Research ArticleOptimization of Fuel Injection Control System of Two-StrokeAeroengine of UAV

Yixuan Wang1 Yan Shi 12 Maolin Cai1 Weiqing Xu 1 Jian Zhang1 Wei Zhong23

and Na Wang 1

1School of Automation Science and Electrical Engineering Beihang University Beijing 100191 China2Jiangsu Provincial Key Laboratory of Advanced Manufacture and Process for Marine Mechanical EquipmentZhenjiang 212003 China3School of Mechanical Engineering Jiangsu University of Science and Technology Zhenjiang 212003 China

Correspondence should be addressed to Yan Shi yesoyougmailcom and Na Wang lion_na987buaaeducn

Received 1 May 2020 Accepted 8 June 2020 Published 9 July 2020

Guest Editor Juan Sandoval

Copyright copy 2020 YixuanWang et alis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Power efficiency of two-stroke spark-ignition engine is generally low because improper amount of fuel injection leads to a lot ofunburned fuel loss during the engine working process However parameters of the fuel injection system are hard to confirm byaviation experiments due to expensive test costs is paper proposes a method of calibrating injection parameters of two-strokespark-ignition engine based on thermodynamic simulation and parameter optimum algorithm Firstly the one-dimensionalthermodynamic model is built according to the internal structure and thermodynamic process of the engine then the modelparameters are corrected according to the operating principle of the injector after experimental verification of the modelconsidering both the engine power sufficiency and fuel economy Analytic Hierarchy Process method is applied to look for theoptimal injection amount and fuel injection advance angle at different engine working speeds finally an aeroengine experimentstation with an electronic fuel injector system is built rough simulation and experiment studies it can be seen that when theengine speed changes from 3000 to 3500 RPM the oil consumption rate of the optimal results is higher than that of the previousones when the aeroengine speed is higher than 4000 RPM the oil consumption rate results of the optimal method are 10 to 27higher than the original results is paper can be a reference in the optimization of UAV aircraft engine

1 Introduction

Two-stroke engine has been widely applied in the powersystem of small aerial equipment fuel-powered UAV becauseof the advantages of strong explosive and small size [1]However model selection of engine is always difficult for thedesign of fuel-powered UAVrsquos power system at is be-cause in the flight simulation environment of UAV theoutput characteristics of the engine are hard to accuratelypredict especially it is hard to find a matching fuel supplysystem Traditional fuel supply method for two-stroke en-gine is using carburetor which canmechanically atomize fuelduring the engine working process [2] Nevertheless au-tomatic control cannot be achieved in engine with a car-buretor and the engine can hardly automatically adapt to

the flight condition variation of UAV Electronic fuel in-jector (EFI) has been widely developed in the area of enginefuel supply due to its superiorities of controllability andfavourable characteristics [3] Performance of the enginewith the EFI system has been generally studied by setting upexperimental stations which can test the output speedtorque air-fuel ratio (AFR) cylinder pressure and exhaustcontents and the researchers do a lot of experiments tooptimize the engine structure or control method [4 5]

Although the engine experiments are designed more andmore realistic in recent time there is still some distancebetween test results to the real application In addition thetraditional two-stroke engine test stations are alwaysdesigned more suitable for the ground vehicles because thetest torque is always added by means of electromagnetism

HindawiComplexityVolume 2020 Article ID 8921320 12 pageshttpsdoiorg10115520208921320

which is hard to test the output power of an aeroengine witha propeller Furthermore in order to get accurate results theexperiment conditions have to be prepared strictly such ashigh precision sensors and stable environment which willgreatly increase the research cost Last but not the least it isdangerous and inaccurate to simulate extreme workingconditions by engine station tests

erefore research studies have paid more and more at-tention to the engine working process simulation by mathe-matical models In order to estimate engine performance suchas cylinder pressure heat release rate and fuel consumptionVenkatraman and Devaradjane [6] build the working math-ematical model of a 4-stroke engine e simulation modelincludes cylinder state equation heat transfer process ignitiondelay combustion duration and NOx formation In additionbased on the mathematical model Venkatraman and Devar-adjane [7] design engine experiments for demonstration Intheir works the heat release rate brake thermal efficiencycarbon monoxide hydrocarbon and so on are predictedthrough the model and the experiments verify that the rec-tification model coincides with the reality Furthermore in thecombustion model Wiebe heat release function is appliedbased on the exponential rate of the chemical reactions Wiebeequations have been implemented by Miyamoto et al [8] andone of the equation factors is considered to be important whichis called ldquorate of heat releaserdquo Ganapathy et al [9] haveemployed a thermodynamic model based on two-zone Wiebeheat release function to simulate the performance of new fuelengine Raut [10] also use an exponential rate-basedWiebe heatrelease model and the Pflaum formula is applied in the esti-mation of empirical coefficient of the heat transfer processFrom these works it can be seen that engine performance studyby using the mathematical model method is effective

GT-Power is the leading engine simulation softwarebased on one-dimensional gas dynamic which represents theflow and transfer in the components of the engine systemandmore andmore scientists and engineers have applied thecomputing tool in engine prediction in order to improve thecontrol performance or reduce the emission Kassa et al [11]have leveraged experimental data from a 6-cylinder engineto a GT-Power model to better understand the distributionof the port-injected fuel across cylinders under severaloperating conditions Rahimi-Gorji et al [12] have opti-mized the performance and fuel consumption according tothe weather conditions by combining the artificial neuralnetwork and GT-Power model and pressure temperatureand humidity of the incoming air are considered in thenetwork to obtain a better engine performance Alves et al[13] apply GT-Power in the engine intake system design andthe best intake runner length and diameter configuration ofeach speed for a four-stroke and single cylinder engine isfound to get the optimum volume efficiency Trajkovic et al[14] build the GT-Power model of a 2-stroke engine to studythe effect of different parameters and their effect onpneumatic hybrid performance From the works above themathematical model built by GT-Power is proved to beeffective to predict and improve the engine characteristicsHowever these papers mainly focus on the engine structurerather than the control strategy of the EFI system

In order to match the power system of a kind ofdownsized fuel-powered UAV the characteristics of theaeroengine including output speed and output powershould be analyzed based on the GT-Power model with afixed structure Furthermore key control parameters of thematched EFI system should be confirmed for the aeroengineapplication Calculations of the engine power based on theGT-Power module have been researched Yang and Zhu [15]have developed a mixed valve and crank-based engine modelfor a dual-stage turbocharged engine Under differentloading states the output torque and released AFR of theengine are simulated and values of the fuel pulse width arecalculated for a reference for the engine control unit (ECU)design Menacer and Bouchetara [16] have applied the GT-Power model to study the effect of the inject fuel mass flowon the brake power and indicate power under the certainignition advanced angle compression ratio and outputspeed In their work the maximum power and economycorresponding to the optimal speed are determined Weiet al [17] have adopted a serial of experiment data in a GT-Power model of a water-cooled four-stroke engine andlengths of the opening and closing delay times are optimizedand an optimal inject fuel mass flow is optimized MoreoverYang et al [18] have designed the controlled fuel process andstudied the different intake air parameters to improve theengine dynamic performances However in these works theengine confirmatory experiments are far away from the realapplication of the aeroengine because the torque propellermainly comes from the propeller air resistance In additionsome of the works are short of detailed experiment de-scription and relative theory basis so it is important for us toprovide a theoretical model reference for the aeroengine fuelsupply system in order to avoid multiple engine parametertests which can cause huge development costs FurthermoreECU controls the injector of the EFI system of the aero-engine and the electrified injector is opened and atomizesthe input high pressure gasoline into the engine manifold[19] However because of the electromagnetic force char-acteristic of the injector the dynamic response of the in-jected fuel mass flow will affect the precision of the suppliedfuel erefore based on the model results of the theory fuelflow it is necessary to analyze the dynamic response of theinjector and compensate the fuel spray and then we can get aconfirmed EFI control parameter which can provide opti-mum performance for the aeroengine

In this paper we firstly analyze the structure of theaeroengine and one-dimensional GT-Power mode of theengine is established Furthermore several parameter cor-rection methods are proposed Based on the simulationresults of the correctedmodel the analytic hierarchy methodis applied to optimize the fuel injection control systemEngine experiment results which use the optimize injectionMAP demonstrate that the oil consumption rate can beimproved differently

2 Methodology of Model

21 Subject Introduction In this paper the studied two-stroke aeroengine with the model of DLE170 has two

2 Complexity

opposing twin cylinders and mainly includes two air cyl-inders chambers two pistons one crankcase and onecrankshaft As shown in Figure 1 each of the cylinders has ascavenging channel and an exhaust vent and all the ports arewithout valves at means that opening and closing of theholes on the cylinder chambers depend on the movement ofthe pistons In addition main parameters of the aeroengineare shown in Table 1

When the two-stroke aeroengine starts to work duringthe first stroke firstly the air-fuel mixture is sucked into thecrankcase and the scavenging port is opened when thepistons move from the bottom dead center (BDC) until thecrankshaft rotates to the intake valve closed (IVC) anglewhich can be seen in Figure 2 e exhaust port is openedfrom BDC until the crankshaft rotates to the emission valveclosed (EVC) angle then the air-fuel mixture is compressedand at the ignition advance angle before the top dead center(TDC) the engine is sparked During the piston powerprocess before the exhaust valve opened (EVO) angle boththe exhaust and scavenging ports are closed and the cylinderchambers are hermetic which can ensure that the piston getsthe maximum power e ignition advanced angle (θ) isusually set to 5sim15 degrees ahead of TDC Because thecompressed ratio of the engine is relatively high and therated engine speed is fast the ignition advanced angle is setat 15 degrees e fuel in the crankcase comes from theelectronic injector as a certain air-fuel ratio (λ) and the ratiois determined by the average intake fuel flow ( _mf ) and airflow into the manifold ( _mman) which is controlled by injectfuel pulse width (Pw) inject fuel pressure (pf ) and throttleopening degree (α) e relative parameters can also be seenin Table 1

e engine working process is designed as shown inFigure 3 according to the working principle of the one-dimensional simulation software GT-Power In this pictureit can be seen that connected to the inlet port there are twosymmetrical crankcase chambers with numbers 1 and 2When the air-fuel mixture is flows into the crankcase it isgenerally assumed that two homogeneous mounts of oil andgas are divided by the crankshaft and then flow into the twocylinders Furthermore there are also symmetrical scav-enging passages intake ports cylinder chambers exhaustports and exhaust passages e opening and closing de-grees of the two kinds of ports determine the intake time ofthe air-fuel mixture and the exhaust time of the emissionsAccording to the actual measurement results the openingareas with the crankshaft angles are as shown in Figures 4(a)and 4(b) It should be noted that in these figures range ofthe x-coordinates is 0 to 180 degrees which is in the firstworking stroke e changing area with the shaft angle issymmetrical in the second working stroke

22 Modeling Method en the one-dimensional GT-Power model of the two-stroke aeroengine can be set asshown in Figure 5 according to the aeroengine workingprocess Structure of the aeroengine is based on the actualmeasure results

Main setting parameters of the fuel injector are ṁf andthe set air-fuel ratio (λset) In practice ECU controls theinjector work and breaks through pulse signal with a certain

TDC (0deg)

BDC (180deg)

EVOEVC

IVOIVC

Exhaust port opens

Scavenging port opens

Crankshaft anglephase

Compress Power

Spark

Exhaust port closes

Scavenging port closes

Ignition advanceangle

Figure 1 Main parts of the two-stroke aeroengine

Table 1 Specifications of DLE170 engine

Parameter ValueCylinder bore (mm) 52Engine stroke (mm) 40Connecting rod length (mm) 175Compression ratio 95TDC clearance height (mm) 2Displacement (cc) 85X2Intake fuel pressure (MPa) 03EVO (degrees) 65IVO (degrees) 123Intake pressure (bar) 1Intake temperature (K) 298Exhaust temperature (K) 700Exhaust pressure (bar) 12

Maximum performance 13 kw7500RPM

Minimum idle (RPM) 1000Range of the throttle opening degree (degrees) 10sim90EVC (degrees) minus65IVC (degrees) minus123

TDC (0deg)

BDC (180deg)

EVOEVC

IVOIVC

Exhaust port opens

Scavenging port opens

Crankshaft anglephase

Compress Power

Spark

Exhaust port closes

Scavenging port closes

Ignitionadvance

angle

Figure 2 Working schematic diagram of the two-strokeaeroengine

Complexity 3

width Relationship between _mf λset and the inject fuel pulsewidth (Pw) is shown in the following equation

