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Original Article

Proc IMechE Part D:J Automobile Engineering2014, Vol. 228(7) 703–718� IMechE 2014Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/0954407014521797pid.sagepub.com

Nonlinear model-based control ofcombustion timing in premixed chargecompression ignition

Lyle E Kocher1, Carrie M Hall2, Dan Van Alstine3, Mark Magee3 andGregory M Shaver3

AbstractOne of the major challenges in the control of advanced combustion modes, such as premixed charge compression igni-tion, is controlling the timing of the combustion event. A nonlinear model-based controller is outlined and experimen-tally shown to be capable of controlling the engine combustion timing during diesel premixed charge compressionignition operation on a modern diesel engine with variable valve actuation by targeting the desired values of the in-cylinder oxygen mass fraction and the start of injection. Specifically, the experimental results show that the strategy iscapable of controlling the start of combustion and the intake oxygen mass fraction to within 1� crank angle and 1%respectively. A stability analysis also demonstrates that this control strategy ensures asymptotically stable errordynamics.

KeywordsEngine control systems, engine emission control, engine valvetrains, heavy-duty diesel engines, low-emission engines

Date received: 15 May 2013; accepted: 9 January 2014

Introduction

Engine developers continually balance the tighteningemissions legislation1 with requirements to maximizethe fuel efficiency. In modern diesel engines, aftertreat-ment systems are deployed to reduce the engine-outemissions to the legislated tailpipe-out levels.2–4 Analternative to this approach is the use of advanced com-bustion modes including diesel premixed charge com-pression ignition (PCCI), homogeneous chargecompression ignition (HCCI), and low-temperaturecombustion (LTC) which offer the potential of reducedemissions while maintaining a high engine efficiency.5–11

In particular, PCCI can be achieved on diesel enginesby lengthening the time period between the start ofinjection (SOI) and the start of combustion (SOC) suchthat there is sufficient time for the fuel and air to premixprior to combustion. Combustion then occurs in onerapid event at a rate governed by the chemical kineticsof the combustion reaction. This leads to lower localtemperatures and lower equivalence ratios and shiftsoperation to regions where particulate matter and nitro-gen oxide emissions are dramatically reduced,12 asdemonstrated in Figure 1. While dramatic reductions inthe emissions can be achieved through this combustion

strategy, the lack of a direct combustion trigger has pre-viously limited the widespread adoption of diesel PCCIand other advanced combustion modes.

Additionally, many of these advanced combustiontechniques are enabled through the use of flexible val-vetrains, as will be considered in this work.13–19 The useof variable valve actuation (VVA) allows alterations inthe effective compression ratio (ECR) of the engine tobe made, thereby enabling changes to the engine’s gasexchange processes to be carried out.

In PCCI, the SOI will be followed by an ignitiondelay period which is significantly affected by the in-cylinder conditions. If the ignition delay period is notsufficiently long, there will not be adequate time forcomplete mixing of the air and fuel prior to combus-tion. While control of the SOI alone can provide some

1Cummins Inc, Columbus, Indiana, USA2Illinois Institute of Technology, Chicago, Illinois, USA3Ray W Herrick Laboratories, Purdue University, West Lafayette, Indiana,

USA

Corresponding author:

Gregory M Shaver, Ray W Herrick Laboratories, Purdue University, 140 S

Martin Jischke Drive, West Lafayette, IN 47907, USA.

Email: [email protected]

combustion phasing control, combustion phasing con-trol which utilizes the SOI as its sole input will not berobust to changes in the in-cylinder contents, the tem-perature, and the pressure. To place the combustionevent accurately, proper control of the nonlinear gasexchange processes as well as control of the fuel injec-tion timing are essential in order to maintain therequired in-cylinder temperatures necessary to achievesuch an LTC mode.

Several key studies have investigated control of thegas exchange processes through the use of a nonlinearmodel-based controller such as that utilized in thiswork. Previous efforts included a paper by Jankovicet al.,20 in which a nonlinear model-based controllerwas developed to regulate the air-to-fuel ratio and theexhaust gas recirculation (EGR) fraction on a dieselengine equipped with a variable-geometry turbocharger(VGT) and an EGR valve. The controller was experi-mentally validated against engine data containing refer-ence set-point steps. Operations of the engine undertypical diesel diffusion combustion and advanced com-bustion modes were not considered. Jung and Glover21

designed and implemented a robust gain-scheduledmodel-based controller which was based upon a third-order linear parameter-varying model of the air path ofa turbocharged diesel engine. The intake manifold pres-sure was utilized to schedule the gains, and the EGRvalve position and the VGT position are used as con-trol inputs. The controller was experimentally validatedagainst engine data containing reference set-point stepsand a portion of the New European Driving Cycle.Operations of the engine under typical diesel diffusioncombustion and advanced combustion modes were notconsidered.

Other studies have investigated control of advancedcombustion modes including a paper by Husted et al.,22

in which a proportional–integral controller was devel-oped to control the combustion phasing of a dieselengine operating in pre-mixed diesel combustion to a

reference set point. The controller utilized the crankangle for 50% burned mass fraction (CA50), calculatedfrom the in-cylinder pressure data, as feedback to adjustthe fuel injection timing. The controller was experimen-tally validated against engine data containing an engineload ramp at a constant engine speed. A stability analy-sis was not included.

