Flatness-based Feedforward and Feedback Control for Fuel Rail System of Gasoline Direct Injection Engine

Advances in Control Preprints, 8th IFAC International on Advances in Automotive Automotive Control Symposium Preprints, 8th IFACNorrköping, International Symposium on on June 19-23, Sweden Preprints, 8th IFAC International Symposium Advances in2016. Automotive Control June 19-23, 2016. Norrköping, Sweden Available online at www.sciencedirect.com Advances in Automotive Control Advances Automotive Control June 19-23,in2016. Norrköping, Sweden June June 19-23, 19-23, 2016. 2016. Norrköping, Norrköping, Sweden Sweden

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IFAC-PapersOnLineFeedforward 49-11 (2016) 775–780 Flatness-based and Feedback Feedback Flatness-based Feedforward and Flatness-based Feedforward and Feedback Flatness-based Feedforward and Control Rail of Gasoline Control for for Fuel Fuel Rail System System of Feedback Gasoline Control for Fuel Rail System of Gasoline Control for Fuel Rail System of Direct Injection Engine Direct Injection Engine Gasoline Direct Injection Engine Direct Injection Engine ∗,∗∗ ∗∗ ∗∗ ∗,∗∗

Q.-F. Liu Liu ∗,∗∗ C.-Y. C.-Y. Wang Wang ∗∗ Y.-F. Y.-F. Hu Hu ∗∗ H. H. Chen Chen ∗,∗∗ Q.-F. ∗,∗∗ ∗∗ ∗∗ Q.-F. Liu C.-Y. Wang Y.-F. Hu H. Chen ∗,∗∗ ∗,∗∗ ∗∗ ∗∗ ∗,∗∗ C.-Y. Wang ∗∗ Y.-F. Hu ∗∗ H. Chen ∗,∗∗ Q.-F. Liu ∗ Q.-F. Liu C.-Y. Wang Y.-F. Hu H. Chen ∗,∗∗Jilin ∗ State Key Laboratory of Automotive Simulation and State Key Laboratory of Automotive Simulation and Control, Control, Jilin ∗ PR China. of Automotive Simulation and Control, Jilin ∗ State Key LaboratoryUniversity, University, PR China. ∗ State Key Key Laboratory Laboratory of Science Automotive Simulation and Control, Jilin ∗∗State of Automotive Simulation and Control, Jilin ∗∗ Department of Control and Engineering, Jilin University, University, PR China. Department of Control Science and Engineering, Jilin University, University, PR China. ∗∗ University, PR China. PR Department of Control Science and Engineering, Jilin University, ∗∗ PR China. China. ∗∗ Department of Control Science and Department of Control Science and Engineering, Engineering, Jilin Jilin University, University, PR China. PR China. China. PR Abstract: For For gasoline gasoline direct direct injection injection (GDI) (GDI) engines, engines, obtaining obtaining desired desired rail rail pressure pressure has has Abstract: become a key prerequisite of fuel injection quantity precise control. Since improved control Abstract: For gasoline direct injection (GDI) engines, obtaining desired rail pressure has become a key prerequisite of fuel injection quantity precise control.desired Since improved control Abstract: For gasoline direct injection (GDI) engines, obtaining rail pressure has Abstract: For gasoline direct injection (GDI) engines, obtaining desired rail economy pressure has performance and robustness will translate into better combustion stability, fuel and become a key prerequisite of fuel injection quantity precise control. Since improved control performance and robustness will translate into better combustion stability, fuel economy and become a key prerequisite of fuel injection quantity precise control. Since improved control become a This keyand prerequisite ofwill fuel injectioninto quantity precise control. Since improved control emissions. paper develops a feedforward-feedback controller based on a nonlinear model of performance robustness translate better combustion stability, fuel economy and emissions. This paper develops a feedforward-feedback controller based on a nonlinear modeland of performance and robustness will translate into into better combustion stability, fuel economy performance and robustness will translate better combustion stability, fuel economy and fuel rail system, where nominal feedforward control is derived by differential flatness and fuel emissions. This paper develops a feedforward-feedback controller based on a nonlinear model of fuel rail system, wheredevelops nominala feedforward control is controller derived bybased differential flatness model and fuel emissions. This paper feedforward-feedback on aa nonlinear of emissions. This paper develops feedforward-feedback controller based ondesign, nonlinear model of rail pressure pressure is selected selected as flat flat aoutput. output. In feedback feedback part, to simplify simplify the the system system is fuel rail system, where nominal feedforward control is derived by differential flatness and fuel rail is as In part, to the design, the is fuel rail system, where nominal feedforward control is derived by differential flatness and fuel fuel rail system, where nominal feedforward control is derived by differential flatness and fuel linearized on equilibrium point using Taylor series expansion, and Lyapunov method is used to rail pressure is selected as flat output. In feedback part, to simplify the design, the system is linearized on equilibrium point using Taylor series expansion, and Lyapunov method is used to rail pressure is selected as flat output. In part, to the the system is rail pressure is selected aspoint flat error output. In feedback feedback part, to simplify simplify the design, design, the is system is ensure stability of closed-loop closed-loop system. Finally, the proposed proposed controller is verified verified by fuel fuel linearized on equilibrium using Taylor series expansion, and Lyapunov method used to ensure stability of error system. Finally, the controller is by linearized on equilibrium point using Taylor series expansion, and Lyapunov method is used to linearized on equilibrium point using Taylor series expansion, and Lyapunov method is used to rail system simulation model established in AMESim software package, the simulation results ensure stability of closed-loop error system. Finally, the proposed controller is verified by fuel rail system simulation model established in AMESim software package, the simulation results ensure stability of error system. Finally, the proposed controller is fuel ensure stability of closed-loop closed-loop error system. Finally, the proposed controller is verified verified by by fuel in different different pressure references demonstrate the effectiveness of the the control system. rail system simulation model established in AMESim software package, the simulation results in pressure references demonstrate the effectiveness of control system. rail system simulation model established in AMESim software package, the simulation results rail system simulation model established in AMESim software package, the simulation results in different pressure references demonstrate the effectiveness of the control system. in in different different pressure pressure references references demonstrate demonstrate the the effectiveness effectiveness of of the the control control system. system. 1.IFAC INTRODUCTION © 2016,1. (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. performance analysis. developing aa virtual INTRODUCTION performance analysis. By By developing virtual prototype prototype using a domain-specific tool, it can be used analyze 1. INTRODUCTION performance analysis. By developing a virtual prototype using a domain-specific tool, it can be used to to analyze 1. INTRODUCTION performance analysis. By developing a virtual prototype 1. INTRODUCTION performance analysis. Bypressure, developing a virtual prototype influence factors of rail verify control strategy using a domain-specific tool, it can be used to analyze With the direct injection technology applying in Diesel influence factors of rail pressure, verify control strategy With the direct injection technology applying in Diesel using a domain-specific tool, it can be used to analyze using a domain-specific tool, it can beof used to strategy analyze and foretell the effects of modification the elements of factors of rail pressure, verify control engines, itdirect achieves perfectly precise mixing mixing of in fuel and influence With the injection technology applying Diesel and foretell the effects of modification of the elements of engines, it achieves perfectly precise of fuel and influence factors of rail pressure, verify control strategy With the direct injection technology applying in Diesel influence factors of rail pressure, verify control strategy With the direct injection technology applying in Diesel the system Corno et al. [2008], di Gaeta et al. [2009]. and foretell the effects of modification of the elements of gas directly in the combustion chamber Kouremenos et al. engines, it achieves perfectly precise mixing of fuel and the system Corno et al. [2008], di Gaeta et al. [2009]. gas directly in the combustion chamber Kouremenos et al. and foretell the effects of modification