Model-Based Control for Mode Transition Between Spark

Shupeng ZhangDepartment of Mechanical Engineering,

Michigan State University (MSU),

East Lansing, MI 48824

e-mail: [email protected]

Ruitao SongDepartment of Mechanical Engineering,




Guoming G. ZhuDepartment of Mechanical Engineering;

Department of Electrical and Computer

Engineering,




Harold SchockDepartment of Mechanical Engineering,




Model-Based Control for ModeTransition Between SparkIgnition and HCCI CombustionWhile the homogeneous charge compression ignition (HCCI) combustion has its advan-tages of high thermal efficiency with low emissions, its operational range is limited inboth engine speed and load. To utilize the advantage of the HCCI combustion, an HCCIcapable spark ignition (SI) engine is required. One of the key challenges of developingsuch an engine is to achieve smooth mode transition between SI and HCCI combustion,where the in-cylinder thermal and charge mixture properties are quite different due tothe distinct combustion characteristics. In this paper, a control strategy for smooth modetransition between SI and HCCI combustion is developed and experimentally validatedfor an HCCI capable SI engine equipped with electrical variable valve timing (EVVT)systems, dual-lift valves, and electronic throttle control (ETC) system. During the modetransition, the intake manifold air pressure is controlled by tracking the desired throttleposition updated cycle-by-cycle; and an iterative learning fuel mass controller, combinedwith sensitivity-based compensation, is used to manage the engine torque in terms of netmean effective pressure (NMEP) at the desired level for smooth mode transition. Notethat the NMEP is directly correlated to the engine output torque. Experiment resultsshow that the developed controller is able to achieve smooth combustion mode transition,where the NMEP fluctuation is kept below 3.8% during the mode transition.[DOI: 10.1115/1.4035093]

Keywords: HCCI, mode transition, model-based control, iterative learning

1 Introduction

Homogeneous charge compression ignition (HCCI) combustionhas the potential of providing higher thermal efficiency and loweremissions than those of the conventional SI combustion due to itsunthrottled operation, flameless, and lean combustion nature [1,2].However, HCCI combustion also has limited operational rangedue to possible misfire at low load and knock at high load. AnHCCI capable SI engine equipped with EVVT actuation and dual-lift valve control is used to demonstrate smooth mode transitionbetween the HCCI and SI combustion [3–5].

It is fairly challenging to achieve smooth mode transitionbetween the SI and HCCI combustion due to the significant thermaland charge mixture differences between the HCCI and SI combus-tion. Note that the unthrottled HCCI combustion reduces pumpingloss with relatively high in-cylinder temperature at intake valveclosing (IVC) required by auto-ignition of the HCCI combustion,while the SI combustion is required to operate in a throttled modewith relatively low manifold pressure and temperature, especiallyaround the combustion mode transition region. In Ref. [6], anexperimental investigation of SI–HCCI–SI mode transition usinghydraulic two-stage profile camshafts is performed, where the valvetiming, step throttle opening (opening the throttle with a step com-mand) timing, and fuel mass are optimized. However, considerableengine torque fluctuation during the combustion mode transition isobserved. In Ref. [7], a state feedback controller is designed basedon a state-space model obtained from system identification, andfuel mass and negative valve overlap (NVO) are used as the controlinputs to track the desired indicated mean effective pressure(IMEP) and combustion phase. The model-based controller reducestorque fluctuation over the traditional proportional and integral (PI)

one, but engine torque output still varies unexpectedly, especially atthe beginning of the mode transition. In Ref. [8], a control-orientedcombustion model is linearized around the steady-state SI andHCCI operational conditions, and a controller, composed of state-feedback and model-based feed-forward components, is used tocontrol the fuel injection timing to track the desired combustionphasing without considering the hybrid combustion mode that startswith SI and ends with HCCI combustion. In Ref. [9], a model-based linear quadratic tracking strategy is used to track a desiredmanifold pressure to achieve a reasonable air-to-fuel ratio, and thefuel mass is controlled by using the iterative learning to maintainthe torque at the desired level. However, the proposed control strat-egy is validated only in hardware-in-the-loop (HIL) simulations.Note that in Ref. [9], the engine manifold air pressure (MAP) iscontrolled based on the linearized intake dynamic model, whichcould lead to significant transition-by-transition variations. Thiscould adversely affect the combustion stability during the modetransition.

In this paper, a model-based control strategy is developed toachieve smooth SI–HCCI combustion mode transition. The con-trol strategy mainly consists of two controllers: manifold pressurecontrol for regulating charge air and fuel mass control for manag-ing engine output torque. By considering the filling dynamics ofthe intake manifold, a feed-forward control based on the predeter-mined desired cycle-by-cycle throttle position is developed, andan linear parameter varying (LPV) closed-loop throttle positioncontrol strategy [10] is implemented to track the desired MAPprofile during the combustion mode transition. For the NMEPcontrol, iterative learning approach is used to obtain the fuel massat each transition cycle to maintain the engine NMEP at thedesired level under any transition condition; and sensitivity-basedfeed-forward control is developed to compensate the potentialNMEP fluctuation due to the cycle-by-cycle variation (such asMAP variations). The developed control strategy is validated on asingle-cylinder HCCI capable SI engine at four different transi-tional engine operational conditions.

Contributed by the Dynamic Systems Division of ASME for publication in theJOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript receivedNovember 4, 2015; final manuscript received October 19, 2016; published onlineFebruary 6, 2017. Assoc. Editor: Douglas Bristow.