Combustion control in partially premixed combus-tion (PPC) modes has been investigated by Tunestaland Lewander23 and Lewander.24 System identificationmethods were used to model the dynamics between thefuel injection and the combustion characteristics.Model-based control was then utilized to enable PPCto occur by maintaining a CA50 that was within a pre-defined region while controlling the injection timingand the injection duration to keep the indicted meaneffective pressure (IMEP) and the ignition delay at thedesired values. This control method utilized in-cylinderpressure measurements to obtain feedback on theCA50, the IMEP, and the ignition delay.

Wang25 developed a hybrid robust nonlinear model-based controller for a modern diesel engine operatingunder multiple combustion modes. The intake mani-fold pressure, the intake manifold oxygen fraction, andthe exhaust manifold pressure were selected as the con-trolled system outputs. Sliding-mode controllers weredeveloped for each combustion mode considered, andthe controllers were switched by a designed supervisorycontroller. The controller was experimentally validatedagainst engine data containing the EGR valve andVGT actuator step changes and the engine load ramps.The controller took into account the advanced combus-tion modes but did not control or estimate the combus-tion phasing.

Unlike these previous efforts, this work uses a non-linear model-based controller to provide control of thegas exchange and fueling processes and to achievetracking of a desired SOC target in diesel PCCI com-bustion. The controller utilizes the VGT actuator tocontrol the intake manifold oxygen fraction to a desiredvalue and additionally modifies the start of injectioncommanded by the engine electronic control module(SOIECM) to achieve the desired SOC. Feedback for theoxygen fraction controller is provided by an oxygenfraction estimator developed by three of the presentauthors and co-workers.26 Stability of the PCCI com-bustion timing controller is shown through applicationof the Lyapunov theory. The controller is designed totrack the desired intake manifold oxygen fraction towithin 1% oxygen with asymptotic stability. Thedesired SOC is achieved by inverting a PCCI combus-tion timing model27 to calculate the necessary SOI com-mand. The desired SOC is controlled to within 1� crankangle (CA). The controller is validated on an engine uti-lizing high-pressure cooled EGR, variable-geometryturbocharging and flexible intake valve actuation. Adirect measurement of the SOC is used for comparisonby utilizing an in-cylinder pressure transducer and aCA encoder processing the cycle data in real time in

Figure 1. Emissions with respect to the local temperatureversus the local equivalence ratio for different operatingmodes.12

LTC: low-temperature combustion; PCCI: premixed charge compression

ignition; HCCI: homogenous charge compression ignition; NO: nitric

oxide.

704 Proc IMechE Part D: J Automobile Engineering 228(7)

dSPACE. Several underlying estimators, which werepreviously developed by the present authors, are used inthis effort and as such will be only briefly covered in thispaper. The nonlinear controller focused on in this workpresents a significant step forward in actually demon-strating control of the combustion timing in PCCI.

Experimental setup

A 2010 Cummins diesel engine outfitted with an elec-trohydraulic VVA system was utilized in this study.The Cummins ISB engine is a 6.7 l, 360 hp six-cylinderdirect-injection diesel engine. As shown in Figure 2, theengine is an in-line six-cylinder configuration equippedwith a Bosch common-rail fuel injection system withmulti-pulse injection capability and a cooled EGRloop. The engine also has a VGT to boost the engineperformance over the entire operating range as well asan electronic EGR valve to allow control of the freshcharge and EGR flows delivered to the cylinder.

The electrohydraulic VVA system, which was manu-factured by Team Corporation and described in moredetail by Modiyani et al.28 and Kocher et al.,29 is capa-ble of modifying the intake valve opening, the peakintake valve lift, and the intake valve closing (IVC) ona cylinder-independent cycle-to-cycle basis. The VVAsystem was used to alter the IVC timings in this work.The ability to control the intake valve actuation pro-vides the capability to alter the ECR which affects the

volumetric efficiency and the amount of piston-motion-induced compression.

The experimental engine data are acquired using adSPACE system. The dSPACE system collects datafrom the engine electronic control module (ECM)such as the commanded fueling quantities and timingsas well as the ECM sensor measurements. The engineis equipped with an open architecture ECM thatallows direct read and write access to the memorylocations at 100 Hz. The dSPACE system also collectsdata from additional temperature, pressure, flow, andemissions measurements instrumented on the enginetest bed. The fresh-air mass flow rate is measuredusing a laminar flow element (LFE) device. Theengine charge flow is calculated using the LFE fresh-air flow measurement and the measured EGR frac-tion. Emission gas analyzers are used to measure thecomposition of the exhaust gases as well as the con-centration of carbon dioxide (CO2) in the intakemanifold. Cambustion nondispersive infrared fastCO2 analyzers were utilized during this testing. TheEGR fraction is computed using the intake andexhaust manifold CO2 measurements. The intakemanifold CO2 is sampled in three locations and aver-aged to provide the best measurement average of thetrue intake manifold CO2, as shown in Figure 2. Auniversal exhaust gas oxygen sensor is mounted in theexhaust pipe shortly after the turbine outlet, as shownin Figure 2.

Figure 2. Schematic diagram of a modern diesel engine.CO2: carbon dioxide; EGR: exhaust gas recirculation; IMT_TEMP: intake manifold temperature; Inj.: injection; CAC:charge air cooler; IVC: intake

valve closing; ECR: effective compression ratio; EXH_PORT_TEMPS: exhaust port temperatures; EGR_CLR_IN_T: exhaust gas recirculation cooler,

temperature in; EGR_CLR_OUT_T: exhaust gas recirculation cooler, temperature out; TURB_IN_T: turbocharger, temperature in; VGT: variable-

geometry turbocharger; LFE: laminar flow element; DELTA_P_SENSOR: Delta pressure sensor; O2: oxygen.

