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Implementation of a robust cruise control using look-ahead method
Preprints, 8th IFAC International Symposium on Advances in Automotive Control Symposium Preprints, IFAC Preprints, 8th IFAC International International on Advances 8th in Automotive Control Symposium on June 19-23,in 2016. Norrköping, Sweden Advances Automotive Control Available online at www.sciencedirect.com 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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Implementation of a robust cruise Implementation Implementation of of a a robust robust cruise cruise control using look-ahead method control using using look-ahead look-ahead method method control ∗ ∗∗ ∗∗∗ P´ e P´ eter ter P´ e P´ eter ter
G´ a a G´ asp´ sp´ arr ∗∗∗ G´ a sp´ a G´ asp´ arr
Bal´ a e Michel Bal´ azs zs N´ N´ emeth meth ∗∗ Michel Basset Basset ∗∗∗ ∗∗ ∗∗∗ ∗∗∗∗∗ Bal´ a zs N´ e meth Rodolfo Orjuela ∗∗∗ Bal´ azs N´ emeth Michel Michel Basset Basset ∗∗∗ Rodolfo Orjuela ∗∗∗ ∗∗∗ Rodolfo Rodolfo Orjuela Orjuela ∗ ∗ Institute for Computer Science and Control, Hungarian Academy of Institute for Computer Science and Control, Hungarian Academy of ∗ ∗ Institute Computer Science and Control, Sciences and MTA-BME Control Research Group, Institute for Computer Science andEngineering Control, Hungarian Hungarian Academy of Sciencesfor and MTA-BME Control Engineering ResearchAcademy Group, of Sciences and MTA-BME Control Engineering Research Budapest, Hungary; E-mail: [email protected] Sciences and MTA-BME [email protected] Engineering Research Group, Group, Budapest, Hungary; E-mail: ∗∗ Budapest, E-mail: and Control Institute ∗∗ Systems Budapest, Hungary; E-mail: [email protected] [email protected] Systems and Hungary; Control Laboratory, Laboratory, Institute for for Computer Computer Science Science ∗∗ ∗∗ Systems and Control Laboratory, Institute for Computer Science and Control, Hungarian Academy of Sciences, Budapest, Hungary; Systems and Control Laboratory, Institute for Computer Science and Control, Hungarian Academy of Sciences, Budapest, Hungary; and Academy of Sciences, Budapest, Hungary; E-mail: [email protected] and Control, Control, Hungarian Hungarian Academy of Sciences, Budapest, Hungary; E-mail: [email protected] ∗∗∗ E-mail: Process ∗∗∗ Modelling Intelligence E-mail: [email protected] [email protected] Modelling Intelligence Process and and Systems Systems (MIPS) (MIPS) Laboratory, Laboratory, ∗∗∗ ∗∗∗ Modelling Intelligence Process and Systems (MIPS) Laboratory, Universit´ e de Haute-Alsace, Mulhouse Cedex, France; Modelling Intelligence Process and Systems (MIPS) Laboratory, Universit´e de Haute-Alsace, Mulhouse Cedex, France; Universit´ e de Haute-Alsace, Mulhouse Cedex, France; E-mail: [michel.basset,rodolfo.orjuela]@uha.fr Universit´ e de Haute-Alsace, Mulhouse Cedex, France; E-mail: [michel.basset,rodolfo.orjuela]@uha.fr E-mail: E-mail: [michel.basset,rodolfo.orjuela]@uha.fr [michel.basset,rodolfo.orjuela]@uha.fr Abstract: The The paper paper proposes proposes the the implementation implementation of of aa robust robust cruise cruise control control system system which which is is Abstract: Abstract: The paper proposes the aa robust cruise which is able to to ensure ensure the fuel-efficient travel of the the vehicle vehicle of with look-ahead control system algorithm. The Abstract: Thethe paper proposes travel the implementation implementation of robust cruise control control system which is able fuel-efficient of with aa look-ahead control algorithm. The able to the of the with control The H∞ -based feedforward-feedback control guarantees robustness against varying vehicle able to ensure ensure the fuel-efficient fuel-efficient travel travel of method the vehicle vehicle with aa look-ahead look-ahead control algorithm. algorithm. The H ∞ -based feedforward-feedback control method guarantees robustness against varying vehicle H -based feedforward-feedback control method guarantees robustness against varying vehicle mass, longitudinal disturbances and the consideration of actuator dynamics. The advantage ∞ H -based feedforward-feedback control method guarantees robustness against varying vehicle ∞ mass, longitudinal disturbances and the consideration of actuator dynamics. The advantage of of mass, longitudinal the of dynamics. The of the is application a number parameters. Therefore, aa method mass, longitudinal disturbances and the consideration consideration of actuator actuator dynamics. The advantage advantage of the method method is the the disturbances application of ofand a small small number of of vehicle vehicle parameters. Therefore, method the method is of number of Therefore, aa method for cars significant modifications is proposed cruise the various method passenger is the the application application of a a small small number of vehicle vehicle parameters. parameters. Therefore, method for various passenger cars without without significant modifications is needed. needed. The The proposed cruise for passenger cars without significant modifications is proposed cruise control and look-ahead implemented in (SIL) environment for various various passenger cars method withoutare significant modifications is needed. needed. The The proposed cruise control and the the look-ahead method are implemented in aa software-in-the-loop software-in-the-loop (SIL) environment control and the look-ahead method are implemented in a software-in-the-loop (SIL) environment using DSpace Autobox, which cooperates with the high-fidelity CarSim software through control and the look-ahead method are implemented in a software-in-the-loop (SIL) environment using DSpace Autobox, which cooperates with the high-fidelity CarSim software through CAN CAN using DSpace communication. using DSpace Autobox, Autobox, which which cooperates cooperates with with the the high-fidelity high-fidelity CarSim CarSim software software through through CAN CAN communication. communication. communication. © 2016, IFAC (International of Automaticcontrol, Control)Software-in-the-loop Hosting by Elsevier Ltd.application All rights reserved. Keywords: Robust controlFederation design, Look-ahead Look-ahead Keywords: Robust control design, control, Software-in-the-loop application Keywords: Keywords: Robust Robust control control design, design, Look-ahead Look-ahead control, control, Software-in-the-loop Software-in-the-loop application application 1. INTRODUCTION INTRODUCTION AND AND MOTIVATION MOTIVATION speed 1. speed design design for for road road vehicles vehicles based based on on road road inclinations, inclinations, 1. speed design road based on road inclinations, vehicle in traveling 1. INTRODUCTION INTRODUCTION AND AND MOTIVATION MOTIVATION speed limits, design aafor forpreceding road vehicles vehicles based on lane roadand inclinations, speed limits, preceding vehicle in the the lane and traveling speed limits, a preceding vehicle in the lane and time is proposed by N´ e meth and G´ a sp´ a r [2013]. A In the last decade, the longitudinal vehicle control based speedislimits, a preceding vehicle the lane and traveling traveling proposed by N´emeth andinG´ asp´ ar [2013]. A road road In the last decade, the longitudinal vehicle control based time time is proposed by N´ e meth and G´ a sp´ a r [2013]. A In the last decade, the longitudinal vehicle control based type and congestion level estimation method is combined on the look-ahead approach has been in the focus of time is proposed by N´ e meth and G´ a sp´ a r [2013]. A road road In the last decade, the longitudinal vehicle control based on the look-ahead approach has been in the focus of type and congestion level estimation method is combined type and congestion level estimation method is combined on the look-ahead approach has been in the focus of with the principal components analysis for a variety the automotive research centers. It is widespread in the type and congestion level estimation method is combined on the look-ahead approach has been in the focus of of the automotive research centers. It is widespread in the with the principal components analysis for a variety of aa variety of the research centers. It in purposes, e.g. information systems, intelligent realcruise control, which which is able able to guarantee guarantee energy-efficient with the the principal principal components analysis for variety of the automotive automotive research centers. It is is widespread widespread in the the with purposes, e.g. traffic trafficcomponents information analysis systems,for intelligent realcruise control, is to energy-efficient purposes, e.g. traffic information systems, intelligent realcruise control, which is able to guarantee energy-efficient time control systems, energy consumption/emissions in driving, see Sciarretta et al. [2015]. Since Adaptive Cruise purposes, e.g. traffic information systems, intelligent realcruise control, which isetable to guarantee energy-efficient driving, see Sciarretta al. [2015]. Since Adaptive Cruise time control systems, energy consumption/emissions in control driving, Sciarretta [2015]. Adaptive Zhu Barth [2006]. Control (ACC) allows et to al. maintain desired travelCruise speed time time control systems, energy consumption/emissions consumption/emissions in in driving, see see Sciarretta et al. [2015]. Since Since Adaptive Cruise Zhu and and Barthsystems, [2006]. energy Control (ACC) allows to maintain aa desired travel speed Zhu and Barth [2006]. Control (ACC) allows to maintain a desired travel speed set by the driver by acting on the throttle and brakes, Zhu and Barth [2006]. Control (ACC) allows to maintain a desired travel speed set by the driver by acting on the throttle and brakes, A test platform for the implementation of look-ahead set by acting the and the combination ofby look-ahead control and ACC ACC is brakes, novel A test platform for the implementation of look-ahead set combination by the the driver driverof by acting on oncontrol the throttle throttle andis brakes, the look-ahead and aa novel A platform for the implementation look-ahead control introduced [2006]. The platform A test test is platform