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Control-Oriented Cyclic Modeling Method for Spark Ignition Engines
5th IFAC Conference on 5th IFAC Conference on Engine Powertrain Simulation and online Modeling 5th IFACand Conference onControl, Available at www.sciencedirect.com Engine Powertrain Simulation and Modeling 5th IFACand Conference onControl, Changchun, China, September 2018 and Modeling Engine and Powertrain Control,20-22, Simulation Changchun, China, September 20-22, 2018 Engine and Powertrain Control, Simulation and Modeling Changchun, China, September 20-22, 2018 Changchun, China, September 20-22, 2018
ScienceDirect
IFAC PapersOnLine 51-31 (2018) 448–453
Control-Oriented Cyclic Modeling Method Control-Oriented Cyclic Modeling Method Control-Oriented Cyclic Modeling Method for Spark Ignition Engines Control-Oriented Cyclic Modeling Method for Spark Ignition Engines for Spark Ignition Engines for Spark Ignition Engines ∗∗ ∗ ∗∗
Mingxin Mingxin Kang Kang ∗ Kota Kota Sata Sata ∗∗ Akio Akio Matsunaga Matsunaga ∗∗ ∗∗ Mingxin Kang ∗∗ Kota Sata ∗∗ ∗∗ Akio Matsunaga ∗∗ Akio Matsunaga ∗ Mingxin Kang Kota Sata ∗ State Key Laboratory of Synthetical Automation for Process ∗ State Key Laboratory of Synthetical Automation for Process Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, China ∗ State Industries, Northeastern University, China (e-mail: (e-mail: State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, China (e-mail: [email protected]) [email protected]) Industries, Northeastern University, China (e-mail: ∗∗ Motor Corporation, Japan (e-mail: ∗∗ Toyota [email protected]) Motor Corporation, Japan (e-mail: ∗∗ Toyota [email protected]) Japan (e-mail: kota akio matsunaga [email protected]) ∗∗ Toyota Motor Corporation, kota [email protected], [email protected], akio matsunaga [email protected]) Toyota Motor Corporation, Japan (e-mail: kota [email protected], akio matsunaga [email protected]) kota [email protected], akio matsunaga [email protected]) Abstract: Abstract: Automotive Automotive engine engine is is a a sophisticated sophisticated dynamical dynamical control control system system involving involving both both Abstract: Automotive engine is and a sophisticated dynamical control system involving both continuous-time dynamic behavior event-based cyclic state transition. To grasp the continuous-time dynamic engine behavior and event-based cyclic state control transition. To grasp the engine engine Abstract: Automotive is a sophisticated dynamical system involving both continuous-time dynamic behavior and event-based cyclic state transition. To grasp the engine dynamics accurately, this paper proposes a hybrid model structure for automotive gasoline dynamics accurately, thisbehavior paper proposes a hybridcyclic modelstate structure for automotive gasoline continuous-time dynamic and event-based transition. To grasp the engine dynamics accurately, paper proposes a hybrid model structure for response automotive gasoline engines that not consists of continuous air model, actuator model, but engines that not only only this consists of the the continuous air path path model, actuator response model, but dynamics accurately, this paper proposes a hybrid model structure for model. automotive gasoline engines that not only consists of the continuous air path model, actuator response model, but also includes the cyclic residual gas mass model and combustion process The proposed also includes the cyclic residual gas mass model and combustion process model. The proposed engines that not only consists ofgas themass continuous air path model, actuator response but also includes the cyclic residual model and combustion process model. Themodel, proposed model adopts an extended Kalman filter to on-line estimate the cyclic state and it has model adoptsthe an cyclic extended Kalman filter model to on-line estimate theprocess cyclic model. state and has the the also includes residual gas mass and combustion Theit proposed model adopts an extended Kalman filter to on-line estimate the cyclic state and it has the potential to be applied for the real-time optimal control design to improve the transient control potential to be an applied for the real-time optimal control design to improve the transient control model adopts extended Kalman filter to on-line estimate the cyclic state and it has the potential to be applied for the real-time optimal control design to improve the transient control performance. The precision of the model has been evaluated by comparing with the measurement performance. The precision of the model has beencontrol evaluated by comparing with the measurement potential to be applied for the real-time optimal design to improve the transient control performance. precision of the model has been evaluated bymodel comparing with behavior. the measurement data and validation results demonstrate the matching data and the the The validation results demonstrate the satisfactory satisfactory matching performance. precision of the model has been evaluated bymodel comparing with behavior. the measurement data and the The validation results demonstrate the satisfactory model matching behavior. data andIFAC the (International validation results demonstrate the Control) satisfactory model matching © 2018, Federation of Automatic Hosting by Elsevier Ltd. behavior. All rights reserved. Keywords: Keywords: cycle-by-cycle cycle-by-cycle modeling, modeling, spark spark ignition ignition engine, engine, Extended Extended Kalman Kalman Filter, Filter, Gauss Gauss Keywords: cycle-by-cycle modeling, spark ignition engine, Extended Kalman Filter, Gauss Process Regression Process Regression Keywords: cycle-by-cycle modeling, spark ignition engine, Extended Kalman Filter, Gauss Process Regression Process Regression 1. INTRODUCTION INTRODUCTION both continuous continuous time-based time-based dynamical dynamical behavior behavior and and disdis1. both 1. INTRODUCTION both continuous time-based dynamical behavior and discrete event-based combustion process. All of these features crete combustiondynamical process. Allbehavior of these and features 1. INTRODUCTION both event-based continuous disThe increasing increasing stringent stringent environmental requirement requirement brings brings crete event-based combustion process. All ofcomputational these features make the accurate accuratetime-based engine model model with lower lower The environmental make the engine with computational crete event-based combustion process. All of these features The increasing stringent environmental requirement brings new challenges to the development of the automotive commake the accurate engine model with lower computational complexity difficult to be obtained. new challenges stringent to the development of the automotivebrings com- complexity difficultengine to be obtained. The increasing environmental requirement make the accurate with lower computational new challenges the development of the automotive com- complexity bustion engines.to The engine control technology is develdifficult to be model obtained. The engine control technology is develbustion engines. new challenges to the development of the automotive comTo adapt the requirement of the controller design, design, the the complexity difficult to be obtained. bustion engines. The engine control technology is developed towards towards to to sophisticated sophisticated and and complex complex that that attempts attempts To adapt the requirement of the controller oped adaptfunction the requirement of first the adopted controllerin design, the bustion engines. The engine control technology is devel- To transfer models were were early stage stage oped towards totransient sophisticated and complex that attempts to control the details of the cyclic combustion transfer function models first adopted in early To adapt the requirement of(Winterbone the adopted controller the of complex the cyclic combustion to control thetotransient detailsand function models were first in design, early stage oped towards sophisticated that attempts for engine controller design et al., 1998). 1998). to control the transient details of theperformance cyclic combustion process, since the transient control has aa transfer for engine controller design (Winterbone et al., transfer function models were first adopted in early stage process, since the transient control performance has enginethe controller designis(Winterbone al., 1998). to controlsince the transient details of theand cyclic However, transfer model model indeed aa kind kind et of ‘black ‘black box‘ process, the on transient control performance has a for significant impact the emission fuelcombustion consumpHowever, the transfer is(Winterbone indeed of box‘ for engine controller design et al., 1998). significant impact on the emission and fuel consumpHowever, the transfer model is indeed a kind of ‘black box‘ process, since the transient control performance has a model (Grondin et al., 2004) without the details of the significant impact on the emission and fuel consumption(Ericson, 2005). 2005). In In this this context, context, model-based model-based developdevelop- model (Grondin et al., 2004) withouta kind the details ofbox‘ the However, the transfer model isand indeed oflower ‘black tion(Ericson, (Grondin et al., 2004) without the adetails of the significant impact on the emission and fuelautomotive consumpinternal state of the the system, it is is with with model tion(Ericson, 2005). In this context, model-based develop- model ment (MBD) has been widely focused in the internal state of system, and it a lower model model (Grondin et al., 2004) without the adetails of the ment (MBD) 2005). has been widely focused in the automotive internal state of the system, and it is with lower exists. model tion(Ericson, In this context, model-based developaccuracy especially when the strong nonlinearity ment (MBD) has 2010), been widely focused in thetoautomotive industry (del Re, Re, because it is capable tackle the theand strong nonlinearity exists. accuracy especially when internal state of the system, it is with a lower model 2010), because it is capable to tackle the industry (del when theforstrong nonlinearity exists. ment (MBD) hasissues beenand widely focused in theto automotive Therefore,especially it is is not not suitable suitable the state-dependent state-dependent conindustry (del Re, 2010), because it is capable tackleperthe accuracy complex control obtain optimal control Therefore, it forstrong the conaccuracy especially when the nonlinearity exists. complex control issues and obtainitthe the optimalto control perTherefore, it is not suitable for the state-dependent conindustry (del Re, 2010), because is capable tackle the troller design. Afterwards, the mean-value engine model complex control issues and obtain the optimal control performance. The The model-based model-based control control schemes schemes such such as as model model troller design. the engine model Therefore, it isAfterwards, not suitable for mean-value the state-dependent conformance. design. Afterwards, mean-value engine model complex control issues andlinear obtain the optimal control per- troller (Hendricks&Sorenson, 1990)the was attracted much attention formance. The model-based control schemes such as (LPV) model predictive control (MPC), parameter varying much attention (Hendricks&Sorenson, 1990) was attracted troller design. Afterwards, the mean-value engine model predictive control (MPC), linear parameter varying (LPV) 1990) precision was attracted formance. The model-based control schemes suchtoasthe model since it it has has aa satisfactory satisfactory withmuch lowerattention compupredictive control (MPC), linear parameter varying (LPV) control, etc, have been investigated and applied applied en- (Hendricks&Sorenson, since precision with lower compu(Hendricks&Sorenson, 1990) was attracted much attention control, etc, have been investigated and to the ensince it has a satisfactory precision with lower compupredictive control (MPC), linear parameter varying (LPV) tational complexity. In such kind of model, the average control, etc, have been investigated and applied to the engine control control system(Hu system(Hu et et al., al., 2018; 2018; Postma&Nagamune, Postma&Nagamune, tational complexity. In suchprecision kind of model, the average since it satisfactory with compugine tational complexity. In suchinstead kind ofofmodel, the average control, etc, have been investigated