Kocher et al. 705

PCCI combustion timing model

As mentioned previously, one of the major challengesin using PCCI is achieving the proper timing of thecombustion event. The controller developed in thiswork utilizes a combustion timing model for dieselPCCI developed by three of the present authors andco-workers.27 A short description of the model is pro-vided below.

PCCI combustion timing model development

The time delay that exists between the SOIECM and theSOC is modeled as three distinct consecutive delaysaccording to

SOIECM+ telec + thyd + tid=SOC ð1Þ

where telec is the delay present in the electrical system,thyd is the hydraulic delay present in the injector, andtid is the ignition delay.

Analysis of the injector current signal reveals a dif-ference between the SOIECM timing and when the injec-tor current actually begins to rise. This average value isthe electrical delay telec given by

telec= �1:3 8CA ð2Þ

This observed delay is due in part to an actual delay inthe electrical subsystem as well as to an offset in topdead center (TDC). The TDC offset is due to a discre-pancy between the TDC location reported by theengine’s crankshaft position sensor and the measuredTDC provided by an AVL 365C position encoder. TheAVL encoder has a resolution of 0.1� CA and allowsprecise knowledge of the true TDC. Since the effect ofthe TDC offset manifests itself in the injector currentsignal, it is included in the electrical delay. The observedelectrical delay was constant in the CA domain.

The next delay in the system is a hydraulic delay inthe injector, which is the time between when the injectorcurrent signal is enabled and when fuel droplets actuallybegin to exit from the injector nozzle. Examination ofthe injection rate-shape profiles allows characterizationof the hydraulic delay for a variety of engine speed andload conditions. The hydraulic delay is essentially con-stant in the time domain at 0:3 ms. As such, in units ofdegrees CA, the hydraulic delay is given by

thyd =0:0018N 8CA ð3Þ

where N is the engine speed in revolutions per minute.The ignition delay tid is modeled using the

Arrhenius-type correlation

tid =0:051F�1:14cyl�P�0:51

e2100=�T ð4Þ

where tid is in milliseconds, Fcyl is the in-cylinder oxy-gen fraction, and P and T are the average in-cylinderpressure and average in-cylinder temperature respec-tively during the ignition delay period.27 The averagepressure and average temperature over the ignition

delay period from the SOI to the SOC can be approxi-mated as

�P=12PimV

npIVC V

�np(SOI+TDC)=2 +V

�npSOI

� �ð5Þ

�T=12PimV

npIVC

mchargeRchargeV�np +1

(SOI+TDC)=2 +V�np +1SOI

� �ð6Þ

in which Pim is the intake manifold pressure, VIVC is thecylinder volume at the IVC, VSOI is the cylinder volumeat the SOI, V(SOI+TDC)=2 is the cylinder volume at themidpoint between top dead center (TDC) and the SOI,np is the polytropic coefficient, mcharge is the chargemass and Rcharge is the gas constant for the charge air.

Combining the tid model in equation (4) with theelectrical delay and hydraulic delay in equation (2) andequation (3) respectively completes the PCCI combus-tion timing model first described in equation (1) andgives the expression for the SOC as

SOC=�1:3+0:0018N+0:006Nð0:051Fcyl

�1:14 �P�0:51

e2100=�TÞ+SOIECM

ð7Þ

in which the SOC is in degrees CA, �P and �T are calcu-lated from equation (5) and equation (6) respectively,and N is in revolutions per minute. Additional detailsregarding the development of this model can be foundin the paper by three of the present authors and co-workers.27 This model expresses the dependence of thecombustion timing in PCCI on the in-cylinder condi-tions as well as the commanded fuel injection timing.

PCCI combustion timing model experimental results

The model detailed above was experimentally validatedby three of the present authors and co-workers27

against 180 PCCI data points collected on the experi-mental engine test bed. SOIECM and IVC sweeps wereperformed at 12 nominal speed–load conditions,namely 271 N m, 203 N m, and 102 N m (200 ft lbf,150 ft lbf, and 75 ft lbf), each at 2400 r/min, 2000 r/min, 1600 r/min, and 1200 r/min. The VGT positionwas varied to provide sufficient EGR to remain in aPCCI combustion mode. All data points presented inthis study have a single main injection of fuel and havea carbon balance error of less than 610%. (The carbonbalance is the difference between the carbon in theintake versus the carbon in the exhaust and was evalu-ated on the basis of the CO2 measurements and theinjected fuel mass.) Note that all timings are reportedin degrees CA after top dead center (ATDC) of firing.

The PCCI combustion timing model in equation (7)maps from the SOIECM to the SOC, given knowledgeof the total in-cylinder oxygen mass fraction (Fim), theaverage pressure ( �P) and the average temperature ( �T)across the ignition delay, and the engine speed N. Themodel predicts the SOC to within 62� CA of theexperimental values for all but three of the 180 datapoints, which represents 98%+ accuracy. The r.m.s.


error is 0.86� CA. Figure 3 shows the model and experi-mental SOC data in a scatter plot for comparison. Thesolid line is the 1:1 line and the dashed lines signify 62�CA. The PCCI combustion timing model will be uti-lized to control the actual SOC in the following sec-tions. As the timing model predicts the SOC to within62� CA, it is expected that the combustion timing con-troller should be able to maintain a similar level ofaccuracy. However, a portion of the observed error inthe controlled SOC will be due to the uncertainty in themodel.