Journal of Dynamic Systems, Measurement, and Control APRIL 2017, Vol. 139 / 041004-1Copyright VC 2017 by ASME

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 05/02/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use

The main contribution of this paper is the proposed multicyclecontrol strategy for mode transition between SI and HCCI com-bustion that takes account of actuator dynamics. The mode transi-tion smoothness is achieved by combining the MAP and NMEPcontrol strategies, and the combined control strategy is validatedon a single-cylinder HCCI capable SI engine. It is demonstratedthat the proposed strategy completes the combustion mode transi-tion within six to eight engine cycles, and the NMEP fluctuationsare below 3.8%. The proposed sensitivity-based iterative learningcontrol scheme is also applicable to the engine calibration processunder both steady-state and transient operation conditions.

The paper is organized as follows: Section 2 describes the com-bustion mode transition control problem and provides a generalcontrol framework; and based on the engine model described inSec. 3, MAP, fuel, and NMEP control are presented in Secs. 4 and5, respectively. The associated experimental validation results areprovided in Sec. 6. Section 7 concludes the paper.

2 Mode Transition Control Problem

2.1 Engine Configuration. The HCCI capable SI engineused for the model-based control of combustion mode transition isa single-cylinder engine equipped with EVVT systems, dual-liftvalve-train, and ETC system. The LPV control strategy is used forprecise throttle position control [10], and an output covarianceconstraint (OCC) controller [11] is used to accurately regulate theintake and exhaust valve timings. The intake air is heated byengine coolant through a heat exchanger installed in the intakemanifold to around 350 K (with 62.5 K error) before enteringboth intake ports to make the auto-ignition possible for the HCCIcombustion. The Siemens production gasoline direct fuel injectorsare used for the target engine with a fuel rail pressure of 150 bar,and the injected fuel quantity is controlled by the injection pulsewidth. The injection timing is 300 before top dead center (BTDC)to have a close-to-homogenous charge since fuel is injected whilethe intake valve is open, which allows the fuel to be mixed duringthe intake and early compression strokes. The engine is equippedwith the in-cylinder pressure sensor for calculating combustioncharacteristics such as NMEP, CA10, CA50, and CA90 (crankposition where 10%, 50%, and 90% trapped fuel are burned) inreal-time and a production MAP sensor is also used. Table 1 liststhe engine specifications.

2.2 Control Problem. SI and HCCI combustion requiresquite different in-cylinder thermoconditions and charge mixtureproperties. For instance, the engine is normally operated undermedium or low load when the mode transition is required betweenSI and HCCI combustion, where the intake manifold pressure isrelatively low due to throttled SI operation and the engine is oper-ated under stoichiometric air-to-fuel ratio (AFR) required by theafter treatment system. On the other hand, the HCCI combustionis normally operated under a relatively lean AFR and largeamount of trapped exhaust gas with widely opened throttle, wherethe NVO is utilized to trap a desired amount of the hot residual

gas to manage the in-cylinder temperature at IVC to enable theauto-ignition. This leads to high percentage of exhaust-gas-recirculation (EGR).

The primary goal of combustion mode transition control is tomaintain the engine output torque (directly related to engineNMEP) at a desired level during the transition cycles when all theengine control parameters gradually migrate from the settingrequired by the SI combustion to the setting required by the HCCIcombustion. Due to the relatively slow engine actuator dynamics,such as the EVVT system, approximately five to ten engine cyclesare needed to complete the mode transition between the SI andHCCI combustion. The transition process and the required numberof engine cycles are also heavily dependent on the engine speed.

Figure 1 shows a set of open-loop control parameters used formode transition from SI to HCCI combustion when the engine isoperated at 2000 rpm with 4.5 bar NMEP. The valve timings forthe SI mode were optimized experimentally to achieve the highestthermal efficiency, or in other words, the highest NMEP with thegiven fuel quantity; the valve timings for the HCCI mode weredetermined to achieve the most stable combustion with the lowestcoefficient of variation (COV) of NMEP and the proper CA50;during the combustion mode transition, the intake valve isretarded by 63 crank deg while the exhaust valve is advanced by80 crank deg from the SI to HCCI combustion mode within eightengine cycles. The valve timings during the mode transitioncycles were determined by the EVVT system response profiles toa step command (63/80 crank deg). Both of the intake and exhaustvalves are switched from high lift to low lift within the first transi-tional cycle. While the change in the valve lifts results in a suddenchange in the in-cylinder temperature owing to the reduced effec-tive compression ratio in the cycle from high to low lift and alsoresults in the increase of residual gas amount, leading to longercombustion duration, the spark timing is advanced significantlyfor the first few transitional cycles to avoid late combustion andretarded gradually from the sixth cycle when the auto-ignitionoccurs and remains at top dead center (TDC) in the HCCI com-bustion mode as a precaution to eliminate misfire; see Ref. [12]for detailed spark timing selection. The sixth to eighth cycles arecalled “hybrid combustion cycles,” which starts with SI combus-tion mode and continues with HCCI combustion when the gasmixture in the unburned zone satisfies the condition for auto-ignition [12]. HCCI combustion is shown by the much faster massburn rate than that of the SI combustion during both hybrid com-bustion mode and steady HCCI combustion mode. Note that fastthrottle opening (such as step opening) immediate after transitionstarts could lead to ultralean AFR, causing partial-burn or misfire

Table 1 Engine specifications

Parameters Model values

Bore/stroke/con-rod length 86 mm/86 mm/151 mmCompression ratio 12.7:1Intake air temperature 350 KIntake/exhaust valve lifts—high 9 mmIntake valve opening (IVO) duration—high 216 crank degExhaust valve opening (EVO) duration—high 216 crank degIntake/exhaust valve lifts—low 5 mmIntake valve opening duration—low 148 crank degExhaust valve opening duration—low 148 crank degDefault IVO with zero intake cam phase 410 deg ATDC

