A two-layer predictive control for hybrid electric vehicles energy management

Proceedings of the 20th World Proceedings of 20th Congress The International Federation of Congress Automatic Control Proceedings of the the 20th World World Congress The International Federation of Automatic Control The International Federation of Automatic Control Toulouse, France, July 9-14, 2017 Proceedings of the 20th World Congress The International Federation of Automatic Control Toulouse, France, France, July July 9-14, 9-14, 2017 2017 Available online at www.sciencedirect.com Toulouse, The International of Automatic Control Toulouse, France,Federation July 9-14, 2017 Toulouse, France, July 9-14, 2017

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IFAC PapersOnLine 50-1 (2017) 10058–10064 A two-layer predictive control for hybrid A two-layer predictive control for hybrid A two-layer predictive control for hybrid A two-layer predictive control for hybrid electric vehicles energy management A electric two-layer predictive control for hybrid vehicles energy management electric vehicles energy management electric vehicles energy management electric vehicles energy management ∗∗∗ Nicoleta Stroe ∗∗ Sorin Olaru ∗∗ ∗∗ Guilaume Colin ∗∗∗

∗∗ Guilaume Colin Nicoleta Stroe Stroe ∗∗ Sorin Sorin Olaru Olaru ∗ ∗∗∗ ∗∗∗ ∗∗ Chamaillard ∗∗∗ Nicoleta Guilaume Colin Karim Ben-Cherif Nicoleta Stroe ∗ Yann ∗∗∗ ∗∗∗ ∗ Sorin Olaru ∗∗ Guilaume Colin ∗ Yann ∗∗∗ Karim Ben-Cherif Nicoleta Stroe Sorin Olaru Guilaume Colin ∗ Yann Chamaillard ∗∗∗ Karim Ben-Cherif Chamaillard Karim Ben-Cherif ∗ Yann Chamaillard ∗∗∗ ∗ Karim Ben-Cherif Yann Chamaillard ∗ Renault SAS, Lardy, France, (e-mail: ∗ Renault SAS, Lardy, France, (e-mail: ∗ Renault SAS, Lardy, France, (e-mail: {nicoleta − alexandra.stroe, karim.ben − cherif }@renault.com) France, (e-mail: ∗ Renault SAS, Lardy, − alexandra.stroe, karim.ben − cherif }@renault.com) ∗∗{nicoleta Renault SAS, Lardy, France, (e-mail: {nicoleta − alexandra.stroe, karim.ben − cherif }@renault.com) Laboratory of Signals and Systems, CentraleSup´ elec-CNRS-Univ. ∗∗{nicoleta − alexandra.stroe, karim.ben − cherif }@renault.com) ∗∗{nicoleta Laboratory of Signals Signals and and Systems, Systems, CentraleSup´ lec-CNRS-Univ. − alexandra.stroe, karim.ben − cherif }@renault.com) ∗∗ Laboratory of CentraleSup´ eeelec-CNRS-Univ. Paris-Sud, Univ. Paris-Saclay, Gif-sur-Yvette, Laboratory of Signals and Systems, CentraleSup´ lec-CNRS-Univ. ∗∗ Paris-Sud, Univ. Paris-Saclay, Gif-sur-Yvette, Laboratory of Signals and Systems, CentraleSup´ e lec-CNRS-Univ. Paris-Sud, Univ. Paris-Saclay, Gif-sur-Yvette, (e-mail:[email protected]) Paris-Sud, Univ. Paris-Saclay, Gif-sur-Yvette, (e-mail:[email protected]) ∗∗∗ Paris-Sud, Univ. Paris-Saclay, Gif-sur-Yvette, (e-mail:[email protected]) Univ. Orl´ e ans, PRISME, France, (e-mail:[email protected]) ∗∗∗ ∗∗∗ Univ. Orl´ eeans, PRISME, France, (e-mail:[email protected]) ∗∗∗ Univ. Orl´ (e-mail:{guillaume.colin, yann.chamaillard}@univ-orleans.fr) eans, ans, PRISME, PRISME, France, France, ∗∗∗ Univ. Orl´ (e-mail:{guillaume.colin, yann.chamaillard}@univ-orleans.fr) Univ. Orl´ e ans, PRISME, France, (e-mail:{guillaume.colin, yann.chamaillard}@univ-orleans.fr) (e-mail:{guillaume.colin, yann.chamaillard}@univ-orleans.fr) (e-mail:{guillaume.colin, yann.chamaillard}@univ-orleans.fr) Abstract: In this paper, a two-layer predictive energy management strategy for hybrid electric Abstract: In this paper, aa two-layer two-layer predictive predictive energy energy management management strategy strategy for for hybrid hybrid electric Abstract: In vehicles without anpaper, external recharge predictive is introduced. The low-level layer exploits data Abstract: In this this paper, a two-layer energy management strategy for telemetry hybrid electric electric vehicles without an external recharge is introduced. The low-level layer exploits telemetry data Abstract: In this paper, a two-layer predictive energy management strategy for hybrid vehicles without an external is introduced. The low-level layer exploits data over a short-term horizon in arecharge model predictive control structure that provides thetelemetry engine electric torque, vehicles without an external recharge is introduced. The low-level layer exploits telemetry data over a short-term horizon in a model predictive control structure that provides the engine torque, vehicles without an external is introduced. low-level layer exploits data over a horizon in model control that provides engine torque, but also the stop-start decision. The predictive upper layer usesThe astructure tuning mechanism withthe a telemetry longer over a short-term short-term horizon in a arecharge model control that provides engine horizon torque, but also also the stop-start stop-start decision. The predictive upper layer layer uses aastructure tuning mechanism mechanism withthe longer horizon over a short-term horizon in a model predictive control structure that provides engine torque, but the decision. The upper uses with aaa longer to calculate the MPC weighting factor that ensures atuning balance between thethe fuel and horizon battery but also the stop-start decision. The upper layer uses a tuning mechanism with longer horizon to calculate calculate the MPC MPC decision. weightingThe factor that ensures balance between with the fuel and horizon battery but also the stop-start upper layer usesprediction aaaatuning mechanism a longer to the weighting factor that ensures balance between the and battery consumption. AnMPC analysis of this upper-level tuning horizon dependence on the drive to calculate the weighting factor that ensures balance between the fuel fuel and battery consumption. An analysis of this upper-level tuning prediction horizon dependence on the drive to calculate the MPC factor thattuning ensures a balance between the fuel and battery consumption. An analysis of this upper-level prediction horizon dependence on the drive cycle characteristics is weighting performed. The robustness with respect to state-of-charge and engine consumption. An analysis of this upper-level tuning prediction horizon dependence on the drive cycle characteristics is performed. The robustness with respect to state-of-charge and engine consumption. An analysis of this by upper-level tuning prediction horizon dependence on theengine drive cycle is The robustness with respect to and torquecharacteristics estimation is also proven a sensitivity analysis. cycle is performed. performed. robustness with respect to state-of-charge state-of-charge and engine torquecharacteristics estimation is is also also proven by by The a sensitivity sensitivity analysis. cycle characteristics is performed. The robustness with respect to state-of-charge and engine torque estimation proven a analysis. torque estimation is also proven by a sensitivity analysis. © 2017, estimation IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. torque is also proven a sensitivity analysis. Keywords: hybrid electric vehicle,byenergy management, predictive control Keywords: hybrid electric vehicle, energy management, predictive control Keywords: hybrid hybrid electric electric vehicle, vehicle, energy energy management, management, predictive predictive control control Keywords: Keywords: hybrid electric vehicle, energy management, predictive control 1. INTRODUCTION is used for feature extraction from accelerometer data, 1. INTRODUCTION INTRODUCTION is used used for for feature feature extraction extraction from from accelerometer accelerometer data, data, 1. is whereas in (Liu et al., 2015) a from metricaccelerometer that characterizes 1. INTRODUCTION is used for feature extraction data, whereas in (Liu et al., 2015) a metric that characterizes 1. INTRODUCTION is usedfluctuations for feature extraction accelerometer data, whereas in (Liu (Liu etisal., al., 2015)using metric thatanalysis. characterizes speed defined Fourier in et 2015) aa from metric that characterizes Fuel consumption