PCCI combustion timing controller

The design of the PCCI combustion timing controllerbegins by examining the relationship between the con-trol inputs and the desired SOC, as described in equa-tion (7). The inputs to the control model include theSOIECM, the in-cylinder oxygen fraction, and the in-cylinder temperature and pressure during the ignitiondelay period. While examining the inputs, it is apparentthat the inputs can be separated on the basis of thespeed of the dynamics associated with the inputs. In thiscase, the in-cylinder oxygen fraction and the pressureand temperature during the ignition delay period areheavily dependent on the gas exchange processes, whilethe commanded SOI is essentially infinitely fast owingto the bandwidth of the fuel system. This separation ofthe dynamics allows a decoupled controller approach tobe made. The slower controller will focus on controllingthe dynamics associated with the gas exchange process,and the faster controller will focus on controlling thedynamics associated with the fuel injection process.Previous work by three of the present authors and co-workers26 has demonstrated that the in-cylinder oxygenfraction is extremely close to the intake manifold oxy-gen fraction. This is due to the small amount of residualexhaust gas that remains in the cylinder. Therefore, the

assumption will be made to neglect the effect of the resi-dual exhaust gas on the in-cylinder oxygen fraction,and the intake manifold oxygen fraction will be utilizeddirectly in equation (7).

Previously developed and validated models of thegas exchange processes26,30 will be employed for thedevelopment of the slower controller which focuses ontracking the desired in-cylinder conditions. As a firststep, only the in-cylinder oxygen fraction is consideredas an input to the PCCI combustion timing controller.The variation in the in-cylinder temperature and pres-sure during the ignition delay period will not be directlycontrolled but instead will be considered as a distur-bance to the system.

The intake manifold oxygen fraction dynamics aredescribed by

_Fim= RTim

PimVimFambWc +FemWEGR � FimWeð Þ ð8Þ

where Fim is the fraction of oxygen in the intake mani-fold, R is the universal gas constant, Tim, Pim, and Vim

are the temperature, pressure, and volume respectivelyin the intake manifold, Wc is the flow through the com-pressor, WEGR is the EGR flow, and We is the flowinto the engine cylinder. The development of thismodel for the intake manifold oxygen dynamics as wellas validation of this model over a wide speed range(1000–2300 r/min) and load range (200–522 N m) havebeen detailed previously by three of the present authorsand co-workers.26

Examination of equation (8) reveals the impor-tance of the flows Wc and WEGR into the intake mani-fold, as well as the flow We leaving the intakemanifold. The traditional control actuators for thegas exchange process include the EGR valve positionand the VGT position. However, PCCI combustionmodes typically require large quantities of EGR,resulting in an EGR valve position of 100% under alloperating conditions. Therefore, the VGT positionwill be the controlling actuator for the intake mani-fold oxygen fraction dynamics. The VGT positionwill have a direct impact on the flow (Wt) through theturbocharger turbine and, in turn, will control thecompressor flow (Wc). As such, recording thedynamics of the turbocharger is essential to properlycontrolling the VGT position such that the desiredintake manifold oxygen fraction is achieved.

The VGT turbine is modeled using analytical func-tions based upon turbine maps provided by the turbo-charger manufacturer to determine the flow throughthe turbine. The analytical functions were derivedand validated by three of the present authors and co-workers31 and allow the turbine speed and mass flowto be found independently of the manufacturer’s maps,reducing the computation time for real-time estimationand control. Turbine maps generally express the tur-bine speed and mass flow in terms of reduced quantitiesto account for the inlet conditions

Figure 3. Scatter plot of the model SOC versus theexperimental SOC (the dashed lines are 62� CA).SOC: start of combustion.

Kocher et al. 707

Wt, red =Wt

ffiffiffiffiffiffiffiffiTem

p

Pemð9Þ

vtc, red =vtcffiffiffiffiffiffiffiffiTem

p ð10Þ

where Wt, red is the reduced turbine mass flow, vtc, red isthe reduced turbine speed, and Tem and Pem are the tur-bine inlet temperature and turbine inlet pressurerespectively.

The reduced turbine flow (Wt:red) is calculatedthrough an analytical function using the pressure ratio(PRt) across the turbine and the turbocharger shaftspeed vtc:red according to

Wt, red=pd2t gRexhð Þ1=2g b1 + b2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2cp, exh 1�PR(1�g)=g

tð Þp=60ð Þdtvtc, red½ �2

r" #

3a1X

2VGT +a2XVGT +a3ð Þ p=60ð Þdtvtc, red½ �(2g�1)=g

4Rexh

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2cp, exh 1�PR(1�g)=g

tð Þp

Here, Rexh and cp, exh are assumed to be constant. Thevalues for bi and ai, which are found via the least-squares method using the manufacturer’s turbochargermaps, are listed in Table 1. The reduction of the turbo-charger maps has been covered in detail previously bythree of the present authors and co-workers.31 Notethat the three inputs to equation (11) are vtc, red, PRt,and XVGT (the VGT position) and result in reducedmass flow. This reduced mass flow can then be used inequation (9) to back out the actual mass flow throughthe turbine.

Equations (9) to (11) represent the link between theVGT position, which will be used as a control input forthe PCCI controller, and the turbine flow.