applied to theisenvalue of has the asystem system states the lower cycle-by-cycle gine control system(Hu et of al.,MBD, 2018;and Postma&Nagamune, 2012). Under the concept a key technique to value of the states instead of the cycle-by-cycle tational complexity. In such kind of model, the average 2012). Undersystem(Hu the concept MBD, aPostma&Nagamune, key technique is to value of the system of the gine control et of al., 2018; transient details are states mainlyinstead focused. For cycle-by-cycle example, the the 2012). Under the concept of MBD, a key is to transient establish an accurate accurate engine model with lowtechnique computational details are mainly focused. For example, value oftorque, the system states instead of in the cycle-by-cycle establish an engine model with low computational transient details are mainly focused. For example, the 2012). Under the concept of MBD, a key technique is to engine emissions are modeled the mean-value establish an accurate engine model with low computational engine complexity. torque, emissions are modeled in theexample, mean-value transient details arepolynomial mainly focused. Forwith complexity. emissions are modeled in the mean-value establish an accurate engine model with low computational engine sense astorque, the static functions respectthe to complexity. sense as the static polynomial functions with respect to engine torque, emissions are modeled in the mean-value However, internal combustion engine is a complicated syssense as the static polynomial functions with respect to complexity. the mean-values of the manifold pressure and air mass mass However, internal combustion engine is a complicated sys- the mean-values of the manifold pressure and air sensemean-values as the static functions with respect to However, internal combustion engine is a and complicated sys- the tem involving involving multi-input multi-output its dynamic dynamic of polynomial the manifold pressure and air mass flow. Although the mean-value model based engine contem multi-input multi-output and its flow. Although the mean-value model based engine conHowever, internal combustion engine is a complicated systhe mean-values of the manifold pressure and air mass tem involving multi-input multi-output and its dynamic behavior is is quite quite difficult be due to Although the model basedetengine control applications, applications, i.e.mean-value speed control(Cairano control(Cairano al., 2012), 2012), difficult to to be characterized characterized due to the the flow. behavior i.e. speed etengine al., tem involving multi-input multi-output and the its dynamic flow.applications, Although the model based conbehavior is of quite to beprocess characterized due to the trol complexity thedifficult combustion and coupling trol i.e.mean-value speed control(Cairano et al., 2012), torque control(Kang&Shen, 2016), airpath control(Xie et complexity of the combustion process and the coupling control(Kang&Shen, 2016), airpath control(Xie et behavior between is of quite difficult tostate beprocess characterized due to the torque trol 2016), applications, i.e.reached speed control(Cairano et al., 2012), complexity thethe combustion andThe the coupling relations inner variables. derivation torque control(Kang&Shen, 2016), airpath control(Xie al., etc have a fruitful achievement, it et is variables. The derivation relations between the inner state al., 2016), etc have reached a fruitful achievement, it is complexity of the combustion process andThe thethe coupling torque control(Kang&Shen, 2016), airpath control(Xie et relations between the inner statehas variables. derivation of conventional physical model to consider multial., 2016), etc have reached a fruitful achievement, it is still incapable to be applied to the cyclic based transient multi- still of conventional physical model has to consider incapable to be reached applied to the cyclic based transient relations between the inner state variables. The the derivation al., 2016), etcsuch have a fruitful achievement, it is of conventional physical model has to consider the multi- still disciplinary knowledge such as thermo-dynamics, thermo-dynamics, chemical incapable to beasapplied to thephase cyclic based and transient control issues combustion control comdisciplinary knowledge such as chemical control issues such as combustion phase control and comof conventional physical model has to consider the multistill incapable to be applied to the cyclic based transient disciplinary knowledge such asand thermo-dynamics, chemical control mechanism, fluid mechanics, mechanical kinematics. issues such as combustion phase control and combustion variation variation rejection rejection issue. issue. mechanism, fluid mechanics, mechanical kinematics. bustion disciplinary knowledge such asand thermo-dynamics, control issues suchrejection as combustion mechanism, fluid and mechanical For example, themechanics, burn zone based method kinematics. ischemical usually bustion variation issue. phase control and comFor example, the burn zone based method is usually mechanism, fluid and mechanical The importance ofrejection the cyclic cyclic transient modeling modeling and and conconbustion variationof issue. For example, themechanics, burn based method kinematics. is usually The adopted to describe describe the zone combustion process (Heywood, importance the transient process (Heywood, adopted to the combustion The importance of the cyclic transient modeling and conFor example, the burn zone based method is usually trol has been aroused much attention recently, and the adopted to describe the combustion process (Heywood, 1988), but but such such kind kind of of model model has has aa very very complicated complicated trol been aroused much transient attentionmodeling recently, and and conthe The has importance of low-cost the cyclic 1988), trol has beenofaroused much attention recently, and the adoptedbut toand describe (Heywood, development the cylinder pressure sensor makes 1988), such kindthe of combustion model has aprocess very complicated structure computation, therefore it is not suitable development of the low-cost cylinder pressure sensor makes trol control-oriented has beenofaroused much attention recently, and the therefore is not suitable development structure and the low-cost cylinder pressure sensor makes 1988), suchcomputation, kind of model has a it very complicated the cyclic modeling possible. Makowicki structure and computation, therefore itAdditionally, is not suitable for thebut real-time control application. the the control-oriented cyclic modeling possible. Makowicki development of the low-cost cylinder pressure sensor makes for the real-time control application. Additionally, the control-oriented cyclic modeling possible. Makowicki structure and computation, therefore itAdditionally, is consisting not suitable et al. al. (2016) proposed proposed combustion cycle model model where for the real-time control application. the combustion engine is aa typical typical hybrid system system of the et (2016) aa combustion cycle where theal. control-oriented cyclic modeling possible. Makowicki combustion engine is hybrid consistingthe of (2016) proposed a combustion cycle model where for the real-time application. Additionally, combustion engine control is a typical hybrid system consisting of et combustion engine is a typical hybrid system consisting of et al. (2016) proposed a combustion cycle model where
2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 487 Peer review©under responsibility of International Federation of Automatic Copyright 2018 IFAC 487Control. Copyright © 2018 IFAC 487 10.1016/j.ifacol.2018.10.101 Copyright © 2018 IFAC 487
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018Mingxin Kang et al. / IFAC PapersOnLine 51-31 (2018) 448–453
Due to the operating mechanism of a SI engine, the engine system has a hybrid model structure consisting of continuous time dynamic behavior and discrete combustion event. Several system dynamics will be considered in this study including intake air-path dynamics, actuator response dynamics, cyclic residual gas transition dynamics, and combustion process model. The model structure is shown in Fig. 1. The manifold pressure (Pim ) is a continuous state influenced by the engine speed (Ne ) and the control inputs such as throttle angle (ϕ), variable valve timing (θ). In each cycle, the fresh air mass flow in the intake manifold will be aspirated into the cylinder and then result in the variations of the manifold pressure. Then, the combustion process is performed with appropriate fuel injection (uf ) and SA control in discrete cycle-by-cycle form to generate the cyclic power output and emissions. Finally, the cyclic power output will be merged in the crankshaft and therefore the power output and emissions will be in general considered in the continuous time domain. Indeed, for each cylinder, the interrelation on cycle-bycycle state involves not only the mass transition (i.e., 488
ma (k ) (k )
VVT actuator model
uf
Cyclic Transition Model Mass transition
imep( k )
1 4
Tivc ( k )
mr (k 1) f min (k ),mr (k )
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1/z
min mr Tivc mrTevc minTim
ncyl
y
e
i
i
CA 50 ( k )
SA(k )
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Time-domain model
Time-domain model
Fig. 1. The proposed model framework for automotive gasoline engines. residual gas remained for next cycle), but also the energy transition (i.e., the in-cylinder temperature or heat influences the combustion process and then influence the state in the next cycle). The residual gas is a very important variable to find the cycle-by-cycle relations. Residual gas has two effects on the properties of the cycle. Firstly, there is the effect that it occupies a volume that cannot be filled with a fresh mixture of air and fuel, and therefore it reduces the volumetric efficiency. Secondly, the residual gas has a mass that influences the temperature rise from the combustion (Eriksson&Nilsen (2014)). However, the residual gas mass is difficult to be measured on board. The conventional estimation method for the residual gas is to apply the iteratively calculation by means of the cylinder pressure signal and the thermodynamics relations(Eriksson&Nilsen, 2014; Heywood, 1988). This calculation process is complex and only carried out off-line. In this regards, the cyclic estimation and modeling of the residual gas mass is quite significant. This study will find the cyclic transition relations for the residual gas mass, and then derive the cyclic temperature of the in-cylinder air-fuel mixture. Finally, the cyclic combustion process variables such as CA50 and IMEP will be further modeled. 3. MODELING Before modeling the cyclic relations, we have to declare the definition of one cycle. As shown in Fig. 2, the starting point (0 deg) of a new cycle is from the intake top dead center (TDC) point. In the follows, the cyclic state transition dynamics will be derived based on this definition. TDC
TDC
25
Cylinder Pressure [bar]
2. THE FRAMEWORK OF THE ENGINE MODEL
120 N e ncyl
ma
···
The rest of the paper is organized as follows. Section II introduces the overall framework of the proposed hybrid engine model. In section III, the derivation procedure of the cyclic model is presented including time domain based air path model, actuator dynamics, and eventbased residual gas transition model, combustion process model,etc. A state estimator based on Extended Kalman Filter (EKF) is proposed to estimate the the cyclic state in section IV. Then, the model validation results are included in section V. Conclusions are provided in the last section.
manifold
dynamics pim
···
This paper proposes a cyclic model for the spark ignition (SI) engine system where the continuous-time based intake airpath dynamics, actuator response dynamics, and the discrete-time based residual gas mass transition model are both considered. An extended Kalman filter is adopted to estimate the state in real time and improve the model precision based on the measurable in-cylinder pressure data, and the data-driven based method (Gauss process regression modeling method) is adopted to model the combustion process quantities including combustion phase (CA50) and indicated mean effective pressure (IMEP). The proposed model is able to represent the mass and energy transition process in the cycle-by-cycle details, and has the potentials to be applied to the cyclic transient controller design.