Fig. 1 Open-loop control parameters

041004-2 / Vol. 139, APRIL 2017 Transactions of the ASME


[9]; and slow throttle opening might lead to quite rich AFR, pre-venting stable HCCI combustion. A reference throttle opening sig-nal, updated cycle-by-cycle, is used to follow a predeterminedMAP trajectory to maintain the normalized air-to-fuel ratio(denoted by k) between 1.0 and 1.3 to make sure that stable hybridcombustion can be initiated by the spark event. As an example,Fig. 2 shows that the AFR increases from stoichiometric SI com-bustion to lean (k ¼ 1:2) steady HCCI combustion mode gradu-ally. It can be seen that as the MAP and k increase, the peak in-cylinder pressure increases gradually due to the increased rate ofheat release in SI–HCCI hybrid and HCCI combustion, and at thesame time, the engine NMEP remains unchanged. Due to theadvancement of the exhaust valve timing, the magnitude of smallpressure peaks between exhaust and intake strokes due to NVOalso increases, which can be observed in Fig. 2 during the modetransition and HCCI combustion periods.

In the case of mode transition from HCCI to SI combustion, allthe open-loop control parameters will be reversed and the descrip-tion figure is omitted.

2.3 Control Framework. Based on the open-loop controlstrategy shown in Fig. 1, the combustion mode transition at agiven operational condition can be considered as a repetitive pro-cess (with fixed open-loop scheduled control parameters, such asspark timing, valve timings, and MAP), where the iteration learn-ing approach can be applied to obtain the fuel mass required totrack the desired NMEP. However, in practical applications, therepeatability of such a process is highly sensitive to the cycle-by-cycle variations, such as fluctuation of combustion timing (causedby turbulent flow, in-cylinder temperature variation, etc.) andMAP tracking variation (caused by intake manifold pressurewave). In order to improve the robustness of the iterative learning,sensitivity-based compensation is utilized to reduce the cycle-by-cycle variations.

Figure 3 shows the architecture of the proposed model-basedcontroller for combustion mode transition. The open-loop feed-forward control parameters are scheduled for spark timing (hST),valve lift (Plift), IVO (hIN), EVO (hEX), the initial fuel mass(mfuelði� 1Þ) to be used for the iterative learning, target CA50(CA50), target NMEP (NMEP), and the reference throttle position(hTPS) to track the target MAP (PMAP, see Sec. 4). The NMEP iscontrolled by regulating the fuel mass through iterative learning,and the sensitivity-based feed-forward controller adjusts the fuelmass to compensate the possible NMEP fluctuations by utilizingthe measured CA50 of the last engine cycle and the MAP of cur-rent cycle, see Sec. 5. Note that NMEP is normally calculatedbased upon the measured in-cylinder pressure. During the enginecalibration process or under steady-state operational conditions,

the iterative learning is turned on; and after the learning processconverges, it could be turned off and the sensitivity-based com-pensation will continue for improved robustness. Note that thesmall iterative learning gain can also be used to make the controlrobust to engine aging and engine-to-engine variations.

As a summary, the open-loop control is used for adjusting sparktiming, valve lifts, and timings during the transition; the enginemanifold pressure is controlled by tracking the desired throttleposition during the mode transition and the NMEP is controlledby regulating the fuel injection quantity using both sensitivity-based feed-forward control and iterative learning feedback con-trol, where the iterative learning can be used during the calibrationprocess to generate the initial calibrations for smooth mode transi-tion and during normal operation with small learning gain to com-pensate for manufacturing engine-to-engine variations and engineaging.

3 Engine Combustion Modeling

In order to investigate the impact of intake charge quantity andinjected fuel mass to the engine combustion characteristics,engine thermodynamics equations are derived for different com-bustion phases over the entire engine cycle. Figure 4 shows thedefinition of the engine cycle and its associated combustionevents, where SOC, EOC, EVO, EVC, IVO, and IVC denote startof combustion, end of combustion, exhaust valve opening, exhaustvalve closing, intake valve opening, and intake valve closing,respectively.

EVO is used as the dividing point between cycles k� 1 and k,and the calculation of in-cylinder thermodynamic characteristicsof cycle k is based on the measured in-cylinder pressure at cyclek� 1 and current intake manifold pressure at the IVC of cycle k.

Fig. 2 Engine performance for the SI to HCCI combustionmode transition Fig. 3 Mode transition control diagram

Fig. 4 Combustion events

Journal of Dynamic Systems, Measurement, and Control APRIL 2017, Vol. 139 / 041004-3


Fuel injection timing is set to 300 deg before TDC that is close toIVO. All the parameters required for feed-forward fuel control aremade available about 30 deg crank angle before fuel injection tim-ing so that the engine control has enough time to schedule the fuelinjection pulse; and the MAP at TDC before IVO is used insteadof the MAP at IVO due to the assumption that the MAP at TDCand IVO is close to each other. Note that assuming the in-cylinderpressure at IVC equal to MAP may lead to certain error but theerror is relatively small, see Ref. [13]. The in-cylinder thermody-namics models under different combustion phases are presentedbelow.

3.1 Polytropic Process. Polytropic process is assumed duringthe exhaust (from exhaust valve opening to intake valve opening),compression, and expansion phases. Under the configuration ofvalve lifts and EVVT strategy, NVO starts from the second transi-tion cycle once the valves have been shifted to the low lift. Forpolytropic process, the in-cylinder temperature at crank angle h isgiven by

Th ¼ TeVe

Vh

� �n�1

(1)

where the index e denotes the event of EVO, EVC, IVC, or EOCwhen h is within the exhaust, NVO, compression, or expansionphases, respectively; V is the in-cylinder volume; and n is thepolytropic exponent. Note that n is a function of in-cylinder tem-perature; however, it is chosen to be a constant during each com-bustion phase to make the real-time calculation possible for thesensitivity-based control (see Sec. 5).