_mf ηvρrefVDλset(CYL)Pw

(1)

where ηv is volumetric efficiency ρref is reference air densityused to calculate volumetric efficiency VD is the enginedisplacement and CYL is the number of cylinders Fromthis equation we can see that Pw directly determines theinjected fuel flow In order to improve the comprehensiveperformance of the aeroengine the inject fuel flow rates arecalibrated under different working conditions So as tomake the setup more intuitive in this paper the calibratingstandard is based on the expected air-fuel ratio and then theECU can calculate the output Pw in the real practiceHowever because the injector is driven by electromagnetic

Env Filter Throttleplate Manifold

Injector

Inlet port

Crankcase system

Scavenging passage 1

Cylinderchamber 2

Exhaust passage 2Exhaust passage 1

EnvEnv

Cylinderchamber 1

Scavenging passage 2

Crankcasechamber 1

Crankcasechamber 2

Load ofthe propeller

Intake port 2Intake port 1

Exhaust port 2Exhaust port 1

055 06 065 07 075 08

10002000

30004000

50006000

05

10152025

ndash1000ndash1500ndash2000

ndash2500ndash3000

ndash3500ndash4000

ndash4500

UAV propeller rotor diameter (m)

ndash5000

ndash5500ndash6000

Engine speed (rpm)

Load

torq

ue (N

m)

Figure 3 Working process of the two-stroke aeroengine

Port

area

(mm

2 )

0

300

600

900

1200

1500

120 140 160 180100Cranksha angle (degree)

(a)

Port

area

(mm

2 )

0

50

100

150

200

80 100 120 140 160 18060Cranksha angle (degree)

(b)

Figure 4 Working process of the two-stroke aeroengine (a) Intake port area (b) Exhaust port area

Intakeports

Exhaustports

Cylinderchambers

Fuelinjector

Propellerload

Throttleplate

Env-1 cranktrain-1

Env-4

Env-2Exhrunner-1

Exhrunner-2

Propeller_N_T-1

exhport-1

exhport-2

Exvalve-1

Exvalve-2

Cylinder-1

Cylinder-2

Invalve-1

Invalve-2

PipeRound-1

PipeRound-2

EngCrankcase-1

EngCrankcase-2

Man-fs-1

ValveCheckConn-2

Intport-1Intrunner-1

ThrottleConn-1

Intrunner-2

AirFilter

Si-inject-1

ValveCheckConn-1

Figure 5 One-dimensional GT-Power model of the two-strokeaeroengine

4 Complexity

force the dynamic action of the needle valve should beconsidered in the compensation of the set pulse width

Fuel injector working progress mainly includes threesteps the injector receives the pulse signal from ECU theelectromagnetic coil is gradually energized and the needlevalve starts to move when overcoming the spring preloadwhen the magnetized solenoid coil is saturated the needlevalve stops at the mechanical limit position when the pulsesignal becomes zero the magnetic flux of the solenoid coilreduces gradually and the needle valve will return to thenormal position Basically all the nozzles of the electro-magnetic type work in this way and the response delayimpact on the dynamic inject fuel flow caused by mechanicalfactors cannot be ignored In order to deeply analyze thedynamic injection and formulate the calibration strategy thedynamic model of the injector is built as follows

U0 Ri + NdΦbdt

when electrified

0 R + R0( 1113857 i + NdΦbdt

when not electrified

(2)

ese equations are magnetic flux when the injector iselectrified and not electrified where R is the basic resistanceof the electrified coil loop R0 is the protective resistance Vbrepresents total magnetic circuitN is the number of the coili is the current in the loop and U0 is the driving voltage eelectromagnetic force (Fm) on the needle valve when the coilis electrified is as follows

Fm μ0(iN)2S

2δ2 (3)

where μ0 represents permeability of vacuum S is cross-section of the air gap and δ means length of the working airgap Kinetic equation of the magnetic needle valve is

Fm minus F0 minus kx + Ffuel mvd2xdt2

(4)

where F0 is the initial tension of spring k is the springstiffness x is the displacement of the needle valve mv is themass of needle valve and Ffuel is fuel pressure force on theneedle valve When the needle valve is opened the highpressure fuel erupts and produces spray into the manifolde equation of the fuel flow is as follows according to orificecompensation principle

_mfi CdA0

2 ρf pf minus pm( 1113857

1113969

(5)

where _mfi is the instantaneous inject fuel mass flow Cd isdischarge coefficient A0 is aperture area ρf is the fueldensity and Pm is the atmosphere pressure Based on theequations the dynamic displacement of the needle valve iscalculated under different spring stiffness values As shownin Figure 6(a) when the initial spring tension force F0 is setat 55N the response of the valve displacement will not keeppace with the control signal However when F0 is set at95N pulse width of the needle displacement is muchshorter than the control signal which can be shown inFigure 6(b) and that will lead to insufficient of the inject fuel

erefore the pulse width of the valve displacement can beadjusted to be the same with that of the control signal bysetting the spring tension force F0 As shown in Figure 6(c)pulse width of the dynamic displacement of the needle valveis approximate to the control signal except at the beginningof the period where there is a rise process which causesinjection control error

is paper proposes a compensation method for theinjection control error As shown in Figure 7 it can be seenthat the displacement compensation time is equal to thecurrent delay time Compensation area of the rise process isapproximate as a triangle erefore the compensationwidth (Pc) is shown in the following equation

Pc Di

2 (6)

where Di is the current time delay Equation (1) can beamended as follows

_mf ηvρ refVDλset

(CYL) Pw + Pc( 1113857 (7)

Propeller load can be calculated according to differentworking conditions based on standard strip analysis Asknown from the calculation load torque of the propellermainly depends on engine speed (n) and propeller rotordiameter (rp) Main formula of the torque is as follows

MR 1113944(ΔD cos β + ΔL sin β)rp (8)

where MR is the propeller torque ΔD is differential form ofthe drag force ΔL is differential form of the lift force β is theintake air flow angle and rp is the propeller radius en theparameters are confirmed according to a blade materialthen we can get the torque MAP in horizontal directionunder different working conditions which is shown inFigure 8 From Figure 8 we can see that the load torque doesnot increase linearly with increasing engine speed and theUAV propeller rotor diameter However we can substitutethe torque MAP into the one-dimensional model by thelinear interpolation method

3 Experiments and Optimization

31ExperimentalVerification Numerical simulation cannotcompletely replace experiment analysis and if we want tomake the simulation results reflect the engine mechanism asprecisely as possible the mathematical simulation and ex-periment analysis should be combined e mathematicalmodel needs to be verified by experiment results whichmainly includes two parts the engine structure and thecombustion model e engine structure can be verified byintake air flow experiments at is because the engine isdriven by the oil and gas combustion and if the detected airflow is consistent with the simulation result in differentconditions we can see that the built engine model structurecan provide an equal inlet air mass flow In addition thecombustion model should be demonstrated by the cylinderpressure test e reason is that the output power of theinternal combustion engine mainly comes from the in-

Complexity 5

0 001 002 003 004 0050

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(a)

0 001 002 003 004 005

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(b)

0005 001 0015 002

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(c)

Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N

Control signalCurrent signalNeedle valve displacement

0

12

Nee

dle v

alve

disp

lace

men

t (m

m)

0

1

Current time delayDisplacement compensation

Approximatetriangle

Cont

rol s

igna

l (V

)

0

1

Curr

ent s

igna

l (A

)

1 2 3 4 5 6 7 8 9 100Time (ms)

Figure 7 Schematic diagram of needle valve displacementcompensation

05506

06507

07508

10002000

30004000

50006000 1000

15002000

25003000

35004000

4500

UAV propeller rotor diameter (m)

5000

5500

6000

Engine speed (rpm)

0

5

10

15

20

25

Load

torq

ue (N

middotm)

Figure 8 Horizontal torque of the propeller under differentworking conditions

6 Complexity

cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective

Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms

rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows

η Po

Pi

nTo

9550 _mfHu

c n

_mf

(9)

where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained

32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable

Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the

simulation the input AFR value is set to every 05 from 12 to155

As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle

Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15

As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation

It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight

Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves

Complexity 7

of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV

Simulation resultsExperiment results

202224262830323436

Air

mas

s flo

w (K

gh)

3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)

(a)

Simulation resultsExperiment results

0

5

10

15

20

25

Cylin

der p

ress

ure (

bar)

ndash50 0 50 100 150 200ndash100Crank angle (degree)

(b)

Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM

ECUWiringharness

OscilloscopeFuel injector

Figure 10 Injector test picture

Current signalPulse signal

Current delay time

0

002

004

006

008

01

012

014

Curr

ent s

igna

l (A

)

0

05

1

15

2

25

3

Vol

tage

pul

se (V

)

20 40 60 800Time (ms)

Figure 11 Results of the current delay time test

Table 2 Results of the GT-power simulation when α 10deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMhKg)Pc

(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687

Table 3 Results of the GT-power simulation when α 40deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128

Table 4 Results of the GT-power simulation when α 80deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391

8 Complexity

33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations

n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857

(10)

where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)

f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c

(11)

where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

8

10

12

14

16

18

20

Out

put t

orqu

e (N

middotm)

3000 4000 5000 60002000Engine speed (RPM)

Figure 12 Output torque at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

2

3

4

5

6

7

8

9

10

Oup

ut p

ower

(Kw

)

Figure 13 Output power at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

01

012

014

016

018

02

022

024

026

028

Pow

er e

ffici

ency

Figure 14 Power efficiency at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000O

il co

nsum

ptio

n ra

te o

f rot

atio

n sp

eed

(RPM

middothK

g)

Figure 15 Oil consumption rate of rotation speed

Complexity 9

matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16

e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5

According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows

(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping

(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed

(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered

(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced

rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17

From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows

(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator

calculate the weight matrixesW1W2W3 and W4

obtain the simulation results

calculate the evaluation function results f (θn)

derive the evaluation function matrix F (θn)

data normalization preprocessing determine the relationship

between throttle openingdegree and engine speedaccording to A and equ(12)

obtain the engine set AFR optimization curve

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Final

determine the set AFRmatrix A according to theevaluation function matrix

Figure 16 Optimization process

Table 5 Definition and explanation of preference weights based onSaatyrsquos theory

Preferenceweights Definition Explanation

1 Equally preferable Two factors contributeequally to the objective

3 Moderate preferredExperience and judgementslightly favour one over

other

5 Strongly preferredExperience and judgementstrongly favour one over the

other

7 Very stronglypreferred

Experience and judgementvery strongly favour one

over the other

9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity

2 4 6 8 Intermediates valuesUsed to represent

compromise between thepreferences listed

Reciprocals Reciprocals forinverse comparison mdash

Table 6 Optimize calibration data of fuel injection parameter

α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135

10 Complexity

(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10

34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded

From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results

4 Conclusion

is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

10 20 30 40 50 60 70 80 90

2500300035004000450050005500600012

13

14

15

16larrlarr6000

Throttle opening degree (deg)Engine speed (RPM)

Targ

et A

FR

Figure 17 Fuel injection MAP

020

4060

80100

20003000

40005000

6000ndash01

ndash005

0

005

01

2500

Throttle opening degree (deg)

300035004000

50004500

55006000

Engine speed (RPM)

Effic

ienc

y er

ror

Figure 18 Efficiency error MAP

Fuel tank

Weightingsensor

Testaeroengine

Analysiscomputer

Remotecontroller

Figure 19 Aeroengine test station

Optimal resultsPrevious results

1800

2000

2200

2400

2600

2800

Oil

cons

umpt

ion

rate

of r

otat

ion

spee

d (R

PMmiddoth

Kg)

3000 3500 4000 4500 5000 5500 60002500

Engine speed (RPM)

Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed

Complexity 11

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity

opposing twin cylinders and mainly includes two air cyl-inders chambers two pistons one crankcase and onecrankshaft As shown in Figure 1 each of the cylinders has ascavenging channel and an exhaust vent and all the ports arewithout valves at means that opening and closing of theholes on the cylinder chambers depend on the movement ofthe pistons In addition main parameters of the aeroengineare shown in Table 1