of the elements engines, it achieves achieves perfectly precise mixing of fuel fuelcould and and foretell the ofetmodification of the elements ofa engines, it perfectly precise mixing of and For system example, in effects Corno al. [2008], [2008], the dynamics of of the Corno et al. [2008], di Gaeta et al. [2009]. [1999]. Only a few years later, the same technology gas directly in the combustion chamber Kouremenos et al. For example, in Corno et al. the dynamics of a [1999]. Onlyina the few combustion years later, chamber the sameKouremenos technology could the system Corno et al. [2008], di Gaeta et al. [2009]. gas directly et al. the system Corno et al. [2008], di Gaeta et al. [2009]. gas directly in the combustion chamber Kouremenos et al. common rail injection system for GDI engines is analyzed For example, in Corno et al. [2008], the dynamics of a be applied to gasoline engines, in which, the fuel is injected [1999]. Only a few years later, the same technology could common rail injection system for GDI engines is analyzed be applied to agasoline engines, which, fuel is injected example, in et [2008], the of [1999]. Only fewcombustion years later,in the samethe technology could For For example, in Corno Cornosystem et al. al. [2008], the dynamics dynamics of aa [1999]. Only agasoline few years later, the same technology could and model parameters are identified using experimental common rail injection for GDI engines is analyzed directly into the chamber of each cylinder, be applied to engines, in which, the fuel is injected and model parameters are identified using experimental directly into the combustion chamber of each cylinder, common rail injection injection system fordeveloping GDI engines engines is analyzed analyzed be applied to gasoline engines, engines, in which, which, the the fuel is is injected injected rail system for GDI is be applied to gasoline in fuel data. Others are with more effective and model are identified using experimental leading to economic fuel consumption, consumption, powerful torque common directly into the combustion chamber of each cylinder, data. Othersparameters are concerned concerned with developing more effective leading to economic fuel powerful torque and model parameters are identified using experimental directly into the combustion chamber of each cylinder, and model parameters are identified using experimental directly into the combustion chamber of each cylinder, control strategy. In paper paper Balluchi Balluchi et al. al. [2006], [2006], based on data. Others are concerned with developing more effective output and efficient emission reduction. Of course, the leading to economic fuel consumption, powerful torque control strategy. In et based on output and efficient emission reduction.powerful Of course, the data. Others are concerned with developing more effective leading to economic fuel consumption, torque data. Others are concerned with developing moreinbased effective leading tothese economic fuel consumption, powerful torque the coupled discrete and continuous interactions the fuel control strategy. In paper Balluchi et al. [2006], on costs of advantages are a more complex system output and efficient emission reduction. Of course, the the coupled discrete and continuous interactions in the fuel costs ofand these advantages are reduction. a more complex system control strategy. In paper Balluchi et al. based on output efficient emission Of course, course, the control strategy. In paper Balluchi et al. [2006], [2006], based on output and efficient emission reduction. Of injection system, aa hybrid control approach is utilized for coupled discrete and continuous interactions in the fuel and more more control degrees of freedom Achleitner et the al. the costs of these advantages are a more complex system injection system, hybrid control approach is utilized for and control degrees of freedom Achleitner et al. the coupled discrete and continuous interactions in the fuel costs of these advantages are a more complex system the coupled discrete and continuous interactions in the fuel costs ofMyung these advantages arefreedom a more complex system the rail pressure control. In paper Lino et al. [2007], aa injection system, a hybrid control approach is utilized for [2007], and Park [2012]. Fuel rail injection system and more control degrees of Achleitner et al. the rail pressure In paperapproach Lino et isal.utilized [2007],for [2007], Myung and degrees Park [2012]. Fuel railAchleitner injection system system, aacontrol. hybrid control and more control of freedom freedom et al. injection injection system,model hybrid control approach isal.utilized for and more control degrees of Achleitner et al. control-oriented of aaIn diesel engine is et developed, and the rail pressure control. paper Lino [2007], aa equipped with the electromagnetic drive injector is a key [2007], Myung and Park [2012]. Fuel rail injection system control-oriented model of diesel engine is developed, and equipped with and the electromagnetic injector issystem a key the rail control. In paper Lino et al. [2007], Myung Park [2012]. Fueldrive rail injection the rail pressure pressure control. In paper Lino et al.is[2007], [2007], a [2007], Myung and Park [2012]. Fuel rail injection system acontrol-oriented controller based on Backstepping technique derived model of a diesel engine is developed, and element for realizing the requirement of flexible cylinder equipped with the electromagnetic drive injector is a key a controller based on Backstepping technique is derived element for realizing the requirement of injector flexible cylinder control-oriented model of aa diesel diesel engineChatlatanagulchai is developed, developed, and and equipped with theGDI electromagnetic drive is aa key key control-oriented model of engine is equipped with the electromagnetic drive injector is for the rail pressure control. In paper a controller based on Backstepping technique is derived injection. In fact, combustion system is very sensitive element for requirement of cylinder the rail pressure In paper Chatlatanagulchai injection. In realizing fact, GDIthe combustion system is very sensitive controller based oncontrol. Backstepping technique is derived derived element for realizing the requirement of flexible flexible cylinder for aafor controller based on Backstepping technique is element for realizing the requirement of flexible cylinder et al. [2010], for the convenience of implementation, an the rail pressure control. In paper Chatlatanagulchai to the the quality quality of the the fuel spray, evensystem a small small size derivation injection. In fact, GDI combustion is very sensitive et al. [2010], for the convenience of implementation, an to of fuel spray, even a size derivation for the rail pressure control. In paper Chatlatanagulchai injection. In fact, GDI combustion system is very sensitive for the rail pressure control. In paper Chatlatanagulchai injection. In fact, GDI combustion system is very sensitive integrator-augmented sliding mode controller integrating et al. [2010], for the convenience of implementation, an of droplets can significantly deteriorate engine emission to the quality of the fuel spray, even a small size derivation integrator-augmented sliding mode controller integrating of droplets can significantly deteriorate engine emission et al. [2010], for the convenience of implementation, an to the quality of the fuel spray, even a small size derivation et al. gain [2010], for the convenience ofcontroller implementation, an to the quality of the fuel spray, even a small size derivation with scheduling and feed-forward term is proposed integrator-augmented sliding mode integrating performance and reduce combustion efficiency Giorgetti of droplets can significantly deteriorate engine emission with gain scheduling and feed-forward term is proposed performance and reduce combustion efficiency Giorgetti integrator-augmented sliding mode controller integrating of droplets can significantly deteriorate engine emission integrator-augmented sliding mode controller integrating of droplets can significantly deteriorate engine emission for accurate common-rail pressure control. In paper Monwith gain scheduling and feed-forward term is proposed et al. [2006], Tang et al. [2009]. The precise control performance reduce combustion efficiency for accurate common-rail pressure control. In paper Monet al. [2006],and Tang et al. [2009]. The preciseGiorgetti control with gain scheduling and feed-forward term is proposed performance and reduce combustion efficiency Giorgetti gain scheduling andpressure feed-forward term is proposed performance and reduce combustion efficiency Giorgetti tanaro et al. [2011], aa model reference adaptive control (Mfor