A regenerative braking control strategy for electric vehicle with four in-wheel motors

Transcription

1 A regeneraive braking conrol sraegy for elecric vehicle wih four in-wheel moors Wei Xu 2, Haiyan Zhao 1,2, Bingao Ren 2, Hong Chen* 1,2 1. Sae Key Laboraory of Auomoive Simulaion and Conrol, Changchun, 1325, P. R. China 2. Jilin Universiy Deparmen of Conrol Science and Engineering,Changchun, 1325, P. R. China Absrac: Regeneraive braking conrol echnology of elecric vehicle plays a vial role in auomoive energy-saving and environmenal proecion. Acually, here are wo imporan aspecs included in regeneraive braking conrol. Firs and foremos is o mainain he vehicle safey during he braking process, and secondly is o maximize he energy recovery and minimize he energy consumpion as far as possible. This paper proposes a regeneraive braking conrol sraegy o mee he above wo aspecs. In his research, he elecric vehicle is assumed o keep sraigh line driving wih a driver. Firs, according o he desired braking orques of he driver during braking process, he brake orque on fron and rear axle respecively are allocaed based on he ire load raio, which makes sure ha maximizing he use of ire adhesion during deceleraion. Second, in order o deal wih muli-objecions and consrains for maximizing he energy recovery and minimizing he energy consumpion, an model predicive conroller is designed o disribue he brake orque beween he hydraulic brake mode and he elecric moor brake mode. In he end, he effeciveness of he proposed sraegy is verified hrough he simulaions of he elecric vehicle model wih four individually driven in-wheel moors based on Malab/Simulink and AMESim sofware. Key Words: elecric vehicle, regeneraive braking, model predicive conrol, opimal conrol 1 Inroducion In order o improve he energy efficiency, energy conservaion and ecological environmen, he research and developmen of elecric vehicles have become a big concern of he public in recen years. Pure elecric vehicle wih four independen drive wheels is especially invesigaed exensively, which hanks o he four wheels can be conrolled no only independenly, bu precisely. Because he orque of he four in-wheel elecric moor can be measured and conrolled accuraely 1. Due o he limiaion of baery and moor echnology, he high coss and shor driving disance seriously hampered he developmen of elecric vehicle 2. However, regeneraive braking sysem could conver he kineic energy and poenial energy of vehicle o elecrical energy sored in energy sorage device for he nex driving. Therefore, regeneraive braking has become he key echnology of elecric vehicles by reducing energy consumpion and exending driving disance in he presen research. The braking mode can be divided ino fully hydraulic braking sysem, fully elecric braking sysem and hybrid braking sysem. The radiional fricion braking sysem, i.e. fully hydraulic braking sysem makes he vehicle deceleraes or sops wih fricion plaes by convering he kineic energy of vehicle o hermal energy dissipaed. This braking mode has no a all abiliy of implemening he energy recovery. Fully elecric braking sysem can recover energy during he enire braking process 3. I indeed bring abou a very fas and accurae brake orque conrol sysem wih only moors as he acuaors for he braking process, bu wha shorcoming of his braking mode is ha he brake orque by elecric moors is limied han he radiional hydraulic braking This work was suppored by he 973 Program (No.212CB82122), he Naional Naural Science Foundaion of China (No , No , No.U156427). mode, so ha would cause a resul of insufficien braking force while high srengh braking force is required. In addiion, fully elecric braking mode demands a higher-level energy sorage sysem. The las one is he hybrid braking sysem, which implemens deceleraion or braking process by boh hydraulic braking mode and elecric moors braking mode. I well compensaes for he disadvanages of he previous radiional fricion braking sysem and fully elecric braking sysem. Therefore, hybrid braking mechanism is employed in his research. The configuraion diagram of hybrid braking sysem is shown in Fig. 1. Wheel 1 Wheel 3 Inverer Inverer Speed sensor Vehicle conrol uni Moor SOC Brake pedal Baery Inverer Inverer Wheel 2 Wheel 4 Fig. 1: Hybrid braking sysem Wheel brake cylinder Considering he hybrid braking mode, he key opic of his approach is how o disribue he hydraulic brake orque and he elecric moor brake orque under he premise of baking safey. Many scholars have done some research on his issue. Srais Kanarachos and Mohsen Alirezaei proposed an allocaion conroller, which maximizes he regeneraive braking energy hrough he sae-dependen Riccai equaion conrol echnique and vehicle sae esimaion 4, where ire sauraion and moor consrains are considered. The allocaion of braking force of a regeneraive braking sysem is devel-