optimization is a priority objective in whereas speed fluctuations fluctuations isal., defined using Fourier analysis. in (Liu etis 2015)using a metric thatanalysis. characterizes speed is defined using Fourier analysis. Fuel consumption consumption optimization optimization is is aa priority priority objective objective in in whereas speed fluctuations defined Fourier Fuel the automotive research, whose isdevelopment during the Fuel consumption optimization a priority objective in speed This paper continues the previous work analysis. (Stroe et al., fluctuations is defined using Fourier the automotive automotive research, whose isdevelopment development during the the This paper paper continues the previous previous work (Stroe (Stroe et et al., al., Fuel consumption optimization a priority objective in This the research, whose during last automotive years has witnessed an increased interest in hybrid continues the work the research, whose development during the 2016b), where an MPC based torque split optimization This paper continues previous work et al., last automotive years has has witnessed witnessed an increased interestduring in hybrid hybrid 2016b), where an MPC MPCthe - based based torque split(Stroe optimization the research, whose development the last years an increased interest in This paper continues the previous work (Stroe et al., vehicles. The research work spans several fields related to 2016b), where an torque split optimization last yearsThe hasresearch witnessed anspans increased interest in hybrid includingwhere stop-start mechanism has been It an MPC - based torque splitintroduced. optimization vehicles. work several fields related related to 2016b), includingwhere stop-start mechanism has been been introduced. It last yearsThe has witnessed anspans increased interest incontrol. hybrid vehicles. The research work spans several fields to 2016b), anthe MPC - based torque splitforeseen optimization this topic: topology, dimensioning, modeling and including stop-start mechanism has introduced. It vehicles. research work several fields related to is assumed that vehicle speed can be up to including stop-start mechanism has been introduced. It this topic: topic:The topology, dimensioning, modeling and control. is assumed that the vehicle speed can be foreseen up to vehicles. research work spans several fields related to this topology, dimensioning, modeling and control. stop-start mechanism has been introduced. It The latter especially the energy management prob- including is assumed that the theand vehicle speed can be foreseen up to to this topic: tackles topology, dimensioning, modeling and control. several kilometers this speed prediction will be incorpoassumed that vehicle can be foreseen up The latter latter tackles especially the energy energy management prob- is several kilometers and this speed prediction will be incorpoincorpothis topic: topology, modeling and control. The tackles especially the management probassumed that the vehicle can be foreseen up to lem, latter whichtackles refers especially to dimensioning, the power distribution between the is several kilometers and this prediction will be The the energy management probrated into a two-layer control structure, that work with kilometers and control this prediction incorpolem, latter whichtackles refers especially to the the power power distribution between the several rated into into a two-layer two-layer structure,will thatbe work with The the energy problem, which refers to distribution between the several kilometers this prediction bework incorpoengine and the additional power source.management rated control structure, that work with lem, which refers to the power distribution between the longer into horizons for and thecontrol higher decision will layers. The lowrated aa two-layer structure, that with engine and the additional power source. longer horizons for the higher decision layers. The lowlem, which refers to the power distribution between the engine and the additional power source. rated into a two-layer control structure, that work with longer horizons for the higher decision layers. The lowengine and the additional power source. level controller handles the power distribution, which is longer horizons for the higher decision layers. The lowThere are currently numerous techniques in the literature longer level controller handles the power distribution, which is engine and the additional power source. horizons forcalculation the the higher layers.of The lowlevel controller handles the power distribution, which is There are are currently currently numerous numerous techniques techniques in in the the literature literature level reduced to torque indecision thedistribution, absence gearshift controller handles power which is There for the power distribution problem: dynamic programreduced to torque calculation in the absence of gearshift There are currently numerous techniques in the literature controller handles power which is reduced to torque torque calculation in the thedistribution, absence of ofThis gearshift for the theare power distribution problem: dynamic program- level optimization, and also thethe stop-start command. probto calculation in absence gearshift There currently numerous techniques in the literature for power distribution problem: dynamic programmingthe(off-line solution, it needs the entire drive cycle), reduced optimization, and also also the stop-start stop-start command. This probfor power distribution problem: dynamic programto torque calculation in thecommand. absencewhose ofThis gearshift optimization, and the command. This probmingthe(off-line (off-line solution, it needs needs the entire entire drive cycle), reduced lem is formulated as an MPC optimization, tuning optimization, and also the stop-start probfor power distribution problem: dynamic programming solution, it the drive cycle), rule-based (Goerke et al., 2015),the Equivalent Consumplem is is formulated formulated as an an MPC MPC optimization, whose tuning ming (off-line solution, it needs entire drive cycle), optimization, also command. Thistuning problem as optimization, whose tuning rule-based (Goerke et al., al., 2015),the Equivalent Consumpparameter is and calculated atstop-start the upper level,whose that uses a is formulated as anthe MPC optimization, ming (off-line solution, it needs entire cycle), rule-based (Goerke et 2015), Equivalent Consumption Minimization Strategy (ECMS), with its drive different ap- lem parameter is calculated at the upper level, that uses aa rule-based (Goerke et al., 2015), Equivalent Consumplem is formulated as an MPC optimization, whose tuning parameter is calculated at the upper level, that uses tion Minimization Strategy (ECMS), with its different aplong-term prediction. The main contribution of this paper parameter is calculated at the upper level, that uses a rule-based (Goerke et al., 2015), Equivalent Consumption Minimization Strategy (ECMS), with its different approaches, such as Adaptive-ECMS (Musardo et al., 2005) long-term prediction. prediction. Theatmain main contribution ofthat thisuses paper tion Minimization Strategy (ECMS), with its different ap- parameter is calculated the upper the level, a long-term The contribution of this paper proaches, such as as Adaptive-ECMS Adaptive-ECMS (Musardo et al., al., 2005) 2005) is to present a method to calculate penalty factor prediction. The main contribution of this paper tion Minimization Strategy (ECMS), with its different ap- long-term proaches, such (Musardo et and Telemetric-ECMS (Sciarretta et(Musardo al., 2004). Model preis to to present present a method method to calculate the penalty penalty factor proaches, such as Adaptive-ECMS et al., 2005) long-term prediction. The main contribution of this paper is a to calculate the factor and Telemetric-ECMS (Sciarretta et al., 2004). Model prein to thepresent MPC design as a to sum of an average-based feeda method calculate the penalty factor proaches, such (MPC) as Adaptive-ECMS al., 2005) and Telemetric-ECMS (Sciarretta et(Musardo al., 2004). 