3.2 Charge Mixing. During the intake phase, the residual gasand intake fresh charge can be considered separately. First, the in-cylinder pressure at IVC is approximated to be equal to the intakemanifold pressure, then the volume of the residual gas and thefresh charge can be obtained sequentially at IVC as follows:

Vres kð Þ ¼ VEVC kð Þ PEVC kð ÞPMAP kð Þ

!1=n

(2)

Vair kð Þ ¼ VIVC kð Þ � VEVC kð Þ PEVC kð ÞPMAP kð Þ

!1=n

(3)

By the ideal gas law, the masses of the fresh charge and the aver-age in-cylinder temperature are

mair kð Þ ¼ PMAP kð ÞVair kð ÞRTMAT

(4)

TIVC kð Þ ¼ PMAP kð ÞVIVC kð Þmres k � 1ð Þ þ mair kð Þ þ mfuel kð Þ½ �R

(5)

respectively.

3.3 Combustion Process. Three combustion modes areinvestigated, and they are SI combustion mode used for transitioncycles 1–3, SI–HCCI hybrid combustion mode for cycles 4–8, andHCCI combustion mode for cycles 9, 10, and beyond. These cyclenumbers are for the mode transition at 2000 rpm, and they vary asa function of engine speed. Note that the in-cylinder temperaturecalculation can be simplified to be a sum of a polytropic volumechange process and a heat release process [13]. In the SI mode,during the combustion process

Th kð Þ ¼ TIVC kð Þ VIVC kð ÞVh

� �n�1

þ gQLHVmfuel kð Þx hð ÞmCv

(6)

where m ¼ mresðkÞ þ mairðkÞ þ mfuelðkÞ is the total in-cylindermass, g is the combustion efficiency, QLHV is the lower heatingvalue of the fuel, and xðhÞ is the mass fraction burned (MFB),which is modeled by the Wiebe function [14] to make the sensitiv-ity analysis possible (see Sec. 5.2.2). Note that MFB can also becalculated based upon the in-cylinder pressure [15] with improvedaccuracy of CA50 sensitivity-based control (see Sec. 5.2.4).

In the HCCI combustion mode, since the combustion durationis much shorter than that in the SI mode, a constant volume heatrelease process is assumed. Therefore, at the EOC

TEOC kð Þ ¼ TIVC kð Þ VIVC kð ÞVEOC kð Þ

!n�1

þ gQLHVmfuel kð ÞmCv

(7)

For the SI–HCCI hybrid combustion mode, the following Arrhe-nius integral [14] is used to determine the start of HCCI(SOHCCI) combustion:

ðhSOC

hIVC

A

Nee� Ea

RTunburned hð Þdh ¼ 1 (8)

where Ea is the activation energy for the auto-ignition reaction,and A is a scaling factor, both are related to fuel composition andexperimentally determined, see Ref. [13] for more details.Tunburned denotes the temperature of the unburned zone, and theMFB is calculated before SOHCCI for SI combustion, which isrepresented by xSIðhÞ. Consequently, prior to the switching point

TSI�HCCI kð Þ ¼ TIVC kð Þ VIVC kð ÞVh

� �n�1

þ gQLHVmfuelxSI hð ÞmCv

(9)

and at the EOC, the in-cylinder temperature has the same expres-sion as Eq. (7). The in-cylinder pressure is obtained by ideal gaslaw for all of these three cases.

4 Manifold Pressure Control

Since the manifold filling dynamics is much slower than that ofthe electronic throttle and pressure wave exists in the intake mani-fold due to the periodic engine intake valve events, a manifoldpressure feed-forward control strategy based on closed-loopcontrol of the throttle position is developed to follow the cycle-by-cycle updated throttle reference signal. By using the ETC sys-tem in Ref. [10], for each engine cycle within the transitioncycles, the throttle is set to a target position to achieve requiredmanifold pressure, and the transient behavior of the throttle posi-tion is ignored due to its fast response time, which simplifies thecalculation.

For the lean combustion circumstance, the fresh air preparedfor combustion in cycle k consists of the newly charged air in Eq.(4) (cycle k) and also the unburned air in the residual gas fromcycle k� 1. Hence, the normalized air-to-fuel ratio in cycle k isobtained by

k kð Þ ¼ mair kð Þ þ mair k � 1ð Þ k k � 1ð Þ � 1½ �14:6mfuel kð Þ

(10)

The fuel mass mfuelðkÞ is expected to lie inside the range of fuelmass in steady SI mode and in steady HCCI mode. Based on apredetermined sequence of kðkÞ and controlled valve timing, therequired MAP can be obtained by Eqs. (3), (4), and (10).