Moving average
Cyclic discretizing
···
the gas-exchange and compression phases described by physics-based and the combustion phase modeled by a data-based approach, and the model was then applied for the optimal fuel injection controller development (Makowicki et al., 2017). Kumar&Shen (2015) proposed a cyclic transition model for the air mass flow including residual gas, burnt gas, etc by means of mass and energy conservation laws. In fact, the transient control quality are mainly determined by the cycle-by-cycle manipulated inputs including the fuel injection mass and the spark advance (SA). Therefore, the cyclic transient modeling becomes quite urgent and necessary to achieve the elaborate control of the modern engines.
449
TDC
TDC
mr ( k )
mr (k � 1)
ma (k ) � m f (k )
ma (k � 1) � m f (k � 1)
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20 15 Tivc (k )
10
Pivc ( k )
Tivc ( k � 1) Pivc ( k � 1)
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EVO
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0
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359
EVO
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k
k+1 539
719 179 Crank Angel [deg]
359
539
719
Fig. 2. A cycle definition: new cycle starts from intake TDC. 3.1 Intake airpath model Based on the ideal gas law and mass conservation, the continuous-time dynamical behavior of fresh air mass flow
IFAC E-CoSM 2018 450 Changchun, China, September 20-22, 2018Mingxin Kang et al. / IFAC PapersOnLine 51-31 (2018) 448–453
through the intake manifold can be described by a meanvalue expression (Eriksson&Nilsen, 2014): Rim Tim dPim = (m ˙ th − m ˙ a) (1) dt Vim where, Pim denotes the intake manifold pressure. As for the air mass flow rate passing through the throttle valve m ˙ th , it can be expressed by (this expression neglects the effects of the throttle shaft): ( ) ) ( cos (ϕ) c ·P πD2 Pim √d a Ψ 1− (2) m ˙ th = 4 cos (ϕ0 ) Pa RTim where cd is discharge coefficient; Pa is the pressure in the upstream of the throttle valve, which is generally regarded the same as the atmospheric pressure; D is the diameter of the throttle plate; ϕ0 is the throttle plate rest angle; Ψ(·) is the piecewise-continuous-function with the following form (Heywood, 1988): √ ) κκ+11 ( κ 2 Pim 2 κ 1 κ ) , for ( < ( ) κ+1 Pa κ+1 Pim � Ψ( )= [ ] κ 1 1 � Pa κ � 2κ κ P P im im � 1−( , otherwise. ) ( Pa ) κ−1 Pa (3) For many working fluids such as intake air, exhaust gas at lower temperature, the approximation can be adopted with κ ≈ 1.4.
In addition, m ˙ a denotes the aspirated air mass flow rate into the cylinder, if ignoring the intake-to-power delay, the mean-value model can be applied with speed-density method: Pim Vd ne Ncyl (4) m ˙ a = ηv (θ, Pim , ne ) Rim Tim 120 where ηv (·) denotes the volumetric efficiency which typically relies on the engine speed, intake manifold pressure and intake valve timing (θ). Vd is the displaced volume, intake air temperature Tim is assumed constant and ne is engine speed in revolution per minute (rpm). Hence, for each cycle the aspirated air-charge into cylinder can be derived from (4) multiplying cyclic period (∆T = 120/ne Ncyl [s]), i.e. Pim Vd ma = η( θ, Pim , ne ) (5) Rim Tim 3.2 Actuator response dynamics In above models, throttle opening angle and variable valve timing (VVT) are two continuous-time control actuators. The first-order lag model are adopted to describe their dynamical behaviors. The response dynamics for throttle and VVT can be formulated as follows: 1 d ϕ(t) = (−ϕ(t) + uϕ (t)) (6) dt τϕ 1 d θ(t) = (−θ(t) + uθ (t − τdθ )) (7) dt τθ where, τdθ denotes the delay time between the command and the actual response, and τϕ , τθ are the time constant for these two actuators. uϕ , uθ denote control commands for the throttle and intake valve timing actuator, respectively.
489
3.3 Fuel injection model In this study, only the direct-injection engine is focused. Then, the fuel mass mf (k) in k-th cycle can be directly given by: mf (k) = uf (k−1), (8) which indicates the actual fuel injection mass always delays in one cycle than fuel injection command uf (k − 1).This is reasonable because the command should be prepared in advance before new injection trigger coming. 3.4 Cyclic model of residual gas mass In this study, we derive the residual gas model in such kind of way. Focusing the exhaust process from k-th cycle to (k+1)-th cycle, there is a relation at the exhaust valve opening (EVO) point according to the ideal gas law: Pevo (k)Vevo (k) , (9) Tevo (k) = mevo (k)Revo (k) where, mevo (k) = ma (k)+mf (k)+mr (k) from mass conversation assumption. ma (k) and mf (k) can be obtained by (5) and (8), respectively. Furthermore, residual gas mass mr (k) is assumed to be the flow mass when exhaust valve closing (EVC), namely, mr (k) = mevc (k). In fact, the EVC point is usually located at/after the intake TDC to pump out the as much burnt gas as possible. Then, at the EVC point, it has Pevc (k+1)Vevc (k+1) Tevc (k+1) = , (10) mevc (k+1)Revc (k+1) where, mevc (k+1) is assumed as the residual gas in (k+1)-th cycle, mevc (k+1) = mr (k+1). Considering the exhaust process can be equivalent to the polytropic process, there is a relationship between temperature and pressure: ( )1− κ1 Tevc (k+1) Pevc (k+1) = . (11) Tevo (k) Pevo (k) Substituting (9), (10) into (11) and supposing the gas property in exhaust process slightly change (i.e. Revo ≈ Revc = R) yields: ( )1 Vevc (k+1) Pevc (k+1) κ mr (k+1) = (maf (k)+mr (k)) Vevo (k) Pevo (k) (12) where maf (k) = ma (k)+mf (k), denotes the fresh mixing charge, it can be represented in the following form by substituting eq.(5), Pim (k)Vd + mf (k). (13) min (k) = η(ne , Pim (k), θ(k)) RTim It should be noted that, eq. (12) represents the cyclic transition of the residual gas, where cylinder pressure, volume, and intake mixtures are measurable parameters. The key-point of this equation is how to get an accurate residual gas in current cycle for next cycle state estimation. 3.5 Cyclic model of in-cylinder charge temperature Now, we consider thermal coupling relation in the intake process. Assuming constant specific heats and the mixing
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018Mingxin Kang et al. / IFAC PapersOnLine 51-31 (2018) 448–453
451
during intake stroke is done under free expansion (i.e., dq = 0 and dU = 0), the temperature at intake valve closing can be calculated based on energy conservation, that is, (min +mr ) Tivc = mr Tevc +min Tim , (14) where the fresh charge temperature Tim can be approximated as the temperature in intake manifold (Eriksson&Nilsen, 2014; Larimore, 2013). Then, according to ideal gas equation, eq. (14) can be written as follows:
IMEP(k) is associate to the components of the in-cylinder mixture, the temperature (Tivc ) and the spark ignition timing: IMEP(k) = GPR2 (ma (k), mf (k), mr (k), Tivc (k), SA(k)). (18) The above GPR models can be trained based on the experimental data under different conditions.
Tivc (k+1) = [ ] 1 Pevc (k+1)Vevc (k+1) +min (k+1)Tim ,(15) mt (k+1) Rem where mt = ma + mf + mr denotes the total mass of the in-cylinder mixture.