2 oped based on fuzzy logic conrol mehod in 5. And a nonlinear model predicive conroller for regeneraive braking sysem is presened in lieraure 6, he conroller improves he energy recovery by disribuing he fron and rear brake orque respecively. Bu he shorcoming is ha i did no allocae he brake orque beween he elecric moor braking mode and he hydraulic braking mode, which limiing he efficiency of energy recovery. In his paper, a sudy on he regeneraive braking disribue issue using model predicive conrol mehod for a elecric vehicle wih four in-wheel moor is presened. The cos funcion considered in his research include hree aspecs. Firs is o racking he driver s expecaion. Second is he energy change of elecric moors, he copper loss is especially considered in his research. The las is he energy consumpion of hydraulic braking mode. Model predicive conrol mehod can efficienly deal wih he muli-consrains online opimizaion problems included in he regeneraive braking conrol sysem. Compared wih general opimal conrol mehod, he model predicive conrol mehod employs finie horizon scrolling opimizaion sraegy, no a global opimizaion objecive. A each sample ime, he model predicive conrol migh solve he opimizaion problem o obain he conrol vecors 7, 8. In he end, he simulaion verificaion of he presened regeneraive braking sraegy is carried ou based on Malab/Simulink and AMESim sofware. The remaining pars of his aricle is organized as follows. The regeneraive braking conrol sysem model is inroduced in he second secion. The hird secion presens he allocaion scheme of brake orque for fron and rear wheels o obain maximum ire adhesion force, and he disribuion sraegy of hydraulic brake orque and he elecric moor brake orque o ensure energy opimizaion. Simulaion resuls and analyzes of he presened regeneraive braking conroller are given in he forh secion, and he conclusions are proposed in he fifh secion. 2 Regeneraive Braking Conrol Sysem Model In his secion a brief descripion of he regeneraive braking conrol sysem model is inroduced. I includes four main secions, vehicle dynamics model, ire model, moor and baery model. 2.1 Vehicle Dynamics Model As laeral performance is negleced in his sudy, considering he vehicle dynamics model adoped here has five degrees of freedom for longiudinal moion and he roaional movemen of he four wheels. A single wheel braking model is shown in Fig. 2. Assuming ha he forces on he lef and he righ ires are he same, hen according o Newons second law 9, he equaions of vehicle dynamic behavior in longiudinal and he roaional direcions can be expressed as M v F xf F xr f air f roll, (1) J ω wi R e F xi T bi, i f, r, (2) where M and v represen he vehicle mass and he longiudinal velociy, F xf, F xr are he longiudinal ire-road fricion force of he fron and rear wheels. f air and f roll are respecively he air resisance and he rolling resisance of he R e ω T b F z F x Fig. 2: Single wheel braking model elecric vehicle which are concerned as zero in his paper. J is he wheel roaion ineria, ω wi are he fron and rear wheel longiudinal roaional speed in radians per second, R e is he effecive rolling radius in meers of he ire, and T bi are he fron and rear brake orque of he wheels. The ire-road fricion force has a relaionship wih he normal force F zi suppored by he wheel, which is described wih he fricion coefficien µ as given in equaion (3). Whereas he fricion coefficien µ is he funcion of he slip raio κ. 2.2 Tire Model F xi µ i (κ)f zi. (3) As he suppor and ransfer uni beween he road and vehicle, he ire characerisics have a direc impac on vehicle sae. The Magic Formula model developed by Pacejka 1, which conains muli-parameers and exacly describes he ire characerisics, is widely used in he lieraures 11. In Magic Formula model, he longiudinal ire fore is expressed as a nonlinear funcion of he normal force F zi and he slip raio κ i, which is shown in he following equaion, F xi 2D x sin{c x arcanb x κ i E x (B x κ i arcan(b x κ i ))}, where B x, C x, D x, E x respecively represen he siffness, shape, peak and curvaure facor, he value of hem can be calculaed hrough model parameers. The longiudinal slip raio was inroduced as an inpu variable insead of he braking or driving force, which denoes he speed difference beween he wheel and he vehicle. The relaionship beween hem is shown in equaion (5). v (4) κ i ω wir e v, (5) v The normal force F zi can calculaed from he deceleraion a x, which is shown in equaions (6) and (7), F zf M(l rg ha x ) l f + l r, (6) F zr M(l f g + ha x ) l f + l r, (7) where g is he acceleraion of graviy, h is he disance of he cener of vehicle mass o ground, l f and l r are he he longiudinal disance from cener of graviy o fron and rear axis.