for in theGustafsson implementation of look-ahead is introduced in Gustafsson [2006]. of The platform the combination of look-ahead control and ACC is a novel trend in the vehicle control design. the combination of look-ahead control and ACC is a novel control trend in the vehicle control design. control is introduced in Gustafsson [2006]. The platform contains the user interface, the controller structure tocontrol is introduced in Gustafsson [2006]. The platform contains the user interface, the controller structure totrend in the vehicle control design. trend in the vehicle control design. contains the user interface, the controller structure together with the look-ahead optimization, CAN softwares Several publications and patents deal with the topics of containswith thethe user interface, optimization, the controllerCAN structure tolook-ahead softwares Several publications and patents deal with the topics of gether gether with the look-ahead optimization, CAN softwares Several publications and patents deal with the topics of and interfaces. The proposed device is in connection with driveline control implementation and look-ahead strategether with the look-ahead optimization, CAN softwares Several publications and patents deal with the topics of driveline control implementation and look-ahead strate- and interfaces. The proposed device is in connection with interfaces. The is with driveline and stratethe bus the vehicle. The method of gies. Thecontrol design implementation and the the implementation implementation of aa predicpredicand interfaces. The proposed device is in in connection connection with driveline control implementation and look-ahead look-ahead strate- and the CAN CAN bus of of theproposed vehicle. device The look-ahead look-ahead method of gies. The design and of the CAN bus of the vehicle. The look-ahead method of gies. The design and the implementation of a predicplatform considers the engine torque, the gear positive speed controller are presented by Hellstr¨ o m et al. the CAN bus of the vehicle. The look-ahead method of gies. The design and the implementation of a predictive speed controller are presented by Hellstr¨ om et al. the platform considers the engine torque, the gear posithe platform considers the engine torque, the gear positive speed controller are presented by Hellstr¨ o m et al. tion and road geometry information. The implementation [2009], Passenberg et al. [2009], Hellstr¨ o m et al. [2010]. the platform engine torque, the gear positive speed controller presented by oHellstr¨ om [2010]. et al. tion and road considers geometry the information. The implementation [2009], Passenberg et are al. [2009], Hellstr¨ m et al. road The implementation [2009], Passenberg al. [2009], oom [2010]. of optimal ACC passenger presented The intervention ofet the look-ahead control is al. connected tion and road geometry geometry information. The is implementation [2009], Passenbergof etthe al. look-ahead [2009], Hellstr¨ Hellstr¨ m et et al. [2010]. tion of an anand optimal ACC for forinformation. passenger cars cars is presented by by The intervention control is connected of an optimal ACC for passenger cars is by The intervention of the look-ahead control is connected Li et al. [2013]. The system uses radar and acceleration to the reference signal of the PID-based speed controller, of an optimal ACC for passenger cars is presented by The intervention of the look-ahead control is connected acceleration to the reference signal of the PID-based speed controller, Li et al. [2013]. The system uses radar andpresented Li et al. [2013]. The system uses radar and acceleration to the reference signal of the PID-based speed controller, sensor measurements, from which the acceleration of the which modifies the fuel injection of the engine. A dynamic Li et al. [2013]. The system uses radar and acceleration to the reference signal of the PID-based speed controller, sensor measurements, from which the acceleration of the which modifies the fuel injection of the engine. A dynamic from the of which the the engine. dynamic preceding vehicle The algorithm longitudinal model for injection the design designof of the speedA controller sensor measurements, measurements, from which which the acceleration acceleration of the the which modifies modifies the fuel fuel injection of of thethe engine. Acontroller dynamic sensor preceding vehicle are are derived. derived. The optimization optimization algorithm longitudinal model for the speed preceding vehicle are derived. The optimization algorithm longitudinal model for the design of the speed controller yields a reference acceleration signal, which is the input is applied by Kiencke and Nielsen [2000]. It influences preceding vehicle are derived. The optimization algorithm longitudinal model for the design of the speed controller of is applied by Kiencke and Nielsen [2000]. It influences yields a reference acceleration signal, which is the input of aa reference acceleration which the input is Kiencke Nielsen [2000]. the dynamic controller together with the engine by torque basedand on the the engine rpm It andinfluences the fuel fuel yields yields reference acceleration signal, which isthe theestimated input of of is applied applied by Kiencke and Nielsen [2000]. It influences the vehicle vehicle dynamic controller signal, together with is the estimated the engine torque based on engine rpm and the dynamic controller the torque on the and fuel preceding acceleration. injection, are control in architecture. The the vehicle vehiclevehicle dynamic controller together together with with the the estimated estimated the engine enginewhich torque based oninputs the engine engine rpm and the the The fuel the preceding vehicle acceleration. injection, which arebased control inputs in the the rpm architecture. vehicle injection, which are control inputs in The The research preceding vehicle acceleration. acceleration. injection, which control by inputs in the the architecture. architecture. The preceding wasare supported the National Research, Develop The research Further automotive industrial was supported by the National Research, DevelopFurther automotive industrial patents patents on on the the predictive predictive ment and Innovation Fund through the projectResearch, ”SEPPAC: Safety The research was supported by the National DevelopFurther automotive industrial patents on the The research was supported by the National Research, Developspeed control algorithms are presented Lattemann et ment and Innovation Fund through the project ”SEPPAC: Safety Further automotive industrial patentsin on the predictive predictive speed control algorithms are presented in Lattemann et al. al. and Economic Platform for Partially Automated Commercial vehiment and Innovation Fund through the project ”SEPPAC: Safety mentEconomic and Innovation Fund through the project ”SEPPAC: speed control algorithms are presented in Lattemann et al. [2004]. The method of Eriksson and Ste´ e n [2003] is based and Platform for Partially Automated CommercialSafety vehispeed control algorithms are presented in Lattemann et al. [2004]. The method of Eriksson and Ste´ e n [2003] is based cles”Economic (VKSZ 14-1-2015-0125). This paper was partially supported by and Platform for for Partially Partially Automated Commercial vehiand Platform Automated Commercial vehicles”Economic (VKSZ 14-1-2015-0125). This paper was partially supported by [2004]. The method of Eriksson and Ste´ e n [2003] is based on the forthcoming terrain characteristics to select gear [2004]. The method of Eriksson and Ste´ e n [2003] is based on the forthcoming terrain characteristics to select gear the J´ a nos Bolyai Research Scholarship of the Hungarian Academy of cles” (VKSZ 14-1-2015-0125). This paper was partially supported by cles”J´ 14-1-2015-0125). This paper wasHungarian partially supported the a(VKSZ nos Bolyai Research Scholarship of the Academy by of on the terrain characteristics select position, according the driver’s on the forthcoming forthcoming terrain characteristics toperformance select gear gear Sciences. position, according to to the required required driver’sto performance the J´ a the J´ anos nos Bolyai Bolyai Research Research Scholarship Scholarship of of the the Hungarian Hungarian Academy Academy of of Sciences. position, according to the required driver’s performance position, according to the required driver’s performance Sciences. Sciences. Copyright © 2016 IFAC 515 Copyright 2016 IFAC 515 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 515 Copyright ©under 2016 responsibility IFAC 515Control. Peer review© of International Federation of Automatic 10.1016/j.ifacol.2016.08.074
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(fuel-consumption, emission, traveling time). An algorithm which computes the optimal driveline torque considering the road inclinations is presented by Takahashi et al. [1998]. In this paper, the implementation of a robust cruise control together with a look-ahead control is proposed. The applied method guarantees robustness against varying vehicle mass, and longitudinal disturbances, such as rolling resistances, aerodynamic forces. Moreover, the dynamic properties of the actuator are considered in the control design phase. In the presented method, the look-ahead strategy and the robust longitudinal control are connected through the reference velocity signal. The output of the look-ahead computation is the optimal velocity, which is considered as an input of the controller. The advantage of the method is the application of a small number of vehicle parameters. Then the method can be applied to various passenger cars without significant modifications. The preliminary results of the cruise control design can be found in N´emeth et al. [2015]. As a novelty, in this paper the cruise control and the look-ahead method are implemented in a software-in-the-loop (SIL) environment using DSpace Autobox. The organization of the paper is the following. Section 2 presents the formulation of the longitudinal vehicle dynamics for the look-ahead cruise control. The robust H∞ control strategy of the cruise control system considering the formulation of the uncertainties is described in Section 3. The concept of the speed design using a look-ahead approach is presented in Section 4. The implementation of the robust control system is found in Section 5. The evaluation of the proposed control method is presented through simulation examples in Section 6. 2. MODELING LONGITUDINAL DYNAMICS