accurate common-rail control. In paper Monof injection injection quantity is mainly mainly dependent on the the stable with et al. [2006], Tang et al. [2009]. The precise control tanaro et al. [2011], model reference adaptive control (Mof quantity is dependent on stable for accurate common-rail pressure control. In paper Monet al. [2006], [2006], Tang et general, al. [2009]. [2009]. The precise precise control for accurate common-rail control. In value paper Monet al. Tang et al. The control RAC) algorithm based on aapressure common rail mean model tanaro et al. [2011], a model reference adaptive control (Mpressure in fuel rail. In insufficient rail pressure of injection quantity is mainly dependent on the stable RAC) algorithm based on common rail mean value model pressure in fuel rail. In general, insufficienton railthe pressure tanaro et al. [2011], a model reference adaptive control (Mof injection quantity is mainly dependent stable tanaro et al.to [2011], a model reference adaptive control (Mof quantity is general, mainly dependent on the stable is designed reduce the residual pressure in the rail. By algorithm based on a common rail mean value model willinjection reduce the spray penetration distance, which may ruin RAC) pressure in fuel rail. In insufficient rail pressure is designed to reduce the residual pressure in the rail. By will reduce the spray penetration distance, which may ruin RAC) algorithm based on a common rail mean value model pressure in fuel rail. In general, insufficient rail pressure RAC) algorithm based on a common rail mean value model pressure in fuel rail. In general, insufficient rail pressure analyzing control structure in engineering, paper Chen is designed to reduce the residual pressure in the rail. By the fuel mixing and break the interaction with airflow will reduce the spray penetration distance, which may ruin analyzing control structure in engineering, paper Chen the fuel mixing and break the interaction with airflow is designed to reduce the residual pressure in the rail. By will reduce the spray spray the penetration distance, which may may ruin is designed to proposes reduce the residual pressurecontrol in paper the method rail. By will reduce the penetration distance, which ruin et al. [2014] a new nonlinear analyzing control structure in engineering, Chen directly. Increasing pressure is an effective way to the fuel mixing and break the interaction with airflow et al. [2014] proposes a new nonlinear control method directly. Increasing the pressure is an effective way to analyzing control structure in engineering, paper Chen the fuel mixing and break the interaction with airflow analyzing control structure in engineering, paper Chen the fuel mixing and break the interaction with airflow (Triple-step method) for rail pressure, and based on the et al. [2014]method) proposes new nonlinear control improve fuel fuel atomization, but high directly. Increasing the pressure is way to foraa rail pressure, and basedmethod on the improve atomization, but the the excessively excessively high pressure pressure et al. proposes new nonlinear control method directly. Increasing the pressure is an an effective effective wayrail to (Triple-step et al. [2014] [2014] proposesand a rail new nonlinear control method directly. Increasing pressure is an effective way to method, the complex time consuming calculations in (Triple-step method) for pressure, and based on often results results in fuel fuel the rebuffed. Therefore, thehigh reliable improve fuel atomization, but the excessively pressure method, the complex and time consuming calculations in often in rebuffed. Therefore, the reliable rail (Triple-step method) for rail rail pressure, and the based on the the improve fuel atomization, but the the excessively excessively high pressure (Triple-step method) for pressure, and based on the improve fuel atomization, but high pressure control law are translated into map. From published method, the complex and time consuming calculations in pressure control is a challenging issue for ensuring the often results in fuel rebuffed. Therefore, the reliable rail control law are translated into map. From the published pressure control is a challenging issue for ensuring the method, the complex and time consuming calculations in often resultsstability in fuel fuel rebuffed. rebuffed. Therefore, the reliable rail method, the complex and control, time consuming calculations in often results in Therefore, the reliable rail researches on rail pressure it is known that modelcontrol law are translated into map. From the published combustion and output efficiency Yan and Wang pressure control is a challenging issue for ensuring the researches on rail pressure control, it is known that modelcombustion stability and output efficiency Yan and Wang control law are translated into map. From the published pressure control is a challenging issue for ensuring the control law are translated into map. From the published pressure control is a challenging issue for ensuring the based development has become the dominant attempts of researches on rail pressure control, is known that model[2011]. combustion development has become theit dominant attempts of [2011]. researches on rail pressure control, it is known that modelcombustion stability stability and and output output efficiency efficiency Yan Yan and and Wang Wang based researches on rail pressure control, it is known that modelcombustion stability and output efficiency Yan and Wang control system design. Following up, in order to get an based development has become the dominant attempts of [2011]. control system design. Following up, in order to get an based development has become become more the dominant dominant attempts of Rail pressure control control has has attracted attracted more more and and more more attenatten- based [2011]. development has the attempts of [2011]. improved control performance, and more nonlinear Rail pressure control system design. Following up, in order to get an improved control performance, more and more to nonlinear control system design. Following up, in order get an tion of researchers. Some of them focus on modeling and Rail pressure control has attracted more and more attencontrol system design. Following up, in order to get an methods are are developed. The investigation investigation pursed in this this tion researchers. of them focus and improved control performance, more and more nonlinear Rail of pressure controlSome has attracted attracted more on andmodeling more attenattenmethods developed. The pursed in Rail pressure control has more and more improved control performance, more and more nonlinear tion of researchers. Some of them focus on modeling and improved control performance, more and more nonlinear paper is motivated by the need for developing robust methods are developed. The investigation pursed in this ⋆ tion of researchers. Some of them focus on modeling and paper is motivated by the need for developing robust is by Nature Science Foundation tion ofwork researchers. Some them focus modeling and methods are developed. The investigation pursed in this ⋆ This methods are developed. The need investigation pursed in this This work is supported supported by the theofNational National Natureon Science Foundation rail pressure control in engineering, and the flatness-based paper is motivated by the for developing robust rail pressure control in engineering, and the flatness-based ⋆ of China (No.61522307, No.61374046), and Jilin Provincial Science paper is motivated by the need for developing robust This work is supportedNo.61374046), by the Nationaland Nature Science Foundation of China (No.61522307, Jilin Provincial Science ⋆ paper is motivated by the need for developing robust control techniques is used to deduce feedforward control. This work is supported by the National Nature Science Foundation ⋆ rail pressure control in engineering, and the flatness-based Foundation of China (No.20140520062JH). This work is China supported by the Nationaland Nature Foundation control techniques is used to deduceand feedforward control. of China (No.61522307, No.61374046), JilinScience Provincial Science rail pressure control engineering, the Foundation of (No.20140520062JH). rail pressure controlisin inused engineering, and the flatness-based flatness-based of China No.61374046), control techniques to deduce feedforward control. of China (No.61522307, (No.61522307, No.61374046), and and Jilin Jilin Provincial Provincial Science Science Foundation of China (No.20140520062JH). control techniques is used to deduce feedforward control techniques is used to deduce feedforward control. control. Foundation Foundation of of China China (No.20140520062JH). (No.20140520062JH).