Then consider the filling dynamic equation of the intakemanifold



PMAP kð Þ ¼ PMAP k � 1ð Þ þ RTMAT

Vman

min k � 1ð Þ � mout k � 1ð Þ½ �

(11)

where TMAT, Vman, min, and mout denote the manifold air tempera-ture, manifold volume, intake air mass through the throttle to themanifold, and the air mass going to the cylinder from the intakemanifold, respectively. Note that mout is easy to obtain by thescheduled nominal target and min can be obtained by the com-pressible flow equation below

_min ¼ hTPS

CdAtP0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2c= c� 1ð Þ

pffiffiffiffiffiffiffiffiRT0

p W PMAPð Þ (12)

where Cd is the discharge coefficient (fixed for simplicity); P0 andT0 are the atmosphere pressure and temperature; At is the throttlereference area; and W is the function of PMAP and thedetailed expression is provided in Ref. [13]. During eachengine cycle, the averaged manifold pressure PMAP (wherePMAP ¼ ðPMAPðk � 1Þ þ PMAPðkÞÞ=2) is used as an approxima-tion of PMAP in Eq. (12); therefore, the target throttle positionhTPSðkÞ (the control reference of the manifold pressure controller)can be obtained by combining Eqs. (10)–(12). Note that hTPSðkÞ isalso dependent on engine speed. Figure 5 shows the MAP trackingresults during the mode transition, and Fig. 1 shows the throttlereference hTPSðkÞ.

5 Fuel and NMEP Control

The NMEP is defined as the engine effective work completedper unit volume over an engine cycle and it can be calculated bythe following integral over an engine cycle:

NMEP ¼þðp=VÞdV (13)

where p is the in-cylinder pressure, and V is the current cylindervolume.

Assume that the in-cylinder pressure can be expressed as afunction of the injected fuel mass, the intake manifold pressure,and the in-cylinder temperature at EVC from the previous model-ing analysis, the engine NMEP can also be written as follows bycombining Eqs. (1)–(9):

NMEPðkÞ ¼ FðmfuelðkÞ;PMAPðkÞ;TEVCðkÞÞ (14)

Note that there are other engine control parameters (such asspark timing and valve timing) that affect the NMEP. Since theyare not used for iterative learning control and sensitivity-based

compensation, these control parameters are not explicitlyexpressed in Eq. (14). The control target is to maintain NMEP atthe desired level by regulating the fuel mass for each transitioncycle during the transition. Due to cyclic operation of the internalcombustion engine, iterative learning control (ILC) [9,16] is anefficient approach to improve the tracking performance (fixed tra-jectory in this case) with a simple control structure.

5.1 Iterative Learning Control

5.1.1 P-Type Iterative Learning Control. As the fuel massmfuel is the only control input, the nonlinear equation (14) can bepartially linearized to obtain a simple state-space model for con-trol purpose since TEVC at cycle k is dependent on the NMEP atcycle k – 1

xðk þ 1Þ ¼ f ðxðkÞÞ þ BðkÞuðkÞyðkÞ ¼ xðkÞ

(15)

where xðkÞ ¼ NMEPðkÞ is the state, and B is the fuel sensitivityfunction that will be discussed in Sec. 5.1.

A P-type [17–19] ILC is used in the form of

uðiþ 1; kÞ ¼ uði; kÞ þ Kðyd � yði; kÞÞ (16)

where indices i and k represent iterative learning number andengine cycle number during the transition, respectively; K is theproportional iterative learning gain; and yd is the desired NMEPoutput. The system is stable if the learning gain satisfies

j1� K � BðkÞj � 1 (17)

which implies that

K � 2=BðkÞ ¼ 2@mfuelðkÞ=@NMEPðkÞ (18)

5.1.2 Robustness Analysis. If the condition (17) holds, thetracking error converges to zero as the iteration steps go toinfinity, assuming that there are no external disturbances or mea-surement errors. However, in real-engine applications, enginecycle-by-cycle variations cannot be neglected. For mode transi-tion, this cycle-by-cycle variation is mainly due to two reasons:One is that the engine combustion is heavily dependent on thecycle-by-cycle varying in-cylinder turbulence for SI and HCCIcombustion, and the other is due to the MAP tracking error andtrapped mixture property variations caused by the previous com-bustion event.

Considering the following system with disturbance:

xðk þ 1Þ ¼ f ðxðkÞÞ þ BðkÞuðkÞ þ wðkÞyðkÞ ¼ xðkÞ

(19)

and the disturbance

wðkÞ ¼ w1ðkÞ þ w2ðkÞ (20)

is a combination of w1, defined as NMEP perturbation due tocycle-by-cycle variations of the turbulence charge-mixing, andw2, defined as the NMEP perturbation due to the trapped mixtureproperty variations of the previous engine cycle. Note that w1 isdifficult to be compensated due to its random nature and w2 canbe compensated by the sensitivity-based feed-forward control tobe discussed in Sec. 5.2. It can also be shown that with boundeddisturbance w1, the convergence of system in Eq. (19) is guaran-teed by the ILC law in Eq. (16) with an output tracking errorbound in the form of

limi!1

supjdyij � f1ðKÞ þ jw1jf2ðKÞ (21)

Fig. 5 Manifold pressure tracking during the mode transitionfrom SI to HCCI at 2000 rpm with 4.5 bar NMEP



where f1ðKÞ and f2ðKÞ are functions of the learning gain K. Moredetails are provided in Ref. [19]. Note that there is a tradeoffbetween the rate of convergence and the ILC robustness. That is,a high learning gain could result in fast learning convergence withlarge steady-state error; while low learning gain leads to a smallsteady-state tracking error but with slow learning convergence.

5.2 Sensitivity-Based Compensator. The purpose of sensitivity-based compensation is twofold: minimizing the effect of cycle-by-cycle variations to the iterative learning process to make itconverge fast and reducing the NMEP fluctuations due to thecycle-by-cycle variations.