When the two-stroke aeroengine starts to work duringthe first stroke firstly the air-fuel mixture is sucked into thecrankcase and the scavenging port is opened when thepistons move from the bottom dead center (BDC) until thecrankshaft rotates to the intake valve closed (IVC) anglewhich can be seen in Figure 2 e exhaust port is openedfrom BDC until the crankshaft rotates to the emission valveclosed (EVC) angle then the air-fuel mixture is compressedand at the ignition advance angle before the top dead center(TDC) the engine is sparked During the piston powerprocess before the exhaust valve opened (EVO) angle boththe exhaust and scavenging ports are closed and the cylinderchambers are hermetic which can ensure that the piston getsthe maximum power e ignition advanced angle (θ) isusually set to 5sim15 degrees ahead of TDC Because thecompressed ratio of the engine is relatively high and therated engine speed is fast the ignition advanced angle is setat 15 degrees e fuel in the crankcase comes from theelectronic injector as a certain air-fuel ratio (λ) and the ratiois determined by the average intake fuel flow ( _mf ) and airflow into the manifold ( _mman) which is controlled by injectfuel pulse width (Pw) inject fuel pressure (pf ) and throttleopening degree (α) e relative parameters can also be seenin Table 1

e engine working process is designed as shown inFigure 3 according to the working principle of the one-dimensional simulation software GT-Power In this pictureit can be seen that connected to the inlet port there are twosymmetrical crankcase chambers with numbers 1 and 2When the air-fuel mixture is flows into the crankcase it isgenerally assumed that two homogeneous mounts of oil andgas are divided by the crankshaft and then flow into the twocylinders Furthermore there are also symmetrical scav-enging passages intake ports cylinder chambers exhaustports and exhaust passages e opening and closing de-grees of the two kinds of ports determine the intake time ofthe air-fuel mixture and the exhaust time of the emissionsAccording to the actual measurement results the openingareas with the crankshaft angles are as shown in Figures 4(a)and 4(b) It should be noted that in these figures range ofthe x-coordinates is 0 to 180 degrees which is in the firstworking stroke e changing area with the shaft angle issymmetrical in the second working stroke

22 Modeling Method en the one-dimensional GT-Power model of the two-stroke aeroengine can be set asshown in Figure 5 according to the aeroengine workingprocess Structure of the aeroengine is based on the actualmeasure results

Main setting parameters of the fuel injector are ṁf andthe set air-fuel ratio (λset) In practice ECU controls theinjector work and breaks through pulse signal with a certain

TDC (0deg)

BDC (180deg)

EVOEVC

IVOIVC

Exhaust port opens

Scavenging port opens

Crankshaft anglephase

Compress Power

Spark

Exhaust port closes

Scavenging port closes

Ignition advanceangle

Figure 1 Main parts of the two-stroke aeroengine

Table 1 Specifications of DLE170 engine

Parameter ValueCylinder bore (mm) 52Engine stroke (mm) 40Connecting rod length (mm) 175Compression ratio 95TDC clearance height (mm) 2Displacement (cc) 85X2Intake fuel pressure (MPa) 03EVO (degrees) 65IVO (degrees) 123Intake pressure (bar) 1Intake temperature (K) 298Exhaust temperature (K) 700Exhaust pressure (bar) 12

Maximum performance 13 kw7500RPM

Minimum idle (RPM) 1000Range of the throttle opening degree (degrees) 10sim90EVC (degrees) minus65IVC (degrees) minus123

TDC (0deg)

BDC (180deg)

EVOEVC

IVOIVC

Exhaust port opens

Scavenging port opens

Crankshaft anglephase

Compress Power

Spark

Exhaust port closes

Scavenging port closes

Ignitionadvance

angle

Figure 2 Working schematic diagram of the two-strokeaeroengine

Complexity 3

width Relationship between _mf λset and the inject fuel pulsewidth (Pw) is shown in the following equation

_mf ηvρrefVDλset(CYL)Pw

(1)

where ηv is volumetric efficiency ρref is reference air densityused to calculate volumetric efficiency VD is the enginedisplacement and CYL is the number of cylinders Fromthis equation we can see that Pw directly determines theinjected fuel flow In order to improve the comprehensiveperformance of the aeroengine the inject fuel flow rates arecalibrated under different working conditions So as tomake the setup more intuitive in this paper the calibratingstandard is based on the expected air-fuel ratio and then theECU can calculate the output Pw in the real practiceHowever because the injector is driven by electromagnetic

Env Filter Throttleplate Manifold

Injector

Inlet port

Crankcase system

Scavenging passage 1

Cylinderchamber 2

Exhaust passage 2Exhaust passage 1

EnvEnv

Cylinderchamber 1

Scavenging passage 2

Crankcasechamber 1

Crankcasechamber 2

Load ofthe propeller

Intake port 2Intake port 1

Exhaust port 2Exhaust port 1

055 06 065 07 075 08

10002000

30004000

50006000

05

10152025

ndash1000ndash1500ndash2000

ndash2500ndash3000

ndash3500ndash4000

ndash4500

UAV propeller rotor diameter (m)

ndash5000

ndash5500ndash6000

Engine speed (rpm)

Load

torq

ue (N

m)

Figure 3 Working process of the two-stroke aeroengine

Port

area

(mm

2 )

0

300

600

900

1200

1500

120 140 160 180100Cranksha angle (degree)

(a)

Port

area

(mm

2 )

0

50

100

150

200

80 100 120 140 160 18060Cranksha angle (degree)

(b)

Figure 4 Working process of the two-stroke aeroengine (a) Intake port area (b) Exhaust port area

Intakeports

Exhaustports

Cylinderchambers

Fuelinjector

Propellerload

Throttleplate

Env-1 cranktrain-1

Env-4

Env-2Exhrunner-1

Exhrunner-2

Propeller_N_T-1

exhport-1

exhport-2

Exvalve-1

Exvalve-2

Cylinder-1

Cylinder-2

Invalve-1

Invalve-2

PipeRound-1

PipeRound-2

EngCrankcase-1

EngCrankcase-2

Man-fs-1

ValveCheckConn-2

Intport-1Intrunner-1

ThrottleConn-1

Intrunner-2

AirFilter

Si-inject-1

ValveCheckConn-1

Figure 5 One-dimensional GT-Power model of the two-strokeaeroengine

4 Complexity

force the dynamic action of the needle valve should beconsidered in the compensation of the set pulse width

Fuel injector working progress mainly includes threesteps the injector receives the pulse signal from ECU theelectromagnetic coil is gradually energized and the needlevalve starts to move when overcoming the spring preloadwhen the magnetized solenoid coil is saturated the needlevalve stops at the mechanical limit position when the pulsesignal becomes zero the magnetic flux of the solenoid coilreduces gradually and the needle valve will return to thenormal position Basically all the nozzles of the electro-magnetic type work in this way and the response delayimpact on the dynamic inject fuel flow caused by mechanicalfactors cannot be ignored In order to deeply analyze thedynamic injection and formulate the calibration strategy thedynamic model of the injector is built as follows

U0 Ri + NdΦbdt

when electrified

0 R + R0( 1113857 i + NdΦbdt

when not electrified

(2)

ese equations are magnetic flux when the injector iselectrified and not electrified where R is the basic resistanceof the electrified coil loop R0 is the protective resistance Vbrepresents total magnetic circuitN is the number of the coili is the current in the loop and U0 is the driving voltage eelectromagnetic force (Fm) on the needle valve when the coilis electrified is as follows

Fm μ0(iN)2S

2δ2 (3)

where μ0 represents permeability of vacuum S is cross-section of the air gap and δ means length of the working airgap Kinetic equation of the magnetic needle valve is

Fm minus F0 minus kx + Ffuel mvd2xdt2

(4)

where F0 is the initial tension of spring k is the springstiffness x is the displacement of the needle valve mv is themass of needle valve and Ffuel is fuel pressure force on theneedle valve When the needle valve is opened the highpressure fuel erupts and produces spray into the manifolde equation of the fuel flow is as follows according to orificecompensation principle

_mfi CdA0

2 ρf pf minus pm( 1113857

1113969

(5)

where _mfi is the instantaneous inject fuel mass flow Cd isdischarge coefficient A0 is aperture area ρf is the fueldensity and Pm is the atmosphere pressure Based on theequations the dynamic displacement of the needle valve iscalculated under different spring stiffness values As shownin Figure 6(a) when the initial spring tension force F0 is setat 55N the response of the valve displacement will not keeppace with the control signal However when F0 is set at95N pulse width of the needle displacement is muchshorter than the control signal which can be shown inFigure 6(b) and that will lead to insufficient of the inject fuel

erefore the pulse width of the valve displacement can beadjusted to be the same with that of the control signal bysetting the spring tension force F0 As shown in Figure 6(c)pulse width of the dynamic displacement of the needle valveis approximate to the control signal except at the beginningof the period where there is a rise process which causesinjection control error

is paper proposes a compensation method for theinjection control error As shown in Figure 7 it can be seenthat the displacement compensation time is equal to thecurrent delay time Compensation area of the rise process isapproximate as a triangle erefore the compensationwidth (Pc) is shown in the following equation

Pc Di

2 (6)

where Di is the current time delay Equation (1) can beamended as follows

_mf ηvρ refVDλset

(CYL) Pw + Pc( 1113857 (7)

Propeller load can be calculated according to differentworking conditions based on standard strip analysis Asknown from the calculation load torque of the propellermainly depends on engine speed (n) and propeller rotordiameter (rp) Main formula of the torque is as follows

MR 1113944(ΔD cos β + ΔL sin β)rp (8)

where MR is the propeller torque ΔD is differential form ofthe drag force ΔL is differential form of the lift force β is theintake air flow angle and rp is the propeller radius en theparameters are confirmed according to a blade materialthen we can get the torque MAP in horizontal directionunder different working conditions which is shown inFigure 8 From Figure 8 we can see that the load torque doesnot increase linearly with increasing engine speed and theUAV propeller rotor diameter However we can substitutethe torque MAP into the one-dimensional model by thelinear interpolation method

3 Experiments and Optimization

31ExperimentalVerification Numerical simulation cannotcompletely replace experiment analysis and if we want tomake the simulation results reflect the engine mechanism asprecisely as possible the mathematical simulation and ex-periment analysis should be combined e mathematicalmodel needs to be verified by experiment results whichmainly includes two parts the engine structure and thecombustion model e engine structure can be verified byintake air flow experiments at is because the engine isdriven by the oil and gas combustion and if the detected airflow is consistent with the simulation result in differentconditions we can see that the built engine model structurecan provide an equal inlet air mass flow In addition thecombustion model should be demonstrated by the cylinderpressure test e reason is that the output power of theinternal combustion engine mainly comes from the in-

Complexity 5

0 001 002 003 004 0050

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(a)

0 001 002 003 004 005

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(b)

0005 001 0015 002

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(c)

Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N

Control signalCurrent signalNeedle valve displacement

0

12

Nee

dle v

alve

disp

lace

men

t (m

m)

0

1

Current time delayDisplacement compensation

Approximatetriangle

Cont

rol s

igna

l (V

)

0

1

Curr

ent s

igna

l (A

)

1 2 3 4 5 6 7 8 9 100Time (ms)

Figure 7 Schematic diagram of needle valve displacementcompensation

05506

06507

07508

10002000

30004000

50006000 1000

15002000

25003000

35004000

4500

UAV propeller rotor diameter (m)

5000

5500

6000

Engine speed (rpm)

0

5

10

15

20

25

Load

torq

ue (N

middotm)

Figure 8 Horizontal torque of the propeller under differentworking conditions

6 Complexity

cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective

Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms

rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows

η Po

Pi

nTo

9550 _mfHu

c n

_mf

(9)

where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained

32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable

Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the

simulation the input AFR value is set to every 05 from 12 to155

As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle

Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15

As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation

It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight

Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves

Complexity 7

of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV

Simulation resultsExperiment results

202224262830323436

Air

mas

s flo

w (K

gh)

3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)

(a)

Simulation resultsExperiment results

0

5

10

15

20

25

Cylin

der p

ress

ure (

bar)

ndash50 0 50 100 150 200ndash100Crank angle (degree)

(b)

Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM

ECUWiringharness

OscilloscopeFuel injector

Figure 10 Injector test picture

Current signalPulse signal

Current delay time

0

002

004

006

008

01

012

014

Curr

ent s

igna

l (A

)

0

05

1

15

2

25

3

Vol

tage

pul

se (V

)

20 40 60 800Time (ms)