2004).etModel Model predictive control has gained in popularity during the is in to thepresent MPC design design as aa to sum of an an average-based average-based feedand Telemetric-ECMS (Sciarretta et al., a method calculate the penaltyhorizon, factor in the MPC as sum of feeddictive control (MPC) (MPC) has has gained in in popularity duringprethe is forward component, calculated over a average-based prediction in the MPC design as a sum of an feedand Telemetric-ECMS (Sciarretta et al., 2004). Model predictive control gained popularity during the last years, it its deterministic form (Cairano et al., 2011), forward component, calculated over a prediction horizon, dictive control (MPC) has gained in popularity during the MPC design calculated as a sum of anaaThe average-based forward component, over prediction horizon, last years, years, it its its deterministic deterministic formin(Cairano (Cairano et during al., 2011), 2011), andthe a SOC feedback corrective term. influence offeedthe forward component, over prediction horizon, dictive has gained popularity the in last it form et al., (Lu years, et control al., it 2013) or stochastic (Ripaccioli et al., 2010), and aa SOC SOC feedback calculated corrective term. term. The influence of the the last its(MPC) deterministic form (Cairano et al., 2011), forward component, calculated over a prediction horizon, and feedback corrective The influence of (Lu et al., 2013) or stochastic (Ripaccioli et al., 2010), prediction horizon on fuel gain is analysed for different and a SOC feedback corrective term. The influence of the last years, it its deterministic form (Cairano et al., 2011), (Lu et al., al.,and 2013) or2014). stochastic (Ripaccioli (Ripaccioli et et al., al., 2010), 2010), prediction horizon on fuel gain is analysed for different (Josevski Abel, (Lu et 2013) or stochastic and a SOC feedback corrective term. The influence of the prediction horizon on fuel gain is analysed for different (Josevski and Abel, 2014). drive cycles. The robustness with torque and horizon on fuel gain is respect analysedto different (Lu et al.,and 2013) or2014). stochastic (Ripaccioli et al., 2010), prediction (Josevski and Abel, 2014). drive cycles. cycles. The robustness robustness with respect tofor torque and (Josevski Abel, horizon on fuelperformed gain is respect analysed for different drive The with respect to torque and Current technologies allow the acquisition of future traffic prediction SOC estimation is equally in order to complete drive cycles. The robustness with to torque and (Josevski and Abel, 2014). Current technologies technologies allow allow the the acquisition acquisition of of future future traffic traffic drive SOC estimation is equally performed in order to complete Current cycles. The with respect to to torque and SOC estimation is robustness equally performed in structure. order to complete data andtechnologies consequently, theirthe exploitation predictive the sensitivity analysis of the proposed Current allow acquisitionwithin of future traffic SOC estimation is equally performed in order complete data and andtechnologies consequently, theirthe exploitation within predictive the sensitivity sensitivity analysis of the the proposed structure. Current allow acquisition of future data consequently, their exploitation within predictive estimationanalysis is equally performed in structure. order to complete the analysis of proposed structure. control strategies, with explicit reconstruction of predictive the traffic speed SOC data and consequently, their exploitation within the sensitivity of the proposed control strategies, with their explicit reconstruction of predictive the speed speed the paper is analysis organized as follows: a powertrain data and consequently, exploitation within control strategies, with explicit reconstruction of the of the proposedfirst, structure. profile or by the use ofexplicit pattern recognition (drive cycle The Thesensitivity paper is is organized organized as follows: follows: first, a powertrain powertrain control strategies, with reconstruction of the speed The paper as first, a profile or by the use of pattern recognition (drive cycle control-oriented model is introduced and next, an MPC paper is organized as follows: and first,next, a powertrain control strategies, withof explicit reconstruction ofthe the future speed profile or by the the use of pattern recognition (drive cycle The profile, or driving style). In (Bender et al., 2014)(drive control-oriented model is introduced an MPC MPC profile by use pattern recognition cycle The paper is organized as follows: first, a powertrain control-oriented model is introduced and next, an profile, or driving style). In pattern (Bender recognition et al., al., 2014) 2014)(drive the future future formulation is presented, for the torque distribution and control-oriented model is introduced and next, an MPC profile by the use of cycle profile, driving style). In (Bender et the target speed reconstructed from the 2014) vehicle formulation is is presented, presented, for the torque torque distribution and profile, drivingis style). In (Bender et al., thecurrent future control-oriented model is introduced and next, an MPC formulation for the distribution and target speed is reconstructed from the vehicle current ICE stop-start, with a focus on the MPC tuning method. formulation is presented, for the torque distribution and profile, driving style). In (Bender et al., 2014) the future target speed is reconstructed from the vehicle current positionspeed and aisdatabase, whereas in (Mayr et al., 2011) a formulation ICE stop-start, with a focus on the MPC tuning method. target reconstructed from the vehicle current is presented, for on thethe torque distribution and stop-start, with focus on the MPC tuning method. method. positionspeed and aaisdatabase, database, whereas in (Mayr (Mayr et al., al., 2011) 2011) a ICE The performance andaarobustness of the proposed strategy stop-start, with focus MPC tuning target reconstructed from the vehicle current position and whereas in et cycle detection based on correlation analysis is al., performed. The performance performance andarobustness robustness of the the proposed strategy position and a database, whereas in (Mayr et 2011) aa ICE ICE stop-start, with focus on the MPC tuning method. The and of proposed strategy cycle detection based on correlation analysis is performed. are evaluated into a model-in-the-loop validation. performance robustness of thevalidation. proposed strategy position andto a database, whereas in (Mayr etis 2011)as a The cycle detection based on transient correlation analysis is al., performed. The ability capture characteristics, such are evaluated evaluated intoand a model-in-the-loop model-in-the-loop cycle detection on correlation analysis performed. performance and robustness of thevalidation. proposed strategy are into validation. The ability ability to based capture transient characteristics, such as as The are evaluated into aa model-in-the-loop cycle detection based on the correlation analysis is performed. The to capture transient characteristics, such abrupt changes, makes frequency analysis a suitable The ability to capture transient characteristics, such as are evaluated into a model-in-the-loop validation. abrupt changes, makes the frequency analysis a suitable The ability capture transient such as abrupt changes, makes the frequency analysis aa analysis suitable approach: into (Wang et al., 2012) acharacteristics, wavelet-based abrupt changes, makes the frequency analysis suitable approach: in (Wang (Wang et al., al., 2012) a wavelet-based wavelet-based analysis abrupt changes, makes the frequency analysis a suitable approach: in et 2012) a analysis approach: in (Wang et al., 2012) a wavelet-based analysis approach: in (Wang et al., 2012) a wavelet-based analysis