The turbine flow is related to the turbine power Pturb

by

Pturb=Wtcp, exhhturbTem 1� Pamb

Pem

� �(gexh�1)=gexh

ð12Þ

The turbine and compressor powers are related byconsidering the turbocharger shaft dynamics accordingto

_vtc =Pturb � Pcomp

Iturbvtcð13Þ

where vtc is the turbocharger shaft speed, Iturb is themoment of inertia of the turbocharger, Pturb is the tur-bine power, and Pcomp is the compressor power.

It is assumed that the turbocharger shaft is in thesteady state. While this simplifying assumption couldinduce minor errors, the steady-state approximation isreasonable, given the large lumped volume between theturbocharger compressor outlet and the intake mani-fold. Furthermore, as will be shown in a subsequentsection, even given this assumption the controller(which is derived from this, and other, models) is shownto perform quite well on an experimental test bed.

Applying the steady-state assumption to the turbo-charger shaft dynamics shown in equation (13), thecompressor power (Pcomp) can be assumed to be equal

to the turbine power (Pturb). The compressor power(Pcomp) can then be utilized to calculate the compressorflow ðWcÞ using

Pcomp=Wccp, ambTamb

hcomp

Pim

Pamb

� �(gamb�1)=gamb

� 1

" #ð14Þ

To simplify the notation, the following substitutionsare made:

Wc = kcompPcomp ð15Þ

kcomp =hcomp

cp, ambTamb Pim=Pambð Þ(gamb�1)=gamb � 1h i ð16Þ

Pturb= kturbWt ð17Þ

kturb=hturbcp, exhTem 1� Pamb

Pem

� �(gexh�1)=gexh

" #ð18Þ

Wc = kcompkturbWt ð19Þ

kFim=

RimTim

PimVimð20Þ

The WEGR term in equation (8) will be treated as a dis-turbance to the system since the main control actuator,namely the EGR valve position, is saturated at its max-imum position. The value of WEGR is provided by anEGR flow estimator developed by Kocher32 and isdependent on the pressure drop across the engine. Theintake manifold oxygen fraction dynamics are now castin the state-space equivalent form

_Fim=kFimFambkcompkturbWt+kFim

FemWEGR � kFimFimWe

ð21Þ

Equation (21) can be expressed as the linear parameter-varying form

_x=A(r)x+B(r)u+G(r) ð22Þ

in which

A(r)= �kFimWe ð23Þ

B(r)= kFimFambkcompkturb ð24Þ

G(r)= kFimFemWEGR ð25Þ

where the system parameters are expressed in r, thestate x is the intake manifold oxygen fraction (Fim), andthe input u is the turbine flow (Wt) which is directlycontrollable by adjusting the VGT position.

With the system dynamics defined, a control lawmay be selected to stabilize the system and to providereference tracking of the desired Fim values. Theselected control law is given by

Table 1. Turbine mass flow constants.

b1 –2.8883 3 1022

b2 1.9318a1 –1.2056a2 2.2198a3 –1.5203 3 1022


u=K(rf � x)+L ð26Þ

where rf is the filtered version of the Fim reference com-mand r after it is filtered by the system dynamics and isgiven by

_rf =Arf � Ar

= � kFimWerf + kFim

Werð27Þ

The usage of the matrix A is a suitable choice since itreflects the dynamics of the physical system.

Substitution of the control law in equation (26) intothe system dynamics equation (21) yields the closed-loop expression

_x=Ax+B K(rf � x)+L� �

+G ð28Þ

With the control law selected for the slower gasexchange dynamics, fixing the values of Fim, �P, and �T,the SOIECM can be determined on the basis of theengine speed and the desired SOC. The SOIECM is cal-culated using

SOIECM=SOC� 1:3� 0:0018N

�0:006N 0:051F�1:14im�P�0:51

e2100=�T

� � ð29Þ

A high-level graphical representation of the control-ler structure is shown in Figure 4. The PCCI controllerrecieves commands for the desired SOC and Fim andutilizes the intake manifold oxygen controller repre-sented by equation (28) to determine the required tur-bine flow input. The VGT position is then calculatedusing equations (9) to (11). The required SOI will bedetermined on the basis of equation (29) and the cur-rent in-cylinder conditions.

Figure 5 shows the PCCI controller structure andincludes the additional models and estimators utilizedin the control. Underlying models of the gas exchangeprocesses including estimates of the volumetric effi-ciency, the EGR flow, the turbine flow, and the intakemanifold oxygen fraction provide inputs to the PCCI

controller which are utilized in the Fim controller aswell as in the SOI calculation.

PCCI combustion timing controller stability

With the closed-loop system dynamics and the refer-ence filter dynamics defined, the stability of the closed-loop system may be analyzed by examining the errordynamics given by

e= rf � x ð30Þ_e= _rf � _x ð31Þ

Substitution of the expressions for _rf and _x into equa-tion (31) yields the equation

_e=Arf � Ar� Ax� B K(rf � x)+L� �

� G ð32Þ

After simplification, the expression for _e is

_e=(A� BK)e� Ar� BL� G ð33Þ

The gain L may be selected to negate the errordynamics associated with the original reference

Figure 5. Block diagram of the PCCI controller structure including the estimators and the models.SOC: start of combustion; SOI; start of injection; SOIECM: start of injection commanded by the engine electronic control module; VGT: variable-

geometry turbocharger; O2: oxygen; EGR: exhaust gas recirculation.