5.2.1 Sensitivity Analysis. Let Sm, SP, and ST represent theNMEP sensitivities with respect to fuel mass, MAP, and exhausttemperature at EVC, respectively, and they can be expressed asfollows:

Sm kð Þ ¼ @NMEP kð Þ@mfuel kð Þ

¼ @F

@mfuel kð Þ

��m fuel kð Þ;T EVC kð Þ;PMAP kð Þ

(22)

SP kð Þ ¼ @NMEP kð Þ@PMAP kð Þ

¼ @F

@PMAP kð Þ


(23)

ST kð Þ ¼ @NMEP kð Þ@TEVC kð Þ

¼ @F

@TEVC kð Þ


(24)

where mfuelðkÞ, TEVCðkÞ, and PMAPðkÞ denote the nominal valuesfor fuel mass, MAP, and exhaust temperature at EVC under thecurrent operational condition, and the same notations will be usedin the rest of the paper. Therefore, the first-order approximation ofthe Taylor expansion of Eq. (14) leads to the following sensitivityfunction:

dNMEPðkÞ ¼ dmfuelðkÞSmðkÞ þ dPMAPðkÞSPðkÞ þ dTEVCðkÞSTðkÞ(25)

Since the sensitivity-based feed-forward control target is to elimi-nate the NMEP fluctuations, by setting dNMEPðkÞ ¼ 0, the fuelmass correction can be obtained by

dmfuel kð Þ ¼ � 1

Sm kð ÞdPMAP kð ÞSP kð Þ þ dTEVC kð ÞST kð Þ½ � (26)

The sensitivity functions SmðkÞ, SPðkÞ, and STðkÞ are derived inSecs. 5.2.2 to 5.2.4.

5.2.2 Sensitivity of Fuel Mass. The small deviation of the in-cylinder pressure and temperature during the compression phasecaused by the evaporation of dmfuel is ignored in this derivation.Then for the SI combustion case, during the combustion phase

Ph kð Þ ¼ mRT IVC kð ÞVh

VIVC kð ÞVh

� �n�1

þ gQLHVmfuel kð Þx hð ÞCvVh

(27)

and as a result, assuming that the MFB does not change due tosmall variation of the fuel mass, the instantaneous in-cylinderpressure deviation is

Ph kð Þ � Ph kð Þ ¼ gQLHVdmfuel kð Þx hð ÞCvVh

(28)

Note that the in-cylinder pressure variation is very small, due tofueling mass change calculated based upon the fuel deviation,between EVO and SOC. Hence, the integral of pressure-to-volume within this period is omitted. Only the integral between

SOC and EVO is considered and it can be expressed by the fol-lowing two equations from SOC to EOC:

ðEOC

SOC

Ph kð Þ � Ph kð Þ� �

dVh ¼ðEOC

SOC

gQLHVdmfuel kð Þx hð ÞCvVh

dVh

¼ dmfuel kð ÞðEOC

SOC

gQLHVx hð ÞCvVh

dVh (29)

and from EOC to EVO

ðEVO

EOC

Ph kð Þ � Ph kð Þ� �

dVh ¼ðEVO

EOC

gQLHVdmfuel kð ÞCvVh

VEOC kð ÞVh

� �n

dVh

¼ dmfuel kð ÞðEVO

EOC

gQLHV

CvVh

VEOC kð ÞVh

� �n

dVh

(30)

Since all the parameters contained in the integrals of Eqs. (29)and (30) are available for offline calculation, the sensitivity func-tion of fuel can be finally obtained as follows:

Sm kð Þ ffiðEOC

SOC

gQLHVx hð ÞCvVh

dVh þðEVO

EOC

gQLHV

CvVh

VEOC kð ÞVh

� �n

dVh

(31)

Note that Cv and n are assumed to be constant within the integralinterval to simplify the calculation. The derivation of SmðkÞ in theHCCI mode and SI–HCCI hybrid mode is similar, thus omitted inthis paper.

5.2.3 Sensitivity of Intake Manifold Pressure. The change ofintake manifold pressure results in variations of air charge mass,the in-cylinder temperature, and air-to-fuel ratio. This conse-quently affects the engine NMEP. Under lean combustion opera-tional condition with high percentage of residual gas, air-to-fuelratio changes, the intake manifold pressure deviation could resultin CA50 deviation, and consequently affect the NMEP. The fol-lowing two equations are results of exponential curve fitting basedon the experimental data. The relationship between CA50 andMAP deviations based on curve fitting is expressed by

dCA50 kð Þ ffi dPMAP kð Þ 1250 k kð Þ � 1� �1:5

e�50 k kð Þ�1½ �2:5

PMAP kð Þ(32)

and the effect of CA50 deviation to NMEP is approximated by

dNMEPðkÞ ffi �0:2½ð1þ 0:0085ðdCA50ðkÞÞ2Þ0:6 � 1�NMEPðkÞ(33)

see similar approximation in Ref. [20]. Finally, the sensitivityfunction of the intake manifold pressure SPðkÞ can be calculatedby combining Eqs. (32) and (33).

In the HCCI combustion mode, since the throttle is widelyopened, the manifold pressure would remain unchanged and SPðkÞis set to zero.

5.2.4 Sensitivity of In-Cylinder Temperature. In the hybridcombustion mode, change of in-cylinder temperature affects theauto-ignition timing, which is the major factor of the NMEP devi-ation. The in-cylinder temperature of cycle k is mainly affected bythe trapped residual gas temperature from the previous cycle(k� 1); the compensated fuel mass dmfuel also leads to tempera-ture variation. While the in-cylinder temperature is not measura-ble, CA50 can be used as a replacement. For brevity, only thefinal calculation results are shown in this section. The in-cylindertemperature variation at EVC can be obtained by



TEVC kð Þ � T EVC kð Þ ffi gQLHV

CvVn�1EVO k � 1ð Þ

� mfuel k � 1ð Þ VCA50 k � 1ð Þn�2� h

�mfuel k � 1ð Þ VCA50

k � 1ð Þn�2� i

(34)