Figure 11 Results of the current delay time test

Table 2 Results of the GT-power simulation when α 10deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMhKg)Pc

(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687

Table 3 Results of the GT-power simulation when α 40deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128

Table 4 Results of the GT-power simulation when α 80deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391

8 Complexity

33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations

n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857

(10)

where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)

f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c

(11)

where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

8

10

12

14

16

18

20

Out

put t

orqu

e (N

middotm)

3000 4000 5000 60002000Engine speed (RPM)

Figure 12 Output torque at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

2

3

4

5

6

7

8

9

10

Oup

ut p

ower

(Kw

)

Figure 13 Output power at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

01

012

014

016

018

02

022

024

026

028

Pow

er e

ffici

ency

Figure 14 Power efficiency at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000O

il co

nsum

ptio

n ra

te o

f rot

atio

n sp

eed

(RPM

middothK

g)

Figure 15 Oil consumption rate of rotation speed

Complexity 9

matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16

e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5

According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows

(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping

(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed

(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered

(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced

rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17

From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows

(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator

calculate the weight matrixesW1W2W3 and W4

obtain the simulation results

calculate the evaluation function results f (θn)

derive the evaluation function matrix F (θn)

data normalization preprocessing determine the relationship

between throttle openingdegree and engine speedaccording to A and equ(12)

obtain the engine set AFR optimization curve

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Final

determine the set AFRmatrix A according to theevaluation function matrix

Figure 16 Optimization process

Table 5 Definition and explanation of preference weights based onSaatyrsquos theory

Preferenceweights Definition Explanation

1 Equally preferable Two factors contributeequally to the objective

3 Moderate preferredExperience and judgementslightly favour one over

other

5 Strongly preferredExperience and judgementstrongly favour one over the

other

7 Very stronglypreferred

Experience and judgementvery strongly favour one

over the other

9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity

2 4 6 8 Intermediates valuesUsed to represent

compromise between thepreferences listed

Reciprocals Reciprocals forinverse comparison mdash

Table 6 Optimize calibration data of fuel injection parameter

α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135

10 Complexity

(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10

34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded

From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results

4 Conclusion

is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

10 20 30 40 50 60 70 80 90

2500300035004000450050005500600012

13

14

15

16larrlarr6000

Throttle opening degree (deg)Engine speed (RPM)

Targ

et A

FR

Figure 17 Fuel injection MAP

020

4060

80100

20003000

40005000

6000ndash01

ndash005

0

005

01

2500

Throttle opening degree (deg)

300035004000

50004500

55006000

Engine speed (RPM)

Effic

ienc

y er

ror

Figure 18 Efficiency error MAP

Fuel tank

Weightingsensor

Testaeroengine

Analysiscomputer

Remotecontroller

Figure 19 Aeroengine test station

Optimal resultsPrevious results

1800

2000

2200

2400

2600

2800

Oil

cons

umpt

ion

rate

of r

otat

ion

spee

d (R

PMmiddoth

Kg)

3000 3500 4000 4500 5000 5500 60002500

Engine speed (RPM)

Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed

Complexity 11

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity

width Relationship between _mf λset and the inject fuel pulsewidth (Pw) is shown in the following equation

_mf ηvρrefVDλset(CYL)Pw

(1)

where ηv is volumetric efficiency ρref is reference air densityused to calculate volumetric efficiency VD is the enginedisplacement and CYL is the number of cylinders Fromthis equation we can see that Pw directly determines theinjected fuel flow In order to improve the comprehensiveperformance of the aeroengine the inject fuel flow rates arecalibrated under different working conditions So as tomake the setup more intuitive in this paper the calibratingstandard is based on the expected air-fuel ratio and then theECU can calculate the output Pw in the real practiceHowever because the injector is driven by electromagnetic

Env Filter Throttleplate Manifold

Injector

Inlet port

Crankcase system

Scavenging passage 1

Cylinderchamber 2

Exhaust passage 2Exhaust passage 1

EnvEnv

Cylinderchamber 1

Scavenging passage 2

Crankcasechamber 1

Crankcasechamber 2

Load ofthe propeller

Intake port 2Intake port 1

Exhaust port 2Exhaust port 1

055 06 065 07 075 08

10002000

30004000

50006000

05

10152025

ndash1000ndash1500ndash2000

ndash2500ndash3000

ndash3500ndash4000

ndash4500

UAV propeller rotor diameter (m)

ndash5000

ndash5500ndash6000

Engine speed (rpm)

Load

torq

ue (N

m)

Figure 3 Working process of the two-stroke aeroengine

Port

area

(mm

2 )

0

300

600

900

1200

1500

120 140 160 180100Cranksha angle (degree)

(a)

Port

area

(mm

2 )

0

50

100

150

200

80 100 120 140 160 18060Cranksha angle (degree)

(b)

Figure 4 Working process of the two-stroke aeroengine (a) Intake port area (b) Exhaust port area

Intakeports

Exhaustports

Cylinderchambers

Fuelinjector

Propellerload

Throttleplate

Env-1 cranktrain-1

Env-4

Env-2Exhrunner-1

Exhrunner-2

Propeller_N_T-1

exhport-1

exhport-2

Exvalve-1

Exvalve-2

Cylinder-1

Cylinder-2

Invalve-1

Invalve-2

PipeRound-1

PipeRound-2

EngCrankcase-1

EngCrankcase-2

Man-fs-1

ValveCheckConn-2

Intport-1Intrunner-1

ThrottleConn-1

Intrunner-2

AirFilter

Si-inject-1

ValveCheckConn-1

Figure 5 One-dimensional GT-Power model of the two-strokeaeroengine

4 Complexity

force the dynamic action of the needle valve should beconsidered in the compensation of the set pulse width

Fuel injector working progress mainly includes threesteps the injector receives the pulse signal from ECU theelectromagnetic coil is gradually energized and the needlevalve starts to move when overcoming the spring preloadwhen the magnetized solenoid coil is saturated the needlevalve stops at the mechanical limit position when the pulsesignal becomes zero the magnetic flux of the solenoid coilreduces gradually and the needle valve will return to thenormal position Basically all the nozzles of the electro-magnetic type work in this way and the response delayimpact on the dynamic inject fuel flow caused by mechanicalfactors cannot be ignored In order to deeply analyze thedynamic injection and formulate the calibration strategy thedynamic model of the injector is built as follows

U0 Ri + NdΦbdt

when electrified

0 R + R0( 1113857 i + NdΦbdt

when not electrified

(2)

ese equations are magnetic flux when the injector iselectrified and not electrified where R is the basic resistanceof the electrified coil loop R0 is the protective resistance Vbrepresents total magnetic circuitN is the number of the coili is the current in the loop and U0 is the driving voltage eelectromagnetic force (Fm) on the needle valve when the coilis electrified is as follows

Fm μ0(iN)2S

2δ2 (3)

where μ0 represents permeability of vacuum S is cross-section of the air gap and δ means length of the working airgap Kinetic equation of the magnetic needle valve is

Fm minus F0 minus kx + Ffuel mvd2xdt2

(4)

where F0 is the initial tension of spring k is the springstiffness x is the displacement of the needle valve mv is themass of needle valve and Ffuel is fuel pressure force on theneedle valve When the needle valve is opened the highpressure fuel erupts and produces spray into the manifolde equation of the fuel flow is as follows according to orificecompensation principle

_mfi CdA0

2 ρf pf minus pm( 1113857

1113969

(5)

where _mfi is the instantaneous inject fuel mass flow Cd isdischarge coefficient A0 is aperture area ρf is the fueldensity and Pm is the atmosphere pressure Based on theequations the dynamic displacement of the needle valve iscalculated under different spring stiffness values As shownin Figure 6(a) when the initial spring tension force F0 is setat 55N the response of the valve displacement will not keeppace with the control signal However when F0 is set at95N pulse width of the needle displacement is muchshorter than the control signal which can be shown inFigure 6(b) and that will lead to insufficient of the inject fuel

erefore the pulse width of the valve displacement can beadjusted to be the same with that of the control signal bysetting the spring tension force F0 As shown in Figure 6(c)pulse width of the dynamic displacement of the needle valveis approximate to the control signal except at the beginningof the period where there is a rise process which causesinjection control error

is paper proposes a compensation method for theinjection control error As shown in Figure 7 it can be seenthat the displacement compensation time is equal to thecurrent delay time Compensation area of the rise process isapproximate as a triangle erefore the compensationwidth (Pc) is shown in the following equation

Pc Di

2 (6)

where Di is the current time delay Equation (1) can beamended as follows

_mf ηvρ refVDλset

(CYL) Pw + Pc( 1113857 (7)

Propeller load can be calculated according to differentworking conditions based on standard strip analysis Asknown from the calculation load torque of the propellermainly depends on engine speed (n) and propeller rotordiameter (rp) Main formula of the torque is as follows

MR 1113944(ΔD cos β + ΔL sin β)rp (8)

where MR is the propeller torque ΔD is differential form ofthe drag force ΔL is differential form of the lift force β is theintake air flow angle and rp is the propeller radius en theparameters are confirmed according to a blade materialthen we can get the torque MAP in horizontal directionunder different working conditions which is shown inFigure 8 From Figure 8 we can see that the load torque doesnot increase linearly with increasing engine speed and theUAV propeller rotor diameter However we can substitutethe torque MAP into the one-dimensional model by thelinear interpolation method

3 Experiments and Optimization

31ExperimentalVerification Numerical simulation cannotcompletely replace experiment analysis and if we want tomake the simulation results reflect the engine mechanism asprecisely as possible the mathematical simulation and ex-periment analysis should be combined e mathematicalmodel needs to be verified by experiment results whichmainly includes two parts the engine structure and thecombustion model e engine structure can be verified byintake air flow experiments at is because the engine isdriven by the oil and gas combustion and if the detected airflow is consistent with the simulation result in differentconditions we can see that the built engine model structurecan provide an equal inlet air mass flow In addition thecombustion model should be demonstrated by the cylinderpressure test e reason is that the output power of theinternal combustion engine mainly comes from the in-

Complexity 5

0 001 002 003 004 0050

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(a)

0 001 002 003 004 005

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(b)

0005 001 0015 002

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(c)

Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N

Control signalCurrent signalNeedle valve displacement

0

12

Nee

dle v

alve

disp

lace

men

t (m

m)

0

1

Current time delayDisplacement compensation

Approximatetriangle

Cont

rol s

igna

l (V

)

0

1

Curr

ent s

igna

l (A

)

1 2 3 4 5 6 7 8 9 100Time (ms)

Figure 7 Schematic diagram of needle valve displacementcompensation

05506

06507

07508

10002000

30004000

50006000 1000

15002000

25003000

35004000

4500

UAV propeller rotor diameter (m)

5000

5500

6000

Engine speed (rpm)

0

5

10

15

20

25

Load

torq

ue (N

middotm)

Figure 8 Horizontal torque of the propeller under differentworking conditions

6 Complexity

cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective

Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms

rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows

η Po

Pi

nTo

9550 _mfHu

c n

_mf

(9)

where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained

32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable

Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the

simulation the input AFR value is set to every 05 from 12 to155

As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle

Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15

As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation

It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight

Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves

Complexity 7

of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV

Simulation resultsExperiment results

202224262830323436

Air

mas

s flo

w (K

gh)

3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)

(a)

Simulation resultsExperiment results

0

5

10

15

20

25

Cylin

der p

ress

ure (

bar)

ndash50 0 50 100 150 200ndash100Crank angle (degree)

(b)

Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM

ECUWiringharness

OscilloscopeFuel injector

Figure 10 Injector test picture

Current signalPulse signal

Current delay time

0

002

004

006

008

01

012

014

Curr

ent s

igna

l (A

)

0

05

1

15

2

25

3

Vol

tage

pul

se (V

)

20 40 60 800Time (ms)

Figure 11 Results of the current delay time test

Table 2 Results of the GT-power simulation when α 10deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMhKg)Pc

(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687

Table 3 Results of the GT-power simulation when α 40deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128

Table 4 Results of the GT-power simulation when α 80deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391

8 Complexity

33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations

n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857

(10)

where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)

f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c

(11)

where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

8

10

12

14

16

18

20

Out

put t

orqu

e (N

middotm)

3000 4000 5000 60002000Engine speed (RPM)

Figure 12 Output torque at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

2

3

4

5

6

7

8

9

10

Oup

ut p

ower

(Kw

)