Figure 4. Block diagram of the PCCI controller structure.SOC: start of combustion; SOI; start of injection; SOIECM: start of

injection commanded by the engine electronic control module; VGT:

variable-geometry turbocharger; EGR: exhaust gas recirculation.

Kocher et al. 709

command r and the disturbance due to the WEGR termand is given by

L=�Ar� G

Bð34Þ

L=Wer� FemWEGR

kcompkturbFambð35Þ

This selection of the gain L will reduce the errordynamics to

_e=(A� BK)e ð36Þ

The selection of the gain K will be determined on thebasis of the experimental controller performance tuningand a Lyapunov analysis will be performed to assessthe stability. A Lyapunov function V is chosen as

V=12e

2 ð37Þ

The derivative of the Lyapunov function is then calcu-lated as

_V= e _e ð38Þ

Substituting the expression for _e in equation (36) intoequation (38) yields the equation

_V= e (A� BK)e½ � ð39Þ

After substituting for A and B in equation (39), theexpression can be simplified to

_V=(� kFimWe � kFim

kcompkturbFambK)e2 ð40Þ

To demonstrate the stability, the Lyapunov functionV needs to be positive definite and the derivative of theLyapunov function _V needs to be negative definite.Examination of equation (40) shows that the errordynamics will be stable and _V will be negative definiteas long as K. 0. The difficulty in selecting the gain Karises when evaluating the controller performancedynamically and assessing the desired performance androbustness tradeoffs associated with the controllerdesign. While the choice of controller gain will influ-ence the transient response, the steady-state error, andthe robustness over the operating conditions examinedin this study, the error dynamics are expected to be sta-ble and to converge asymptotically for any positivegain value (as shown in the analysis). In order to vali-date the control strategy experimentally, the gain wastuned to 3000 in order to give a good balance betweenthe transient response, the error, and the robustnessover different operating conditions. Care was taken toavoid engine damage that might result from misfire oroverly advanced combustion timing.

Experimental results for the PCCIcombustion timing controller

The PCCI combustion timing controller developed wasimplemented using a dSPACE control system. The

controller was then tested in multiple operating condi-tions to demonstrate its performance. A variety of tran-sitions were investigated including steps in the intakemanifold oxygen fraction, steps in the commandedSOC, steps in the VC, and steps in the fueling.

Performance during commanded intake manifoldoxygen steps

It is essential that the controller tracks changes in thedesired intake manifold oxygen fraction while alsotracking the desired SOC.

Figure 6 shows the controller operating at an enginespeed of 1600 r/min and an engine torque of 140 ft lbf.The desired SOC was fixed at –5� CA ATDC, and theFim command was stepped from 20% oxygen to 16%oxygen. In Figure 6, the upper left-hand plot shows theoxygen fraction in both the intake manifold and theexhaust manifold. The solid black curve is the referencefiltered commanded intake manifold oxygen fraction.The dashed red curve is the estimated intake manifoldoxygen fraction, and the dot-dashed blue curve is themeasured exhaust oxygen fraction. The manifold oxy-gen fraction plot shows the step change in the desiredintake manifold oxygen fraction and the estimatedintake manifold oxygen fraction tracking the referencecommand. The estimated value of Fim tracks the desiredoxygen fraction to within 1% oxygen as desired. Theupper right-hand plot shows the desired SOC as a solidblack line. The dashed red line is the measured SOCbased upon the in-cylinder pressure trace and the bluedot-dashed curve is the commanded SOI. Figure 6shows that the SOC is controlled to the desired SOC towithin 1� CA while Fim is being step changed. The com-manded SOI is adjusted by the controller to compen-sate for the change in Fim, as evidenced by examiningthe SOI command during the Fim step changes. Thebottom left-hand plot shows the gas exchange actuatorpositions. The VGT position is shown as a solid blackcurve. The VGT position is adjusted to control the esti-mated Fim to the desired Fim. The EGR valve positionis shown as a dashed red line at 100% open. As a largeamount of EGR is required to ensure sufficiently longignition delays in PCCI, the EGR valve is required tobe fully open during all tests. The IVC timing is shownas a blue dot-dashed line and is fixed at 565� CAATDC, which is the nominal IVC timing. The bottomright-hand plot shows the commanded turbine flow asa solid black curve. The dashed red curve shows theactual turbine flow as calculated by the turbochargeranalytical functions described by three of the presentauthors and co-workers.31 The calculated turbine flowis controlled to the commanded turbine flow by adjust-ing the VGT position. A larger VGT position, reportedas the percentage closed, allows less flow to passthrough the turbine when compared with a smallerVGT position, allowing the turbine flow to be con-trolled through adjustment of the VGT position. Note


that, when a smaller amount of intake manifold oxygenis required, the VGT closes, thereby reducing the tur-bine flow and providing a higher EGR flow and thedesired intake manifold oxygen level.

Figure 7 shows the controller operating at an enginespeed of 1200 r/min and an engine torque of 140 ft lbf.The desired SOC was held constant at 0� CA ATDC,and the Fim command was stepped between 20% oxy-gen and 16% oxygen. The IVC timing was held con-stant at 565� CA ATDC. The effects on the system atthis lower engine speed are handled by the controller.In both of these cases, the desired Fim and the desiredSOC are achieved.

Performance during commanded SOC steps

The previous results demonstrated that different SOCvalues could be tracked during steps in the desired intakemanifold oxygen fraction. Next, the controller’s abilityto track steps in the desired SOC is evaluated.