Copyright © 2017 IFAC 10473 Copyright © 2017, 2017 IFAC 10473 2405-8963 © IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright 10473 Copyright © © 2017 2017 IFAC IFAC 10473 Peer review under responsibility of International Federation of Automatic Control. Copyright © 2017 IFAC 10473 10.1016/j.ifacol.2017.08.1777

Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Nicoleta Stroe et al. / IFAC PapersOnLine 50-1 (2017) 10058–10064

NOTATIONS • • • • • • • • • • •

ICE - Internal Combustion Engine EM - Electric Machine DCT - Dual-Clutch Transmission Ri - gear ratio engaged on ith shaft (includes neutral definition), i ∈ {1 : odd, 2 : even} Ci - clutch status (0 - open, 1 - closed) Ni = min(Ri , 1) - used to define the case where one of the shafts is decoupled Rf( Ri ) - axle ratio corresponding to ith shaft w rice/em - ratio between the ICE/EM torque at wheel level and the component (ICE/ EM) torque ratem - ratio between the EM and the corresponding shaft where it is connected ctrl ωice - idle speed or 0 rpm, in case of engine stop Rw - wheel radius

2. POWERTRAIN CONTROL-ORIENTED MODEL

Fig. 1. DCT hybrid configuration Vehicle dynamics is expressed using a backward approach, where the reference speed and acceleration are known and from which the required torque can be determined. Hence, the wheel torque demand can be calculated from the velocity (v), environment data, such as slope (α), air density (ρair ) and vehicle parameters, such as the mass (m), frontal area (Af ), aerodynamic drag coefficient (cd ), rolling friction coefficients (cr0 , cr1 ): 1 Tw = ρair Af cd v 2 + (cr1 v + cr0 )mgcos(α) 2 (1)  +mgsin(α) + mv˙ Rw

A wheel level supervisory control is the most appropriate for an HEV, where the EM can be connected to different driveline positions. Shafts inertias and clutch dynamics are neglected and, therefore, a static model for torque and rotational speeds of the components is introduced, as in (2)-(6). The purpose of the model is to define a relation between the components torques and the total torque demand and for the rotational speeds, a dependence of velocity and driveline states (clutches states and gear engaged). The architecture considered here is a dual-clutch transmission hybrid with the EM connected to the even primary shaft, as in Fig. 1. In (Stroe et al., 2016a) it was shown

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Table 1. Hybrid DCT modes as functions of clutches states and N2 C1 0 0 0 0 1 1 1