Figure 13 Output power at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

01

012

014

016

018

02

022

024

026

028

Pow

er e

ffici

ency

Figure 14 Power efficiency at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000O

il co

nsum

ptio

n ra

te o

f rot

atio

n sp

eed

(RPM

middothK

g)

Figure 15 Oil consumption rate of rotation speed

Complexity 9

matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16

e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5

According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows

(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping

(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed

(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered

(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced

rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17

From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows

(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator

calculate the weight matrixesW1W2W3 and W4

obtain the simulation results

calculate the evaluation function results f (θn)

derive the evaluation function matrix F (θn)

data normalization preprocessing determine the relationship

between throttle openingdegree and engine speedaccording to A and equ(12)

obtain the engine set AFR optimization curve

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Final

determine the set AFRmatrix A according to theevaluation function matrix

Figure 16 Optimization process

Table 5 Definition and explanation of preference weights based onSaatyrsquos theory

Preferenceweights Definition Explanation

1 Equally preferable Two factors contributeequally to the objective

3 Moderate preferredExperience and judgementslightly favour one over

other

5 Strongly preferredExperience and judgementstrongly favour one over the

other

7 Very stronglypreferred

Experience and judgementvery strongly favour one

over the other

9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity

2 4 6 8 Intermediates valuesUsed to represent

compromise between thepreferences listed

Reciprocals Reciprocals forinverse comparison mdash

Table 6 Optimize calibration data of fuel injection parameter

α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135

10 Complexity

(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10

34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded

From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results

4 Conclusion

is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

10 20 30 40 50 60 70 80 90

2500300035004000450050005500600012

13

14

15

16larrlarr6000

Throttle opening degree (deg)Engine speed (RPM)

Targ

et A

FR

Figure 17 Fuel injection MAP

020

4060

80100

20003000

40005000

6000ndash01

ndash005

0

005

01

2500

Throttle opening degree (deg)

300035004000

50004500

55006000

Engine speed (RPM)

Effic

ienc

y er

ror

Figure 18 Efficiency error MAP

Fuel tank

Weightingsensor

Testaeroengine

Analysiscomputer

Remotecontroller

Figure 19 Aeroengine test station

Optimal resultsPrevious results

1800

2000

2200

2400

2600

2800

Oil

cons

umpt

ion

rate

of r

otat

ion

spee

d (R

PMmiddoth

Kg)

3000 3500 4000 4500 5000 5500 60002500

Engine speed (RPM)

Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed

Complexity 11

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity

force the dynamic action of the needle valve should beconsidered in the compensation of the set pulse width

Fuel injector working progress mainly includes threesteps the injector receives the pulse signal from ECU theelectromagnetic coil is gradually energized and the needlevalve starts to move when overcoming the spring preloadwhen the magnetized solenoid coil is saturated the needlevalve stops at the mechanical limit position when the pulsesignal becomes zero the magnetic flux of the solenoid coilreduces gradually and the needle valve will return to thenormal position Basically all the nozzles of the electro-magnetic type work in this way and the response delayimpact on the dynamic inject fuel flow caused by mechanicalfactors cannot be ignored In order to deeply analyze thedynamic injection and formulate the calibration strategy thedynamic model of the injector is built as follows

U0 Ri + NdΦbdt

when electrified

0 R + R0( 1113857 i + NdΦbdt

when not electrified

(2)

ese equations are magnetic flux when the injector iselectrified and not electrified where R is the basic resistanceof the electrified coil loop R0 is the protective resistance Vbrepresents total magnetic circuitN is the number of the coili is the current in the loop and U0 is the driving voltage eelectromagnetic force (Fm) on the needle valve when the coilis electrified is as follows

Fm μ0(iN)2S

2δ2 (3)

where μ0 represents permeability of vacuum S is cross-section of the air gap and δ means length of the working airgap Kinetic equation of the magnetic needle valve is

Fm minus F0 minus kx + Ffuel mvd2xdt2

(4)

where F0 is the initial tension of spring k is the springstiffness x is the displacement of the needle valve mv is themass of needle valve and Ffuel is fuel pressure force on theneedle valve When the needle valve is opened the highpressure fuel erupts and produces spray into the manifolde equation of the fuel flow is as follows according to orificecompensation principle

_mfi CdA0

2 ρf pf minus pm( 1113857

1113969

(5)

where _mfi is the instantaneous inject fuel mass flow Cd isdischarge coefficient A0 is aperture area ρf is the fueldensity and Pm is the atmosphere pressure Based on theequations the dynamic displacement of the needle valve iscalculated under different spring stiffness values As shownin Figure 6(a) when the initial spring tension force F0 is setat 55N the response of the valve displacement will not keeppace with the control signal However when F0 is set at95N pulse width of the needle displacement is muchshorter than the control signal which can be shown inFigure 6(b) and that will lead to insufficient of the inject fuel

erefore the pulse width of the valve displacement can beadjusted to be the same with that of the control signal bysetting the spring tension force F0 As shown in Figure 6(c)pulse width of the dynamic displacement of the needle valveis approximate to the control signal except at the beginningof the period where there is a rise process which causesinjection control error

is paper proposes a compensation method for theinjection control error As shown in Figure 7 it can be seenthat the displacement compensation time is equal to thecurrent delay time Compensation area of the rise process isapproximate as a triangle erefore the compensationwidth (Pc) is shown in the following equation

Pc Di

2 (6)

where Di is the current time delay Equation (1) can beamended as follows

_mf ηvρ refVDλset

(CYL) Pw + Pc( 1113857 (7)

Propeller load can be calculated according to differentworking conditions based on standard strip analysis Asknown from the calculation load torque of the propellermainly depends on engine speed (n) and propeller rotordiameter (rp) Main formula of the torque is as follows

MR 1113944(ΔD cos β + ΔL sin β)rp (8)

where MR is the propeller torque ΔD is differential form ofthe drag force ΔL is differential form of the lift force β is theintake air flow angle and rp is the propeller radius en theparameters are confirmed according to a blade materialthen we can get the torque MAP in horizontal directionunder different working conditions which is shown inFigure 8 From Figure 8 we can see that the load torque doesnot increase linearly with increasing engine speed and theUAV propeller rotor diameter However we can substitutethe torque MAP into the one-dimensional model by thelinear interpolation method

3 Experiments and Optimization

31ExperimentalVerification Numerical simulation cannotcompletely replace experiment analysis and if we want tomake the simulation results reflect the engine mechanism asprecisely as possible the mathematical simulation and ex-periment analysis should be combined e mathematicalmodel needs to be verified by experiment results whichmainly includes two parts the engine structure and thecombustion model e engine structure can be verified byintake air flow experiments at is because the engine isdriven by the oil and gas combustion and if the detected airflow is consistent with the simulation result in differentconditions we can see that the built engine model structurecan provide an equal inlet air mass flow In addition thecombustion model should be demonstrated by the cylinderpressure test e reason is that the output power of theinternal combustion engine mainly comes from the in-

Complexity 5

0 001 002 003 004 0050

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(a)

0 001 002 003 004 005

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(b)

0005 001 0015 002

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(c)

Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N

Control signalCurrent signalNeedle valve displacement

0

12

Nee

dle v

alve

disp

lace

men

t (m

m)

0

1

Current time delayDisplacement compensation

Approximatetriangle

Cont

rol s

igna

l (V

)

0

1

Curr

ent s

igna

l (A

)

1 2 3 4 5 6 7 8 9 100Time (ms)

Figure 7 Schematic diagram of needle valve displacementcompensation

05506

06507

07508

10002000

30004000

50006000 1000

15002000

25003000

35004000

4500

UAV propeller rotor diameter (m)

5000

5500

6000

Engine speed (rpm)

0

5

10

15

20

25

Load

torq

ue (N

middotm)

Figure 8 Horizontal torque of the propeller under differentworking conditions

6 Complexity

cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective

Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms

rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows

η Po

Pi

nTo

9550 _mfHu

c n

_mf

(9)

where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained

32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable

Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the

simulation the input AFR value is set to every 05 from 12 to155

As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle

Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15

As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation

It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight

Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves

Complexity 7

of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV

Simulation resultsExperiment results

202224262830323436

Air

mas

s flo

w (K

gh)

3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)

(a)

Simulation resultsExperiment results

0

5

10

15

20

25

Cylin

der p

ress

ure (

bar)

ndash50 0 50 100 150 200ndash100Crank angle (degree)

(b)

Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM

ECUWiringharness

OscilloscopeFuel injector

Figure 10 Injector test picture

Current signalPulse signal

Current delay time

0

002

004

006

008

01

012

014

Curr

ent s

igna

l (A

)

0

05

1

15

2

25

3

Vol

tage

pul

se (V

)

20 40 60 800Time (ms)

Figure 11 Results of the current delay time test

Table 2 Results of the GT-power simulation when α 10deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMhKg)Pc

(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687

Table 3 Results of the GT-power simulation when α 40deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128

Table 4 Results of the GT-power simulation when α 80deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391

8 Complexity

33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations

n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857

(10)

where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)

f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c

(11)

where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

8

10

12

14

16

18

20

Out

put t

orqu

e (N

middotm)

3000 4000 5000 60002000Engine speed (RPM)

Figure 12 Output torque at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

2

3

4

5

6

7

8

9

10

Oup

ut p

ower

(Kw

)

Figure 13 Output power at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

01

012

014

016

018

02

022

024

026

028

Pow

er e

ffici

ency

Figure 14 Power efficiency at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000O

il co

nsum

ptio

n ra

te o

f rot

atio

n sp

eed

(RPM

middothK

g)

Figure 15 Oil consumption rate of rotation speed

Complexity 9

matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16

e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5

According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows

(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping

(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed

(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered

(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced

rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17

From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows

(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator

calculate the weight matrixesW1W2W3 and W4

obtain the simulation results

calculate the evaluation function results f (θn)

derive the evaluation function matrix F (θn)

data normalization preprocessing determine the relationship

between throttle openingdegree and engine speedaccording to A and equ(12)

obtain the engine set AFR optimization curve

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Final

determine the set AFRmatrix A according to theevaluation function matrix

Figure 16 Optimization process

Table 5 Definition and explanation of preference weights based onSaatyrsquos theory

Preferenceweights Definition Explanation

1 Equally preferable Two factors contributeequally to the objective

3 Moderate preferredExperience and judgementslightly favour one over

other

5 Strongly preferredExperience and judgementstrongly favour one over the

other

7 Very stronglypreferred

Experience and judgementvery strongly favour one

over the other

9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity

2 4 6 8 Intermediates valuesUsed to represent

compromise between thepreferences listed

Reciprocals Reciprocals forinverse comparison mdash

Table 6 Optimize calibration data of fuel injection parameter

α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135

10 Complexity

(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10

34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded

From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results

4 Conclusion

is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

10 20 30 40 50 60 70 80 90

2500300035004000450050005500600012

13

14

15

16larrlarr6000

Throttle opening degree (deg)Engine speed (RPM)

Targ

et A

FR

Figure 17 Fuel injection MAP

020

4060

80100

20003000

40005000

6000ndash01

ndash005

0

005

01

2500

Throttle opening degree (deg)

300035004000

50004500

55006000

Engine speed (RPM)

Effic

ienc

y er

ror

Figure 18 Efficiency error MAP

Fuel tank

Weightingsensor

Testaeroengine

Analysiscomputer

Remotecontroller

Figure 19 Aeroengine test station

Optimal resultsPrevious results

1800

2000

2200

2400

2600

2800

Oil

cons

umpt

ion

rate

of r

otat

ion

spee

d (R

PMmiddoth

Kg)

3000 3500 4000 4500 5000 5500 60002500

Engine speed (RPM)

Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed

Complexity 11

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity

0 001 002 003 004 0050

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(a)

0 001 002 003 004 005

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(b)

0005 001 0015 002

3

6

9

12

15

Time (s)

Con

trol s

igna

l (V

)

0

05

1

15

2

25

3 times10ndash4

Nee

dle d

ispla

cem

ent (

m)

Control signalNeedle displacement

(c)

Figure 6 Dynamic displacement of the needle valve with different spring initial tension F0 (a) F0 55N (b) F0 95N (c) F0 80N

Control signalCurrent signalNeedle valve displacement

0

12

Nee

dle v

alve

disp

lace

men

t (m

m)