actual mass m of the vehicle such as: m = m0 + mv . Thus the longitudinal motion equation is reformulated in the following way: m0 ξ¨0 = Fl1 − Fd1 − mv ξ¨0 (3) Considering that ξ¨0 , the actual longitudinal acceleration, is a measurable and bounded signal of the vehicle, mv ξ˙ is handled as a disturbance of the vehicle. Combining it with Fd1 , the next expression is yielded: (4) Fd1 + mv ξ¨0 = Fd1,1 + mv fd,2 2 ˙ where Fd1,1 = Ca ξ0 + Cr gm0 cos ϑ + m0 g sin ϑ and fd,2 = Cr g cos ϑ + g sin ϑ + ξ¨0 . Fd1,1 and fd,2 incorporate measurable signals, such as velocity, road slope and longitudinal acceleration. Thus, Fd1,1 is handled in this approach as a measured disturbance. Since there is no information about the mass variation mv , the term mv fd,2 is considered as an unknown disturbance - where actually fd,2 is a measurable part of the disturbance expression. 3. ROBUST CONTROL STRATEGY In this section, the control design for the longitudinal velocity tracking control problem is proposed. The realized total longitudinal control force on the wheels Fl1 is divided into two elements: (5) Fl1 = Fl1,0 + Fl1,1 where the purpose of Fl1,1 is to compensate for the measured disturbance Fd1,1 , while Fl1,0 guarantees the unknown disturbance rejection and the performances. In the following, a robust control design method is presented, which combines the advantages of the feedforward and feedback control design. 3.1 Design of the feedforward control
In this section the modeling of longitudinal dynamics is presented. The longitudinal dynamics is described in the approach by the following simplified model: (1) mξ¨0 = Fl1 − Fd1
where m is the mass of the vehicle, ξ0 is the vehicle position, Fl1 is the realized longitudinal force on the wheels. Fd1 includes the longitudinal disturbances, such as the aerodynamic forces, rolling resistance and road slope: (2) Fd1 = Ca ξ˙2 + Cr gm cos ϑ + mg sin ϑ 0
where ϑ is road slope and Ca , Cr are vehicle parameters related to aerodynamic and resistances forces. In the following the transformation of the vehicle model has two focuses. Firstly, the mass of the vehicle is an uncertain parameter of the vehicle. The mass has a nominal value m0 , which is known, but the variation of the mass mv is unknown. However, the variation is assumed to be a bounded parameter, e.g. mv /m0 = ±15%. Secondly, the road inclination is assumed to be known. In practice, the slope of the road can be obtained in two ways: either a contour map which contains the level lines is used or an estimation method is applied, see e.g., Bae et al. [2001], Hahn et al. [2004]. Since the handling of vehicle mass uncertainty is a requirement for the control system, it is necessary to define the 516
In the first step the feedforward control is designed. If Fd1,1 is fully compensated for, then the feedforward control input is u1 = Fl1,1 , (6) where ξ˙0 , ϑ are measured and estimated parameters, see Vahidi et al. [2005]. Thus, the efficiency of the feedforward disturbance compensation is based on the accuracy of the measured signals. Since the measurement of the speed and the estimation of the road slope are inaccurate, the feedforward compensation has an error Fd,11 . The longitudinal motion of the vehicle is formed in the following way: m0 ξ¨0 = Fl1,0 − Fd1,11 − mv fd,2 (7) In the next step a feedback control input Fl1,0 is designed, which is able to handle the disturbances Fd1,11 , fd,2 . 3.2 Design of the feedback control The feedback control input Fl1,0 has three main goals in the control strategy: the rejection of unknown disturbances (Fd1,11 , fd,2 mv ), the handling of the unmodelled actuator dynamics and the guarantee of the performance. The statespace representation of the system is the following: 1 1 1 Fd1,11 ¨ ˙ − + Fl,0 (8) ξ0 = [0] ξ0 + − Fd1,2 m0 m0 m0
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where the disturbances are compressed to a vector Fd,f b = T [Fd1,11 Fd1,2 ] , where Fd1,2 = fd,2 mv . The measured output of the system is the velocity ξ˙0 , which is also the state in the formulation. The performance of the system is expressed by the tracking of the reference velocity λ and the minimization of the control input u0 . Note that the influence on the control input is necessary to avoid the extremely high actuation of the longitudinal control. The performance signals are (9) |z1 | = |λ − ξ˙0 | → min |z2 | = |u0 | → min
(10)
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Wu
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Wp,1
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Wp,2
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Fig. 1. Closed-loop interconnection The augmented-plant for the H∞ design is illustrated in Figure 1. The weighting functions of z1 and z2 are formulated as Wp,i = (b1,i s + b0,i )/(a1,i s + a0,i ) where b1,i , b0,i , a1,i , a0,i are design parameters. The selection of these parameters has significant relevance. Firstly, the parameters determine the accuracy of the velocity tracking and the limitation of the actuator intervention. Secondly, the overshot of the velocity signal is also determined by the parameters. Generally, the actuators delay the controlled action and provide additional dynamic motion. This dynamics can be handled as an input multiplicative uncertainty of the system, where Wu = −τ s/(τ s + 1) is the uncertainty of the system. In this form the value τ is related to the dynamics of the actuation of the driveline/braking systems. In Figure 1 the measured signal is y = ξ˙0 . The sensor noise Fd,s on the velocity measurement is considered as a disturbance, which must be rejected by the robust controller. Thus, Fd,f b is extended with the signal Fd,s . The objective of H∞ control is to minimize the inf-norm of the transfer function Tz∞ w . More precisely, the problem can be stated as follows [Scherer and Weiland, 2000, Boyd et al., 1997]. The LMI problem of H∞ performance is formulated as: the closed-loop RMS gain from w to z∞ does not exceed γ if and only if there exists a symmetric and definite positive matrix X∞ such that T Acl X∞ + X∞ ATcl X∞ Bcl Ccl T T <0 (11) Bcl X∞ −γI Dcl Ccl Dcl −γI with γ > 0 and state space components of the closed-loop control system Acl , Bcl , Ccl1 , Dcl1 .
Finally, a robust dynamic K controller is yielded. The feedback control input is formally computed as u0 = 517
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K(vref − ξ˙0 ). As a result of the combined feedforwardfeedback strategy, the control law of the system, using (6), is yielded as u = u0 + u1 , where u0 represents the feedback control input and u1 the feedforward control. 4. SPEED GENERATION BASED ON THE LOOK-AHEAD CONTROL 4.1 The basics of look-ahead control In this section the design of a cruise control system, in which the longitudinal control incorporates the brake and traction forces is proposed in order to achieve the designed velocity profile. By choosing the appropriate speed according to the road and traffic information, the number of unnecessary accelerations and brakings and their durations can be significantly reduced. A detailed description of the speed profile design is found in N´emeth and G´asp´ar [2013]. In this section only a brief summary of the look-ahead control is presented. The road ahead of the vehicle is divided into several segments, which are of different lengths consistent with the topography of the road. The rates of the slopes of the road and the speed limits are assumed to be known at each segment. The reference speeds at the segment points are predefined. The current speed requires information systems installed along the road. In the method, the vehicle is assumed to be traveling in a segment from the initial point to the first division point. The aim is to calculate the speed at the same initial point at which the reference speed of the first point can be reached. This method is applied to the next segments and division points. In the case of n segments and n + 1 points, n equations are formulated between the first and the end points. It is assumed that the acceleration of the vehicle may change in the different intervals, but within a single interval it is approximated by a constant. The reference speeds at the section points are predefined: vref,0 , vref,1 , ..., vref,n . The speed of the vehicle at point i ∈ (1, n) is written as: i ξ˙i2 = ξ˙02 + m20 j=1 sj (Flj − Fdj,r − Fdj,o ), where ξ˙0 is the speed of the vehicle at the initial point, ξ˙i is the speed of the vehicle at the ith point and sj is the distance of the interval [j − 1, j]. Moreover, Flj is the longitudinal force, Fdj,r = m0 g sin αi is the force resistance from the road slope, Fdj,o represents other resistances such as rolling resistance and aerodynamic forces. At the calculation of the control force, it is assumed that only the control force Fl1 affects the vehicle, i.e., Fli = 0, i > 1. The aim is that at every segment point the speed ξ˙i 2 must reach the predefined reference speed: ξ˙i2 → vref,i . The equations of the vehicle speeds at the segment points are calculated in the following way: ξ˙i2 = ξ˙02 + i 2 2 2 j=1 sj Fdj,r . Prediction weights m0 s1 Fl1 − m0 s1 Fd1,o − m0 Q, γ1 , γ2 , ..., γn are applied to the sections (γ1 + γ2 + ... + γn + Q = 1). While the prediction weights γi represent the rate of the road conditions, weight Q has an essential role: it determines the tracking requirement of the current reference speed vref,0 . By increasing Q the momentary speed
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where parameter λ is calculated in the following way based on the designed ϑ: λ = ϑ − 2s1 (1 − Q)(ξ¨0 + gsinα). (12) shows that the modified speed ξ˙0 depends on the prediction weights (Q and γi ). By choosing these values the effects of road conditions can be tuned.