C2 0 0 1 1 0 0 1

N2 0 1 1 0 0 1 0

Case standstill, sailing electric driving, regenerative braking hybrid or conventional, even gear engaged charge during standstill conventional driving, odd gear engaged hybrid driving take-off, charge during driving

that with a proper parametrization, this configuration can represent all types of hybrid parallel architectures. For a better understanding of the system and of the proposed model, Table 1 summarizes the clutches states with respect to functional modes. The variable N2 is introduced in order to correctly define special cases when one of the shafts is decoupled from the wheel (to charge the battery via the ICE at standstill or during driving, with odd gear engaged). For the present configuration, only the even shaft is concerned, due to EM position. The engine is disconnected from the drive not only for the case when C1 = C2 = 0, but also for the charge at standstill, where C2 = 1, but N2 = 0. Therefore, the ICE speed will be ctrl defined by ωice when C1 + N2 C2 = 0, as expressed in (5). w w Tw = rice Tice + rem Tem (2) w (3) rice = Rf(R1 ) R1 C1 + Rf(R2 ) R2 C2 w = Rf(R1 C1 C2 +R2 ) (R1 C1 C2 + R2 ) ratem (4) rem w v ctrl ωice = rice + (1 − C1 − N2 C2 ) ωice (5) Rw v ctrl w + ratem C2 (1 − C1 ) (1 − N2 ) ωice (6) ωem = rem Rw The battery SOC is the only considered state of the system, for which an internal resistance model has been retained in this paper. Its dynamics is described by the integrator-like relation below, involving its open circuit voltage (OCV ), internal resistance (R), battery capacity (Qmax ).  2 − 4R(SOC) Pb OCV(SOC) − OCV(SOC) ˙ =− (7) SOC 2R(SOC) Qmax π ωem Tem + loss (ωem , Tem ) is the battery where Pb = 30 power.

The engine fuel rate is given as a non linear map with respect to torque and rotational speed, but in view of control design, an analytical expression with an explicit appearance of the control variable, is needed. The vehicle considered for this case-study is equipped with a turbocharged 1.2 L SI engine, whose fuel rate dependence on torque is illustrated in Fig. 2, via a parametrization of curves with respect to ωice . In this paper, a piecewise linear approximation with respect to torque is introduced, as expressed below: m˙ f = αj (ωice )Tice + βj (ωice ), for j = 1 . . . Npart (8) where Npart is the number of torque partitions. 3. MPC- BASED ENERGY MANAGEMENT The focus of this work is the optimization-based decision making for torque distribution between the engine and the electric machine with respect to fuel consumption, for a

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Proceedings of the 20th IFAC World Congress 10060 Nicoleta Stroe et al. / IFAC PapersOnLine 50-1 (2017) 10058–10064 Toulouse, France, July 9-14, 2017

is introduced, resulting into a Linear Time-Varying (LTV) prediction model:

12

xk+1 = xk + Bk uk + Dk

10

where x = SOC, uk = TICE (k), Dk is a residual term due to linearisation. It can be noticed that the model is representing practically an integrator-like dynamics, with Bk and Dk time-varying, dependent on wheel torque demand Tw (k) and EM rotational speed ωEM (k). The variations of open circuit voltage and internal resistance with respect to SOC are neglected during the prediction. With this simplification, the optimization problem introduced before can be formulated as a quadratic programming:

m ˙ f [g/s]

8

ωICE = 6000 rpm 6

ωICE

4

2

1 T U HU + F T U U 2  Aineq U ≤ bineq s.t. Aeq U = beq

ωICE = 1200 rpm 0

20

40

60

80

100

120

140

160

180

200

Fig. 2. Fuel consumption [g/s] with respect to torque; curves for different engine speeds hybrid vehicle without an external recharge. It is assumed that the future vehicle speed profile can be extracted from the navigation data system for a preview distance of several kilometers. 3.1 Optimization criterion The choice of the cost function should reflect the tradeoff between fuel and battery consumption. A local fuelfriendly strategy would be to use the battery as much as possible, but the absence of an external recharge would imply to charge the battery later, via the engine, if the regenerative braking phases are not enough. A cost function defined as a weighted sum of the two power sources is given by PMP (Pontryagin’s Minimum Principle): min Pfk + λk Pek uk (9) ˙ Pfk = HLV m ˙ fk , Pek = OCVk SOC where k is the current step, HLV is the lower heating value of the fuel, uk is the engine torque and λk is a penalty, usually called equivalence factor. The choice of the optimization criterion in the present developments is inspired from the above design, but with the squared values of the powers: u

k+N M P C −1 i=k

(12a)

min

Torque[Nm]

min

(11)

Pf2 (i) + λ2k (Pek (i) − Pemink (i))

2

(12b)

With the definitions from (9) and (8), the expressions of the matrices involved in the QP formulation are given below: ¯2 ¯ k2 + qk2 B (13a) Hk = α k ¯k Ukmax Fk = α (13b) ¯ k β¯k − qk2 B 1 ¯k = diag (Bk+i−1 ), where qk = λk HLV Qmax OCVk , B   αj1 (ωicek ) · · · 0   .. .. ..  . . α¯k =   .  ,  0 · · · αjNmpc −1 ωicek+Nmpc −1

   β¯k = βj1 (ωicek ) · · · βjNmpc −1 ωicek+Nmpc −1 ,

where the index ji denotes the fuel consumption region j (8) for the ith element in the array Uk and Ukmax is an array with the control upper bounds. The constraints are defined with respect to physical limitations of torque and power, but the SOC balance problem needs to be handled separately. For a hybrid without an external recharge, it is usually imposed to have at the end at the drive cycle the same SOC value as in the beginning. In this way, a fair comparison with a conventional vehicle or between different strategies can be done. The solution proposed here is the use of distance-varying limits: 1−

SOCkmin

(10)

where NM P C is the prediction horizon, u is a vector with ICE torques of length NM P C and Pemink is the electrochemical power minimal value. This latter element is used as a displacement term, in order to properly include the sign information of the electrochemical power, that would otherwise be lost if only the squared value were used. 3.2 Problem formulation As mentioned in the first section, the only system dynamics is the battery SOC, whose nonlinear model is defined by (7). In this work, a linearisation at the operating point