Combining eqs. (1), (8) and (13), and writing the cyclic transition models in a compact form, we can obtain:
If the temperature Tivc and residual gas mr are obtained, the cylinder pressure at IVC timing can be calculated by: RTivc (k) [maf (k)+mr (k)] . (16) Pivc (k) = Vivc (k) It is obvious in eq.(15) the cylinder temperature Tivc (k) is coupled with residual gas mr (k) , Pim (k) and uf (k −1). And the initial mr (k) is crucial to the model accuracy. To predict Tivc , and mr , an Extended Kalman Filter (EKF) was adopted in this study, see details in the following section.. 3.6 Combustion process modeling The combustion process is associate with the some initial conditions including the components of the air-fuel mixture, in-cylinder temperature, and spark ignition timing, etc. If the residual gas mass and the temperature of the mass flow at IVC timing can be obtained cycle-by-cycle, the combustion process model can be easily modeled as the function of these proposed cyclic states. Considering the combustion is a quite complicated stochastic process and it is difficult to derive a physical relations, the Gauss process regression (GPR) method is adopted in this study. GPR is a powerful Bayesian and non-parametric modeling approach which assumes Gaussian distributions on function classes and sampled data. Non-parametric means that the GPR model contains no parameters to fit the data through the measurement values as opposed to the weights of a polynomial model. The probabilistic approach allows information to be given about the predictive uncertainty of the model with respect to prior beliefs of the function properties(Tietze, 2015). Instead of minimizing an error to optimize the model parameters as shown for the polynomial model, the probabilistic approach maximizes the probability of the model values, given the measurement. By means of the GPR method, combustion phase and IMEP are mainly considered. Combustion phase CA50 defined as the location of 50% of mass fraction burned is an important indicator to evaluate the combustion status, and it can be determined by the cylinder temperature (Tivc ) and spark ignition timing SA (Larimore, 2015), i.e., (17) CA50 (k) = GPR1 (Tivc (k), SA(k)). Similarly, another important variable about the combustion status denoted by the indicate mean effective pressure 490
4. EKF-BASED STATE ESTIMATION
Pim (k+1) = f1 (Pim (k), ϕ(k), θ(k))
(19)
mr (k+1) = f2 (mr (k), Pim (k), θ(k), mf (k), p(θ(k))) (20) mf (k+1) = uf (k)
(21)
and the system output is Pivc from (15): Pivc (k) = g(mr (k), Tivc (k), Pim (k), mf (k), p(θ(k))) (22) where p(θ) denotes the VVT-dependent parameters such as Pevc , Pevo , Vevc , Vevo ; in fact, Vevc , Vevo are explicit functions of valve timing θ, and Pevc , Pevo can be calibrated based on different θ. For the sake of the simplicity, denote x = [Pim , mr , mf ]T , u = [ϕ, θ, uf ]T , y = Pivc , and suppose the cylinder pressure is measurable with Guassian white noise, then the state equations (19)-(21) and the output equation (22) can be linearized as follows: xk ≈˜ xk + A(xk−1 − x ˆk−1 ) + W wk−1 , ˆk−1 ) + V vk . yk ≈ y˜k + H(xk−1 − x
(23) (24)
˜k , y˜k are where xk , yk is the true values at time k. x approximate state and measurement vectors from x ˜k = f (ˆ xk−1 , uk−1 , 0) and y˜k = g(˜ xk , 0), x ˆ is the estimator of the state. wk , vk denotes the noise. A, W, H, V are Jacobians with the following form: ∂f[i] ∂f[i] (ˆ xk−1 , uk−1 , 0), W[i,j] = (ˆ xk−1 , uk−1 , 0), A[i,j] = ∂x[j] ∂w[j] H[i,j] =
∂g[i] ∂g[i] (˜ xk , 0), V[i,j] = (˜ xk , 0). ∂x[j] ∂v[j]
˜k , and e˜yk = yk − y˜k , then error Define e˜xk = xk − x dynamics can be deduced from (23) and (24): e˜xk ≈ A(xk−1 − x ˆk−1 ) + ϵk , e˜yk ≈ H e˜xk + ηk
(25) (26)
where ϵk and ηk denote new independent random variables having zero mean and covariance matrices W QW T and V RV T , Q, R are process and measurement noise covariance, respectively. (that is, ϵk : p(ϵ) ∼ N (0, W QW T ).) It should be noticed that (25) and (26) are linear which can use conventional Kalman filter by means of the measurable e˜yk : x ˆk = x ˜k + Kk e˜yk = x ˜k + Kk (yk − y˜k ) where Kk is Kalman filter gain. The Kk updating algorithm of Kalman filter has been summarized as follows (Welch, 1995):
IFAC E-CoSM 2018 452 Changchun, China, September 20-22, 2018Mingxin Kang et al. / IFAC PapersOnLine 51-31 (2018) 448–453
(0) Initialization: Given x ˆk−1 and Pk−1 (a) Time update equations (here denote x ˆ− ˜k ) k := x
0.2 m r [g]
0.15
x r (model)
xr (approx)
0.1
x− x ˆ− k=f (ˆ k−1 , uk−1 )
(27)
Pk−=Ak Pk−1 ATk + Wk Qk−1 WkT (b) State update equations
(28)
TDC
(29) (30)
Cylinder Pressure [bar]
ma (k ) m f (k )
ma (k 1) m f (k 1)
TDC
Tivc ( k )
10 5
Pivc ( k )
EVC
Tivc ( k 1) Pivc ( k 1)
Tevo ( k )
IG
EVO
EVC
Tevo ( k 1)
179
359
Pevo (k )
719 179 Crank Angel [deg]
359
u (k ) Cyclic Transition Model Eqs.(19) (20) (21)
z
1
xˆ(k +1)
x(k +1)
+
+
2500 T ivc (approx)
200 0.8
Output Model Eq.(22)
0
500
1000
1500
2000
2500 P ivc [bar]
Pivc [bar]
0.6 0.4 0.2
0
500
1000
1500
SA[deg]
CA [deg](measured) 50
40
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2500
CA [deg](model) 50
20 0 6
0
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1500 IMEP[bar](model)
500
1000
1500
2000
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IMEP[bar](measured)
2000
2500 speed[rpm]
500
1000
1500
2000
2500
1500
2000
2500
θ[deg]
10 539
719
0
Pivc (k 1)
Pevc (k +1)
2000 T ivc [K](model)
φ[deg]
k+1 539
1500
300
EVO
IVC
k 0
1000
400
2 0 2500 2000 1500 1000 0 20
IG
IVC
500
4
15
0
uf ( k )
TDC
mr ( k 1)
20
-5
(k ) (k )
TDC
mr ( k )
0 700 500
(31) The estimation diagram is illustrated in Fig. 3. Based on this algorithm, the residual gas mass mr and the temperature of mass flow Tivc can be obtained at IVC point. The early knowledge about the in-cylinder state before spark ignition will be helpful for applying the accurate SA and fuel injection control. TDC
0
600
Kk=Pk− HkT (Hk Pk− HkT + Vk Rk VkT )−1 ˆ− x− x ˆk=x k + Kk (yk − g(ˆ k )) − Pk=(I − Kk Hk )Pk
25
0.05
0
500
1000 Cycle No.
+
y (k +1)
-
Fig. 4. Case 1 (load torque at 60Nm): Estimation results of residual gas and cylinder temperature.
Extended Kalman Filter
Fig. 3. Diagram of the EKF estimator. 5. MODEL VALIDATION The model validations have been conducted based on the experimental data collected from a 3.5 Liter V6 type gasoline engine. Considering the actual residual gas mass is unmeasurable, the residual gas fraction xr is introduced as an evaluation index and defined by xr (k) = mr (k)/mt (k). Suppose the total aspirated mass in the adjacent cycles are the same under the steady operating condition, i.e. mt (k−1) ≈ mt (k), then based on the polytropic assumption during the exhaust stroke, the residual gas fraction can be approximated as, ( ) κ1 Vevc (k) Pevc (k) mr (k) = (32) xr (k) ≈ mt (k−1) Vevo (k−1) Pevo (k−1) In fact, the above approximation is only effective under the steady operating condition and has been adopted in (Kumar&Shen, 2015) to model the cyclic transition of mass flow. Hence, the approximation is adopted in this study to compare and verify the precision of the proposed modeling method. Two case studies have been investigated including the transient experiments under the fixed load torque, and the fixed engine speed. In the first case, the load torque is fixed at 60Nm, throttle angle and VVT are changed in transient 491
mode. The proposed model outputs are shown in Fig.4. In the another case, the engine speed is fixed at 1200rpm, and the estimation results is shown in Fig.5. In both cases, it is obvious the residual gas fraction xr and the temperature of mass flow Tivc estimated by the proposed model are matching to the approximated values under steady condition, although there are relative large fluctuation. The combustion phase (CA50 ) and IMEP model show the good precision. To observer the transient details of the model, the enlarged figure about the step change of the throttle is illustrated Fig. 5(b). In general, the combustion variations is inevitable because of the stochasticity of the combustion process. The proposed model demonstrates the satisfactory transient cyclic behavior. 6. CONCLUSION In this paper, a spark ignition (SI) engine model with a hybrid structure is presented where the continuoustime based intake airpath dynamics, actuator response dynamics, and discrete-time based residual gas mass transition model are considered. An extended Kalman filter is adopted to estimate the cyclic state (residual gas mass, and the temperature of the mass flow) in real time and improve the model precision based on the measurable incylinder pressure data. Meanwhile, the combustion process models including combustion phase CA50 and IMEP are modeled based on the GPR method. The proposed model is capable to represent the mass and energy transition
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018Mingxin Kang et al. / IFAC PapersOnLine 51-31 (2018) 448–453
Fig. 5. Case 2(engine speed at 1200rpm): Estimation results of residual gas and cylinder temperature. process in the cycle-by-cycle details, and it is suitable for the cyclic transient controller design. However, because the proposed model relies on the cylinder pressure information in current cycle, it can only perform one-step ahead prediction for the status of the combustion process. This drawback restricts the wide application to the model based optimal controller design. To improve this model, the model of the cylinder pressure should be studied in the future work. ACKNOWLEDGEMENTS The first author would like to express his thanks to SHEN Laboratory of Sophia University for the experimental data and technical support. REFERENCES C. Ericson, B. Westerberg, R.Egnell. Transient emission predictions with quasi stationary models. SAE Technical Paper No. 2005-01-3852, 2005. Del Re, L. (Eds.)(2010). Automotive model predictive control : models, methods and applications. Verlag Berlin Heidelberg, Springer. Grondin, O., Stobart, R., Chafouk, H., & Maquet, J. (2004). Modelling the Compression Ignition Engine for Control: Review and Future Trends. SAE World Congress. Winterbone, D. E., Thiruarooran, C., & Wellstead, P. E. (1977). A wholly dynamic model of a turbocharged 492
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diesel engine for transfer function evaluation.SAE Technical Paper, (770124). Postma, M., & Nagamune, R. (2012). Air-fuel ratio control of spark ignition engines using a switching LPV controller. IEEE Transactions on Control Systems Technology, 20(5), 1175-1187. Hu, Y., Chen, H., Wang, P., Chen, H., & Ren, L. (2018). Nonlinear model predictive controller design based on learning model for turbocharged gasoline engine of passenger vehicle . Mechanical Systems & Signal Processing, 109, 74-88. Shen T., Zhang J., Jiao X., Kang M., Kako J., Ohata A. Transient Control of Gasoline Engines. CRC Press, 2015. Eriksson, Lars, and Lars Nielsen. Modeling and control of engines and drivelines. John Wiley & Sons, 2014. Heywood, John. Internal combustion engine fundamentals. McGraw-Hill Education, 1988. Hendricks, E. and Sorenson, S., Mean Value Modelling of Spark Ignition Engines, SAE Technical Paper 900616, 1990, doi: 10.4271/900616. Cairano, S. D., Yanakiev, D., Bemporad, A., Kolmanovsky, I. V., & Hrovat, D. (2012). Model predictive idle speed control: design, analysis, and experimental evaluation. IEEE Transactions on Control Systems Technology, 20(1), 84-97. Kang, M., & Shen, T. (2016). Receding horizon online optimization for torque control of gasoline engines. Isa Transactions. Xie, H., Song, K., Yang, S., Tatsumi, J., Zheng, Q., & Zhang, H., et al. (2016). On decoupling control of the vgt-egr system in diesel engines: a new framework. IEEE Transactions on Control Systems Technology, 24(5), 1788-1796. Makowicki, T., Bitzer, M., Kotman, P., & Graichen, K. (2016). A combustion cycle model for stationary and transient engine operation. Ifac Papersonline, 49(11), 469-475. Makowicki, T., Bitzer, Graichen, K., & Grodde S. (2017). Cycle-by-Cycle Optimization of the Combustion during Transient Engine Operation.IFAC World Congress, Toulouse, 2017. Kumar, M., & Shen, T. (2015). Estimation and feedback control of air-fuel ratio for gasoline engines. Control Theory and Technology, 13(2), 151-159. Larimore, J., Jade, S., Hellstrm, E., Stefanopoulou, A. G., Vanier, J., & Jiang, L. Online adaptive residual mass estimation in a multicylinder recompression HCCI engine. In Proceedings of ASME 2013 Dynamic Systems and Control Conference, pp.1-9,2013. Larimore, J., Hellstrm, E., Jade, S., Stefanopoulou, A. G., & Jiang, L. (2015). Real-time internal residual mass estimation for combustion with high cyclic variability. International Journal of Engine Research, 16(3), 474484. Guzzella L, Onder C. Introduction to modeling and control of internal combustion engine systems. Springer Science & Business Media, 2009. Welch, G., & Bishop, G. (1995). An introduction to the Kalman filter. Tietze N. Model-based Calibration of Engine Control Units Using Gaussian Process Regression[D]. Ph.D dissertation, Technische Universitt, 2015
