design of rail pressure tracking controller for novel fuel injection system

J. Shanghai Jiaotong Univ. (Sci.), 2013, 18(3): 264-270

DOI: 10.1007/s12204-013-1392-3

Design of Rail Pressure Tracking Controller forNovel Fuel Injection System

HUA Hai-de∗ (��), MA Ning (� �), MA Jie (� �), HUANG He (� �)(State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China)

© Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg 2013

Abstract: This paper proposes a rail pressure tracking controller based on a novel common rail system. Amathematical model, based on physical equations, is developed and used for feed forward control design. Railpressure peak sampling mechanism is designed to remove the disturbance of rail pressure due to fuel injection. Anenhanced tracking differentiator is designed to get smooth tracking signal and exact differential signal from signalwith noise. Double loop control strategy is designed to decouple the system and to improve dynamic performanceof the system. Experimental results indicate that fluctuation of rail pressure is within ±1MPa in steady condition,while within ±3MPa in transient condition, which verifies the effectiveness of the proposed rail pressure controlstrategy.Key words: accumulating distribution fuel injection system (ADFIS), rail pressure control, tracking differentiator,double loop controlCLC number: U 664.121 Document code: A

0 Introduction

High pressure common rail injection system has beenstudied and developed to reduce noise, emissions andfuel consumption and to improve performances at thesame time. Nevertheless, if rail pressure is poorly con-trolled, system performance may be degraded. Railpressure control is significant to the precision of fuelcontrol and emission control. There are many studieson rail pressure control algorithm and control strategyin our country[1-4]. However, rail pressure control is asystematic engineering, and control performance wouldbe influenced by signal sampling, signal processing, con-trol strategy and algorithm, and features of actuator.These researchers have only studied on control strat-egy, without comprehensive consideration of rail pres-sure sampling mechanism, signal processing, control al-gorithm designing, and features of actuator.

There are mature products in this field in foreigncountries, but there are few documents. Catania etal.[5] designed a complicated mathematical model offuel injection system based on hydraulic analysis; Linoet al.[6] built a state space model for control, and haddesigned sliding mode control law; Gupta et al.[7] de-signed a rail pressure compensator for the periodic dis-

Received date: 2013-03-20Foundation item: the National Natural Science Founda-

tion of China (No. 51179102)∗E-mail: [email protected]

turbances caused by injection, and proposed a time-varying control algorithm to suppress the disturbance;Shiraishi et al.[8] adopted cerebellar model articulationcontroller to control rail pressure. However, intelligentcontrol method has higher requirements for hardware,while modern control theory requires accurate math-ematical model and its complex design process is notconducive to practical application.

This paper studies and designs a rail pressure con-troller based on a novel common rail fuel injectionsystem. Mathematical model is built; integrated con-trol strategy of the system is designed, including railpressure sampling mechanism, rail pressure signal pro-cessing algorithm, and rail pressure closed-loop controlalgorithm.

1 System Description

The principle of accumulating distribution fuel injec-tion system (ADFIS) is shown in Fig. 1. The systemmainly includes high pressure pump, rail, distributorand injector. There are three valves: inlet meteringvalve (IMV), high pressure valve (HPV) and fuel re-lease valve (FRV). Its work principle is as follows.

Low pressure part The fuel is inhaled by the lowpressure pump from the tank. Volume of the fuel thatflows into high pressure pump is adjusted by IMV, andrail pressure is regulated by controlling the fuel volumethrough the IMV.

J. Shanghai Jiaotong Univ. (Sci.), 2013, 18(3): 264-270 265

Electroniccontrol unit

Rail

IMV

Distributor

HPV

FRV

Injector

Fueltanker

Low-pressure

fuel pump

High-pressure

fuel pump

Fig. 1 Scheme of the ADFIS

High pressure part The high pressure fuel fromthe rail flows through the HPV. The injection fuel quan-tity is controlled by adjusting pulse width of HPV, andinjection time is adjusted by controlling the open timeof HPV. Also, an FRV is downstream of the HPV. Me-chanical principle of FRV is similar to HPV. Its mainrole is to regulate the injection pressure waveform. Inorder to reduce the complexity of controlling, the pulsewidth of the FRV can be set to a maximum value (inthis system for 2ms) to ensure the spare high-pressurefuel back to tank. Another function of FRV is that itcan enhance injection efficiency of the system. Postpon-ing the open time of the FRV can improve the efficiencyof the system. Fuel is distributed to each cylinder by amechanical distributor.