Copyright 789 Copyright © © 2016 2016 IFAC IFAC 789 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016, 2016 IFAC 789 Hosting by Elsevier Ltd. All rights reserved. Copyright © 2016 IFAC 789 Peer review under responsibility of International Federation of Automatic Copyright © 2016 IFAC 789Control. 10.1016/j.ifacol.2016.08.113

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That differential flatness has been applied in other control systems of engine in the last decade Chladny and Koch [2008], Aschemann et al. [2011]. Moreover, in order to simplify the control system design and stability analysis, the feedback control law is obtained by the tracking error system linearized at reference points. The work is structured as follows. Section 2 describes overall architecture of the fuel rail system and gives a control-oriented model and control specifications. The feedforward-feedback controller is designed and the detailed derivation is described in Section 3. In Section 4, the effectiveness of the controller is verified under different conditions in order to ensure the control performance. Finally, conclusions are in Section 5. 2. MODELING AND CONTROL STATEMENT The fuel rail system is one of the most important parts in GDI engine fuel-path system, which provides the requested injection pressure for injectors to realize gasoline direct injection. In this paper, we take a four-cylinder four-stroke GDI engine as the plant. As shown in Fig. 1, the fuel rail system is mainly composed of a low pressure circuit, a high pressure pump (HPP), a fuel rail, injectors, a rail pressure sensor and an electronic control unit (ECU). rail pressure sensor