Figure 8 shows the controller operating at an enginespeed of 1600 r/min and an engine torque of 140 ft lbf.The desired SOC was stepped and the Fim commandwas held constant at 20% oxygen. In Figure 8, themanifold oxygen fraction plot shows the desired intakemanifold oxygen fraction and the estimated intakemanifold oxygen fraction tracking the reference

command. The estimated value of Fim tracks thedesired oxygen fraction. The upper right-hand plotshows that the SOC is controlled to the desired steppedSOC while Fim is held constant. The commanded SOI,shown as a dot-dashed blue curve, is adjusted to com-pensate for the change in the desired SOC. The bottomleft-hand plot shows the VGT position being adjustedto control the estimated Fim to the desired Fim. TheEGR valve position is shown as a dashed red line at100% open. The IVC timing is shown as a dot-dashedblue line and is fixed at 565� CA ATDC. The bottomright-hand plot shows that the actual turbine flow iscontrolled to the commanded turbine flow by adjustingthe VGT position.

Figure 9 shows the controller operating at an enginespeed of 1200 r/min and an engine torque of 140 ft lbf.The desired SOC was stepped, and the Fim commandwas held constant at 16% oxygen in Figure 9. The IVCtiming was held constant at 565� CA ATDC.

Performance during IVC steps

The valvetrain flexibility is another key enabler ofPCCI, and changes in the valve timings will have adirect impact on the ECR of the engine and the volu-metric efficiency of the engine. In this section, steps inthe IVC are considered.

Figure 6. PCCI combustion timing controller (SOC, –5� CA ATDC; Fim, stepped; IVC, 565� CA ATDC at 1600 r/min and 140 ft lbf).O2: oxygen: Cmd: command; SOC: start of combustion; atdc: after top dead center; SOI; start of injection; EGR: exhaust gas recirculation; VGT:

variable-geometry turbocharger; IVC; intake valve closing. Wt: turbine flow.

Kocher et al. 711

Figure 7. PCCI combustion timing controller (SOC, 0� CA ATDC; Fim, stepped; IVC, 565� CA ATDC at 1200 r/min and 140 ft lbf).O2: oxygen: Cmd: command; SOC: start of combustion; atdc: after top dead center; SOI; start of injection; EGR: exhaust gas recirculation; VGT:


Figure 8. PCCI combustion timing controller (SOC, stepped; Fim = 20%; IVC, 565� CA ATDC at 1600 r/min and 140 ft lbf).O2: oxygen: Cmd: command; SOC: start of combustion; atdc: after top dead center; SOI; start of injection; EGR: exhaust gas recirculation; VGT:



Figure 10 shows the controller operating at anengine speed of 1200 r/min and an engine torque of 140ft lbf. The desired SOC was held constant at –5� CAATDC and the Fim command was held constant at18% oxygen. The IVC timing was stepped from 565�CA ATDC to 535� CA ATDC and then back to 565�CA ATDC. This corresponds to a change in the ECRfrom the nominal ECR of 18.7 at the conventional IVCtiming (565� CA ATDC) to a reduced ECR of 15.9 atthe early IVC timing (535� CA ATDC). In Figure 10,the manifold oxygen fraction plot shows the desiredintake manifold oxygen fraction and the estimatedintake manifold oxygen fraction tracking the referencecommand. The estimated value of Fim tracks the desiredoxygen fraction despite a disturbance to the system inthe form of a change in the ECR of the engine. Theupper right-hand plot shows control of the SOC to thedesired SOC while Fim is held constant. The com-manded SOI is adjusted to control the desired SOCowing to the changes in the in-cylinder pressure and inthe temperature. The bottom left-hand plot shows theadjustment of the VGT position to control the esti-mated Fim to the desired Fim. The EGR valve positionis shown as a dashed red line at 100% open. The IVC

timing is shown as a dot-dashed blue curve and isstepped between 565� CA ATDC and 535� CA ATDC.The bottom right-hand plot shows that the actual tur-bine flow is controlled to the commanded turbine flowby adjusting the VGT position. The controller is capa-ble of controlling the desired Fim and the desired SOCduring the IVC step change.

Performance during fueling and load steps

While changes in the desired oxygen levels, the SOCtiming, and the IVC timing are commonly encounteredparticularly in PCCI, it is also essential to considerchanges in the engine load conditions.

Figure 11 shows the controller performance during afueling step change. The desired SOC was held constantat –5� CA ATDC, and the Fim command was held con-stant at 18% oxygen. The IVC timing was held con-stant at 535� CA ATDC. While the engine speed washeld constant at 1600 r/min, the fueling command wasstepped from 19 mg/stroke to 39 mg/stroke at 12 s andthen back to 19 mg/stroke at 26 s. This fueling com-mand step results in a load step from 80 ft lbf to 200 ftlbf and back. Figure 11 demonstrates the controller’s

Figure 9. PCCI combustion timing controller (SOC, stepped; Fim = 16%; IVC, 565� CA ATDC at 1200 r/min and 140 ft lbf).O2: oxygen: Cmd: command; SOC: start of combustion; atdc: after top dead center; SOI; start of injection; EGR: exhaust gas recirculation; VGT:


Kocher et al. 713

Figure 10. PCCI combustion timing controller (SOC, –5� CA ATDC; Fim = 16%; IVC, stepped at 1200 r/min and 140 ft lbf).O2: oxygen: Cmd: command; SOC: start of combustion; atdc: after top dead center; SOI; start of injection; EGR: exhaust gas recirculation; VGT:


Figure 11. PCCI combustion timing controller (SOC, –5� CA ATDC; Fim = 18%; IVC, 565� CA ATDC at 1600 r/min and stepped fueling).O2: oxygen: Cmd: command; SOC: start of combustion; atdc: after top dead center; SOI; start of injection; EGR: exhaust gas recirculation; VGT: variable-

geometry turbocharger; IVC; intake valve closing. Wt: turbine flow.


ability to control the desired Fim and SOC under enginefueling step changes.