0

1

Current time delayDisplacement compensation

Approximatetriangle

Cont

rol s

igna

l (V

)

0

1

Curr

ent s

igna

l (A

)

1 2 3 4 5 6 7 8 9 100Time (ms)

Figure 7 Schematic diagram of needle valve displacementcompensation

05506

06507

07508

10002000

30004000

50006000 1000

15002000

25003000

35004000

4500

UAV propeller rotor diameter (m)

5000

5500

6000

Engine speed (rpm)

0

5

10

15

20

25

Load

torq

ue (N

middotm)

Figure 8 Horizontal torque of the propeller under differentworking conditions

6 Complexity

cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective

Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms

rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows

η Po

Pi

nTo

9550 _mfHu

c n

_mf

(9)

where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained

32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable

Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the

simulation the input AFR value is set to every 05 from 12 to155

As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle

Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15

As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation

It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight

Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves

Complexity 7

of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV

Simulation resultsExperiment results

202224262830323436

Air

mas

s flo

w (K

gh)

3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)

(a)

Simulation resultsExperiment results

0

5

10

15

20

25

Cylin

der p

ress

ure (

bar)

ndash50 0 50 100 150 200ndash100Crank angle (degree)

(b)

Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM

ECUWiringharness

OscilloscopeFuel injector

Figure 10 Injector test picture

Current signalPulse signal

Current delay time

0

002

004

006

008

01

012

014

Curr

ent s

igna

l (A

)

0

05

1

15

2

25

3

Vol

tage

pul

se (V

)

20 40 60 800Time (ms)

Figure 11 Results of the current delay time test

Table 2 Results of the GT-power simulation when α 10deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMhKg)Pc

(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687

Table 3 Results of the GT-power simulation when α 40deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128

Table 4 Results of the GT-power simulation when α 80deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391

8 Complexity

33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations

n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857

(10)

where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)

f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c

(11)

where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

8

10

12

14

16

18

20

Out

put t

orqu

e (N

middotm)

3000 4000 5000 60002000Engine speed (RPM)

Figure 12 Output torque at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

2

3

4

5

6

7

8

9

10

Oup

ut p

ower

(Kw

)

Figure 13 Output power at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

01

012

014

016

018

02

022

024

026

028

Pow

er e

ffici

ency

Figure 14 Power efficiency at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000O

il co

nsum

ptio

n ra

te o

f rot

atio

n sp

eed

(RPM

middothK

g)

Figure 15 Oil consumption rate of rotation speed

Complexity 9

matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16

e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5

According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows

(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping

(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed

(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered

(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced

rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17

From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows

(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator

calculate the weight matrixesW1W2W3 and W4

obtain the simulation results

calculate the evaluation function results f (θn)

derive the evaluation function matrix F (θn)

data normalization preprocessing determine the relationship

between throttle openingdegree and engine speedaccording to A and equ(12)

obtain the engine set AFR optimization curve

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Final

determine the set AFRmatrix A according to theevaluation function matrix

Figure 16 Optimization process

Table 5 Definition and explanation of preference weights based onSaatyrsquos theory

Preferenceweights Definition Explanation

1 Equally preferable Two factors contributeequally to the objective

3 Moderate preferredExperience and judgementslightly favour one over

other

5 Strongly preferredExperience and judgementstrongly favour one over the

other

7 Very stronglypreferred

Experience and judgementvery strongly favour one

over the other

9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity

2 4 6 8 Intermediates valuesUsed to represent

compromise between thepreferences listed

Reciprocals Reciprocals forinverse comparison mdash

Table 6 Optimize calibration data of fuel injection parameter

α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135

10 Complexity

(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10

34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded

From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results

4 Conclusion

is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

10 20 30 40 50 60 70 80 90

2500300035004000450050005500600012

13

14

15

16larrlarr6000

Throttle opening degree (deg)Engine speed (RPM)

Targ

et A

FR

Figure 17 Fuel injection MAP

020

4060

80100

20003000

40005000

6000ndash01

ndash005

0

005

01

2500

Throttle opening degree (deg)

300035004000

50004500

55006000

Engine speed (RPM)

Effic

ienc

y er

ror

Figure 18 Efficiency error MAP

Fuel tank

Weightingsensor

Testaeroengine

Analysiscomputer

Remotecontroller

Figure 19 Aeroengine test station

Optimal resultsPrevious results

1800

2000

2200

2400

2600

2800

Oil

cons

umpt

ion

rate

of r

otat

ion

spee

d (R

PMmiddoth

Kg)

3000 3500 4000 4500 5000 5500 60002500

Engine speed (RPM)

Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed

Complexity 11

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity

cylinder pressure and if the detected pressure fits well withthe simulation result it can be seen that the combustionprediction model in the simulation is effective erefore anengine intake air flowmeter is connected with the intakemanifold and a high frequency pressure sensor is setup onthe engine cylinder en we can get the air mass flow andcylinder pressure compare curves as shown in Figures 9(a)and 9(b) From these two pictures we can see that the resulterrors are no more than 5 and can demonstrate themathematic model to be effective

Injection fuel compensation can be demonstrated byECU experiments ECU gets trigger signal and outputs pulsesignal with a certain pulse width According to above re-search result the inject fuel pulse is compensated by thedelay time of the current through the electrified coil loopAccording to Figure 10 an ECU with the above function isdesigned and tested e current signal as well as the controlvoltage through the fuel injector is tested According toFigure 11 we can obtain that the current delay time is about4ms erefore in the model we compensate for the injectpulse by 2ms Repetitive experiments with different controlsignal widths are conducted and according to the real ap-plication the signal width is controlled within the range of35ms to 50ms and we obtain that the current delay time isthe same at is because their lowering processes of thecurrent are the same So in the simulation model we can setthe current delay time as constant 2ms

rough the simulation based on the model above therelative working parameters can be calculated e basicsimulation setting parameters are throttle opening degree(α) and the set air-fuel ratio (λset) Generally the mostconcerned characteristics and evaluation indicators of theengine mainly include engine speed (n) output power (Po)power efficiency (η) and rotational fuel consumption (c) ηand c can be calculated as follows

η Po

Pi

nTo

9550 _mfHu

c n

_mf

(9)

where Pi is the input power of the engine To is the outputtorque of the engine andHu is the gas calorific value which isabout 46000KJkg By changing the setting parameters α andλset a group of output parameters are obtained

32 Simulation Results As shown in Tables 2ndash4 there areseveral arrays of input and output parameters In additionall the parameters are recorded when the engine simulationstend to be stable

Tables 2ndash4 represent a part of simulation results In thispaper the throttle opening degree (α) is changed from 10deg to90deg and the engine speed is from 2500 RPM to 6000RPMaccording to the real application What needs illustration isthat according to our a large number of experiment resultsthe output AFR of the engine can only be controlled within aprecision of 05 and the general range of AFR during theengine working process is from 12 to 155 erefore in the

simulation the input AFR value is set to every 05 from 12 to155

As shown in the three tables To reflects the load-carryingcapacity and generally it is considered as the main indicatorof grade ability in the area of ground gasoline However inthe application of the rotorcraft UAV field the lift force ofthe UAV is primarily determined by the engine speed Sothe parameter To is mainly considered in the start and ac-celeration processes Po is the output power of the engineand in the case of the same displacement output powershould be bigger However in this paper the fuel economy istreated as a priority so in the engine fuel injection controlweight of η should be put more Considering that the enginespeed directly influences the lift of the UAV the rotationalfuel consumption c reflects the fuel consumption rate atconstant speed In addition Pc is the maximum cylinderpressure of one crankshaft rotate cycle

Since these output characteristics affect each other theinfluence rules of the injection parameter should be analyzedin order to assist in the formulation of the optimizationstrategies e set AFR directly affects the oil injection flowrate and its value always combines with that of the throttleopening degree (α) Here α is controlled stably as 40deg be-cause the single opening degrees value can reflect the wholeprinciple Engine speed (n) which is as the final controlquantity of the UAV power system should be simulated bystages According to the application requirement the in-terval is set as 500 RPM from 2500RPM to 6000 RPMenthe tendency charts which show the relationships betweenthe input parameters and the output characteristics areobtained as shown in Figures 12ndash15

As shown in Figures 12 and 13 it can be seen that whenthe throttle opening degree is constant the output torquecurves and output power curves will have a peak at a samespeed However it is difficult to find a regular rule betweenthe set AFR and these two output characteristics at isbecause when the throttle opening degree is set constantlythere must be a primal AFR setting value with differentworking conditions which is in accordance with the engineexternal characteristics According to the settled weight theoptimization should be comprehensively considered Inaddition from the two figures the curve trends are almostthe same so only one of the items can be considered whensetting weights in order to reduce the amount of calculation

It is a bit of mess in Figure 14 which represents theefficiency of the engine system Curves in Figure 14 almosthave peak values and the peak values basically independentof the output torque and powererefore the characteristicof power efficiency can be considered independently Powerefficiency is significant for the fuel economy improvementNevertheless it should be secondary to the torque and powerin the startup and acceleration processes in order to ensurethe safety of the UAV flight

Since the engine speed is kept steady during the flightthe oil consumption of rotation speed (c) is the most im-portant characteristic for fuel saving and flight enduranceextension As shown in Figure 15 the curves have troughs atthe same speed point with the torque and power curvesHowever in Figure 15 the arrange regular way of the curves

Complexity 7

of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV

Simulation resultsExperiment results

202224262830323436

Air

mas

s flo

w (K

gh)

3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)

(a)

Simulation resultsExperiment results

0

5

10

15

20

25

Cylin

der p

ress

ure (

bar)

ndash50 0 50 100 150 200ndash100Crank angle (degree)

(b)

Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM

ECUWiringharness

OscilloscopeFuel injector

Figure 10 Injector test picture

Current signalPulse signal

Current delay time

0

002

004

006

008

01

012

014

Curr

ent s

igna

l (A

)

0

05

1

15

2

25

3

Vol

tage

pul

se (V

)

20 40 60 800Time (ms)

Figure 11 Results of the current delay time test

Table 2 Results of the GT-power simulation when α 10deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMhKg)Pc

(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687

Table 3 Results of the GT-power simulation when α 40deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128

Table 4 Results of the GT-power simulation when α 80deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391

8 Complexity

33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations

n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857

(10)

where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)

f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c

(11)

where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

8

10

12

14

16

18

20

Out

put t

orqu

e (N

middotm)

3000 4000 5000 60002000Engine speed (RPM)

Figure 12 Output torque at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

2

3

4

5

6

7

8

9

10

Oup

ut p

ower

(Kw

)

Figure 13 Output power at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

01

012

014

016

018

02

022

024

026

028

Pow

er e

ffici

ency

Figure 14 Power efficiency at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000O

il co

nsum

ptio

n ra

te o

f rot

atio

n sp

eed

(RPM

middothK

g)

Figure 15 Oil consumption rate of rotation speed

Complexity 9

matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16

e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5

According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows

(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping

(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed

(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered

(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced

rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17

From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows

(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator

calculate the weight matrixesW1W2W3 and W4

obtain the simulation results

calculate the evaluation function results f (θn)

derive the evaluation function matrix F (θn)

data normalization preprocessing determine the relationship

between throttle openingdegree and engine speedaccording to A and equ(12)

obtain the engine set AFR optimization curve

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Final

determine the set AFRmatrix A according to theevaluation function matrix

Figure 16 Optimization process

Table 5 Definition and explanation of preference weights based onSaatyrsquos theory

Preferenceweights Definition Explanation

1 Equally preferable Two factors contributeequally to the objective

3 Moderate preferredExperience and judgementslightly favour one over

other

5 Strongly preferredExperience and judgementstrongly favour one over the

other

7 Very stronglypreferred

Experience and judgementvery strongly favour one

over the other

9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity

2 4 6 8 Intermediates valuesUsed to represent

compromise between thepreferences listed

Reciprocals Reciprocals forinverse comparison mdash

Table 6 Optimize calibration data of fuel injection parameter

α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135

10 Complexity

(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10

34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded

From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results

4 Conclusion

is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

10 20 30 40 50 60 70 80 90

2500300035004000450050005500600012

13

14

15

16larrlarr6000

Throttle opening degree (deg)Engine speed (RPM)

Targ

et A

FR

Figure 17 Fuel injection MAP

020

4060

80100

20003000

40005000

6000ndash01

ndash005

0

005

01

2500

Throttle opening degree (deg)