fuel rail

injector

limiting pressure valve

tank

check valve pressure control valve

low pressure pump

for modeling the main dynamics including high pressure pump, fuel rail and injector. First of all, some assumptions are considered before modeling: 1) Ignoring the effects of the air-contenting and pressure in fuel oil on elastic modulus; 2) Ignoring the impact of temperature changes on the component volume; 3) Ignoring pressure wave propagation in rail pipe. For high pressure pump, as we known, its main role in GDI fuel injection system is to regulate injection pressure. One of the common structures of high pressure pump is four-lobes cam-driven which mounted on the camshaft of the engine. In one injection cycle, the operating process of HPP includes the suck flow phase, the back flow phase and the pump flow phase. In the suck flow process, the pressure control valve remains open, the fuel flows into the high pressure pump, and duration of the suction phase is a half cycle. In back flow phase, the pressure control valve is still open, the fuel flow back to the low pressure circuit along with the plunger upward movement. While the rail pressure regulation main occurs in the pump flow phase, which appears in the case that the cam runs to the pump top dead center from the pump bottom dead center, and that the pressure control valve keeps close, the fuel flows into the rail. Hence, according to the bulk modulus of elasticity equation and the fluid dynamics basic principles Chen et al. [2014], and considering the dynamics of fuel rail system in pump flow phase (ı.e. the case of pp > pr ), due to movement of cam and on/off behavior of valve, the fuel pressure change in high pressure pump is caused by fuel inflow-outflow and volume change. Then the fuel pressure equation in the HPP can be written directly as follows. ( ) dVp (θ) Kf p p˙ p = − + qu − qpr − q0 , (1) Vp (θ) dt

where Kf p is the bulk modulus of elasticity, qu is defined as the inlet fuel flow of the high pressure pump, here its sign is negative, which represents back oil amount. q0 is the fuel leakage, and the qpr is the supply flow to the fuel rail. The related calculations in eq. (1) are listed as