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The design of the vehicle speed poses two optimization problems: the longitudinal force must be minimized and the deviation from the reference velocity must be minimized. The minimization of the longitudinal control force 2 → min leads to a quadratic optimization problem: Fl1 2 ¯ + β1 (Q)¯ ¯ γ1 + . . . + βn (Q)¯ ¯ γn )2 → min (15) ¯ Fl1 = (β0 (Q) ¯ γ¯i = ¯ γ¯i ≤ 1 and Q+ with the following constrains 0 ≤ Q, 1. In the first criterion the road inclinations and speed limits are taken into consideration by using appropriately ¯ γ¯i . chosen weights Q, The minimization of the difference between the current velocity and the reference velocity |vref,0 − ξ˙0 | → min (16) leads to the optimal solution, which is achieved by select˘ = 1 and γ˘i = 0, i ∈ [1, n], since in this ing the weights: Q case the vehicle tracks the predefined speed. These optimization criteria lead to different solutions. Two further performance weights, R1 and R2 (R1 + R2 = 1), are introduced in order to achieve a balance between the optimal results. Performance weight R1 (0 ≤ R1 ≤ 1) is related to the importance of the minimization of the longitudinal control force (15) while performance weight R2 (0 ≤ R2 ≤ 1) is related to the minimization (16). 4.3 Effects of the vehicle mass The mass of the vehicle has an important role in the velocity profile optimization through ϑ, see (13). However, the mass of the vehicle is uncertain. Since the mass mv is not measured, the variation is not considered in the lookahead control. In the following section, a simulation-based analysis is shown, which presents the velocity profile of the vehicle, depending on different mass values. 518
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In order to take the road conditions into consideration in the control design (12) is applied as a performance of the controlled system. Finally, a speed tracking problem is deduced, whose reference signal contains the predicted road information (road slopes, speed limits): (14) ξ˙0 → λ
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Force (N)
Taking the weights into consideration the following formula is yielded: 2 2 s1 (1 − Q)Fl1 − s1 (1 − Q)Fd1,o = ϑ (12) ξ˙02 + m0 m0 where value ϑ depends on the road slopes, the reference speeds and the weights n n n 2 2 2 γi vref,i + γj . (13) + si Fdi,r ϑ = Qvref,0 m0 i=1 i=1 j=i
For the testing phase four vehicle masses are analyzed, such as 1000 kg, 3500 kg, 8000 kg and 12000 kg. The road profile is illustrated in Figure 2(a). The velocity profiles of the vehicles with different mass values are found in Figure 2(b). The results show that the increased mass causes a higher variation in velocity. Furthermore, the saved energy of the vehicle with increased mass is higher, see Figure 2(c).
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becomes more important while road conditions become less important.
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(d) Actuated force of vehicle
Fig. 2. Analysis of dependence on mass Table 1 summarizes the energy saving of the vehicle. It can be seen that approximately 6 − 7% of energy can be saved by considering predicted road conditions. The control force and energy represent the same as the change of velocity; it changes slightly with an increase in the mass of the vehicle. Mass (kg) 1000 3500 8000 12000
∆
|Fl1 | (%) 5.82 6.57 7.6 7.95
∆
|El1 | 6.32 7.02 7.66 7.86
Velocity diff. (%) 2.83 2.96 3.39 3.70
Table 1. Dependence of the mass on performances
5. IMPLEMENTATION OF THE METHOD IN THE DRIVING/BRAKING SYSTEM The command variable of the robust control design is the longitudinal force input u = Fl1 . However, the real physical system has two inputs, such as driveline and brake inputs. In the following section the transformation of Fl1 to the real physical inputs is presented. In the conventional engine-powered driveline system the gear positioning and the throttle are the intervention possibilities. The proposed method considers an automatic transmission, where the positioning of the gear is determined by the engine speed and the throttle ∈ [0 . . . 1]. Thus, it is necessary to find an appropriate , which guarantees the realization of Fl1 . Since the driveline dynamics is faster than the longitudinal dynamics, the transients of the driveline are ignored in the computations. The conversion between Fl1 and is based on static relations.
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The required torque of the engine is computed with the following expression as: Meng = Fl1 Rw /k0 /kg , where Rw is wheel radius, k0 and kg are the ratio of the driven axle and the transmission. The value of kg depends on the current gear position. The conversion between Meng and is performed through the engine characteristics. This computation requires the measurement of the engine speed ω, and the inversion of the characteristics based on Meng and ω. The braking system in the paper is a conventional hydraulic construction. The dynamics of the braking hydraulics τ is faster than the longitudinal motion, therefore the relationship between Fl and brake cylinder pressures is described by static equations. Firstly, the longitudinal force is divided at the left and right sides of the front and rear axles using the following expression, see Zomotor [1991]. Second, the wheel longitudinal forces are converted into the cylinder braking pressures, such as pi = Fi Rw /CpM,i where Fi is the longitudinal force of the wheel, and CpM,i is the constant, which depends on the wheel brake construction.
509
vehicle simulator, the dSPACE environment, in which the controller is implemented. In the workstation the CarSim works together with Matlab/Simulink. The CarSim simulator with the Matlab/Simulink software, which are standard industrial tools, simulate the vehicle dynamics with high accuracy. The communication between the workstation and the dSPACE is realized through the CAN bus. Before the SIL simulation the designed control system is set on the real-time equipment. The control signal is computed in dSPACE by the discrete-time solver of the differential equations with 0.01s sampling time.
5.1 SIL implementation of the controller In the following section, the implementation of the proposed system in a SIL environment is presented. The control algorithm has three layers, which are illustrated in Figure 3.
Fig. 4. Software-in-the-loop simulation
road infomation
Look-ahead method ξ˙0
6. SIMULATION SCENARIOS
Robust cruise controller
In this section a simulation example of the implemented robust longitudinal cruise control is proposed. The simulation is performed on the SIL environment, see Section 5. A minivan vehicle is used in the example, whose nominal mass is m0 = 2037kg and the maximum mass in the simulation is 2637kg. The vehicle has a 150kW engine together with a 6-speed automatic transmission. The vehicle is driven along a highway between Mulhouse and Belfort, which is a hilly section of the highway A36 in France, Europe, see Figure 5(a). The altitude and road geometry coordinates are derived from Google Earth. There are also velocity limitations along the 35km-long road section.
Fl1
Low-level control
ǫ, pi
measurements
Fig. 3. Architecture of the cruise control • The high layer contains the look-ahead control strategy, which generates the reference velocity signal of the cruise control. It is based on the information about the forthcoming road intersections, e.g. the road slopes. It guarantees the fuel-efficiency of the vehicle cruising. • The middle layer is the feedforward-feedback H∞ controller. It guarantees the velocity tracking and the robustness against mass variation and longitudinal disturbances. The output of the controller is the Fl1 signal. • The low layer incorporates the transformation of the control force Fl1 to the engine throttle . Moreover, it realizes the distribution of the driving and braking forces on the wheels of the vehicle. The scheme of the SIL environment is illustrated in Figure 4. The SIL consists of a workstation with the CarSim 519
Two scenarios are compared in the simulation example. In the first case, the look-ahead approach in the determination of the reference velocity profile is not considered. Thus, the reference velocity is equal to the current maximum speed limit, such as λ = vref,0 . In the second scenario, the computation of λ is based on (14), which represents a look-ahead control strategy. The predicted road horizon in the look-ahead control is 300 m long, which is divided into n = 10 subsections. The velocity profiles of the vehicles are shown in Figure 5(b). If the road topography is not considered in the cruise control, the vehicle is driven at the maximum regulated velocity. However, in the look-ahead scenario the velocity varies according to the uphill and downhill sections, see e.g. the cruising in the valley at around 13 km. The control input Fl1 is presented in Figure 5(c). Using the look-ahead cruise control the high peaks of Fl1 are avoided.
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through the reference velocity signal. In the control, the mass variation and the longitudinal disturbances have been handled through the robustness of the system. The information about the forthcoming road topography has been incorporated to improve the efficiency of the controller. The presented method has been implemented in a software-in-the-loop (SIL) environment using DSpace Autobox, which cooperates with the high-fidelity CarSim software through CAN communication. The efficiency of the cruise control has been shown through simulation scenarios on the test environment.