300035004000

50004500

55006000

Engine speed (RPM)

Effic

ienc

y er

ror

Figure 18 Efficiency error MAP

Fuel tank

Weightingsensor

Testaeroengine

Analysiscomputer

Remotecontroller

Figure 19 Aeroengine test station

Optimal resultsPrevious results

1800

2000

2200

2400

2600

2800

Oil

cons

umpt

ion

rate

of r

otat

ion

spee

d (R

PMmiddoth

Kg)

3000 3500 4000 4500 5000 5500 60002500

Engine speed (RPM)

Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed

Complexity 11

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity

of different set AFR values is different from those inFigures 12 and 13 So in the optimization work the oilconsumption of rotation speed (c) can be independentlyconsidered according to the setting weight in the stable flightprocess of UAV

Simulation resultsExperiment results

202224262830323436

Air

mas

s flo

w (K

gh)

3000 4000 5000 60002000 2500 3500 4500 5500Enigne speed (rpm)

(a)

Simulation resultsExperiment results

0

5

10

15

20

25

Cylin

der p

ress

ure (

bar)

ndash50 0 50 100 150 200ndash100Crank angle (degree)

(b)

Figure 9 Air mass flow and cylinder pressure compare curves (a) Air mass flow at different engine speeds (b) Cylinder pressure whenengine speed is 5000 RPM

ECUWiringharness

OscilloscopeFuel injector

Figure 10 Injector test picture

Current signalPulse signal

Current delay time

0

002

004

006

008

01

012

014

Curr

ent s

igna

l (A

)

0

05

1

15

2

25

3

Vol

tage

pul

se (V

)

20 40 60 800Time (ms)

Figure 11 Results of the current delay time test

Table 2 Results of the GT-power simulation when α 10deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMhKg)Pc

(MPa)10 2500 12 9551 2501 0177 2257016 306610 3000 12 7352 2310 0175 2892084 204510 3500 12 7195 3633 0189 2316357 278610 4000 12 8874 3717 0185 2537999 321910 4500 12 14272 6725 0204 1736989 398710 5000 12 10635 5568 0194 2219936 298610 5500 12 6053 3486 0163 3280692 276010 6000 12 5634 3539 0156 3362353 2687

Table 3 Results of the GT-power simulation when α 40deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)40 2500 145 9122 2388 0149 1987442 314240 3000 145 8869 2786 0140 1918287 230840 3500 145 12132 4447 0213 2134503 322840 4000 145 12926 5414 0206 1934364 380640 4500 145 15451 7281 0179 1410437 405440 5000 145 13459 7047 0179 1621358 395240 5500 145 10109 5823 0203 2445253 366040 6000 145 9111 5725 0165 2201615 3128

Table 4 Results of the GT-power simulation when α 80deg

α(deg)

n(RPM) λset

To(Nm)

Po(kw) η c

(RPMmiddothKg)Pc

(MPa)80 2500 155 7003 1833 0141 2453110 251080 3000 155 9582 3010 0194 2457778 242480 3500 155 11009 4035 0229 2529551 297480 4000 155 13881 5815 0231 2020441 386980 4500 155 14826 6987 0167 1368566 429380 5000 155 12003 6285 0188 1904895 410780 5500 155 8315 4789 0138 2018235 304480 6000 155 6094 3829 0205 4088545 2391

8 Complexity

33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations

n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857

(10)

where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)

f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c

(11)

where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

8

10

12

14

16

18

20

Out

put t

orqu

e (N

middotm)

3000 4000 5000 60002000Engine speed (RPM)

Figure 12 Output torque at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

2

3

4

5

6

7

8

9

10

Oup

ut p

ower

(Kw

)

Figure 13 Output power at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

01

012

014

016

018

02

022

024

026

028

Pow

er e

ffici

ency

Figure 14 Power efficiency at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000O

il co

nsum

ptio

n ra

te o

f rot

atio

n sp

eed

(RPM

middothK

g)

Figure 15 Oil consumption rate of rotation speed

Complexity 9

matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16

e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5

According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows

(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping

(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed

(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered

(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced

rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17

From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows

(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator

calculate the weight matrixesW1W2W3 and W4

obtain the simulation results

calculate the evaluation function results f (θn)

derive the evaluation function matrix F (θn)

data normalization preprocessing determine the relationship

between throttle openingdegree and engine speedaccording to A and equ(12)

obtain the engine set AFR optimization curve

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Final

determine the set AFRmatrix A according to theevaluation function matrix

Figure 16 Optimization process

Table 5 Definition and explanation of preference weights based onSaatyrsquos theory

Preferenceweights Definition Explanation

1 Equally preferable Two factors contributeequally to the objective

3 Moderate preferredExperience and judgementslightly favour one over

other

5 Strongly preferredExperience and judgementstrongly favour one over the

other

7 Very stronglypreferred

Experience and judgementvery strongly favour one

over the other

9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity

2 4 6 8 Intermediates valuesUsed to represent

compromise between thepreferences listed

Reciprocals Reciprocals forinverse comparison mdash

Table 6 Optimize calibration data of fuel injection parameter

α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135

10 Complexity

(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10

34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded

From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results

4 Conclusion

is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

10 20 30 40 50 60 70 80 90

2500300035004000450050005500600012

13

14

15

16larrlarr6000

Throttle opening degree (deg)Engine speed (RPM)

Targ

et A

FR

Figure 17 Fuel injection MAP

020

4060

80100

20003000

40005000

6000ndash01

ndash005

0

005

01

2500

Throttle opening degree (deg)

300035004000

50004500

55006000

Engine speed (RPM)

Effic

ienc

y er

ror

Figure 18 Efficiency error MAP

Fuel tank

Weightingsensor

Testaeroengine

Analysiscomputer

Remotecontroller

Figure 19 Aeroengine test station

Optimal resultsPrevious results

1800

2000

2200

2400

2600

2800

Oil

cons

umpt

ion

rate

of r

otat

ion

spee

d (R

PMmiddoth

Kg)

3000 3500 4000 4500 5000 5500 60002500

Engine speed (RPM)

Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed

Complexity 11

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity

33 Optimization Method rough the improved modelthe optimization work is conducted Several key perfor-mance parameters are selected as the multiple optimizationobjectives such as output power (Pout) output speed (n)power efficiency (η) and oil consumption of rotation speed(c) In this paper firstly we calculate the key characteristicsby using the engine model while changing the input enginecontrol parameters en according to the usersrsquo require-ment we can artificially set the engine control parametersbased on the engine working conditions e basic principleof the optimization is as the following equations

n α1( 1113857lt n α2( 1113857lt middot middot middot middot middot middot lt n αn( 1113857 α1 lt α2 lt middot middot middot middot middot middot lt αn( 1113857

(10)

where n (αi) (i 1 2 n) means engine speed with throttledegree of αi Equation (10) represents that the higher theengine speed is risen the larger the throttle opening degreeis e evaluation system of the set fuel injection parameterrelies on the developed evaluation function f (θ n)

f(θ n) W1(θ n)To + W2(θ n)Po + W3(θ n)η + W4(θ n)c

(11)

where Wi (θ n) (i 1 2 3 and 4) represents evaluationweight function of To Po η and c respectively In this paperthe weights to be calculated can be expressed as matrixesW1W2 W3 and W4 and Wi (i 1 2 3 and 4) isinRatimesb where aand b are the numbers of different throttle opening degreevalues and engine speed values respectively en the

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

8

10

12

14

16

18

20

Out

put t

orqu

e (N

middotm)

3000 4000 5000 60002000Engine speed (RPM)

Figure 12 Output torque at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

2

3

4

5

6

7

8

9

10

Oup

ut p

ower

(Kw

)

Figure 13 Output power at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

01

012

014

016

018

02

022

024

026

028

Pow

er e

ffici

ency

Figure 14 Power efficiency at different engine speeds

AFR = 12AFR = 125AFR = 13AFR = 135

AFR = 14AFR = 145AFR = 15AFR = 155

3000 4000 5000 60002000Engine speed (RPM)

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000O

il co

nsum

ptio

n ra

te o

f rot

atio

n sp

eed

(RPM

middothK

g)

Figure 15 Oil consumption rate of rotation speed

Complexity 9

matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16

e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5

According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows

(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping

(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed

(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered

(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced

rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17

From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows

(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator

calculate the weight matrixesW1W2W3 and W4

obtain the simulation results

calculate the evaluation function results f (θn)

derive the evaluation function matrix F (θn)

data normalization preprocessing determine the relationship

between throttle openingdegree and engine speedaccording to A and equ(12)

obtain the engine set AFR optimization curve

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Final

determine the set AFRmatrix A according to theevaluation function matrix

Figure 16 Optimization process

Table 5 Definition and explanation of preference weights based onSaatyrsquos theory

Preferenceweights Definition Explanation

1 Equally preferable Two factors contributeequally to the objective

3 Moderate preferredExperience and judgementslightly favour one over

other

5 Strongly preferredExperience and judgementstrongly favour one over the

other

7 Very stronglypreferred

Experience and judgementvery strongly favour one

over the other

9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity

2 4 6 8 Intermediates valuesUsed to represent

compromise between thepreferences listed

Reciprocals Reciprocals forinverse comparison mdash

Table 6 Optimize calibration data of fuel injection parameter

α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135

10 Complexity

(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10

34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded

From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results

4 Conclusion

is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

10 20 30 40 50 60 70 80 90

2500300035004000450050005500600012

13

14

15

16larrlarr6000

Throttle opening degree (deg)Engine speed (RPM)

Targ

et A

FR

Figure 17 Fuel injection MAP

020

4060

80100

20003000

40005000

6000ndash01

ndash005

0

005

01

2500

Throttle opening degree (deg)

300035004000

50004500

55006000

Engine speed (RPM)

Effic

ienc

y er

ror

Figure 18 Efficiency error MAP

Fuel tank

Weightingsensor

Testaeroengine

Analysiscomputer

Remotecontroller

Figure 19 Aeroengine test station

Optimal resultsPrevious results

1800

2000

2200

2400

2600

2800

Oil

cons

umpt

ion

rate

of r

otat

ion

spee

d (R

PMmiddoth

Kg)

3000 3500 4000 4500 5000 5500 60002500

Engine speed (RPM)

Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed

Complexity 11

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity

matrix of the evaluation function can be expressed as F (θn) isinRatimesb MatrixA is the set AFRmatrixe basic principleof the optimization method is as shown in Figure 16

e most important step is Step 2 which aims to obtainthe weight matrixes is paper applies a well-knownmulticriteria decision-making method named Analytic Hi-erarchy Process (AHP) to obtain evaluation weights fordifferent groups of throttle opening degree and engine speed[20] e above four alternatives are compared with eachother based on self-defined Saaty scale as shown in Table 5

According to the experimental experience of the aero-engine characteristics in the application of aircraft flightprinciples of setting the weights are as follows

(a) When the aeroengine starts the speed gets to idlestate and the throttle degree is relative small theoutput power of the engine should be firstly ensuredand oil consumption should be adequate in order toavoid engine speed suddenly dropping

(b) When the engine works from idle state to inter-mediate speed (approximate 4000 RPM) accordingto Figure 8 the load increase is not obviousHowever the engine noise is big which means theload efficiency is relatively low e load efficiency isdefined as load torqueoutput torque At the sametime this process is general when the aircraft takesoff and lands and in order to prevent accidents theoutput torque should be primarily guaranteed and acertain amount of fuel consumption is to besacrificed

(c) When the engine speed transits to the rated valuethe fuel injection is always controlled based on theoutput AFR [21 22] However in spite of the rel-evant regulation of the AFR control the small aer-oengine always leaves out the three-way catalyticunit so as to reduce the whole weight of the aircrafterefore the stoichiometric AFR value is usuallynot the control target When the aircraft regularlyworks the fuel consumption is the first item toconsider because load efficiency of this stage which isrelatively high according to the experiment results[23 24] at is because the working noise is regularand varies uniformity along with the rising speed Itcan be inferred that it is an uncommon occurrence ofdrop speed of aeroengine [25 26] As for the ap-plication in UAV a certain speed is corresponding toa certain lift force so the oil consumption of rotationspeed (c) should be firstly considered