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IFAC PapersOnLine 51-31 (2018) 448–453
Control-Oriented Cyclic Modeling Method Control-Oriented Cyclic Modeling Method Control-Oriented Cyclic Modeling Method for Spark Ignition Engines Control-Oriented Cyclic Modeling Method for Spark Ignition Engines for Spark Ignition Engines for Spark Ignition Engines ∗∗ ∗ ∗∗
Mingxin Mingxin Kang Kang ∗ Kota Kota Sata Sata ∗∗ Akio Akio Matsunaga Matsunaga ∗∗ ∗∗ Mingxin Kang ∗∗ Kota Sata ∗∗ ∗∗ Akio Matsunaga ∗∗ Akio Matsunaga ∗ Mingxin Kang Kota Sata ∗ State Key Laboratory of Synthetical Automation for Process ∗ State Key Laboratory of Synthetical Automation for Process Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, China ∗ State Industries, Northeastern University, China (e-mail: (e-mail: State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, China (e-mail: [email protected]) [email protected]) Industries, Northeastern University, China (e-mail: ∗∗ Motor Corporation, Japan (e-mail: ∗∗ Toyota [email protected]) Motor Corporation, Japan (e-mail: ∗∗ Toyota [email protected]) Japan (e-mail: kota akio matsunaga [email protected]) ∗∗ Toyota Motor Corporation, kota [email protected], [email protected], akio matsunaga [email protected]) Toyota Motor Corporation, Japan (e-mail: kota [email protected], akio matsunaga [email protected]) kota [email protected], akio matsunaga [email protected]) Abstract: Abstract: Automotive Automotive engine engine is is a a sophisticated sophisticated dynamical dynamical control control system system involving involving both both Abstract: Automotive engine is and a sophisticated dynamical control system involving both continuous-time dynamic behavior event-based cyclic state transition. To grasp the continuous-time dynamic engine behavior and event-based cyclic state control transition. To grasp the engine engine Abstract: Automotive is a sophisticated dynamical system involving both continuous-time dynamic behavior and event-based cyclic state transition. To grasp the engine dynamics accurately, this paper proposes a hybrid model structure for automotive gasoline dynamics accurately, thisbehavior paper proposes a hybridcyclic modelstate structure for automotive gasoline continuous-time dynamic and event-based transition. To grasp the engine dynamics accurately, paper proposes a hybrid model structure for response automotive gasoline engines that not consists of continuous air model, actuator model, but engines that not only only this consists of the the continuous air path path model, actuator response model, but dynamics accurately, this paper proposes a hybrid model structure for model. automotive gasoline engines that not only consists of the continuous air path model, actuator response model, but also includes the cyclic residual gas mass model and combustion process The proposed also includes the cyclic residual gas mass model and combustion process model. The proposed engines that not only consists ofgas themass continuous air path model, actuator response but also includes the cyclic residual model and combustion process model. Themodel, proposed model adopts an extended Kalman filter to on-line estimate the cyclic state and it has model adoptsthe an cyclic extended Kalman filter model to on-line estimate theprocess cyclic model. state and has the the also includes residual gas mass and combustion Theit proposed model adopts an extended Kalman filter to on-line estimate the cyclic state and it has the potential to be applied for the real-time optimal control design to improve the transient control potential to be an applied for the real-time optimal control design to improve the transient control model adopts extended Kalman filter to on-line estimate the cyclic state and it has the potential to be applied for the real-time optimal control design to improve the transient control performance. The precision of the model has been evaluated by comparing with the measurement performance. The precision of the model has beencontrol evaluated by comparing with the measurement potential to be applied for the real-time optimal design to improve the transient control performance. precision of the model has been evaluated bymodel comparing with behavior. the measurement data and validation results demonstrate the matching data and the the The validation results demonstrate the satisfactory satisfactory matching performance. precision of the model has been evaluated bymodel comparing with behavior. the measurement data and the The validation results demonstrate the satisfactory model matching behavior. data andIFAC the (International validation results demonstrate the Control) satisfactory model matching © 2018, Federation of Automatic Hosting by Elsevier Ltd. behavior. All rights reserved. Keywords: Keywords: cycle-by-cycle cycle-by-cycle modeling, modeling, spark spark ignition ignition engine, engine, Extended Extended Kalman Kalman Filter, Filter, Gauss Gauss Keywords: cycle-by-cycle modeling, spark ignition engine, Extended Kalman Filter, Gauss Process Regression Process Regression Keywords: cycle-by-cycle modeling, spark ignition engine, Extended Kalman Filter, Gauss Process Regression Process Regression 1. INTRODUCTION INTRODUCTION both continuous continuous time-based time-based dynamical dynamical behavior behavior and and disdis1. both 1. INTRODUCTION both continuous time-based dynamical behavior and discrete event-based combustion process. All of these features crete combustiondynamical process. Allbehavior of these and features 1. INTRODUCTION both event-based continuous disThe increasing increasing stringent stringent environmental requirement requirement brings brings crete event-based combustion process. All ofcomputational these features make the accurate accuratetime-based engine model model with lower lower The environmental make the engine with computational crete event-based combustion process. All of these features The increasing stringent environmental requirement brings new challenges to the development of the automotive commake the accurate engine model with lower computational complexity difficult to be obtained. new challenges stringent to the development of the automotivebrings com- complexity difficultengine to be obtained. The increasing environmental requirement make the accurate with lower computational new challenges the development of the automotive com- complexity bustion engines.to The engine control technology is develdifficult to be model obtained. The engine control technology is develbustion engines. new challenges to the development of the automotive comTo adapt the requirement of the controller design, design, the the complexity difficult to be obtained. bustion engines. The engine control technology is developed towards towards to to sophisticated sophisticated and and complex complex that that attempts attempts To adapt the requirement of the controller oped adaptfunction the requirement of first the adopted controllerin design, the bustion engines. The engine control technology is devel- To transfer models were were early stage stage oped towards totransient sophisticated and complex that attempts to control the details of the cyclic combustion transfer function models first adopted in early To adapt the requirement of(Winterbone the adopted controller the of complex the cyclic combustion to control thetotransient detailsand function models were first in design, early stage oped towards sophisticated that attempts for engine controller design et al., 1998). 1998). to control the transient details of theperformance cyclic combustion process, since the transient control has aa transfer for engine controller design (Winterbone et al., transfer function models were first adopted in early stage process, since the transient control performance has enginethe controller designis(Winterbone al., 1998). to controlsince the transient details of theand cyclic However, transfer model model indeed aa kind kind et of ‘black ‘black box‘ process, the on transient control performance has a for significant impact the emission fuelcombustion consumpHowever, the transfer is(Winterbone indeed of box‘ for engine controller design et al., 1998). significant impact on the emission and fuel consumpHowever, the transfer model is indeed a kind of ‘black box‘ process, since the transient control performance has a model (Grondin et al., 2004) without the details of the significant impact on the emission and fuel consumption(Ericson, 2005). 2005). In In this this context, context, model-based model-based developdevelop- model (Grondin et al., 2004) withouta kind the details ofbox‘ the However, the transfer model isand indeed oflower ‘black tion(Ericson, (Grondin et al., 2004) without the adetails of the significant impact on the emission and fuelautomotive consumpinternal state of the the system, it is is with with model tion(Ericson, 2005). In this context, model-based develop- model ment (MBD) has been widely focused in the internal state of system, and it a lower model model (Grondin et al., 2004) without the adetails of the ment (MBD) 2005). has been widely focused in the automotive internal state of the system, and it is with lower exists. model tion(Ericson, In this context, model-based developaccuracy especially when the strong nonlinearity ment (MBD) has 2010), been widely focused in thetoautomotive industry (del Re, Re, because it is capable tackle the theand strong nonlinearity exists. accuracy especially when internal state of the system, it is with a lower model 2010), because it is capable to tackle the industry (del when theforstrong nonlinearity exists. ment (MBD) hasissues beenand widely focused in theto automotive Therefore,especially it is is not not suitable suitable the state-dependent state-dependent conindustry (del Re, 2010), because it is capable tackleperthe accuracy complex control obtain optimal control Therefore, it forstrong the conaccuracy especially when the nonlinearity exists. complex control issues and obtainitthe the optimalto control perTherefore, it is not suitable for the state-dependent conindustry (del Re, 2010), because is capable tackle the troller design. Afterwards, the mean-value engine model complex control issues and obtain the optimal control performance. The The model-based model-based control control schemes schemes such such as as model model troller design. the engine model Therefore, it isAfterwards, not suitable for mean-value the state-dependent conformance. design. Afterwards, mean-value engine model complex control issues andlinear obtain the optimal control per- troller (Hendricks&Sorenson, 1990)the was attracted much attention formance. The model-based control schemes such as (LPV) model predictive control (MPC), parameter varying much attention (Hendricks&Sorenson, 1990) was attracted troller design. Afterwards, the mean-value engine model predictive control (MPC), linear parameter varying (LPV) 1990) precision was attracted formance. The model-based control schemes suchtoasthe model since it it has has aa satisfactory satisfactory withmuch lowerattention compupredictive control (MPC), linear parameter varying (LPV) control, etc, have been investigated and applied applied en- (Hendricks&Sorenson, since precision with lower compu(Hendricks&Sorenson, 1990) was attracted much attention control, etc, have been investigated and to the ensince it has a satisfactory precision with lower compupredictive control (MPC), linear parameter varying (LPV) tational complexity. In such kind of model, the average control, etc, have been investigated and applied to the engine control control system(Hu system(Hu et et al., al., 2018; 2018; Postma&Nagamune, Postma&Nagamune, tational complexity. In suchprecision kind of model, the average since it satisfactory with compugine tational complexity. In suchinstead kind ofofmodel, the average control, etc, have been investigated applied to theisenvalue