420 400
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380 360 340 320 300 280 260 240 0
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REFERENCES
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Fig. 5. Simulation results - longitudinal signals The actuation of the engine throttle is illustrated in Figure 6(a). Since is derived from the control force Fl1 , the lookahead control requires smaller throttle interventions, due to the less control force. During the road section the lookahead control reaches 7% fuel saving compared to the other vehicle. The consumption signal is generated by CarSim, using the fuel consumption characteristics of the engine. Instead of the 7% fuel saving, the increase of the trip time is only 1 minute along the 35km route. 1
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Fig. 6. Simulation results - engine signals 7. CONCLUSIONS In the paper, the design and the implementation of a robust cruise control have been presented. The velocity profile of the vehicle has been generated by a look-ahead control algorithm, which interacts with the cruise control 520
H. S. Bae, J. Ruy, and J. Gerdes. Road grade and vehicle parameter estimation for longitudinal control using gps. 4th IEEE Conference on Intelligent Transportation Systems, 2001. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics, Philadelphia, 1997. A. Eriksson and M. Ste´ en. Styrning av v¨ axling i motorfordon. Swedish patent, SE 520 228 C2, 2003. N. Gustafsson. The Use of Positioning Systems for Look-Ahead Control in Vehicles. Ph.D. thesis, Department of Electrical Engineering, Link¨ oping University, Sweden, 2006. J.O. Hahn, R. Rajamani, S.H. You, and K.I. Lee. Real-time identification of road-bank angle using differential GPS. IEEE Transactions on Control Systems Technology, 12:589–599, 2004. E. Hellstr¨ om, M. Ivarsson, J. ˚ Aslund, and L. Nielsen. Lookahead control for heavy trucks to minimize trip time and fuel consumption. Control Engineering Practice, 17(2):245–254, 2009. E. Hellstr¨ om, J. ˚ Aslund, and L. Nielsen. Horizon length and fuel equivalents for fuel-optimal look-ahead control. Munich, 2010. U. Kiencke and L. Nielsen. Automotive control systems for engine, driveline and vehicle. Springer, 2000. F. Lattemann, K. Neiss, S. Terwen, and T. Connolly. The predictive cruise control - a system to reduce fuel consumption of heavy duty trucks. SAE Technical Paper, 2004. doi: 10.4271/2004-01-2616. S.E. Li, K. Li, and J. Wang. Economy-oriented vehicle adaptive cruise control with coordinating multiple objectives function. Vehicle System Dynamics, 51(1):1–17, 2013. B. N´ emeth and P. G´ asp´ ar. Design of vehicle cruise control using road inclinations. Int. J. Vehicle Autonomous Systems, 11(4):313–333, 2013. B. N´ emeth, P. G´ asp´ ar, R. Orjuela, and M. Basset. Robust H∞ design of an automotive cruise control system. IFAC Workshop on Engine and Powertrain Control, Simulation and Modeling, Columbus, 2015. B. Passenberg, P. Kock, and O. Stursberg. Combined time and fuel optimal driving of trucks based on a hybrid model. European Control Conference, Budapest, 2009. C. Scherer and S. Weiland. Lecture Notes DISC Course on Linear Matrix Inequalities in Control. Delft University of Technology, Delft, Netherlands, 2000. A. Sciarretta, G. De Nunzio, and L.L. Ojeda. Optimal ecodriving control: Energy-efficient driving of road vehicles as an optimal control problem. Control Systems, IEEE, 35(5):71–90, 2015. H. Takahashi, H. Kidokoro, and A. Shiratori. Controlling vehicular driving force in anticipation of road situation on which vehicle is to run utilizing vehicular navigation system. United States patent, US 5 832 400, 1998. A. Vahidi, A. Stefanopoulou, and H. Peng. Recursive least squares with forgetting for online estimation of vehicle mass and road grade: theory and experiments. Vehicle System Dynamics, 43(1): 31–55, 2005. W. Zhu and M. Barth. Vehicle trajectory-based road type and congestion recognition using wavelet analysis. IEEE Intelligent Transportation Systems Conference, Toronto, 2006. A. Zomotor. Fahrwerktechnik, Fahrverhalten. Vogel Verlag Und Druck, 1991.
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Implementation of a robust cruise Implementation Implementation of of a a robust robust cruise cruise control using look-ahead method control using using look-ahead look-ahead method method control ∗ ∗∗ ∗∗∗ P´ e P´ eter ter P´ e P´ eter ter
G´ a a G´ asp´ sp´ arr ∗∗∗ G´ a sp´ a G´ asp´ arr
Bal´ a e Michel Bal´ azs zs N´ N´ emeth meth ∗∗ Michel Basset Basset ∗∗∗ ∗∗ ∗∗∗ ∗∗∗∗∗ Bal´ a zs N´ e meth Rodolfo Orjuela ∗∗∗ Bal´ azs N´ emeth Michel Michel Basset Basset ∗∗∗ Rodolfo Orjuela ∗∗∗ ∗∗∗ Rodolfo Rodolfo Orjuela Orjuela ∗ ∗ Institute for Computer Science and Control, Hungarian Academy of Institute for Computer Science and Control, Hungarian Academy of ∗ ∗ Institute Computer Science and Control, Sciences and MTA-BME Control Research Group, Institute for Computer Science andEngineering Control, Hungarian Hungarian Academy of Sciencesfor and MTA-BME Control Engineering ResearchAcademy Group, of Sciences and MTA-BME Control Engineering Research Budapest, Hungary; E-mail: [email protected] Sciences and MTA-BME [email protected] Engineering Research Group, Group, Budapest, Hungary; E-mail: ∗∗ Budapest, E-mail: and Control Institute ∗∗ Systems Budapest, Hungary; E-mail: [email protected] [email protected] Systems and Hungary; Control Laboratory, Laboratory, Institute for for Computer Computer Science Science ∗∗ ∗∗ Systems and Control Laboratory, Institute for Computer Science and Control, Hungarian Academy of Sciences, Budapest, Hungary; Systems and Control Laboratory, Institute for Computer Science and Control, Hungarian Academy of Sciences, Budapest, Hungary; and Academy of Sciences, Budapest, Hungary; E-mail: [email protected] and Control, Control, Hungarian Hungarian Academy of Sciences, Budapest, Hungary; E-mail: [email protected] ∗∗∗ E-mail: Process ∗∗∗ Modelling Intelligence E-mail: [email protected] [email protected] Modelling Intelligence Process and and Systems Systems (MIPS) (MIPS) Laboratory, Laboratory, ∗∗∗ ∗∗∗ Modelling Intelligence Process and Systems (MIPS) Laboratory, Universit´ e de Haute-Alsace, Mulhouse Cedex, France; Modelling Intelligence Process and Systems (MIPS) Laboratory, Universit´e de Haute-Alsace, Mulhouse Cedex, France; Universit´ e de Haute-Alsace, Mulhouse Cedex, France; E-mail: [michel.basset,rodolfo.orjuela]@uha.fr Universit´ e de Haute-Alsace, Mulhouse Cedex, France; E-mail: [michel.basset,rodolfo.orjuela]@uha.fr E-mail: E-mail: [michel.basset,rodolfo.orjuela]@uha.fr [michel.basset,rodolfo.orjuela]@uha.fr Abstract: The The paper paper proposes proposes the the implementation implementation of of aa robust robust cruise cruise control control system system which which is is Abstract: Abstract: The paper proposes the aa robust cruise which is able to to ensure ensure the fuel-efficient travel of the the vehicle vehicle of with look-ahead control system algorithm. The Abstract: Thethe paper proposes travel the implementation implementation of robust cruise control control system which is able fuel-efficient of with aa look-ahead control algorithm. The able to the of the with control The H∞ -based feedforward-feedback control guarantees robustness against varying vehicle able to ensure ensure the fuel-efficient fuel-efficient travel travel of method the vehicle vehicle with aa look-ahead look-ahead control algorithm. algorithm. The H ∞ -based feedforward-feedback control method guarantees robustness against varying vehicle H -based feedforward-feedback control method guarantees robustness against varying vehicle mass, longitudinal disturbances and the consideration of actuator dynamics. The advantage ∞ H -based feedforward-feedback control method guarantees robustness against varying vehicle ∞ mass, longitudinal disturbances and the consideration of actuator dynamics. The advantage of of mass, longitudinal the of dynamics. The of the is application a number parameters. Therefore, aa method mass, longitudinal disturbances and the consideration consideration of actuator actuator dynamics. The advantage advantage of the method method is the the disturbances application of ofand a small small number of of vehicle vehicle parameters. Therefore, method the method is of number of Therefore, aa method for cars significant modifications is proposed cruise the various method passenger is the the application application of a a small small number of vehicle vehicle parameters. parameters. Therefore, method for various passenger cars without without significant modifications is needed. needed. The The proposed cruise for passenger cars without significant modifications is proposed cruise control and look-ahead implemented in (SIL) environment for various various passenger cars method withoutare significant modifications is needed. needed. The The proposed cruise control and the the look-ahead method are implemented in aa software-in-the-loop software-in-the-loop (SIL) environment control and the look-ahead method are implemented in a software-in-the-loop (SIL) environment using DSpace Autobox, which cooperates with the high-fidelity CarSim software through control and the look-ahead method are implemented in a software-in-the-loop (SIL) environment using DSpace Autobox, which cooperates with the high-fidelity CarSim software through CAN CAN using DSpace communication. using DSpace Autobox, Autobox, which which cooperates cooperates with with the the high-fidelity high-fidelity CarSim CarSim software software through through CAN CAN communication. communication. communication. © 2016, IFAC (International of Automaticcontrol, Control)Software-in-the-loop Hosting by Elsevier Ltd.application All rights reserved. Keywords: Robust controlFederation design, Look-ahead Look-ahead Keywords: Robust control design, control, Software-in-the-loop application Keywords: Keywords: Robust Robust control control design, design, Look-ahead Look-ahead control, control, Software-in-the-loop Software-in-the-loop application application 1. INTRODUCTION INTRODUCTION AND AND MOTIVATION MOTIVATION speed 1. speed design design for for road road vehicles vehicles based based on on road road inclinations, inclinations, 1. speed design road based on road inclinations, vehicle in traveling 1. INTRODUCTION INTRODUCTION AND AND MOTIVATION MOTIVATION speed limits, design aafor forpreceding road vehicles vehicles based on lane roadand inclinations, speed limits, preceding vehicle in the the lane and traveling speed limits, a preceding vehicle in the lane and time is proposed by N´ e meth and G´ a sp´ a r [2013]. A In the last decade, the longitudinal vehicle control based speedislimits, a preceding vehicle the lane and traveling traveling proposed by N´emeth andinG´ asp´ ar [2013]. A road road In the last decade, the longitudinal vehicle control based time time is proposed by N´ e meth and G´ a sp´ a r [2013]. A In the last decade, the longitudinal vehicle control based type and congestion level estimation method is combined on the look-ahead approach has been in the focus of time is proposed by N´ e meth and G´ a sp´ a r [2013]. A road road In the last decade, the longitudinal vehicle control based on the look-ahead approach has been in the focus of type and