high pressure pump

cam

Fig. 1. The structure diagram of the fuel rail system of GDI engines The low pressure circuit provides low pressure fuel coming from the tank to the high pressure pump. The pressure control valve is equipped at the inlet port of high pressure pump, and it allows the authority to regulate the amount of intake fuel. When the plunger in the HPP moves upward and the pressure control valve is closed, the fuel is compressed to high pressure and delivered to the rail by camshaft motion. The check valve can avoid undesired refluxes. The limiting pressure valve equipped at the outlet port of HPP prevents the rail from the damage by excessive pressure. The fuel rail connects the high pressure pump and the injectors, providing a suitable injection pressure for fuel injection and absorbing the pressure pulsation. The fuel with high pressure is injected directly into the combustion chamber by electro-injectors. The pressure in fuel rail rises when the fuel is pumped to the fuel rail, and the pressure drop occurs due to the injecting output. By analyzing the working principle, the key components with direct influence on rail pressure should be considered 790

(2a) Vp (θ) = Vpmax − Ap hp (θ) , dVp (θ) dhp = −Ap ωrpm , (2b) dt dθ where Vpmax is the maximum volume of the high pressure pump chamber, Ap is the piston bore, hp is the piston instantaneous axial displacement, ωrpm is the camshaft dh speed, and dθp is a nonlinear function depending on the angle and the profile of camshaft. In the case of pp > pr , the fuel flow qpr is computed by √ 2(pp − pr ) , (3) qpr = cpr Apr ρ where Apr is the cross-sectional area of outlet of HPP, and cpr is flow coefficient. For fuel rail pipe, its main effect is to absorb pressure waves and to build up the required injection pressure for injectors. As a storage component, the fuel rail can be considered as a certain volume container. That means the fuel volume change is solely caused by inflow and outflow. Hence, we have rail pressure dynamics as

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Kf r (qpr − qri ) , (4) Vr where Kf r is the bulk modulus of elasticity in rail pipe, Vr is the liquid volume of the fuel rail, and qri is the sum of injection flows. p˙ r =

For injectors, because of the actuators of the fuel injection system, they can guarantee fast response time and high fuel injection precision. In general, the injectors can be considered as valve driven by ECU, and a complete injection cycle takes place in a 360o camshaft angular interval. In considered plant, it consists of four injectors starting every 90o , and each injector is a dynamics element, which means injector will be a fourth order system. In fact, the injection interval is very short and the injection is a very fast dynamics process compared with the fuel rail dynamics. Hence, in order to reduce the controller design complexity, in this paper, the detailed injector dynamics is ignored, and the impact of fuel injection on rail pressure is described in parameter qri . From the above derivation, system dynamics consists of eqs.(1) -(4), the control problem considered in this paper is to make the actual rail pressure tracking the desired rail pressure by controlling the pressure control valve, the smaller tracking error indicates pressure fluctuation is smaller. Obviously, system controlled output is rail pressure. Moreover, according to some design experience of engineering staffs, the refined control specifications are described as • Tracking error in steady-state condition is less than 1 bar, the overshoot in step response should be as low as possible; • The step response rise time is lower than 100 ms; • Tracking error in time-varying condition is less than 5 bar. 3. DESIGN OF NONLINEAR CONTROLLER In Section 2, the control-oriented model has been given, in the following, controller is developed. Based on control requirements, it has been known that the rail pressure is selected as control output y. Due to the closed duration of the pressure control valve determines the fuel flow into the rail, then choose the fuel flow qu of the high pressure pump inlet as control input u. The state variables are selected as x1 = pp and x2 = pr . Assuming that bulk modulus in HPP are equal to that in fuel rail, i.e.Kf p = Kf r =: Kf , the system state-space equations can be rewritten as ( ) √ dhp Kf Ap ωrpm +u−a2 x1 −x2−q0 , x˙ 1 = (5a) Vp(θ) dθ ) Kf ( √ a2 x1 −x2 −qri , (5b) x˙ 2 = Vr √ where a2 = cpr Apr ρ2 . In this paper, the adopted control scheme can be found as shown in Fig. 2. Because the fuel rail system is a fast regulation system and engine operating conditions changes can be reflected on the reference rail pressure, the introduction of feedforward control can guarantee that the control system has a response as quickly as possible to engine demand. Meanwhile, it is very necessary that using feedback control to improve control performance, because of existing 791

777

   

    

+



−     

+ 

 △ + 

      

Fig. 2. The control block diagram of the fuel rail system external disturbance (such as temperature), unmodeled dynamics, and even modeling errors. The derivation process of flatness-based feedforward-feedback control law is described in detail. A: system flat output Differential flatness is an effective mean of feedback control design, the primary work of design is to determine whether the designed system is flat system and to find a flat output. Differentiating y = x2 and inserting the state equation (5a) give ) Kf ( √ y˙ = a2 x1 −x2 −qri , (6a) Vr ( dhp Kf Kf Kf a2 √ Ap ωrpm − q0 (6b) y¨ = dθ Vp (θ) 2Vr x1 −x2 Vp (θ) ) Kf √ Kf Kf Kf u−a2 ( + − ) x1 −x2 + qri . Vp (θ) Vp (θ) Vr Vr