of has the asystem system states the lower cycle-by-cycle gine control system(Hu et of al.,MBD, 2018;and Postma&Nagamune, 2012). Under the concept a key technique to value of the states instead of the cycle-by-cycle tational complexity. In such kind of model, the average 2012). Undersystem(Hu the concept MBD, aPostma&Nagamune, key technique is to value of the system of the gine control et of al., 2018; transient details are states mainlyinstead focused. For cycle-by-cycle example, the the 2012). Under the concept of MBD, a key is to transient establish an accurate accurate engine model with lowtechnique computational details are mainly focused. For example, value oftorque, the system states instead of in the cycle-by-cycle establish an engine model with low computational transient details are mainly focused. For example, the 2012). Under the concept of MBD, a key technique is to engine emissions are modeled the mean-value establish an accurate engine model with low computational engine complexity. torque, emissions are modeled in theexample, mean-value transient details arepolynomial mainly focused. Forwith complexity. emissions are modeled in the mean-value establish an accurate engine model with low computational engine sense astorque, the static functions respectthe to complexity. sense as the static polynomial functions with respect to engine torque, emissions are modeled in the mean-value However, internal combustion engine is a complicated syssense as the static polynomial functions with respect to complexity. the mean-values of the manifold pressure and air mass mass However, internal combustion engine is a complicated sys- the mean-values of the manifold pressure and air sensemean-values as the static functions with respect to However, internal combustion engine is a and complicated sys- the tem involving involving multi-input multi-output its dynamic dynamic of polynomial the manifold pressure and air mass flow. Although the mean-value model based engine contem multi-input multi-output and its flow. Although the mean-value model based engine conHowever, internal combustion engine is a complicated systhe mean-values of the manifold pressure and air mass tem involving multi-input multi-output and its dynamic behavior is is quite quite difficult be due to Although the model basedetengine control applications, applications, i.e.mean-value speed control(Cairano control(Cairano al., 2012), 2012), difficult to to be characterized characterized due to the the flow. behavior i.e. speed etengine al., tem involving multi-input multi-output and the its dynamic flow.applications, Although the model based conbehavior is of quite to beprocess characterized due to the trol complexity thedifficult combustion and coupling trol i.e.mean-value speed control(Cairano et al., 2012), torque control(Kang&Shen, 2016), airpath control(Xie et complexity of the combustion process and the coupling control(Kang&Shen, 2016), airpath control(Xie et behavior between is of quite difficult tostate beprocess characterized due to the torque trol 2016), applications, i.e.reached speed control(Cairano et al., 2012), complexity thethe combustion andThe the coupling relations inner variables. derivation torque control(Kang&Shen, 2016), airpath control(Xie al., etc have a fruitful achievement, it et is variables. The derivation relations between the inner state al., 2016), etc have reached a fruitful achievement, it is complexity of the combustion process andThe thethe coupling torque control(Kang&Shen, 2016), airpath control(Xie et relations between the inner statehas variables. derivation of conventional physical model to consider multial., 2016), etc have reached a fruitful achievement, it is still incapable to be applied to the cyclic based transient multi- still of conventional physical model has to consider incapable to be reached applied to the cyclic based transient relations between the inner state variables. The the derivation al., 2016), etcsuch have a fruitful achievement, it is of conventional physical model has to consider the multi- still disciplinary knowledge such as thermo-dynamics, thermo-dynamics, chemical incapable to beasapplied to thephase cyclic based and transient control issues combustion control comdisciplinary knowledge such as chemical control issues such as combustion phase control and comof conventional physical model has to consider the multistill incapable to be applied to the cyclic based transient disciplinary knowledge such asand thermo-dynamics, chemical control mechanism, fluid mechanics, mechanical kinematics. issues such as combustion phase control and combustion variation variation rejection rejection issue. issue. mechanism, fluid mechanics, mechanical kinematics. bustion disciplinary knowledge such asand thermo-dynamics, control issues suchrejection as combustion mechanism, fluid and mechanical For example, themechanics, burn zone based method kinematics. ischemical usually bustion variation issue. phase control and comFor example, the burn zone based method is usually mechanism, fluid and mechanical The importance ofrejection the cyclic cyclic transient modeling modeling and and conconbustion variationof issue. For example, themechanics, burn based method kinematics. is usually The adopted to describe describe the zone combustion process (Heywood, importance the transient process (Heywood, adopted to the combustion The importance of the cyclic transient modeling and conFor example, the burn zone based method is usually trol has been aroused much attention recently, and the adopted to describe the combustion process (Heywood, 1988), but but such such kind kind of of model model has has aa very very complicated complicated trol been aroused much transient attentionmodeling recently, and and conthe The has importance of low-cost the cyclic 1988), trol has beenofaroused much attention recently, and the adoptedbut toand describe (Heywood, development the cylinder pressure sensor makes 1988), such kindthe of combustion model has aprocess very complicated structure computation, therefore it is not suitable development of the low-cost cylinder pressure sensor makes trol control-oriented has beenofaroused much attention recently, and the therefore is not suitable development structure and the low-cost cylinder pressure sensor makes 1988), suchcomputation, kind of model has a it very complicated the cyclic modeling possible. Makowicki structure and computation, therefore itAdditionally, is not suitable for thebut real-time control application. the the control-oriented cyclic modeling possible. Makowicki development of the low-cost cylinder pressure sensor makes for the real-time control application. Additionally, the control-oriented cyclic modeling possible. Makowicki structure and computation, therefore itAdditionally, is consisting not suitable et al. al. (2016) proposed proposed combustion cycle model model where for the real-time control application. the combustion engine is aa typical typical hybrid system system of the et (2016) aa combustion cycle where theal. control-oriented cyclic modeling possible. Makowicki combustion engine is hybrid consistingthe of (2016) proposed a combustion cycle model where for the real-time application. Additionally, combustion engine control is a typical hybrid system consisting of et combustion engine is a typical hybrid system consisting of et al. (2016) proposed a combustion cycle model where
2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 487 Peer review©under responsibility of International Federation of Automatic Copyright 2018 IFAC 487Control. Copyright © 2018 IFAC 487 10.1016/j.ifacol.2018.10.101 Copyright © 2018 IFAC 487
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018Mingxin Kang et al. / IFAC PapersOnLine 51-31 (2018) 448–453
Due to the operating mechanism of a SI engine, the engine system has a hybrid model structure consisting of continuous time dynamic behavior and discrete combustion event. Several system dynamics will be considered in this study including intake air-path dynamics, actuator response dynamics, cyclic residual gas transition dynamics, and combustion process model. The model structure is shown in Fig. 1. The manifold pressure (Pim ) is a continuous state influenced by the engine speed (Ne ) and the control inputs such as throttle angle (ϕ), variable valve timing (θ). In each cycle, the fresh air mass flow in the intake manifold will be aspirated into the cylinder and then result in the variations of the manifold pressure. Then, the combustion process is performed with appropriate fuel injection (uf ) and SA control in discrete cycle-by-cycle form to generate the cyclic power output and emissions. Finally, the cyclic power output will be merged in the crankshaft and therefore the power output and emissions will be in general considered in the continuous time domain. Indeed, for each cylinder, the interrelation on cycle-bycycle state involves not only the mass transition (i.e., 488
ma (k ) (k )
VVT actuator model
uf
Cyclic Transition Model Mass transition
imep( k )
1 4
Tivc ( k )
mr (k 1) f min (k ),mr (k )
Thermal coupling m f (k )
1/z
min mr Tivc mrTevc minTim
ncyl
y
e
i
i
CA 50 ( k )
SA(k )
Event-based Model
Time-domain model
Time-domain model
Fig. 1. The proposed model framework for automotive gasoline engines. residual gas remained for next cycle), but also the energy transition (i.e., the in-cylinder temperature or heat influences the combustion process and then influence the state in the next cycle). The residual gas is a very important variable to find the cycle-by-cycle relations. Residual gas has two effects on the properties of the cycle. Firstly, there is the effect that it occupies a volume that cannot be filled with a fresh mixture of air and fuel, and therefore it reduces the volumetric efficiency. Secondly, the residual gas has a mass that influences the temperature rise from the combustion (Eriksson&Nilsen (2014)). However, the residual gas mass is difficult to be measured on board. The conventional estimation method for the residual gas is to apply the iteratively calculation by means of the cylinder pressure signal and the thermodynamics relations(Eriksson&Nilsen, 2014; Heywood, 1988). This calculation process is complex and only carried out off-line. In this regards, the cyclic estimation and modeling of the residual gas mass is quite significant. This study will find the cyclic transition relations for the residual gas mass, and then derive the cyclic temperature of the in-cylinder air-fuel mixture. Finally, the cyclic combustion process variables such as CA50 and IMEP will be further modeled. 3. MODELING Before modeling the cyclic relations, we have to declare the definition of one cycle. As shown in Fig. 2, the starting point (0 deg) of a new cycle is from the intake top dead center (TDC) point. In the follows, the cyclic state transition dynamics will be derived based on this definition. TDC
TDC
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2. THE FRAMEWORK OF THE ENGINE MODEL
120 N e ncyl
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The rest of the paper is organized as follows. Section II introduces the overall framework of the proposed hybrid engine model. In section III, the derivation procedure of the cyclic model is presented including time domain based air path model, actuator dynamics, and eventbased residual gas transition model, combustion process model,etc. A state estimator based on Extended Kalman Filter (EKF) is proposed to estimate the the cyclic state in section IV. Then, the model validation results are included in section V. Conclusions are provided in the last section.
manifold
dynamics pim
···
This paper proposes a cyclic model for the spark ignition (SI) engine system where the continuous-time based intake airpath dynamics, actuator response dynamics, and the discrete-time based residual gas mass transition model are both considered. An extended Kalman filter is adopted to estimate the state in real time and improve the model precision based on the measurable in-cylinder pressure data, and the data-driven based method (Gauss process regression modeling method) is adopted to model the combustion process quantities including combustion phase (CA50) and indicated mean effective pressure (IMEP). The proposed model is able to represent the mass and energy transition process in the cycle-by-cycle details, and has the potentials to be applied to the cyclic transient controller design.