congestion level estimation method is combined type and congestion level estimation method is combined on the look-ahead approach has been in the focus of with the principal components analysis for a variety the automotive research centers. It is widespread in the type and congestion level estimation method is combined on the look-ahead approach has been in the focus of of the automotive research centers. It is widespread in the with the principal components analysis for a variety of aa variety of the research centers. It in purposes, e.g. information systems, intelligent realcruise control, which which is able able to guarantee guarantee energy-efficient with the the principal principal components analysis for variety of the automotive automotive research centers. It is is widespread widespread in the the with purposes, e.g. traffic trafficcomponents information analysis systems,for intelligent realcruise control, is to energy-efficient purposes, e.g. traffic information systems, intelligent realcruise control, which is able to guarantee energy-efficient time control systems, energy consumption/emissions in driving, see Sciarretta et al. [2015]. Since Adaptive Cruise purposes, e.g. traffic information systems, intelligent realcruise control, which isetable to guarantee energy-efficient driving, see Sciarretta al. [2015]. Since Adaptive Cruise time control systems, energy consumption/emissions in control driving, Sciarretta [2015]. Adaptive Zhu Barth [2006]. Control (ACC) allows et to al. maintain desired travelCruise speed time time control systems, energy consumption/emissions consumption/emissions in in driving, see see Sciarretta et al. [2015]. Since Since Adaptive Cruise Zhu and and Barthsystems, [2006]. energy Control (ACC) allows to maintain aa desired travel speed Zhu and Barth [2006]. Control (ACC) allows to maintain a desired travel speed set by the driver by acting on the throttle and brakes, Zhu and Barth [2006]. Control (ACC) allows to maintain a desired travel speed set by the driver by acting on the throttle and brakes, A test platform for the implementation of look-ahead set by acting the and the combination ofby look-ahead control and ACC ACC is brakes, novel A test platform for the implementation of look-ahead set combination by the the driver driverof by acting on oncontrol the throttle throttle andis brakes, the look-ahead and aa novel A platform for the implementation look-ahead control introduced [2006]. The platform A test test is platform for in theGustafsson implementation of look-ahead is introduced in Gustafsson [2006]. of The platform the combination of look-ahead control and ACC is a novel trend in the vehicle control design. the combination of look-ahead control and ACC is a novel control trend in the vehicle control design. control is introduced in Gustafsson [2006]. The platform contains the user interface, the controller structure tocontrol is introduced in Gustafsson [2006]. The platform contains the user interface, the controller structure totrend in the vehicle control design. trend in the vehicle control design. contains the user interface, the controller structure together with the look-ahead optimization, CAN softwares Several publications and patents deal with the topics of containswith thethe user interface, optimization, the controllerCAN structure tolook-ahead softwares Several publications and patents deal with the topics of gether gether with the look-ahead optimization, CAN softwares Several publications and patents deal with the topics of and interfaces. The proposed device is in connection with driveline control implementation and look-ahead strategether with the look-ahead optimization, CAN softwares Several publications and patents deal with the topics of driveline control implementation and look-ahead strate- and interfaces. The proposed device is in connection with interfaces. The is with driveline and stratethe bus the vehicle. The method of gies. Thecontrol design implementation and the the implementation implementation of aa predicpredicand interfaces. The proposed device is in in connection connection with driveline control implementation and look-ahead look-ahead strate- and the CAN CAN bus of of theproposed vehicle. device The look-ahead look-ahead method of gies. The design and of the CAN bus of the vehicle. The look-ahead method of gies. The design and the implementation of a predicplatform considers the engine torque, the gear positive speed controller are presented by Hellstr¨ o m et al. the CAN bus of the vehicle. The look-ahead method of gies. The design and the implementation of a predictive speed controller are presented by Hellstr¨ om et al. the platform considers the engine torque, the gear posithe platform considers the engine torque, the gear positive speed controller are presented by Hellstr¨ o m et al. tion and road geometry information. The implementation [2009], Passenberg et al. [2009], Hellstr¨ o m et al. [2010]. the platform engine torque, the gear positive speed controller presented by oHellstr¨ om [2010]. et al. tion and road considers geometry the information. The implementation [2009], Passenberg et are al. [2009], Hellstr¨ m et al. road The implementation [2009], Passenberg al. [2009], oom [2010]. of optimal ACC passenger presented The intervention ofet the look-ahead control is al. connected tion and road geometry geometry information. The is implementation [2009], Passenbergof etthe al. look-ahead [2009], Hellstr¨ Hellstr¨ m et et al. [2010]. tion of an anand optimal ACC for forinformation. passenger cars cars is presented by by The intervention control is connected of an optimal ACC for passenger cars is by The intervention of the look-ahead control is connected Li et al. [2013]. The system uses radar and acceleration to the reference signal of the PID-based speed controller, of an optimal ACC for passenger cars is presented by The intervention of the look-ahead control is connected acceleration to the reference signal of the PID-based speed controller, Li et al. [2013]. The system uses radar andpresented Li et al. [2013]. The system uses radar and acceleration to the reference signal of the PID-based speed controller, sensor measurements, from which the acceleration of the which modifies the fuel injection of the engine. A dynamic Li et al. [2013]. The system uses radar and acceleration to the reference signal of the PID-based speed controller, sensor measurements, from which the acceleration of the which modifies the fuel injection of the engine. A dynamic from the of which the the engine. dynamic preceding vehicle The algorithm longitudinal model for injection the design designof of the speedA controller sensor measurements, measurements, from which which the acceleration acceleration of the the which modifies modifies the fuel fuel injection of of thethe engine. Acontroller dynamic sensor preceding vehicle are are derived. derived. The optimization optimization algorithm longitudinal model for the speed preceding vehicle are derived. The optimization algorithm longitudinal model for the design of the speed controller yields a reference acceleration signal, which is the input is applied by Kiencke and Nielsen [2000]. It influences preceding vehicle are derived. The optimization algorithm longitudinal model for the design of the speed controller of is applied by Kiencke and Nielsen [2000]. It influences yields a reference acceleration signal, which is the input of aa reference acceleration which the input is Kiencke Nielsen [2000]. the dynamic controller together with the engine by torque basedand on the the engine rpm It andinfluences the fuel fuel yields yields reference acceleration signal, which isthe theestimated input of of is applied applied by Kiencke and Nielsen [2000]. It influences the vehicle vehicle dynamic controller signal, together with is the estimated the engine torque based on engine rpm and the dynamic controller the torque on the and fuel preceding acceleration. injection, are control in architecture. The the vehicle vehiclevehicle dynamic controller together together with with the the estimated estimated the engine enginewhich torque based oninputs the engine engine rpm and the the The fuel the preceding vehicle acceleration. injection, which arebased control inputs in the the rpm architecture. vehicle injection, which are control inputs in The The research preceding vehicle acceleration. acceleration. injection, which control by inputs in the the architecture. architecture. The preceding wasare supported the National Research, Develop The research Further automotive industrial was supported by the National Research, DevelopFurther automotive industrial patents patents on on the the predictive predictive ment and Innovation Fund through the projectResearch, ”SEPPAC: Safety The research was supported by the National DevelopFurther automotive industrial patents on the The research was supported by the National Research, Developspeed control algorithms are presented Lattemann et ment and Innovation Fund through the project ”SEPPAC: Safety Further automotive industrial patentsin on the predictive predictive speed control algorithms are presented in Lattemann et al. al. and Economic Platform for Partially Automated Commercial vehiment and Innovation Fund through the project ”SEPPAC: Safety mentEconomic and Innovation Fund through the project ”SEPPAC: speed control algorithms are presented in Lattemann et al. [2004]. The method of Eriksson and Ste´ e n [2003] is based and Platform for Partially Automated CommercialSafety vehispeed control algorithms are presented in Lattemann et al. [2004]. The method of Eriksson and Ste´ e n [2003] is based cles”Economic (VKSZ 14-1-2015-0125). This paper was partially supported by and Platform for for Partially Partially Automated Commercial vehiand Platform Automated Commercial vehicles”Economic (VKSZ 14-1-2015-0125). This paper was partially supported by [2004]. The method of Eriksson and Ste´ e n [2003] is based on the forthcoming terrain characteristics to select gear [2004]. The method of Eriksson and Ste´ e n [2003] is based on the forthcoming terrain characteristics to select gear the J´ a nos Bolyai Research Scholarship of the Hungarian Academy of cles” (VKSZ 14-1-2015-0125). This paper was partially supported by cles”J´ 14-1-2015-0125). This paper wasHungarian partially supported the a(VKSZ nos Bolyai Research Scholarship of the Academy by of on the terrain characteristics select position, according the driver’s on the forthcoming forthcoming terrain characteristics toperformance select gear gear Sciences. position, according to to the required required driver’sto performance the J´ a the J´ anos nos Bolyai Bolyai Research Research Scholarship Scholarship of of the the Hungarian Hungarian Academy Academy of of Sciences. position, according to the required driver’s performance position, according to the required driver’s performance Sciences. Sciences. Copyright © 2016 IFAC 515 Copyright 2016 IFAC 515 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 515 Copyright ©under 2016 responsibility IFAC 515Control. Peer review© of International Federation of Automatic 10.1016/j.ifacol.2016.08.074