= SOC0 − (SOC0 − SOCmin ) e

SOCkmax = SOC0 + (SOCmax − SOC0 ) e

1−

1 dk dT ot

1− 1−

1 dk dT ot

(14)

where SOCmin , SOCmax are the physical lower and upper bound (usually take values of 20% and 90%, respectively), dk is the current distance and dT ot is the drive cycle total distance. The purpose is to force the SOC trajectory to approach the initial value, as the vehicle reaches its destination. This condition implies the knowledge of the total distance, which is not always realistic. An alternative is the use of a reset distance, as depicted in Fig. 3. In simulation, this can be set to standard drive cycles distance, but in practice it can be extracted from the driver’s history data. The constraints are hence expressed as below:

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Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Nicoleta Stroe et al. / IFAC PapersOnLine 50-1 (2017) 10058–10064

100 90

its dependence on the drive cycle. Given the lower and upper bound of the command at each predicted step i, the solution explored in the present study is to express λ as a ratio of the 2 powers variations between these bounds, as expressed below, where k is the optimization step: Pf (uk,i ) − Pf (uk,i ) λk,i = − (17) Pe (uk,i ) − Pe (uk,i )

Total distance known Reset distance at 10 km

SOC[%]

80 70 60 50 40 30 20 0

2

4

6

8

10061

10

Distance[km]

12

14

16

Fig. 3. SOC limits for 2 cases: total distance known and reset distance fixed at 10 km, respectively min max (ωice ) ≤ Tice ≤ Tice (ωice ) Tice

Moreover, the navigation data system can provide information about future traffic conditions over a longer horizon than the one used for MPC. Thus, the proposed solution can use an average-based calculation over this penalty-adaption horizon, in combination with a proportional feedback SOC control: k+N λ −1  1 λk,i + kr (SOCsp − SOCk ) λk = Nλ − Nλstop i=k Nλstop - number of predicted steps of vehicle standstill SOCsp - SOC setpoint (18)

(15a)

min max Tem (ωem ) ≤ Tem ≤ Tem (ωem ) (15b) π min max Pem (ωem ) ≤ ωem Tem ≤ Pem (ωem ) (15c) 30 SOCkmin − k ≤ Xk ≤ SOCkmax + k (15d) where k is a slack variable used to soften the constraints, in order to avoid infeasibility problems that may occur when SOC variation range is too narrow.

where λk,i is given by (17). The expression contains therefore, 2 terms: a feed-forward component (the average in λk,i ) and a feedback part (the proportional SOC control). The purpose of the latter is to adjust the penalty factor with respect to an SOC setpoint: • if the trajectory is below the setpoint, λ increases, thus penalizing more the use of the battery • if the trajectory is greater than the reference, λ will diminish and this will be translated into a greater use of the battery.

3.3 ICE stop-start strategy It is assumed that the drivelines states (gears and clutches) are calculated at the supervisory level and used as inputs by the MPC controller. The ICE can be stopped during standstill and regenerative braking, but also during pure electric traction. The inclusion of stop-start functionality makes the optimization more complex due to the discrete nature of the problem. In order to avoid the introduction of an additional optimization variable, an a-posteriori stop decision based on the sequence of calculated future commands is introduced here. Let tidle be the number of seconds of idling that translate the cost of a restart, ∆topt the MPC sampling time and cton the number of steps after an ICE restart. Then, the condition to stop the engine is given by: thr Uk (1 : Nstop ) ≤ Tice (16a) cton > Nstart (16b) tidle thr where Nstop = ∆t and Tice is an ICE torque threshold opt below which is preferable to stop the engine. The condition (16b) is introduced in order to avoid frequent stops. With this approach, the cost of a restart is implicitly included by the length of the considered subsequence of commands.

The access to a sequence of future commands allows the Non - step restart anticipation, in order to improve speed tracking. If the value of the command on the position 1 + Non exceeds the ICE torque threshold, then a restart command is activated. For the current study, a sampling time of 0.5 s is used and thus, Non is set to 1. 4. TUNING METHOD The penalty factor λ has a tremendous impact on the performance and the main difficulty of tuning arises from

In this case, the setpoint was chosen constant and equal to the initial value. The goal is not to track a certain SOC reference, but to allow the trajectory to freely vary and to avoid overcharge or discharge. The braking phases need to be included in the average calculation, but in this case λk,i can no longer be expressed as a ratio of differences, because these modes are preimposed: the maximum possible energy is recovered and the rest is dissipated in the friction brakes. Therefore, a particular relationship is adopted in the present study: λk,i =

Pfidle regen Pe (k|k

+ i)

,

for Tw (k + i) < 0

(19)

where Pfidle = HLV m ˙ idle and Peregen (k|k + i) is the f predicted electrochemical power obtained by regenerative braking. With this formulation λ will decrease if braking phases are anticipated. Thus, the use of the electric motor is encouraged if is possible to compensate the electric consumption by regenerative braking. 4.1 Choice of the horizon in the tuning procedure The feed-forward component should encapsulate the tradeoff between general tendency and aggressiveness of the drive cycle along a receding window. The longer the horizon Nλ , the smoother the feed-forward component becomes. MPC performs a local optimization and therefore, λ should be able to adapt fast enough with respect to

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1

NEDC Artemis urban FTP−75 Traffic jam

Ratio[−]