Accordingly, the relative degree of the system equals the system order, which implies that the system (5) is flat and z = x2 is a flat output candidate. Then, the system state x as well as the system input u can be expressed at the output z and a finite number of its time derivatives as Vr 1 z˙ + qri )2 , (7a) x1 = z + ( Kf a 2 a2 (7b) x2 = z , (

) Vp (θ) 2Vr Vp (θ) Vr 1 u = − a2 + + z¨ ( z˙ + qri ) Vr Kf2 a2 Kf a 2 a2 + Ap ωrpm

dhp Vp (θ) − q0 + qri . dθ Vr

(8)

B: feedforward control law Based on eq. (8), inserting the desired system output z ∗ i.e. reference rail pressure x2d and its time derivatives, nominal feedforward control is hence given by ) ( Vr Vp (θ) 2Vr Vp (θ) 1 ud = − a2 + + x ¨2d ( x˙ 2d + qri ) Vr Kf2 a2 Kf a2 a2 dhp Vp (θ) − q0 + qri , (9) dθ Vr and the desired tracking of x1 is given by 1 Vr x˙ 2d + qri )2 . (10) x1d = x2d + ( Kf a 2 a2 + Ap ωrpm

C: feedback control law To facilitate engineering implementation and robust performance analysis, based on the nominal feedforward control, linearizing system (5) using Taylor expansion in the desired point x1d , x2d , ud , redefine

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( ) √ dhp Kf Ap ωrpm +u−a2 x1−x2−q0 , x˙ 1 =: f1 (x1 , x2 , u) = Vp(θ) dθ (11a) ( ) √ Kf x˙ 2 =: f2 (x1 , x2 ) = a2 x1 −x2 −qri . (11b) Vr It yields x˙ 1 = f1d +A11 (x1 −x1d )+A12 (x2 −x2d )+B1 (u−ud )+O1h , (12a) x˙ 2 = f2d +A21 (x1 −x1d ) + A22 (x2 −x2d ) + O2h , (12b) where f1d = f1 |(x1d ,x2d ,ud ) = x˙ 1d , f2d = f2 |(x1d ,x2d ,ud ) = x˙ 2d , Kf a √ 2 A11 = − , Vp (θ) 2 x1d −x2d a Kf √ 2 , A12 = Vp (θ) 2 x1d −x2d Kf , B1 = Vp (θ) K a √f 2 A21 = , 2Vr x1d −x2d K a √f 2 . A22 = − 2Vr x1d −x2d Ignore the high order terms O1h (x1 , x2 , u), O2h (x1 , x2 ), and define system errors e1 = x1 − x1d , e2 = x2 − x2d , ∆u = u − ud . Then the linear approximation error system in point (x1d , x2d , ud ) can be written as 1 Kf a2 √ e˙ 2 = [e1 −e2 ] , (14a) 2Vr x1d −x2d 1 Kf a2 Kf √ ∆u , (14b) [e2 −e1 ]+ e˙ 1 = 2Vp (θ) x1d −x2d Vp (θ)

selecting Lyapunov function as V = tem (14), differentiating it yields

1 2 2 e1

+ 12 e22 for sys-

Kf e1 ∆u V˙ = −M e21 − N e22 + (M + N )e1 e2 + Vp (θ) K a

(15)

K a

whereM = 2Vp (θ)√fx 2 −x , N = 2Vr √xf 2−x , the term 1d 2d 1d 2d √ x1d −x2d can be calculated by eq. (10) and M, N > 0. In order to ensure V˙ < 0, feedback control law ∆u can be selected as Vp (θ) [(M + N )e2 − ke1 ]. (16) ∆u = − Kf here, k > 0, hence (17) V˙ = −(M + k)e2 − N e2 < 0 . 1

2

This implies that the closed nominal error system is exponentially stable, and the designed whole control law consists of eqs. (9) and (16).

system parameters (given in Tab. 1). In the following, some simulation results are discussed to show that control objectives are achieved for different working points.

Fig. 3. Fuel rail system AMESim simulation model

Table 1. Model parameters Quantity

value High Pressure Pump spring stiffness of PCV* 5 × 104 N/m spring initial force of PCV* 40 N pump volume 2.3 × 10−7 m3 plunger diameter 0.01 m fuel leak gap 1 × 10−5 m Fuel Rail main body length 0.29 m main body internal diameter 0.17 m orifice area of Inlet port 1.2566 × 10−8 m3 Injector spring elastic coefficient 4 × 108 N/m spring damping coefficient 14.97 N · s/m injector internal diameter 0.005 m needle valve internal diameter 1.5 × 10−3 m nozzle diameter 1.8 × 10−4 m nozzle number 6 *pressure control valve

In the simulation below, we set different pressure reference points, which are associated with engine speed and the injection pressure. The injection sequence of the four injectors is set as 1-3-4-2. The camshaft angle degree corresponding to each injection cycle is 90o . And the pressure in the low pressure circle is set at 6 bar. The controller gains are selected as k = 1500. 4.1 Flow-angle Conversion

4. SIMULATION VERIFICATION In this section, in order to test the effectiveness of the proposed controller, the simulation testing model is established by commercial software AMESim for fluid dynamic simulation, as shown in Fig. 3. The plant model, representing a typical electronic fuel injection system equipped in GDI engines, allows to capture the important transient and static dynamics of the injection directly with actual 792

In the controller design, we neglect the pressure control valve dynamics and define the inlet flow rate of high pressure pump qu as our control input, but in fact physical quantity qu can not be implemented directly. Within one period, the valve action signal is typically implemented by a cam angle. The conversion logic diagram is shown as Fig. 4.