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(fuel-consumption, emission, traveling time). An algorithm which computes the optimal driveline torque considering the road inclinations is presented by Takahashi et al. [1998]. In this paper, the implementation of a robust cruise control together with a look-ahead control is proposed. The applied method guarantees robustness against varying vehicle mass, and longitudinal disturbances, such as rolling resistances, aerodynamic forces. Moreover, the dynamic properties of the actuator are considered in the control design phase. In the presented method, the look-ahead strategy and the robust longitudinal control are connected through the reference velocity signal. The output of the look-ahead computation is the optimal velocity, which is considered as an input of the controller. The advantage of the method is the application of a small number of vehicle parameters. Then the method can be applied to various passenger cars without significant modifications. The preliminary results of the cruise control design can be found in N´emeth et al. [2015]. As a novelty, in this paper the cruise control and the look-ahead method are implemented in a software-in-the-loop (SIL) environment using DSpace Autobox. The organization of the paper is the following. Section 2 presents the formulation of the longitudinal vehicle dynamics for the look-ahead cruise control. The robust H∞ control strategy of the cruise control system considering the formulation of the uncertainties is described in Section 3. The concept of the speed design using a look-ahead approach is presented in Section 4. The implementation of the robust control system is found in Section 5. The evaluation of the proposed control method is presented through simulation examples in Section 6. 2. MODELING LONGITUDINAL DYNAMICS
actual mass m of the vehicle such as: m = m0 + mv . Thus the longitudinal motion equation is reformulated in the following way: m0 ξ¨0 = Fl1 − Fd1 − mv ξ¨0 (3) Considering that ξ¨0 , the actual longitudinal acceleration, is a measurable and bounded signal of the vehicle, mv ξ˙ is handled as a disturbance of the vehicle. Combining it with Fd1 , the next expression is yielded: (4) Fd1 + mv ξ¨0 = Fd1,1 + mv fd,2 2 ˙ where Fd1,1 = Ca ξ0 + Cr gm0 cos ϑ + m0 g sin ϑ and fd,2 = Cr g cos ϑ + g sin ϑ + ξ¨0 . Fd1,1 and fd,2 incorporate measurable signals, such as velocity, road slope and longitudinal acceleration. Thus, Fd1,1 is handled in this approach as a measured disturbance. Since there is no information about the mass variation mv , the term mv fd,2 is considered as an unknown disturbance - where actually fd,2 is a measurable part of the disturbance expression. 3. ROBUST CONTROL STRATEGY In this section, the control design for the longitudinal velocity tracking control problem is proposed. The realized total longitudinal control force on the wheels Fl1 is divided into two elements: (5) Fl1 = Fl1,0 + Fl1,1 where the purpose of Fl1,1 is to compensate for the measured disturbance Fd1,1 , while Fl1,0 guarantees the unknown disturbance rejection and the performances. In the following, a robust control design method is presented, which combines the advantages of the feedforward and feedback control design. 3.1 Design of the feedforward control
In this section the modeling of longitudinal dynamics is presented. The longitudinal dynamics is described in the approach by the following simplified model: (1) mξ¨0 = Fl1 − Fd1
where m is the mass of the vehicle, ξ0 is the vehicle position, Fl1 is the realized longitudinal force on the wheels. Fd1 includes the longitudinal disturbances, such as the aerodynamic forces, rolling resistance and road slope: (2) Fd1 = Ca ξ˙2 + Cr gm cos ϑ + mg sin ϑ 0
where ϑ is road slope and Ca , Cr are vehicle parameters related to aerodynamic and resistances forces. In the following the transformation of the vehicle model has two focuses. Firstly, the mass of the vehicle is an uncertain parameter of the vehicle. The mass has a nominal value m0 , which is known, but the variation of the mass mv is unknown. However, the variation is assumed to be a bounded parameter, e.g. mv /m0 = ±15%. Secondly, the road inclination is assumed to be known. In practice, the slope of the road can be obtained in two ways: either a contour map which contains the level lines is used or an estimation method is applied, see e.g., Bae et al. [2001], Hahn et al. [2004]. Since the handling of vehicle mass uncertainty is a requirement for the control system, it is necessary to define the 516
In the first step the feedforward control is designed. If Fd1,1 is fully compensated for, then the feedforward control input is u1 = Fl1,1 , (6) where ξ˙0 , ϑ are measured and estimated parameters, see Vahidi et al. [2005]. Thus, the efficiency of the feedforward disturbance compensation is based on the accuracy of the measured signals. Since the measurement of the speed and the estimation of the road slope are inaccurate, the feedforward compensation has an error Fd,11 . The longitudinal motion of the vehicle is formed in the following way: m0 ξ¨0 = Fl1,0 − Fd1,11 − mv fd,2 (7) In the next step a feedback control input Fl1,0 is designed, which is able to handle the disturbances Fd1,11 , fd,2 . 3.2 Design of the feedback control The feedback control input Fl1,0 has three main goals in the control strategy: the rejection of unknown disturbances (Fd1,11 , fd,2 mv ), the handling of the unmodelled actuator dynamics and the guarantee of the performance. The statespace representation of the system is the following: 1 1 1 Fd1,11 ¨ ˙ − + Fl,0 (8) ξ0 = [0] ξ0 + − Fd1,2 m0 m0 m0
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where the disturbances are compressed to a vector Fd,f b = T [Fd1,11 Fd1,2 ] , where Fd1,2 = fd,2 mv . The measured output of the system is the velocity ξ˙0 , which is also the state in the formulation. The performance of the system is expressed by the tracking of the reference velocity λ and the minimization of the control input u0 . Note that the influence on the control input is necessary to avoid the extremely high actuation of the longitudinal control. The performance signals are (9) |z1 | = |λ − ξ˙0 | → min |z2 | = |u0 | → min
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Fig. 1. Closed-loop interconnection The augmented-plant for the H∞ design is illustrated in Figure 1. The weighting functions of z1 and z2 are formulated as Wp,i = (b1,i s + b0,i )/(a1,i s + a0,i ) where b1,i , b0,i , a1,i , a0,i are design parameters. The selection of these parameters has significant relevance. Firstly, the parameters determine the accuracy of the velocity tracking and the limitation of the actuator intervention. Secondly, the overshot of the velocity signal is also determined by the parameters. Generally, the actuators delay the controlled action and provide additional dynamic motion. This dynamics can be handled as an input multiplicative uncertainty of the system, where Wu = −τ s/(τ s + 1) is the uncertainty of the system. In this form the value τ is related to the dynamics of the actuation of the driveline/braking systems. In Figure 1 the measured signal is y = ξ˙0 . The sensor noise Fd,s on the velocity measurement is considered as a disturbance, which must be rejected by the robust controller. Thus, Fd,f b is extended with the signal Fd,s . The objective of H∞ control is to minimize the inf-norm of the transfer function Tz∞ w . More precisely, the problem can be stated as follows [Scherer and Weiland, 2000, Boyd et al., 1997]. The LMI problem of H∞ performance is formulated as: the closed-loop RMS gain from w to z∞ does not exceed γ if and only if there exists a symmetric and definite positive matrix X∞ such that T Acl X∞ + X∞ ATcl X∞ Bcl Ccl T T <0 (11) Bcl X∞ −γI Dcl Ccl Dcl −γI with γ > 0 and state space components of the closed-loop control system Acl , Bcl , Ccl1 , Dcl1 .
Finally, a robust dynamic K controller is yielded. The feedback control input is formally computed as u0 = 517
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K(vref − ξ˙0 ). As a result of the combined feedforwardfeedback strategy, the control law of the system, using (6), is yielded as u = u0 + u1 , where u0 represents the feedback control input and u1 the feedforward control. 4. SPEED GENERATION BASED ON THE LOOK-AHEAD CONTROL 4.1 The basics of look-ahead control In this section the design of a cruise control system, in which the longitudinal control incorporates the brake and traction forces is proposed in order to achieve the designed velocity profile. By choosing the appropriate speed according to the road and traffic information, the number of unnecessary accelerations and brakings and their durations can be significantly reduced. A detailed description of the speed profile design is found in N´emeth and G´asp´ar [2013]. In this section only a brief summary of the look-ahead control is presented. The road ahead of the vehicle is divided into several segments, which are of different lengths consistent with the topography of the road. The rates of the slopes of the road and the speed limits are assumed to be known at each segment. The reference speeds at the segment points are predefined. The current speed requires information systems installed along the road. In the method, the vehicle is assumed to be traveling in a segment from the initial point to the first division point. The aim is to calculate the speed at the same initial point at which the reference speed of the first point can be reached. This method is applied to the next segments and division points. In the case of n segments and n + 1 points, n equations are formulated between the first and the end points. It is assumed that the acceleration of the vehicle may change in the different intervals, but within a single interval it is approximated by a constant. The reference speeds at the section points are predefined: vref,0 , vref,1 , ..., vref,n . The speed of the vehicle at point i ∈ (1, n) is written as: i ξ˙i2 = ξ˙02 + m20 j=1 sj (Flj − Fdj,r − Fdj,o ), where ξ˙0 is the speed of the vehicle at the initial point, ξ˙i is the speed of the vehicle at the ith point and sj is the distance of the interval [j − 1, j]. Moreover, Flj is the longitudinal force, Fdj,r = m0 g sin αi is the force resistance from the road slope, Fdj,o represents other resistances such as rolling resistance and aerodynamic forces. At the calculation of the control force, it is assumed that only the control force Fl1 affects the vehicle, i.e., Fli = 0, i > 1. The aim is that at every segment point the speed ξ˙i 2 must reach the predefined reference speed: ξ˙i2 → vref,i . The equations of the vehicle speeds at the segment points are calculated in the following way: ξ˙i2 = ξ˙02 + i 2 2 2 j=1 sj Fdj,r . Prediction weights m0 s1 Fl1 − m0 s1 Fd1,o − m0 Q, γ1 , γ2 , ..., γn are applied to the sections (γ1 + γ2 + ... + γn + Q = 1). While the prediction weights γi represent the rate of the road conditions, weight Q has an essential role: it determines the tracking requirement of the current reference speed vref,0 . By increasing Q the momentary speed
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where parameter λ is calculated in the following way based on the designed ϑ: λ = ϑ − 2s1 (1 − Q)(ξ¨0 + gsinα). (12) shows that the modified speed ξ˙0 depends on the prediction weights (Q and γi ). By choosing these values the effects of road conditions can be tuned.