Compared with the traditional common rail injectionsystem, the system does not need injector with high ac-curacy. It is more adaptive to fuel quality with lowercost, and system efficiency is enhanced due to doublevalve designing. Furthermore, safe function can be re-alized by the injection width of FRV covering that ofHPV.

2 Mathematical Model

According to the definition of the bulk modulus ofelasticity[6] and Bernoulli’s simplified flow equation, thesystem model is

dp

dt=

Kf

V(qV,pmp − qV,inj − qV,back − qV,leak), (1)

Kf = 12 000(1 + 0.6

p

600

), (2)

Iimv(s) =

1Rimv

1 +Limv

Rimvs

Uimv(s), (3)

Feimv(s) = KeimvIimv(s), (4)

ximv(s) =

1kimv

1 +vimv

kimvs +

mimv

kimvs2

Feimv(s), (5)

qV,imv = CqimvSimv

√2Δpi

ρ, (6)

Cqimv = Cqmaxtanh

( 2hdximv

vimv

√2Δpi

ρ

acfn

), (7)

qV,pmp = Gpmp(s)qV,imv, (8)

where, p is rail pressure; Kf is the bulk modulus; V isthe rail and pipes volume; qV,pmp, qV,inj, qV,back, qV,leak

and qV,imv are the high pressure pump flow, the injectorflow, the back flow, the leak flow, and the flow throughIMV, respectively; mimv, Simv, Uimv(s), Iimv(s), Rimv

and Limv are the moving mass, flow area, the voltageapplied to the coil, the current through the coil, theresistance of the coil, and the inductance of the coilof the IMV, respectively; s denoting Laplace variable;Feimv(s) is the electromagnetic force of the IMV; Keimv

is a coefficient, which can be considered as a constant(due to the IMV design); ximv(s) is the position of themass; kimv is the sum of the two springs stiffness; ρand νimv are the fuel density and the fuel viscosity, re-spectively; Cqimv is the flow coefficient; Cqmax is themaximum flow coefficient; Δpi is the absolute valueof pressure difference on each side of the IMV; hd isthe hydraulic diameter; acfn is the critical flow number;Gpmp(s) is the dynamics of the high pressure pump.

Effective area of the IMV is controlled by the elec-tromagnetic force. The effective area is relevant to theaperture and position of the hole. The aperture dif-fers with different IMVs. It is difficult to build the

266 J. Shanghai Jiaotong Univ. (Sci.), 2013, 18(3): 264-270

mathematical model of IMVs. The flow through IMV,qV,imv, can be regarded as the function of qV,imv =f(Iimv). Therefore, the relationship of current and ac-tual output volume flow can be described by the exper-imental results, as shown in Fig. 2.

50100150200250300350

0 0.5 1.0 1.5 2.0Iimv/A

q V,im

v/(L

·h−

1 )

Fig. 2 Inlet metering unit curve

Thus, a simplified model can be derived by

dp

dt=

Kf

V(qV,imv − qV,inj − qV,back − qV,leak)

qV,imv = f(Iimv)dIimv

dt= −Rimv

LimvIimv +

Ubatt

Limvu

⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭

, (9)

where u is duty cycle control output, and Ubatt is thebattery voltage.

The control goal is to ensure that actual pressureshould track the target pressure closely. In view ofEq. (9), the system can be regarded as an approximatecascade system. The model can be used for designingopen loop controller to improve transient performance.

3 Control Law

The incoming and outgoing flows from the pump andthe injector induce sudden drop of the pressure in therail. In order to avoid pressure disturbances in the rail,rail pressure peak value is passed through a low passfilter, and is recorded at intervals of 10ms. Thus, railpressure peaking value is obtained for controlling.3.1 Signal Processing Based on Enhanced

Tracking DifferentiatorDifferentiation of signals is an old and well-known

problem and has attracted more and more attentionin recent years. Differential signal of both target railpressure and actual rail pressure is necessary for theproportion-integral-derivative (PID) controller adoptedin this research. Thus, the precision improvement of thedifferentiator is significant. Several works have beenconducted. Mahmoud and Kahlil[9] designed a linearhigh-gain observer; Han and Wang[10] proposed a non-linear tracking differentiator; Wang et al.[11] proposed afinite time convergent differentiator. Levant[12-13] pro-posed a differentiator via second-order (or high-order)

sliding modes algorithm (hereinafter referred to Levantdifferentiator). Principle of Levant differentiator is

x1 = x2 − λ |x1 − v(t)|12 sign(x1 − v(t))

x2 = α sign(x1 − v(t))