IFAC AAC 2016 June 19-23, 2016. Norrköping, Sweden

÷

 

Commomn Rail Pressure Deviation(bar)

 

 

  

Fig. 4. Flow-angle conversion logic diagram 4.2 Control Performance Evaluation

Common Rail Pressure(bar)

Common Rail Pressure Deviation(bar)

First of all, we consider a steady test condition that the rail pressure reference is given as step signal, and the reference pressure changes from 100 bar to 120 bar. Fig. 5 shows the regulating performance of rail pressure, and it can be seen the rail pressure tracks the reference with steadystate error less than 1 bar. Due to the initial settings, rail pressure changes relatively large in the beginning, but soon rail pressure returns to the set point, and the setting time is less than 100 ms, which meets the requirements of the state control performance.

Common Rail Pressure(bar)

+

 

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779

6 4 2 0 −2 −4 −6 0

0.2

0.4

0.6 0.8 Time(s)

1

1.2

Actual Rail Pressure Reference Rail Pressure

200

150

100

50 0

0.2

0.4

0.6 0.8 Time(s)

1

1.2

Fig. 6. Simulation results in varying rail pressure reference.

12 10

controller is tested on the AMESim simulation model, and the simulation results demonstrate the effectiveness and robustness of the controller.

8 6 4

Moreover, there are still some work that need to be solved in the future. Firstly, system robustness with respect to the unavoidable parameters uncertainties, implementation uncertainties, and unmodeled dynamics, needs to be analyzed so that the closed-loop error system is input-to-state stable. Secondly, the benchmark or real vehicles tests will be finished further to verify the effectiveness and real-time performance of the controller.

2 0 −2 0

0.2

0.4

0.6 0.8 Time(s)

1

1.2

Actual Rail Pressure Reference Rail Pressure

130 120

REFERENCES

110 100 0

0.2

0.4

0.6 0.8 Time(s)

1

1.2

Fig. 5. Simulation results of step rail pressure reference. In order to verify dynamic response, the case of the tracking of a time-varying reference signal is considered. When the reference is a random variation wave, amplitude changes from 60 bar to 150 bar. Fig. 6 shows the rail pressure tracking performance. In this case the rail pressure is regulated fast to track the reference, and the tracking error maximum value is below 4 bar, which is within rail pressure fluctuations extent permitted. 5. CONCLUSION This paper discusses rail pressure control of the fuel injection system of GDI engines. A control oriented mathematical model is established for fuel injection system, in which some assumptions are given for designing easily. Moreover, the nonlinear control law is developed, using differential flatness control technique, gives nominal feedforward control law. Then the nonlinear system is linearized approximation by taylor expansion. Finally, the designed 793

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of a common rail injection system for gasoline engines. In Proceedings of the 17th IFAC World Congress, pages 8481–8486, Seoul, Korea, 2008. A. di Gaeta, G. Fiengo, A. Palladino, and V. Giglio. A control oriented model of a common-rail system for gasoline direct injection engine. In Proceedings of the 28th Chinese Control Conference, pages 6614–6619, Shanghai, China, 2009. N. Giorgetti, G. Ripaccioli, A. Bemporad, I. V. Kolmanovsky, and D. Hrovat. Hybrid model predictive control of direct injection stratified charge engines. IEEE/ASME Transactions Mechatronics, 11(5): 499–506, 2006. D. A. Kouremenos, D. T. Hountalas, and A. D. Kouremenos. Development and validation of a detailed fuel injection system simulation model for diesel engines. SAE Technical Paper, no. 1999-01-0527, pages 1–9, 1999. P. Lino, B. Maione, and A. Rizzo. Nonlinear modelling and control of a common rail injection system for diesel engines. Applied Mathematical Modelling, 31(9):1770– 1784, 2007. U. Montanaro, A. di Gaeta, and V. Giglio. An MRAC approach for tracking and ripple attenuation of the common rail pressure for GDI engines. In Proceedings of the 18th IFAC World Congress, pages 4173–4180, Milano, Italy, 2011. C. L. Myung and S. Park. Exhaust nanoparticle emissions from internal combustion engines: a review. International Journal of Automotive Technology, 13(1):9–22, 2012. H. J. Tang, L. Weng, Dong Z. Y., and R. Yan. Adaptive and learning control for SI engine model with uncertainties. IEEE/ASME Transactions on Mechatronics, 14:93–104, 2009. F. Yan and J. Wang. Common rail injection system iterative learning control based parameter calibration for accurate fuel injection quantity control. International Journal of Automotive Technology, 12(2):149–157, 2011.

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