Moving average
Cyclic discretizing
···
the gas-exchange and compression phases described by physics-based and the combustion phase modeled by a data-based approach, and the model was then applied for the optimal fuel injection controller development (Makowicki et al., 2017). Kumar&Shen (2015) proposed a cyclic transition model for the air mass flow including residual gas, burnt gas, etc by means of mass and energy conservation laws. In fact, the transient control quality are mainly determined by the cycle-by-cycle manipulated inputs including the fuel injection mass and the spark advance (SA). Therefore, the cyclic transient modeling becomes quite urgent and necessary to achieve the elaborate control of the modern engines.
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Fig. 2. A cycle definition: new cycle starts from intake TDC. 3.1 Intake airpath model Based on the ideal gas law and mass conservation, the continuous-time dynamical behavior of fresh air mass flow
IFAC E-CoSM 2018 450 Changchun, China, September 20-22, 2018Mingxin Kang et al. / IFAC PapersOnLine 51-31 (2018) 448–453
through the intake manifold can be described by a meanvalue expression (Eriksson&Nilsen, 2014): Rim Tim dPim = (m ˙ th − m ˙ a) (1) dt Vim where, Pim denotes the intake manifold pressure. As for the air mass flow rate passing through the throttle valve m ˙ th , it can be expressed by (this expression neglects the effects of the throttle shaft): ( ) ) ( cos (ϕ) c ·P πD2 Pim √d a Ψ 1− (2) m ˙ th = 4 cos (ϕ0 ) Pa RTim where cd is discharge coefficient; Pa is the pressure in the upstream of the throttle valve, which is generally regarded the same as the atmospheric pressure; D is the diameter of the throttle plate; ϕ0 is the throttle plate rest angle; Ψ(·) is the piecewise-continuous-function with the following form (Heywood, 1988): √ ) κκ+11 ( κ 2 Pim 2 κ 1 κ ) , for ( < ( ) κ+1 Pa κ+1 Pim � Ψ( )= [ ] κ 1 1 � Pa κ � 2κ κ P P im im � 1−( , otherwise. ) ( Pa ) κ−1 Pa (3) For many working fluids such as intake air, exhaust gas at lower temperature, the approximation can be adopted with κ ≈ 1.4.
In addition, m ˙ a denotes the aspirated air mass flow rate into the cylinder, if ignoring the intake-to-power delay, the mean-value model can be applied with speed-density method: Pim Vd ne Ncyl (4) m ˙ a = ηv (θ, Pim , ne ) Rim Tim 120 where ηv (·) denotes the volumetric efficiency which typically relies on the engine speed, intake manifold pressure and intake valve timing (θ). Vd is the displaced volume, intake air temperature Tim is assumed constant and ne is engine speed in revolution per minute (rpm). Hence, for each cycle the aspirated air-charge into cylinder can be derived from (4) multiplying cyclic period (∆T = 120/ne Ncyl [s]), i.e. Pim Vd ma = η( θ, Pim , ne ) (5) Rim Tim 3.2 Actuator response dynamics In above models, throttle opening angle and variable valve timing (VVT) are two continuous-time control actuators. The first-order lag model are adopted to describe their dynamical behaviors. The response dynamics for throttle and VVT can be formulated as follows: 1 d ϕ(t) = (−ϕ(t) + uϕ (t)) (6) dt τϕ 1 d θ(t) = (−θ(t) + uθ (t − τdθ )) (7) dt τθ where, τdθ denotes the delay time between the command and the actual response, and τϕ , τθ are the time constant for these two actuators. uϕ , uθ denote control commands for the throttle and intake valve timing actuator, respectively.
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3.3 Fuel injection model In this study, only the direct-injection engine is focused. Then, the fuel mass mf (k) in k-th cycle can be directly given by: mf (k) = uf (k−1), (8) which indicates the actual fuel injection mass always delays in one cycle than fuel injection command uf (k − 1).This is reasonable because the command should be prepared in advance before new injection trigger coming. 3.4 Cyclic model of residual gas mass In this study, we derive the residual gas model in such kind of way. Focusing the exhaust process from k-th cycle to (k+1)-th cycle, there is a relation at the exhaust valve opening (EVO) point according to the ideal gas law: Pevo (k)Vevo (k) , (9) Tevo (k) = mevo (k)Revo (k) where, mevo (k) = ma (k)+mf (k)+mr (k) from mass conversation assumption. ma (k) and mf (k) can be obtained by (5) and (8), respectively. Furthermore, residual gas mass mr (k) is assumed to be the flow mass when exhaust valve closing (EVC), namely, mr (k) = mevc (k). In fact, the EVC point is usually located at/after the intake TDC to pump out the as much burnt gas as possible. Then, at the EVC point, it has Pevc (k+1)Vevc (k+1) Tevc (k+1) = , (10) mevc (k+1)Revc (k+1) where, mevc (k+1) is assumed as the residual gas in (k+1)-th cycle, mevc (k+1) = mr (k+1). Considering the exhaust process can be equivalent to the polytropic process, there is a relationship between temperature and pressure: ( )1− κ1 Tevc (k+1) Pevc (k+1) = . (11) Tevo (k) Pevo (k) Substituting (9), (10) into (11) and supposing the gas property in exhaust process slightly change (i.e. Revo ≈ Revc = R) yields: ( )1 Vevc (k+1) Pevc (k+1) κ mr (k+1) = (maf (k)+mr (k)) Vevo (k) Pevo (k) (12) where maf (k) = ma (k)+mf (k), denotes the fresh mixing charge, it can be represented in the following form by substituting eq.(5), Pim (k)Vd + mf (k). (13) min (k) = η(ne , Pim (k), θ(k)) RTim It should be noted that, eq. (12) represents the cyclic transition of the residual gas, where cylinder pressure, volume, and intake mixtures are measurable parameters. The key-point of this equation is how to get an accurate residual gas in current cycle for next cycle state estimation. 3.5 Cyclic model of in-cylinder charge temperature Now, we consider thermal coupling relation in the intake process. Assuming constant specific heats and the mixing
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018Mingxin Kang et al. / IFAC PapersOnLine 51-31 (2018) 448–453
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during intake stroke is done under free expansion (i.e., dq = 0 and dU = 0), the temperature at intake valve closing can be calculated based on energy conservation, that is, (min +mr ) Tivc = mr Tevc +min Tim , (14) where the fresh charge temperature Tim can be approximated as the temperature in intake manifold (Eriksson&Nilsen, 2014; Larimore, 2013). Then, according to ideal gas equation, eq. (14) can be written as follows:
IMEP(k) is associate to the components of the in-cylinder mixture, the temperature (Tivc ) and the spark ignition timing: IMEP(k) = GPR2 (ma (k), mf (k), mr (k), Tivc (k), SA(k)). (18) The above GPR models can be trained based on the experimental data under different conditions.
Tivc (k+1) = [ ] 1 Pevc (k+1)Vevc (k+1) +min (k+1)Tim ,(15) mt (k+1) Rem where mt = ma + mf + mr denotes the total mass of the in-cylinder mixture.