⎫⎬⎭ , (10)

where v(t) is input signal, x1 is tracking value, x2 isdifferential value, and λ and α are the coefficient pa-rameters. A variant of super-twisting differentiator wasproposed in Ref. [14] (hereinafter referred to Denis dif-ferentiator). The differentiator is equipped with hybridadaptation algorithm, which ensures global differentia-tion ability independently of amplitude of the differen-tiated signal and measurement noise. Principle of Denisdifferentiator is

x1 = x2 − k1 |x1 − v(t)|12 sign(x1 − v(t))

x2 = −k2 sign(x1 − v(t)) − x2 − k3 sign(x2)

⎫⎬⎭ , (11)

k1 > 0, k2 > k3 � 0,

where k1, k2 and k3 are the coefficient parameters.For further improvement of the precision of the differ-

entiator, a continuous Denis differentiator is presented(hereinafter referred to enhanced Denis differentiator)in this paper. It can be used to obtain smooth trackingsignal and precise differential signal of target rail pres-sure and actual rail pressure. Principle of the enhancedDenis differentiator is

x1 = x2 − k1 |x1 − v(t)|α+1

2 sign(x1 − v(t))

x2 = −k2 |x1 − v(t)|α sign(x1 − v(t))−x2 − k3 sign(x2)

⎫⎪⎪⎬⎪⎪⎭

. (12)

Its ability of restraining noise will be studied in thefollowing Section 4.

Substituting the target rail pressure into v(t) ofEq. (12), we get the tracking signal of target rail pres-sure z11 and the appropriable differentiator signal oftarget pressure z12. Substituting the actual rail pres-sure into v(t) of Eq. (12), we get the tracking signal ofactual rail pressure z21 and the differentiator signal ofactual rail pressure z22.3.2 Double Loop Control Strategy

In order to control the system as described in Eq. (9),double loop control strategy is designed. The scheme isshown in Fig. 3. Where, d1 and d2 are the disturbanceson fuel metering valve and on fuel injection system, re-spectively; ptgt and pact are target rail pressure andactual rail pressure, respectively; Itgt and Iact are tar-get current and actual current on fuel metering valve,respectively.

Both loops are for first-order plant, so control prob-lem of the high order plant is converted to that of first-order plant. In this paper, the rail pressure loop is used


Fuelinjection system

ControllerFuel

metering valve

Precontrolptgt

qV,imv Itgt Iact

d1 d2

pactuf (Iimv)

Controller

+

Fig. 3 Double loop control strategy

as primary loop, while current closed loop is as auxiliaryloop. The current loop can quickly overcome the dis-turbances plugged into it, thus improving performanceof the control system. The current loop is for coarseregulation, while the rail pressure loop is used for fineregulation.

Specific control steps are listed as follows.(1) The primary loop.A precontrol based on the operating point is used

for the governor to reduce delay time and to keep thegovernor deviation small:

qV,pre = qV,inj + qV,back + qV,leak. (13)

The primary loop is designed for fine regulation ofrail pressure. The dynamic of the rail pressure systemis nonlinear. In this paper, a nonlinear controller isdesigned for regulating:

e1(k) = z11(k) − z21(k)

e2(k) = z12(k) − z22(k)

e0(k) =k∑

j=0

e1(j)

qV,ctrl = β0 fal(e0, α1, δ) + β1fal(e1, α1, δ)+

β2 fal(e2, α2, δ)

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

, (14)

where

fal(e, α, δ) =

{e/δ1−α, |e| > δ

|e|αsgn(e), |e| � δ

is a nonlinear function, k represents the sampling num-ber, qV,ctrl is control effort, α1 = 0.25, α2 = 0.75, andβ0, β1 and β2 are coefficient parameters of the nonlinearfunction. The control effort of the primary loop qV,pmp

is the sum of precontrol volume qV,pre and the controleffort of non-linear PID qV,ctrl, i.e.

qV,pmp = qV,pre + qV,ctrl. (15)