0.8 0.6 0.4 0.2 0

20

40 N [s]

60

80

λ

Fig. 5. Ratio of the frequency content for different prediction horizon values and drive cycles and therefore, the prediction horizon choice is drive - cycle dependent. 5. SIMULATION AND RESULTS The strategy was validated in Matlab/Simulink, in cosimulation with a high-fidelity model for the vehicle, designed in AMEsim. The cost of a restart was set to tidle = 2s, MPC sampling time ∆topt = 0.5s and thus, Nstop = 4. Several drive cycles were considered, whose speed profiles are depicted in Fig. 6. Fig. 4. Generic representation of the control structure; in present study, SOCsp was set constant. S&S stands for stop & start drive cycle aggressiveness. In (Liu et al., 2015), a measurement of traffic and driver aggressiveness based on jerk periodograms has been introduced. The periodogram is an estimate of the spectral density and it is given by the squared modulus of the Discrete Fourrier Transform. In this paper, the periodogram of the wheel power will be used to analyse the aggressiveness information incorporated into λ, by using the frequency cumulative content for different prediction horizon values as in the expression below, where p stands for periodogram.  12 fNλ f =0 p(f )df (20) r =  fs 2 p(f )df f =0

where fs is the sampling frequency (here: fs = 1Hz), fNλ = N1λ . This definition implies that for Nλ = 1s, the ratio is 1, that is, all drive cycle variations are included because no averaging is performed. If Nλ increases, the ratio diminishes due to smoothing. This can be observed in Fig. 5, where the evolution of the aggressiveness indicator with respect to the prediction horizon is depicted for several drive cycles. For values superior to 60s, the smoothing is significant for all the scenarios considered. In certain cases, such as ARTEMIS urban and traffic jam, the loss of aggressiveness information occurs at even lower horizons

The influence of the upper layer horizon was analyzed for a MPC control horizon of 5s which is long enough to include the stop-start decision (Stroe et al., 2016b). The consumption sensitivity with respect to Nλ is illustrated in Fig. 7. NEDC shows a decrease in consumption until Nλ = 40s and then, an increase (final SOC is the same for all the cases). For Artemis urban, Nλ = 5s gives the lowest normalized consumption, for a final SOC slightly greater than the one for the other horizons (SOCf = 52.58% for Nλ = 5s vs SOCf = 51.15% for the other values). FTP-75 shows an improvement up to 20s, and then a constant degradation, with a final SOC that slightly decreases starting with Nλ . For the traffic jam, an horizon of 10s provides the lowest consumption value, with a nonmonotonic behavior for the higher horizons. These results can be interpreted through the aggressiveness analysis introduced in the previous section. From Fig. 5 it is possible to extract a limit for the upper layer horizon and its optimal value can be determined by empirically choosing the value of 0.5 for the ratio defined by (20), which would translate the trade-off between average and transient behavior. This gives Nλ = 40s for NEDC, 5s for Artemis urban, 20s for FTP-75 and 10s for traffic jam. The values are therefore around 30s, which is coherent with the current availability of accurate preview data. A comparison with a PMP - based method, as defined in (9), is summarized in Table 2, where for the MPC strategy the Nλ with the best consumption was retained. In PMP case, a constant equivalence factor was determined offline

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NEDC

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100

40

200

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400

600

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2000

Time[s]

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1000 1200 1400 1600 1800

200

400

Time[s]

600

800

Consump. [L/100km]

Consump. [L/100km]

Consump. [L/100km]

Fig. 6. Speed profile for different drive cycles

Consump. [L/100km]

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Artemis urban

Nλ = 10 s

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N = 20 s λ

40 0

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20 0 0

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SOC[%]

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0 SOC[%]

50 0

NEDC

Nλ = 40 s

λ

WLTC

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10063

Nλ = 20 s

N =5s

50 0 0

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0 SOC[%]

Speed[km/h] Speed[km/h]

0 0

Speed[km/h]

Speed[km/h]

Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Nicoleta Stroe et al. / IFAC PapersOnLine 50-1 (2017) 10058–10064

70 60 50 40 0

200

400

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N = 10 s

800 1000 Time[s]

1200

1400

λ

1800

Traffic jam

N = 20 s λ

100

1600

200

300

400 500 Time[s]

600

700

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900

Fig. 8. SOC trajectories for 2 different Nλ ; black curves represent SOC limits 5.1 Robustness analysis

5

NEDC

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20

30

40

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60

10

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40 N [s] 50 λ

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The MPC controller, as shown in Fig. 4, receives at each optimization step the estimated engine torque and the battery SOC from the vehicle high-fidelity model. The former is used in the model linearization at the operating point and the latter represent the current state which interferes in the calculation of the model parameters (OCV and R in (7)) and also in the feedback correction term of the penalty factor. The technical specifications state that the SOC can be estimated with a precision of ±1% of its value, whereas for the torque, the estimation accuracy is of ±5%. For each drive cycle, the 5 scenarios listed below have been considered and the results summarized in Tables 3 and 4 for two different Nλ values. (1) positive offset for Tice , accurate SOC (2) negative offset for Tice , accurate SOC (3) signed offset for Tice , but with a random distribution, accurate SOC (4) random offset of ±1% of its current value for SOC, accurate Tice (5) random offsets on both inputs

Traffic jam 10

20

30

40

50

N [s]

60

70

80

90

λ

Fig. 7. Evolution of the normalized consumption w.r.t. Nλ for different drive - cycles Table 2. Fuel consumption [L/100km] and final SOC[%], PMP and MPC  Strategy Relative  PMP MPC Cycle difference  NEDC Artemis urban FTP-75 Traffic jam

4.5 (70.26%) 5.61 (52.76%) 4.5 (55.74%) 5.55 (50.12%)

4.76 (70.57%) 6.11 (52.58%) 4.82 (55.16%) 6.16 (50.32%)

5.77% 8.9% 7.11% 11%

for each drive cycle while the engine stop was performed for the electric traction phases.

The fuel consumption degradation is less than 2% for the considered scenarios. It can be noticed that the first scenario, with a positive offset for the engine torque, shows a more important increase in consumption, whereas the second (negative offset) may lead to a decrease, as it is the case for Artemis urban. This is due to the impact on the stop decision, which may be favored by the latter. Disturbances on SOC have a stronger impact on trajectories where the constraints are active: Artemis urban, Nλ = 10s and FTP-75, Nλ = 20s, as it is depicted in Fig. 8. For Artemis urban, the lower constraints are activated during a proportionally longer amount of time than for FTP-75, which explains the difference in the consumption degradation. It can be noticed that SOC limitations are sometimes violated, but this is due to the use of slack variables, as in (15d).