Then, the deviation of in-cylinder pressure at IVC is in the formof

TIVC kð Þ � T IVC kð Þ ffi dTEVC

PMAP kð ÞVIVC kð Þm k � 1ð ÞR

1

TEVC

� Pnþ1ð Þ=n

MAP kð ÞP 1�nð Þ=nEVC k � 1ð Þ

nTMAT

" #

¼: g kð ÞdTEVC (35)

The deviation of auto-ignition timing with respect to thedeviation of TIVC is provided in Ref. [21] through first-orderapproximation. The complete sensitivity function is

ST kð Þ ffiðSOC

IVC

VIVC kð ÞVh

� �n

dVh þðEVO

SOC

mRg

Vh

VIVC kð ÞVh

� �n�1

dVh

þ PEOC kð Þ � PSOH kð Þ� � lg kð ÞEA

RT2

IVC kð Þe� EA

RTSOH

kð ÞðSOH

IVC

Vh

VIVC kð Þ

� �1�n

e� EA

RTh kð Þdh (36)

where the index SOH denotes the crank position associated withthe start of auto-ignition (HCCI mode) during the hybrid combus-tion cycles, and l ¼ @Vh=@hjSOH .

In the SI combustion mode, the effect of in-cylinder tempera-ture of cycle k� 1 to the combustion of cycle k is minimum, andhence, STðkÞ is set to zero.

6 Experimental Validation

The finalized controller shown in Fig. 3 is then implementedinto the MSU Opal-RT based prototype engine controller, andtests are conducted on an HCCI capable single-cylinder SI enginedescribed in Sec. 2. The instantaneous engine performance param-eters are measured (such as valve timing, manifold pressure, andin-cylinder pressure) and calculated (such as NMEP and CA50)by Opal-RT engine controller in real-time.

First, the mode transition from SI to HCCI is studied at2000 rpm with 4.5 bar NMEP. Figure 5 shows the manifold pres-sure tracking results for a sequence of ten mode transition cases. Itcan be seen that the manifold pressure follows the desired trajec-tory very well, the maximum tracking error (mostly occursbetween the fifth and seventh cycles) is about 0.03 bar (5%), andthe maximum resulting air-to-fuel ratio tracking error is also about0.05 (5%). This error is small enough for the sensitivity-basedcontrol to compensate the resulting deviation.

Figure 6 shows the iterative learning results without sensitivity-based fuel compensation, and the learning gain is selected asfollows:

K ¼ SmðkÞ ¼ @NMEPðkÞ=@mfuelðkÞ

The initial fuel mass for the first three single injection cycles is setto be the same as that under steady SI combustion, and for the lat-ter five engine cycles dual injection pulse widths are set to beidentical to that under steady HCCI combustion. It can be seenthat at the first learning iteration, the deviation of NMEP is fairly

large, especially around fourth to fifth cycles, where the chargemixture is relatively lean with a large percentage of residual gas.With the selected learning gain, the NMEP error reduces very fastbut remains within a range of about 0.5 bar thereafter.

Figure 7 shows a much better learning performance with thesensitivity-based compensation under the same operational condi-tion with a low learning gain

K ¼ SmðkÞ=2

The engine NMEP of all the transition cycles converges to the tar-get in a little bit slower pace, but remains within a smaller errorwindow of around 0.1 bar, comparing with the previous case.Note that there are still NMEP fluctuations during the transitionespecially for cycles 4 and 5, where the fuel sensitivity is far awayfrom the linear range; however, the learning still shows a goodconvergence at the end.

From Fig. 8, it can be observed that during the learning itera-tions, for each learning iteration the updated fuel mass reduces forthe first three cycles and increases for the next five cycles. Afterfive learning iterations, the resulted fuel mass uniformly reducesfrom the first cycle to the last cycle during the mode transition.The reason is that as the throttle is opened, the pumping loss isgradually reduced, leading to improved fuel economy. That is,less fuel is required to have the same NMEP.

Taking the fuel mass learning process for the sixth cycle as anexample, Fig. 9 shows the uniform fuel mass convergence as afunction of the learning iteration number. Note that the nominal

Fig. 6 Iterative learning w/o sensitivity compensation, duringthe mode transition from SI to HCCI at 2000 rpm with 4.5 barNMEP

Fig. 7 Iterative learning with sensitivity compensation, duringthe mode transition from SI to HCCI at 2000 rpm with 4.5 barNMEP



fuel is provided by the ILC, compensated fuel is due to thesensitivity-based control, and the total fuel is the sum of both. Thesensitivity-based compensation is used to reduce possible cycle-by-cycle variations caused by the deviation of manifold pressureand in-cylinder temperature at EVC. The bottom subplot in Fig. 9splits the NMEP deviation caused by sensitivity terms SPðkÞ �dPMAP and STðkÞ � dTEVCðkÞ in Eqs. (23) and (24). In this case, thesensitivity due to PMAP dominates the sensitivity-based fuelcontrol.

Figure 10 shows the normalized air-to-fuel ratio during the iter-ative learning process. As discussed early, with the given initialfuel mass (see first learning iteration in Fig. 8), the learning leadsto significant reduction of NMEP in cycles 4, 5, and 6 due toinsufficient fuel mass. Figure 10 shows that the lean combustionoccurs in these cycles for the first two learning iterations; and after

five learning iterations, the air-to-fuel ratio (k) gradually increasesfrom the SI combustion (cycle 1) to the HCCI combustion (cycle9). This matches the gradually reduction of fuel mass shown inFig. 8.