(2) The auxiliary loop.The set volume flow of the pressure governor is con-

verted to the set current by the inverse metering unitcurve and then sent to the subsequent current governor:

Itgt = f−1(qV,imv). (16)

The inlet metering unit is controlled by the model ofIMV in open loop mode. The duty cycle control outputof the feed forward controller is

u0 =ItgtRimv + Limv

dItgt

dtUbatt

=

ItgtRimv

Ubatt+

Limv

Ubatt

dItgt

dt. (17)

Since the coil of the metering unit undergoes a changein resistance based on temperature, the coil current ismeasured and the change in resistance is counteractedby current regulation. The total duty cycle control out-put is

u = u0C

k∑j=0

(Itgt − Iact)j , (18)

where C is feedback controller calibration coefficient.

4 Simulation Results

4.1 Verification of IMV ModelIn order to study the accuracy of the auxiliary

loop model, the model of IMV is built in MAT-LAB/Simulink. Parameters of IMV, Rimv = 2.8 Ω andLimv = 9 mH, are substituted into the model. Controlsignal u is input, as shown in Fig. 4; the detected actualcurrent is compared with the simulated current of IMV;ΔIimv is the current error on IMV between modeledcurrent and measured current. Figure 4 shows that the

1.551.601.651.70

350 400 450 500 550 6000.2100.2150.2200.225

u

t/s

−50

0

50

ΔI i

mv/

mA

I im

v/A

ModeledMeasured

Fig. 4 Comparison of the modeled and measured current


two results are almost the same. When the current ishigh, the actual current is lower than the simulated one,because of the changes of resistance in the condition ofhigh current. Thus integrator compensation shown inEq. (18) should be added to the control system.4.2 Verification of the Enhanced Tracking Dif-

ferentiatorThe following simulation experiment is to study ro-

bustness of enhanced Denis differentiator to noise. Theorigin signal with noise is sinusoidal signal with ran-dom noise. The results obtained from the traditionaldifferentiator are shown in Fig. 5(a); u0 is used as ori-gin signal; the differential signal d0 is poor and can-not be used. The results obtained from Levant dif-

ferentiator, Denis differentiator and enhanced Denisdifferentiator are shown in Figs. 5(b)—5(d), respec-tively; u is used as tracking signal, while d is differ-ential signal. Parameters of Levant differentiator areα = 18, λ = 6. Parameters of Denis differentiator arek1 = 1.5, k2 = 8, k3 = 0.1. Parameters of enhancedDenis differentiator are α = 0.6, k1 = 1.5, k2 = 12, k3 =0.2.

Figures 5(b)—5(d) show that there is no significantdifference among these differentiators, all of which per-form well. The tracking signal is almost the same, whilethe differential signal obtained from enhanced Denis dif-ferentiator performs best.

−2

0

2

0 2 4 6 8 10−1000

0

1000

t/s t/s

d0

u0

Differential signal

sint

−2

0

2

u

0 2 4 6 8 10−2

0

2

d

−2

0

2

u

−2

0

2

u

−2

0

2

d

−1

0

1

2

d

costDifferential signal


sintTracking signal

sintTracking signal

sintTracking signal


(a) Traditional differentiator (b) Levant differentiator

0 2 4 6 8 10t/s t/s

0 2 4 6 8 10

(c) Denis differentiator (d) Enhanced Denis differentiator

Fig. 5 Comparison of the differentiators

5 Experimental Results

Choose MC9S12XEP100 microprocessor as the core,use MATLAB/Simulink to establish control algorithmof the system, use TARGETLINK to generate codeautomatically, and build a test bench of the controlsystem for rail pressure control experiment. The test

bench is shown in Fig. 6. The experimental data iscollected through CANape. The parameters of thepump are: pump chamber diameter of 8mm, cam liftof 3 mm×14.5 mm, maximum rail pressure of 160MPa,and pump maximum speed of 1 200 r/min.

The first experiment uses traditional control method.Traditional low-pass filter is adopted for the signal


Fig. 6 Test bench of the ADFIS

processing of rail pressure signal. Control algorithmuses the conventional proportion-integral (PI) con-troller. The proportion and integral coefficients of PIcontroller are set as 12 and 15, respectively. CANapeis used to collect data. The step experiments are con-ducted with 15MPa as step. The experimental datais shown in Fig. 7; Δp is the error between target railpressure and actual rail pressure. In the step process,the overshoot is large and the error in the high railpressure steady state is big. When the rail pressureis 80MPa, fluctuation of rail pressure reaches ±5MPaand fluctuation of control effort is relatively large.