Performance during combined changes

The previous results indicate that independent changesin the commands and the disturbances to the system arehandled well with this control strategy. Next, the con-troller’s performance is considered during simultaneouschanges in the commands and the disturbances.

Figure 12 shows the controller operating at anengine speed of 1600 r/min and an engine torque of 140ft lbf. The desired Fim was held constant at 18% oxygenand the desired SOC command was stepped. The IVCtiming was held constant at 535� CA ATDC. Recallthat changes in the IVC from the nominal value (565�CA ATDC) serve as a disturbance to this system byaltering the ECR and the volumetric efficiency. InFigure 12, the controller’s tracking performance is simi-lar to the previously described cases with Fim being con-trolled to within 1% oxygen and the SOC beingcontrolled to within 1� CA even with a disturbance tothe system in the form of an early IVC timing.

Similar results are observed at the operating pointfor 1200 r/min and 140 ft lbf. Figure 13 shows the

controller operating at an engine speed of 1200 r/minand an engine torque of 140 ft lbf. The desired SOCwas held constant at –5� CA ATDC and the Fim com-mand was stepped between 20% oxygen and 16% oxy-gen. The IVC timing was held constant at 535� CAATDC. In Figure 13, the Fim controller is unable todrive the estimated Fim completely to the desired Fim

command under the 20% oxygen command condition.In this case, the controller still achieves an error of lessthan 1% oxygen but is unable to reduce the error anyfurther. The reason for the degraded controller perfor-mance is due to the uncertainty in the models used inthe nonlinear model-based controller. The controllerrelies on the accuracy of the models in generating thecontroller commands, and inaccuracy of these modelsleads to degradation in the controller performance.

Conclusions

The controller developed in this work was shown to becapable of accurately controlling the combustion phas-ing of a modern diesel engine operating in PCCI. Thecontroller’s stability was demonstrated throughLyapunov analysis, and the controller’s functionality wasexperimentally validated at multiple operating

Figure 12. PCCI combustion timing controller (SOC, stepped; Fim = 0.18; IVC, 535� CA ATDC at 1600 r/min and 140 ft lbf).O2: oxygen: Cmd: command; SOC: start of combustion; atdc: after top dead center; SOI; start of injection; EGR: exhaust gas recirculation; VGT:


Kocher et al. 715

conditions. The results demonstrate that this controller iscapable of controlling the SOC to within 1� CA of adesired value while also controlling the intake oxygenfraction to within 1% of a desired oxygen fraction value.

Future work

In order to enable PCCI to occur and thereby to reduceemissions, VVA capabilities can also be utilized. Futurework will explore the combined actuation of valve tim-ings together with VGT and EGR settings for moreaccurate tracking of desired trajectories and fasterresponse times. The models employed in this effort willalso be used to explore transitions between PCCI andconventional diesel combustion in future studies.

Funding

This work was supported by the US Department ofEnergy (grant number DE-EE0003403).

Disclaimer

This report was prepared as an account of work spon-sored by an agency of the US Government. Neither theUS Government nor any agency thereof, nor any oftheir employees, makes any warranty, express orimplied, or assumes any legal liability or responsibility

for the accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed,or represents that its use would not infringe privatelyowned rights. Reference herein to any specific commer-cial product, process, or service by trade name, trade-mark, manufacturer, or otherwise does not necessarilyconstitute or imply its endorsement, recommendation,or favoring by the US Government or any agencythereof. The views and opinions of the authorsexpressed herein do not necessarily state or reflect thoseof the US Government or any agency thereof.

Declaration of conflict of interest

The authors declare that there is no conflict of interest.

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Appendix 1

Notation

Famb ambient air oxygen fractionFcyl in-cylinder oxygen fractionFem exhaust manifold oxygen fraction

Kocher et al. 717

Fim intake manifold oxygen fractionmcharge charge massN speed of the engineP average pressure during ignition

delayPamb ambient pressurePcomp compressor powerPem exhaust manifold pressurePim intake manifold pressurePturb turbine powerR universal gas constant�T average temperature during ignition

delayTamb ambient temperatureTem exhaust manifold temperatureTim intake manifold temperatureVim intake manifold volumeVIVC volume at intake valve closingV(SOI+TDC)=2 volume at midpoint between the

start of injection and top dead centerWc fresh air flow from the compressorWe charge flow from the intake

manifold to the cylinders

WEGR exhaust gas recirculation flowWt flow from the exhaust manifold

through the turbineWt, red reduced turbine mass flowXVGT position of the variable-geometry

turbocharger

hcomp efficiency of the compressorhturb efficiency of the turbinetelec electrical delaythyd hydraulic delaytid ignition delayvtc turbocharger shaft speedvtc, red reduced turbocharger shaft speed

Abbreviations

SOC start of combustionSOIECM start of injection commanded by the

engine electronic control modulePRt pressure ratio across the turbine


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