Combining eqs. (1), (8) and (13), and writing the cyclic transition models in a compact form, we can obtain:
If the temperature Tivc and residual gas mr are obtained, the cylinder pressure at IVC timing can be calculated by: RTivc (k) [maf (k)+mr (k)] . (16) Pivc (k) = Vivc (k) It is obvious in eq.(15) the cylinder temperature Tivc (k) is coupled with residual gas mr (k) , Pim (k) and uf (k −1). And the initial mr (k) is crucial to the model accuracy. To predict Tivc , and mr , an Extended Kalman Filter (EKF) was adopted in this study, see details in the following section.. 3.6 Combustion process modeling The combustion process is associate with the some initial conditions including the components of the air-fuel mixture, in-cylinder temperature, and spark ignition timing, etc. If the residual gas mass and the temperature of the mass flow at IVC timing can be obtained cycle-by-cycle, the combustion process model can be easily modeled as the function of these proposed cyclic states. Considering the combustion is a quite complicated stochastic process and it is difficult to derive a physical relations, the Gauss process regression (GPR) method is adopted in this study. GPR is a powerful Bayesian and non-parametric modeling approach which assumes Gaussian distributions on function classes and sampled data. Non-parametric means that the GPR model contains no parameters to fit the data through the measurement values as opposed to the weights of a polynomial model. The probabilistic approach allows information to be given about the predictive uncertainty of the model with respect to prior beliefs of the function properties(Tietze, 2015). Instead of minimizing an error to optimize the model parameters as shown for the polynomial model, the probabilistic approach maximizes the probability of the model values, given the measurement. By means of the GPR method, combustion phase and IMEP are mainly considered. Combustion phase CA50 defined as the location of 50% of mass fraction burned is an important indicator to evaluate the combustion status, and it can be determined by the cylinder temperature (Tivc ) and spark ignition timing SA (Larimore, 2015), i.e., (17) CA50 (k) = GPR1 (Tivc (k), SA(k)). Similarly, another important variable about the combustion status denoted by the indicate mean effective pressure 490
4. EKF-BASED STATE ESTIMATION
Pim (k+1) = f1 (Pim (k), ϕ(k), θ(k))
(19)
mr (k+1) = f2 (mr (k), Pim (k), θ(k), mf (k), p(θ(k))) (20) mf (k+1) = uf (k)
(21)
and the system output is Pivc from (15): Pivc (k) = g(mr (k), Tivc (k), Pim (k), mf (k), p(θ(k))) (22) where p(θ) denotes the VVT-dependent parameters such as Pevc , Pevo , Vevc , Vevo ; in fact, Vevc , Vevo are explicit functions of valve timing θ, and Pevc , Pevo can be calibrated based on different θ. For the sake of the simplicity, denote x = [Pim , mr , mf ]T , u = [ϕ, θ, uf ]T , y = Pivc , and suppose the cylinder pressure is measurable with Guassian white noise, then the state equations (19)-(21) and the output equation (22) can be linearized as follows: xk ≈˜ xk + A(xk−1 − x ˆk−1 ) + W wk−1 , ˆk−1 ) + V vk . yk ≈ y˜k + H(xk−1 − x
(23) (24)
˜k , y˜k are where xk , yk is the true values at time k. x approximate state and measurement vectors from x ˜k = f (ˆ xk−1 , uk−1 , 0) and y˜k = g(˜ xk , 0), x ˆ is the estimator of the state. wk , vk denotes the noise. A, W, H, V are Jacobians with the following form: ∂f[i] ∂f[i] (ˆ xk−1 , uk−1 , 0), W[i,j] = (ˆ xk−1 , uk−1 , 0), A[i,j] = ∂x[j] ∂w[j] H[i,j] =
∂g[i] ∂g[i] (˜ xk , 0), V[i,j] = (˜ xk , 0). ∂x[j] ∂v[j]
˜k , and e˜yk = yk − y˜k , then error Define e˜xk = xk − x dynamics can be deduced from (23) and (24): e˜xk ≈ A(xk−1 − x ˆk−1 ) + ϵk , e˜yk ≈ H e˜xk + ηk
(25) (26)
where ϵk and ηk denote new independent random variables having zero mean and covariance matrices W QW T and V RV T , Q, R are process and measurement noise covariance, respectively. (that is, ϵk : p(ϵ) ∼ N (0, W QW T ).) It should be noticed that (25) and (26) are linear which can use conventional Kalman filter by means of the measurable e˜yk : x ˆk = x ˜k + Kk e˜yk = x ˜k + Kk (yk − y˜k ) where Kk is Kalman filter gain. The Kk updating algorithm of Kalman filter has been summarized as follows (Welch, 1995):
IFAC E-CoSM 2018 452 Changchun, China, September 20-22, 2018Mingxin Kang et al. / IFAC PapersOnLine 51-31 (2018) 448–453
(0) Initialization: Given x ˆk−1 and Pk−1 (a) Time update equations (here denote x ˆ− ˜k ) k := x
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Pk−=Ak Pk−1 ATk + Wk Qk−1 WkT (b) State update equations
(28)
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(29) (30)
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u (k ) Cyclic Transition Model Eqs.(19) (20) (21)
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(31) The estimation diagram is illustrated in Fig. 3. Based on this algorithm, the residual gas mass mr and the temperature of mass flow Tivc can be obtained at IVC point. The early knowledge about the in-cylinder state before spark ignition will be helpful for applying the accurate SA and fuel injection control. TDC
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Kk=Pk− HkT (Hk Pk− HkT + Vk Rk VkT )−1 ˆ− x− x ˆk=x k + Kk (yk − g(ˆ k )) − Pk=(I − Kk Hk )Pk
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Fig. 4. Case 1 (load torque at 60Nm): Estimation results of residual gas and cylinder temperature.
Extended Kalman Filter
Fig. 3. Diagram of the EKF estimator. 5. MODEL VALIDATION The model validations have been conducted based on the experimental data collected from a 3.5 Liter V6 type gasoline engine. Considering the actual residual gas mass is unmeasurable, the residual gas fraction xr is introduced as an evaluation index and defined by xr (k) = mr (k)/mt (k). Suppose the total aspirated mass in the adjacent cycles are the same under the steady operating condition, i.e. mt (k−1) ≈ mt (k), then based on the polytropic assumption during the exhaust stroke, the residual gas fraction can be approximated as, ( ) κ1 Vevc (k) Pevc (k) mr (k) = (32) xr (k) ≈ mt (k−1) Vevo (k−1) Pevo (k−1) In fact, the above approximation is only effective under the steady operating condition and has been adopted in (Kumar&Shen, 2015) to model the cyclic transition of mass flow. Hence, the approximation is adopted in this study to compare and verify the precision of the proposed modeling method. Two case studies have been investigated including the transient experiments under the fixed load torque, and the fixed engine speed. In the first case, the load torque is fixed at 60Nm, throttle angle and VVT are changed in transient 491
mode. The proposed model outputs are shown in Fig.4. In the another case, the engine speed is fixed at 1200rpm, and the estimation results is shown in Fig.5. In both cases, it is obvious the residual gas fraction xr and the temperature of mass flow Tivc estimated by the proposed model are matching to the approximated values under steady condition, although there are relative large fluctuation. The combustion phase (CA50 ) and IMEP model show the good precision. To observer the transient details of the model, the enlarged figure about the step change of the throttle is illustrated Fig. 5(b). In general, the combustion variations is inevitable because of the stochasticity of the combustion process. The proposed model demonstrates the satisfactory transient cyclic behavior. 6. CONCLUSION In this paper, a spark ignition (SI) engine model with a hybrid structure is presented where the continuoustime based intake airpath dynamics, actuator response dynamics, and discrete-time based residual gas mass transition model are considered. An extended Kalman filter is adopted to estimate the cyclic state (residual gas mass, and the temperature of the mass flow) in real time and improve the model precision based on the measurable incylinder pressure data. Meanwhile, the combustion process models including combustion phase CA50 and IMEP are modeled based on the GPR method. The proposed model is capable to represent the mass and energy transition
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018Mingxin Kang et al. / IFAC PapersOnLine 51-31 (2018) 448–453
Fig. 5. Case 2(engine speed at 1200rpm): Estimation results of residual gas and cylinder temperature. process in the cycle-by-cycle details, and it is suitable for the cyclic transient controller design. However, because the proposed model relies on the cylinder pressure information in current cycle, it can only perform one-step ahead prediction for the status of the combustion process. This drawback restricts the wide application to the model based optimal controller design. To improve this model, the model of the cylinder pressure should be studied in the future work. ACKNOWLEDGEMENTS The first author would like to express his thanks to SHEN Laboratory of Sophia University for the experimental data and technical support. REFERENCES C. Ericson, B. Westerberg, R.Egnell. Transient emission predictions with quasi stationary models. SAE Technical Paper No. 2005-01-3852, 2005. Del Re, L. (Eds.)(2010). Automotive model predictive control : models, methods and applications. Verlag Berlin Heidelberg, Springer. Grondin, O., Stobart, R., Chafouk, H., & Maquet, J. (2004). Modelling the Compression Ignition Engine for Control: Review and Future Trends. SAE World Congress. Winterbone, D. E., Thiruarooran, C., & Wellstead, P. E. (1977). A wholly dynamic model of a turbocharged 492
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diesel engine for transfer function evaluation.SAE Technical Paper, (770124). Postma, M., & Nagamune, R. (2012). Air-fuel ratio control of spark ignition engines using a switching LPV controller. IEEE Transactions on Control Systems Technology, 20(5), 1175-1187. Hu, Y., Chen, H., Wang, P., Chen, H., & Ren, L. (2018). Nonlinear model predictive controller design based on learning model for turbocharged gasoline engine of passenger vehicle . Mechanical Systems & Signal Processing, 109, 74-88. Shen T., Zhang J., Jiao X., Kang M., Kako J., Ohata A. Transient Control of Gasoline Engines. CRC Press, 2015. Eriksson, Lars, and Lars Nielsen. Modeling and control of engines and drivelines. John Wiley & Sons, 2014. Heywood, John. Internal combustion engine fundamentals. McGraw-Hill Education, 1988. Hendricks, E. and Sorenson, S., Mean Value Modelling of Spark Ignition Engines, SAE Technical Paper 900616, 1990, doi: 10.4271/900616. Cairano, S. D., Yanakiev, D., Bemporad, A., Kolmanovsky, I. V., & Hrovat, D. (2012). Model predictive idle speed control: design, analysis, and experimental evaluation. IEEE Transactions on Control Systems Technology, 20(1), 84-97. Kang, M., & Shen, T. (2016). Receding horizon online optimization for torque control of gasoline engines. Isa Transactions. Xie, H., Song, K., Yang, S., Tatsumi, J., Zheng, Q., & Zhang, H., et al. (2016). On decoupling control of the vgt-egr system in diesel engines: a new framework. IEEE Transactions on Control Systems Technology, 24(5), 1788-1796. Makowicki, T., Bitzer, M., Kotman, P., & Graichen, K. (2016). A combustion cycle model for stationary and transient engine operation. Ifac Papersonline, 49(11), 469-475. Makowicki, T., Bitzer, Graichen, K., & Grodde S. (2017). Cycle-by-Cycle Optimization of the Combustion during Transient Engine Operation.IFAC World Congress, Toulouse, 2017. Kumar, M., & Shen, T. (2015). Estimation and feedback control of air-fuel ratio for gasoline engines. Control Theory and Technology, 13(2), 151-159. Larimore, J., Jade, S., Hellstrm, E., Stefanopoulou, A. G., Vanier, J., & Jiang, L. Online adaptive residual mass estimation in a multicylinder recompression HCCI engine. In Proceedings of ASME 2013 Dynamic Systems and Control Conference, pp.1-9,2013. Larimore, J., Hellstrm, E., Jade, S., Stefanopoulou, A. G., & Jiang, L. (2015). Real-time internal residual mass estimation for combustion with high cyclic variability. International Journal of Engine Research, 16(3), 474484. Guzzella L, Onder C. Introduction to modeling and control of internal combustion engine systems. Springer Science & Business Media, 2009. Welch, G., & Bishop, G. (1995). An introduction to the Kalman filter. Tietze N. Model-based Calibration of Engine Control Units Using Gaussian Process Regression[D]. Ph.D dissertation, Technische Universitt, 2015