40

80

120

−20

0

20

20 25 30 35 40 45 500.180.190.200.21

t/s

p/M

Pa

Δp/

MPa

u

Target railActual rail

Fig. 7 Trajectory of rail pressure with traditional PI

controller

The second experiment is conducted on the testbench by adopting the control strategy proposed inSection 3. Peak sampling mechanism is used for sam-pling the rail pressure, and the maximum value is ex-tracted in every ten analog-digital (AD) value. Targetrail pressure and actual rail pressure adopt enhancedDenis differentiator for signal processing. Parametersof enhanced Denis differentiator are: α = 0.6, k1 = 2,k2 = 15, k3 = 0.2. Control algorithm uses the nonlinearPID controller proposed in Ref. [10]. Parameters of thenonlinear PID controller are: β0 = 25, β1 = 2, β2 = 8.

The step experiments are conducted with 5MPa as step(non-violent experiment for preventing damage to thecircuit). The target rail pressure changes in range of70 to 80MPa, which is the commonly used pressurefor real condition. The experimental results are shownin Fig. 8. The steady state error is within ±1MPa,the overshoot is within ±3.5MPa, and control effort issmooth.

60708090

p/M

Pa

−5

0

5

Δp/

MPa

7.08 7.09 7.10 7.11 7.12 7.13 7.14 7.150.17

0.18

0.19

t×10−3/s

u


Fig. 8 Trajectory of rail pressure with proposed control

strategy

To further validate the transient operating condi-tions, governor experiment is conducted on a diesel en-gine with the novel pump system. The engine parame-ters are shown in Table 1. The accelerator is fixed at themaximum position. Three unload experiments are con-ducted by adjusting the load through the dynamometer.The same rail pressure control strategy and parametersare used as in the second experiment. The experimen-tal results are shown in Fig. 9; n is engine speed. Theactual rail pressure tracks rapidly and the steady stateerror is within ±1MPa, while in transient conditiontracking error is within ±3MPa and control effort issmooth.

50

75

100

p/M

Pa

2.2

2.42.6

n×10−

3 /(r

·min−

1 )

500 510 520 530 540 550 560 5700.15

0.20

0.25

t/s

u


Fig. 9 Trajectory of rail pressure on engine test bench


Table 1 Parameters for diesel engine

Parameter Value Parameter Value

Engine displacement/L 8.3 Rated power/kW 192

Bore & stroke/mm 114 & 135 Rated speed/(r · min−1) 2 200

Low idle/(r · min−1) 700 Maximum torque/(kN · m) 1

Maximum cylinder pressure/MPa 1.4 Maximum torque speed/(r · min−1) 1 300—1 500

6 Conclusion

This paper proposes a rail pressure controller for anovel common rail fuel injection system. Characteris-tics of solenoid valve, signal processing method, controlalgorithms and control parameters affect the rail pres-sure control accuracy. An enhanced tracking differen-tiator with robust to noise is presented in this paper,which can get smooth tracking signal and resume differ-ential signal. When the enhanced tracking differentia-tor is applied to the PID control, the control accuracyand dynamic response of the system can be improved.Since rail pressure control system can be approximatelyregarded as a cascade system, double loop control strat-egy is adopted to decouple the control system. In ad-dition, the rail pressure peak sampling mechanism, thenonlinear PID algorithm and the feed forward controlare adopted to improve the controller performance. Ex-perimental results on both fuel pump test bench andengine test bench verify the controller performance.

References

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[2] Wang Hong-rong, Zhang You-tong, Wang Jun, et al.Pressure control of high pressure common rail dieselengine [J]. Transactions of Beijing Institute of Tech-nology, 2008, 28(9): 778-781 (in Chinese).

[3] Chen Lin, Yang Fu-yuan, Yang Xue-qing, et al.Model-based controller framework for a common raildiesel engine [J]. Journal of Tsinghua University: Sci-ence and Technology, 2010, 50(7): 1077-1081 (in Chi-nese).

[4] Chen Hai-long, Ouyang Guang-yao, Xu Hai-cheng.Research on simulation of rail pressure control basedon pump control valve [J]. Chinese Internal Combus-

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design of rail pressure tracking controller for novel fuel injection system

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