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of speed profiles. Here, the wheel power periodogram was introduced in order to define an indicator of the aggressiveness content of the upper layer horizon and thus, providing a tool to determine the horizon value that satisfies the aforementioned requirement.

Table 3. Fuel consumption [L/100km] and final SOC[%], different Nλ , Tice offset 

 Case Baseline 

1

Cycle

20s NEDC 40s 5s A. urban 10s 10s FTP-75 20s 10s T. jam 20s

2

3

4.87

4.875

4.81

4.86

(70.57%)

(70.57%)

(70.57%)

(70.57%)

4.76

4.78

4.75

(70.57%)

(70.57%)

(70.57%)

6.11

6.115

6.113

4.77 (70.57%) 6.11

(52.58%)

(52.58%)

(52.54%)

(52.68%)

6.14

6.15

6.07

6.12

(51.15%)

(51.15%)

(51.16%)

(51.16%)

4.82

4.82

4.82

4.82

(57.07%)

(57.1%)

(57.1%)

(57.06%)

4.82

4.83

4.81

4.83

(55.16%)

(54.91%)

(55%)

(55.04%)

6.16

6.2

6.17

6.16

(50.32%)

(50.33%)

(50.32%)

(50.32%)

6.48

6.58

6.5

6.51

(50.28%)

(50.29%)

(50.28%)

(50.29%)

A sensitivity analysis was also performed, that proved the robustness of the control with respect to SOC and to engine torque estimation. The influence of the driver behavior and of the slope, as well as the introduction of sailing functionality represent topics of a future work. REFERENCES

Table 4. Fuel consumption [L/100km] and final SOC[%], different Nλ , SOC disturbance and combined disturbance (Tice and SOC)   Case Baseline 4 5  Cycle 20s NEDC 40s 5s A. urban 10s 10s FTP-75 20s 10s T. jam 20s

4.87 (70.57%) 4.76 (70.57%) 6.11 (52.58%) 6.14 (51.15%) 4.82 (57.07%) 4.82 (55.16%) 6.16 (50.32%) 6.48 (50.28%)

4.85 (70.33%) 4.76 (70.33%) 6.11 (52.26%) 6.25 (50.62%) 4.81 (56.88%) 4.85 (55.9%) 6.2 (50.52%) 6.52 (50.53%)

4.85 (70.32%) 4.77 (70.32%) 6.11 (52.28%) 6.22 (51.04%) 4.82 (57%) 4.83 (55.88%) 6.21 (50.52%) 6.54 (50.56%)

6. CONCLUSIONS AND PROSPECTS In this paper, a two-layer predictive control structure for the energy management of a hybrid electric vehicle was proposed. The MPC low-level controller handles the torque distribution and the engine ON/OFF decision. The latter was introduced without the use of a discrete optimization variable, but as a model-based a-posteriori decision. A short-term prediction horizon was used for the MPC problem, which is suitable for real-time implementation and also for reducing the impact of inaccuracies of the linearized prediction model. The MPC cost function translates the trade-off between the engine and the battery use and it was expressed as a weighted sum of the squared consumptions of these two elements. The tuning factor dependence on the drive cycle makes its choice a difficult problem and in this paper, a novel approach was proposed. The tuning is handled at an upper layer, using on a longterm traffic prediction (speed and wheel torque), in an average-based framework, which allows the integration of drive cycle characteristics. The preview horizon should provide a trade-off between transient and average behavior, which is not ensured by an unique value for all types

Bender, F.A., Uzuner, H., and Sawodny, O. (2014). An adaptive driver model for driving cycle prediction in the intelligent truck. 19th World Congress IFAC. Cairano, S.D., Liang, W., Kolmanosky, I., Kuang, M., and Phillips, A. (2011). Engine power smoothing energy management strategy for a series hybrid electric vehicle. American Control Conf. Goerke, D., Bargende, M., Keller, U., Ruzicka, N., and Schmiedler, S. (2015). Optimal control based calibration of rule-based energy management for parallel hybrid electric vehicles. SAE Tech. Paper, 2015-01-1220. Josevski, M. and Abel, D. (2014). Energy management of a parallel hybrid electric vehicles based on stochastic model predictive control. 19th World Congress, IFAC. Liu, Z., Ivanco, A., and Filipi, Z. (2015). Quantification of drive cycles rapid speed fluctuations using Fourier analysis. SAE International, doi: 10.4271/2015-01-1213. Lu, Z., Song, J., Yuan, H., and Shen, L. (2013). MPC based torque distribution strategy for energy management of power-split hybrid electric vehicles. Proc. 32nd Chinese Control Conf. Mayr, C.H., Fleck, A., and Jakubek, S. (2011). Hybrid powertrain control using optimization and cycle based predictive control algorithms. IEEE International Conference on Control and Automation. Musardo, C., Rizzoni, G., Guezennec, Y., and Staccia, B. (2005). A-ECMS: an adaptive algorithm for hybrid electric vehicle energy management. European Journal of Control. Ripaccioli, G., Bernardini, D., Cairano, S., Bemporad, A., and Kolmanovsky, I. (2010). A stochastic MPC approach for series hybrid electric vehicle power management. American Control Conf. Sciarretta, A., Guzzella, L., and Back, M. (2004). A realtime optimal control strategy for parallel hybrid vehicles with on-board estimation of the control parameters. Proc. IFAC Symp. Adv. Automotive Control. Stroe, N., Colin, G., Ben-Cherif, K., Olaru, S., and Chamaillard, Y. (2016a). Towards a generic controloriented model for HEV predictive energy management. 8th IFAC Int. Symp. Advances Automotive Control. Stroe, N., Olaru, S., Colin, G., Ben-Cherif, K., and Chamaillard, Y. (2016b). Time-varying MPC-based energy management for hev including engine stop & start. 20th International Conference on System Theory, Control and Computing Joint Conference SINTES 20, SACCS 16, SIMSIS 20. Wang, S., Kodagoda, S., and Khushaba, R. (2012). Towards speed-independent road-type classification. 12th International Conference on Control, Automation, Robotics & Vision.

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