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The design of the vehicle speed poses two optimization problems: the longitudinal force must be minimized and the deviation from the reference velocity must be minimized. The minimization of the longitudinal control force 2 → min leads to a quadratic optimization problem: Fl1 2 ¯ + β1 (Q)¯ ¯ γ1 + . . . + βn (Q)¯ ¯ γn )2 → min (15) ¯ Fl1 = (β0 (Q) ¯ γ¯i = ¯ γ¯i ≤ 1 and Q+ with the following constrains 0 ≤ Q, 1. In the first criterion the road inclinations and speed limits are taken into consideration by using appropriately ¯ γ¯i . chosen weights Q, The minimization of the difference between the current velocity and the reference velocity |vref,0 − ξ˙0 | → min (16) leads to the optimal solution, which is achieved by select˘ = 1 and γ˘i = 0, i ∈ [1, n], since in this ing the weights: Q case the vehicle tracks the predefined speed. These optimization criteria lead to different solutions. Two further performance weights, R1 and R2 (R1 + R2 = 1), are introduced in order to achieve a balance between the optimal results. Performance weight R1 (0 ≤ R1 ≤ 1) is related to the importance of the minimization of the longitudinal control force (15) while performance weight R2 (0 ≤ R2 ≤ 1) is related to the minimization (16). 4.3 Effects of the vehicle mass The mass of the vehicle has an important role in the velocity profile optimization through ϑ, see (13). However, the mass of the vehicle is uncertain. Since the mass mv is not measured, the variation is not considered in the lookahead control. In the following section, a simulation-based analysis is shown, which presents the velocity profile of the vehicle, depending on different mass values. 518
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Taking the weights into consideration the following formula is yielded: 2 2 s1 (1 − Q)Fl1 − s1 (1 − Q)Fd1,o = ϑ (12) ξ˙02 + m0 m0 where value ϑ depends on the road slopes, the reference speeds and the weights n n n 2 2 2 γi vref,i + γj . (13) + si Fdi,r ϑ = Qvref,0 m0 i=1 i=1 j=i
For the testing phase four vehicle masses are analyzed, such as 1000 kg, 3500 kg, 8000 kg and 12000 kg. The road profile is illustrated in Figure 2(a). The velocity profiles of the vehicles with different mass values are found in Figure 2(b). The results show that the increased mass causes a higher variation in velocity. Furthermore, the saved energy of the vehicle with increased mass is higher, see Figure 2(c).
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Fig. 2. Analysis of dependence on mass Table 1 summarizes the energy saving of the vehicle. It can be seen that approximately 6 − 7% of energy can be saved by considering predicted road conditions. The control force and energy represent the same as the change of velocity; it changes slightly with an increase in the mass of the vehicle. Mass (kg) 1000 3500 8000 12000
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Table 1. Dependence of the mass on performances
5. IMPLEMENTATION OF THE METHOD IN THE DRIVING/BRAKING SYSTEM The command variable of the robust control design is the longitudinal force input u = Fl1 . However, the real physical system has two inputs, such as driveline and brake inputs. In the following section the transformation of Fl1 to the real physical inputs is presented. In the conventional engine-powered driveline system the gear positioning and the throttle are the intervention possibilities. The proposed method considers an automatic transmission, where the positioning of the gear is determined by the engine speed and the throttle ∈ [0 . . . 1]. Thus, it is necessary to find an appropriate , which guarantees the realization of Fl1 . Since the driveline dynamics is faster than the longitudinal dynamics, the transients of the driveline are ignored in the computations. The conversion between Fl1 and is based on static relations.
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The required torque of the engine is computed with the following expression as: Meng = Fl1 Rw /k0 /kg , where Rw is wheel radius, k0 and kg are the ratio of the driven axle and the transmission. The value of kg depends on the current gear position. The conversion between Meng and is performed through the engine characteristics. This computation requires the measurement of the engine speed ω, and the inversion of the characteristics based on Meng and ω. The braking system in the paper is a conventional hydraulic construction. The dynamics of the braking hydraulics τ is faster than the longitudinal motion, therefore the relationship between Fl and brake cylinder pressures is described by static equations. Firstly, the longitudinal force is divided at the left and right sides of the front and rear axles using the following expression, see Zomotor [1991]. Second, the wheel longitudinal forces are converted into the cylinder braking pressures, such as pi = Fi Rw /CpM,i where Fi is the longitudinal force of the wheel, and CpM,i is the constant, which depends on the wheel brake construction.
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vehicle simulator, the dSPACE environment, in which the controller is implemented. In the workstation the CarSim works together with Matlab/Simulink. The CarSim simulator with the Matlab/Simulink software, which are standard industrial tools, simulate the vehicle dynamics with high accuracy. The communication between the workstation and the dSPACE is realized through the CAN bus. Before the SIL simulation the designed control system is set on the real-time equipment. The control signal is computed in dSPACE by the discrete-time solver of the differential equations with 0.01s sampling time.
5.1 SIL implementation of the controller In the following section, the implementation of the proposed system in a SIL environment is presented. The control algorithm has three layers, which are illustrated in Figure 3.
Fig. 4. Software-in-the-loop simulation
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In this section a simulation example of the implemented robust longitudinal cruise control is proposed. The simulation is performed on the SIL environment, see Section 5. A minivan vehicle is used in the example, whose nominal mass is m0 = 2037kg and the maximum mass in the simulation is 2637kg. The vehicle has a 150kW engine together with a 6-speed automatic transmission. The vehicle is driven along a highway between Mulhouse and Belfort, which is a hilly section of the highway A36 in France, Europe, see Figure 5(a). The altitude and road geometry coordinates are derived from Google Earth. There are also velocity limitations along the 35km-long road section.
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Fig. 3. Architecture of the cruise control • The high layer contains the look-ahead control strategy, which generates the reference velocity signal of the cruise control. It is based on the information about the forthcoming road intersections, e.g. the road slopes. It guarantees the fuel-efficiency of the vehicle cruising. • The middle layer is the feedforward-feedback H∞ controller. It guarantees the velocity tracking and the robustness against mass variation and longitudinal disturbances. The output of the controller is the Fl1 signal. • The low layer incorporates the transformation of the control force Fl1 to the engine throttle . Moreover, it realizes the distribution of the driving and braking forces on the wheels of the vehicle. The scheme of the SIL environment is illustrated in Figure 4. The SIL consists of a workstation with the CarSim 519
Two scenarios are compared in the simulation example. In the first case, the look-ahead approach in the determination of the reference velocity profile is not considered. Thus, the reference velocity is equal to the current maximum speed limit, such as λ = vref,0 . In the second scenario, the computation of λ is based on (14), which represents a look-ahead control strategy. The predicted road horizon in the look-ahead control is 300 m long, which is divided into n = 10 subsections. The velocity profiles of the vehicles are shown in Figure 5(b). If the road topography is not considered in the cruise control, the vehicle is driven at the maximum regulated velocity. However, in the look-ahead scenario the velocity varies according to the uphill and downhill sections, see e.g. the cruising in the valley at around 13 km. The control input Fl1 is presented in Figure 5(c). Using the look-ahead cruise control the high peaks of Fl1 are avoided.
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through the reference velocity signal. In the control, the mass variation and the longitudinal disturbances have been handled through the robustness of the system. The information about the forthcoming road topography has been incorporated to improve the efficiency of the controller. The presented method has been implemented in a software-in-the-loop (SIL) environment using DSpace Autobox, which cooperates with the high-fidelity CarSim software through CAN communication. The efficiency of the cruise control has been shown through simulation scenarios on the test environment.
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Fig. 5. Simulation results - longitudinal signals The actuation of the engine throttle is illustrated in Figure 6(a). Since is derived from the control force Fl1 , the lookahead control requires smaller throttle interventions, due to the less control force. During the road section the lookahead control reaches 7% fuel saving compared to the other vehicle. The consumption signal is generated by CarSim, using the fuel consumption characteristics of the engine. Instead of the 7% fuel saving, the increase of the trip time is only 1 minute along the 35km route. 1
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Fig. 6. Simulation results - engine signals 7. CONCLUSIONS In the paper, the design and the implementation of a robust cruise control have been presented. The velocity profile of the vehicle has been generated by a look-ahead control algorithm, which interacts with the cruise control 520
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