(d) When the engine speed is over the rated value thereason can be firstly there is an urgent externaldisturbance such as mutations in the air and theflight attitude should be adjusted secondly UAVmeets the obstacle while moving forward At thismoment the consideration of output torque andpower should be enhanced

rough the AHP optimizing calculation the calibrationresults of fuel injection parameter can be obtained as shownin Table 6 and the fuel injection MAP is shown in Figure 17

From Figure 17 results of the control target of the outputAFR of the two-stroke aeroengine of UAV can be sum-marized as follows

(1) Engine working conditions are corresponding todifferent control values in order to achieve the op-timal optimization indicator

calculate the weight matrixesW1W2W3 and W4

obtain the simulation results

calculate the evaluation function results f (θn)

derive the evaluation function matrix F (θn)

data normalization preprocessing determine the relationship

between throttle openingdegree and engine speedaccording to A and equ(12)

obtain the engine set AFR optimization curve

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Final

determine the set AFRmatrix A according to theevaluation function matrix

Figure 16 Optimization process

Table 5 Definition and explanation of preference weights based onSaatyrsquos theory

Preferenceweights Definition Explanation

1 Equally preferable Two factors contributeequally to the objective

3 Moderate preferredExperience and judgementslightly favour one over

other

5 Strongly preferredExperience and judgementstrongly favour one over the

other

7 Very stronglypreferred

Experience and judgementvery strongly favour one

over the other

9 Extremely preferrede evidence favour oneover the other is of thehighest possible validity

2 4 6 8 Intermediates valuesUsed to represent

compromise between thepreferences listed

Reciprocals Reciprocals forinverse comparison mdash

Table 6 Optimize calibration data of fuel injection parameter

α (deg)n (RPM) 2500 3000 3500 4000 4500 5000 5500 600010 155 15 155 155 155 155 155 15520 15 14 155 155 155 155 155 15530 145 125 15 15 155 155 155 15540 15 155 15 155 155 15 155 15550 155 155 125 15 155 155 13 15560 15 155 145 155 155 155 15 14570 15 155 155 155 15 135 135 1480 135 15 15 15 14 15 145 15590 155 155 155 155 145 155 135 135

10 Complexity

(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10

34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded

From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results

4 Conclusion

is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

10 20 30 40 50 60 70 80 90

2500300035004000450050005500600012

13

14

15

16larrlarr6000

Throttle opening degree (deg)Engine speed (RPM)

Targ

et A

FR

Figure 17 Fuel injection MAP

020

4060

80100

20003000

40005000

6000ndash01

ndash005

0

005

01

2500

Throttle opening degree (deg)

300035004000

50004500

55006000

Engine speed (RPM)

Effic

ienc

y er

ror

Figure 18 Efficiency error MAP

Fuel tank

Weightingsensor

Testaeroengine

Analysiscomputer

Remotecontroller

Figure 19 Aeroengine test station

Optimal resultsPrevious results

1800

2000

2200

2400

2600

2800

Oil

cons

umpt

ion

rate

of r

otat

ion

spee

d (R

PMmiddoth

Kg)

3000 3500 4000 4500 5000 5500 60002500

Engine speed (RPM)

Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed

Complexity 11

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity

(2) rough the optimization method based on analytichierarchy process efficiency values under the wholeworking conditions can get a promotion as shown inFigure 18 At the rated engine working condition(when the engine speed is at the range of 4500 to6000 rpm) the improved efficiency is at the range of5 to over 10

34 Optimization Results Experiments of the aeroengineare designed so as to test the optimal results in the realapplication In Figure 19 the analysis computer is con-nected to a data acquisition card which can gather real-time data from the AFR ratio and engine speed sensorse oil consumption rate of rotation speed can be cal-culated according to the collected data including the speedand the fuel consumption within a certain period of timeAccording to the characteristics of the aeroengine thepower of the load is constant at a certain engine speederefore in the experiments the throttle opening degreeis stair-stepping settled and the corresponding oil con-sumption is recorded

From Figure 20 results of the aeroengine experimentsare obtained through the comparison of the previousopen-loop control when the injection width is constantlyat 45ms When the engine speed changes from 3000 to3500 RPM the oil consumption rate of the optimal resultsis higher than that of the previous ones because at low-level speed the engine needs more fuel to guarantee theoutput power when the engine starts When the aero-engine speed is higher than 4000 RPM the oil con-sumption rate results of the optimal method are 10 to27 higher than the original results

4 Conclusion

is paper proposes a method to optimize the fuel injectioncontrol system of two-stroke aeroengine of UAV based onone-dimensional fluid model and analytic hierarchy processKey parameters of the one-dimensional model are calibratedand verified by calculation reasoning and experimentationExpert experience is integrated into the rules of the analytichierarchy calculation process rough the optimizationresults from the experiments it can be seen that when theengine speed changes from 3000 to 3500RPM the oilconsumption rate of the optimal results is higher than that ofthe previous ones when the aeroengine speed is higher than4000 RPM the oil consumption rate results of the optimalmethod are 10 to 27 higher than the original results ismethod can be a reference for the efficiency optimization ofthe engine control system

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

10 20 30 40 50 60 70 80 90

2500300035004000450050005500600012

13

14

15

16larrlarr6000

Throttle opening degree (deg)Engine speed (RPM)

Targ

et A

FR

Figure 17 Fuel injection MAP

020

4060

80100

20003000

40005000

6000ndash01

ndash005

0

005

01

2500

Throttle opening degree (deg)

300035004000

50004500

55006000

Engine speed (RPM)

Effic

ienc

y er

ror

Figure 18 Efficiency error MAP

Fuel tank

Weightingsensor

Testaeroengine

Analysiscomputer

Remotecontroller

Figure 19 Aeroengine test station

Optimal resultsPrevious results

1800

2000

2200

2400

2600

2800

Oil

cons

umpt

ion

rate

of r

otat

ion

spee

d (R

PMmiddoth

Kg)

3000 3500 4000 4500 5000 5500 60002500

Engine speed (RPM)

Figure 20 Comparison results of the optimal and previous oilconsumption rate of the engine speed

Complexity 11

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity

Acknowledgments

is work was supported by the Open Project Funding ofJiangsu Provincial Key Laboratory of Advanced Manufac-ture and Process for Marine Mechanical Equipment

References

[1] C Stocker R Bennett F Nex M Gerke and J ZevenbergenldquoReview of the current state of UAV regulationsrdquo RemoteSensing vol 9 no 5 p 459 2017

[2] A D Sonparate S P Gadpayle and P P Bajpai ldquoPerfor-mance testing of 2-stroke SI engine by using external va-porized carburetorrdquo International Research Journal ofEngineering and Technology (IRJET) vol 2 no 8 pp 1470ndash1478 2015

[3] H W Gitano R Chim and J Loh ldquoe application of aresistive type O2 sensor to a small engine EFI systemrdquo inProceedings of the SAE Technical Paper Series No 2014-32-0073 Pisa Italy November 2014

[4] M K Balki C Sayin and M Canakci ldquoe effect of differentalcohol fuels on the performance emission and combustioncharacteristics of a gasoline enginerdquo Fuel vol 115 pp 901ndash906 2014

[5] N Kumar ldquoPerformance evaluation and emission analysis ofvariable compression ratio direct injection diesel enginerdquoMATTER International Journal of Science and Technologyvol 2 no 2 pp 32ndash47 2016

[6] M Venkatraman and G Devaradjane ldquoComputer modelingof a CI engine for optimization of operating parameters suchas compression ratio injection timing and injection pressurefor better performance and emission using diesel-dieselbiodiesel blendsrdquo American Journal of Applied Sciences vol 8no 9 pp 897ndash902 2011

[7] M Venkatraman and G Devaradjane ldquoSimulation studies ofa CI engine for better performance and emission using diesel-diesel biodiesel blendsrdquo International Journal on Design andManufacturing Technologies vol 5 no 2 pp 14ndash21 2011

[8] N Miyamoto T Chikahisa T Murayama and R SawyerldquoDescription and analysis of diesel engine rate of combustionand performance using Wiebersquos functionsrdquo in Proceedings ofthe SAE Technical Paper Detroit MI USA No 850107Detroit MI USA 1985

[9] T Ganapathy K Murugesan and R P Gakkhar ldquoPerfor-mance optimization of Jatropha biodiesel engine model usingTaguchi approachrdquo Applied Energy vol 86 no 11pp 2476ndash2486 2009

[10] L P Raut ldquoComputer simulation of CI engine for diesel andbiodiesel blendsrdquo International Journal of Innovative Tech-nology and Exploring Engineering vol 3 no 2 pp 2278ndash30752013

[11] M Kassa C Hall A Ickes and T Wallner ldquoCylinder-to-cylinder variations in power production in a dual fuel internalcombustion engine leveraging late intake valve closingsrdquo SAEInternational Journal of Engines vol 9 no 2 pp 1049ndash10582016

[12] M Rahimi-Gorji M Ghajar A-H Kakaee and D DomiriGanji ldquoModeling of the air conditions effects on the powerand fuel consumption of the SI engine using neural networksand regressionrdquo Journal of the Brazilian Society of MechanicalSciences and Engineering vol 39 no 2 pp 375ndash384 2017

[13] L O F Alves M G D dos Santos A B UrquizaJ H Guerrero J C de Lira and V Abramchuk ldquoDesign of anew intake manifold of a single cylinder engine with three

stagesrdquo in Proceedings of the SAE Technical Paper No 2017-36-0172 Sao Paulo Brazil November 2017

[14] S Trajkovic P Tunestal and B Johansson ldquoSimulation of apneumatic hybrid powertrain with VVT in GT-power andcomparison with experimental datardquo in Proceedings of theSAE Technical Paper No 2009-01-1323 Detroit MI USA2009

[15] X Yang and G G Zhu ldquoA mixed mean-value and crank-based model of a dual-stage turbocharged SI engine forhardware-in-the-loop simulationrdquo in Proceedings of the 2010American Control Conference (ACC) pp 3791ndash3796 IEEEBaltimore MD USA 2010

[16] B Menacer and M Bouchetara ldquoParametric study of theperformance of a turbocharged compression ignition enginerdquoSimulation vol 90 no 12 pp 1375ndash1384 2014

[17] C Wei M Chen and Y Jiang ldquoElectronic control fuel in-jection system based on GT-POWER and MotoTronrdquo Pro-cedia Engineering vol 174 pp 773ndash779 2017

[18] X Yang C Liao and J Liu ldquoHarmonic analysis and opti-mization of the intake system of a gasoline engine using GT-powerrdquo Energy Procedia vol 14 pp 756ndash762 2012

[19] J H Spurk T Betzel and N Simon ldquoInteraction of nonlineardynamics and unsteady flow in fuel injectorsrdquo in Proceedingsof the SAE Technical Paper No 920621 Detroit MA USA1992

[20] T L Saaty Ee Analytic Hierarchy Process Planning PrioritySetting Resource Allocation McGraw-Hill International BookCo Columbus OH USA 1980

[21] Y Wang Y Shi M Cai W Xu and Q Yu ldquoOptimization ofair-fuel ratio control of fuel-powered UAV engine usingadaptive fuzzy-PIDrdquo Journal of the Franklin Institute vol 355no 17 pp 8554ndash8575 2018

[22] Y Wang Y Shi M Cai W Xu and Q Yu ldquoEfficiencyoptimized fuel supply strategy of aircraft engine based on air-fuel ratio controlrdquo Chinese Journal of Aeronautics vol 32no 2 pp 489ndash498 2018

[23] Z Li C-Y Su G Li and H Su ldquoFuzzy approximation-basedadaptive backstepping control of an exoskeleton for humanupper limbsrdquo IEEE Transactions on Fuzzy Systems vol 23no 3 pp 555ndash566 2014

[24] H Su C Yang G Ferrigno and E De Momi ldquoImprovedhuman-robot collaborative control of redundant robot forteleoperated minimally invasive surgeryrdquo IEEE Robotics andAutomation Letters vol 4 no 2 pp 1447ndash1453 2019

[25] H Yang W Qi C Yang J Sandoval G Ferrigno andE D Momi ldquoDeep neural network approach in robot tooldynamics identification for bilateral teleoperationrdquo IEEERobotics and Automation Letters vol 5 no 2 pp 2943ndash29492020

[26] W Qi and A Aliverti ldquoA multimodal wearable system forcontinuous and real-time breathing pattern monitoringduring daily activityrdquo IEEE Journal of Biomedical and HealthInformatics vol 99 pp 1ndash10 2020

12 Complexity