Fig. 8 Iterative learning of injected fuel mass during the modetransition from SI to HCCI at 2000 rpm with 4.5 bar NMEP

Fig. 9 Fuel mass learning in the sixth cycle corresponding toFig. 8

Fig. 10 Normalized air-to-fuel ratio during the iterative learningassociated with Fig. 8

Fig. 11 Mode transition comparison of with and withoutsensitivity-based compensation

Fig. 12 Mode transition from SI to HCCI at 1500 rpm with5.0 bar NMEP with the same legend as Fig. 7



Once the iterative learning is converged, the fuel quantity can befixed or the learning gain can be reduced significantly to compensatefor engine aging, for example. Figure 11 shows a continuous ten tran-sitions under the learned fuel control parameters obtained from ILCwith or without sensitivity-based compensation. Due to the cycle-by-cycle variations caused by uncontrolled flow characteristics, certainNMEP fluctuation is expected for both cases; however, the maxi-mum NMEP error reduces greatly from 60:424 bar to 60:171 bar (a60% reduction) when the sensitivity-based compensation control isturned on. Significant improvement is achieved especially for thosecycles in the middle of transition, where the cycle-by-cycle variationis dominated by the manifold pressure fluctuations.

In Figs. 12–14, other combustion mode transition cases arestudied under different engine operational conditions, includingtransition from SI to HCCI at 1500 rpm with 5.0 bar NMEP, tran-sition from HCCI to SI at 2000 rpm with 4.5 bar NMEP, and at1500 rpm with 5.0 bar NMEP. Due to the figure size limitation,legend is omitted in these figures but they are the same as those inFig. 7. Good convergences are shown for all of these cases withinfive to six learning iterations.

Note that six engine cycles are needed for the transition from SIto HCCI at 1500 rpm. The initial fuel mass is set to the level forthe steady SI mode for the first two cycles and HCCI mode for thelast four cycles. Similar performance is observed at 2000 rpm;NMEP drops in the middle of transition in the first iteration, andafter the iterative learning converges, the total learned fuel massuniformly decreases from transition cycles 1 to 6.

For combustion mode transition from HCCI to SI, as the actionsof all the actuators and the initial fuel mass are set opposite to thecase of transition from SI and HCCI, NMEP drops between cycles1 and 5 as the pumping loss increases and increases suddenly atcycle 6 as fuel mass in steady-state SI combustion is used. Afterfive learning iterations, the fuel mass increases for cycles 1–8 asexpected.

Fig. 14 Mode transition from HCCI to SI at 1500 rpm, 5.0 barwith the same legend as Fig. 7

Fig. 15 Successful mode transition from SI to HCCI at2000 rpm, 4.5 bar

Fig. 13 Mode transition from HCCI to SI at 2000 rpm, 4.5 barwith the same legend as Fig. 7

Fig. 16 MFB curves during mode transition from SI to HCCI at2000 rpm with 4.5 bar NMEP

Fig. 17 Burning duration (CA10–CA 90) during mode transitionfrom SI to HCCI at 2000 rpm with 4.5 bar NMEP



For the case of 1500 rpm, other initial fuel conditions are alsotried to study the ILC robustness. Fuel mass for steady-state HCCIcombustion is used for all the transition cycles. The sudden“jump” of NMEP occurring in the first learning iteration is elimi-nated, and the learning converges in five iterations. The similarresult is obtained at 2000 rpm. This indicates that the ILC is robustto the initial fuel parameters.

The in-cylinder pressure and corresponding NMEP of a suc-cessful mode transition from SI to HCCI combustion at 2000 rpmwith 4.5 bar NMEP are shown in Fig. 15. During the combustionmode transition, the in-cylinder pressure trace shows a similartrend to that in Fig. 2, and the NMEP fluctuation is about 3.8%that is comparable with cycle-by-cycle variations of the SI com-bustion. This means that the combustion mode transition will beundetectable by the driver as far as torque fluctuations are con-cerned. The MFB curves of a sample mode transition cycles areshown in Fig. 16, where the dark-solid circles denote the auto-ignition in the hybrid combustion cycles (cycles 5–7). The MFBcurves also show that the HCCI combustion has a much fasterburn rate than that of the SI combustion. Figure 17 shows theburning duration (represented by crank degrees between CA10and CA90) during the combustion mode transition, where Fig.17(b) shows a zoomed view of Fig. 17(a) for the transition cyclesshown in Fig. 16 and cycle is also renumbered to match these inFig. 16. Before the mode transition starts (cycles 1–4), SI combus-tion has a burn duration of around 30 crank degrees; during themode transition when auto-ignition occurs (cycles 5–7), the burnduration is gradually reduced down to 12 deg; after the mode tran-sition (cycle 8), the HCCI burn duration is around 12 crankdegrees. Note that the burn duration also provides additionalinformation regarding mode transition properties.

7 Conclusions

A model-based control strategy for spark-ignition (SI) and homo-geneously charge compression ignition (HCCI) combustion modetransition is proposed in this paper. The net mean effective pressure(NMEP) regulation consists of manifold pressure control,sensitivity-based fuel compensation control, and iterative learningof transient fuel control. The NMEP sensitivity to the injected fuelmass is derived based upon the control-oriented combustion model.Experiment results show that the proposed manifold pressure anditerative learning controllers with sensitivity-based compensationare able to achieve smooth mode transition both from SI to HCCIand from HCCI to SI combustion at a range of operational condi-tions, and the mode transition robustness under cycle-by-cycle varia-tions has been greatly enhanced by utilizing the sensitivity-basedfeed-forward fuel compensation. The NMEP (an indication ofengine output torque) fluctuations during the combustion mode tran-sition are kept below 3.8% for all the tests. That is close to the fluctu-ation level of the SI combustion. At the same time, the combustionmode transition is completed within five to eight cycles.

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