3 2.3 Moor and Baery Model We assume ha each in-wheel moor has a orque conroller. As he elecric machine is reversible, i works eiher as a moor or as a generaor. The abiliy of energy recovery during braking process is associaed wih he maximum moor brake orque of he moor under he curren roary velociy. In his research, he maximum moor roary velociy can achieve 9 rpm, he maximum brake orque is 118 Nm, and he gear raio g is 5. Anoher key elemen affecs he abiliy of energy recovery is he moor-o-baery efficiency η 6, which can be described by η U c I c T mf ω mf + T mr ω mr, (8) where U c and I c represen he baery charging volage and curren during he regeneraive braking process, and he charging power of he baery P c can be described in equaion (9). T mf and T mr are respecively he absolue value of he moor brake orque, ω mf and ω mr are he elecric moor angular velociy of fron and rear wheel, which can described in equaion (1). P c U c I c, (9) ω mi g ω wi, (1) According o DC moor performance, he relaion beween moor curren I a and orque T m can be described as I a T m C T φ αt m, (11) where C T is he moor orque consan, and φ is he moor pole magneic flux, which is assumed a consan in his research. Then he energy consumpion of he moor resisance R, i.e. copper loss can be described as follows. P loss α 2 RT 2 m. (12) 3 Regeneraive Braking Conroller Design This secion propose a brake orque allocaion conroller for regeneraive braking sysem of elecric vehicle wih four in-wheel moors. The regeneraive braking sysem include several modules, brake orque demand calculaion module, brake orque disribuion module, brake orque racking module, and baery managemen uni. The srucure of regeneraive braking conrol sysem is shown in Fig. 3. In his aricle, we focus on he research of brake orque disribuion module. This module mainly consiss of wo pars work, one aspec is o allocae he brake orque on fron and rear axis, and he oher is disribuing he brake orque beween hydraulic braking mode and elecric braking mode. Noe ha he brake orque demand calculaion and racking module, and baery managemen uni are assumed useful and beneficial, we will conduc research on hese issues in he fuure. 3.1 Braking Torque Allocaion of Fron and Rear Wheels Safey is he premise of energy recovery of he whole braking process. Experience has shown ha, vehicle would be unsable if rear wheel locks before fron wheel. A shock roaion or ail flick migh appear while vehicle is driven in high speed on low fricion coefficien road. In order o ensure vehicle in a safe sae, a large adhesion beween ire and road is expeced. As he muaive ire load raio of fron and rear axis have he saple impac on ire-road adhesion, we consider allocaing he brake orque based on he muaive ire load raio of fron and rear axis. According o he previously menioned ire model, we can easily ge he muaive ire load raio of fron and rear axis based on normal force equaions. F zf F zr l rg ha x l f g + ha x. (13) Therefore, he brake orque coefficien of fron and rear axis K can be described as K F zf F zr T mf T mr T hf T hr. (14) 3.2 Torque Allocaion of Hydraulic Brake and Elecric Brake Based on MPC In his secion, a model predicive conroller is designed for orque allocaion of hydraulic brake and elecric brake. Firs, he conroller design model is given based on vehicle dynamics equaions. Then he cos funcion is esablished for he purpose of braking safey and energy Opimizaion, nex he conrol consrains are inroduced. Finally, he approach for solving he cos funcion is presened. According o he curren measuremen informaion obained, model predicive conrol mehod solve he finie horizon open loop opimizaion problems online a each sampling ime, and he firs elemen of he obained conrol vecors from opimal soluion would be applied o he elecric vehicle model. On he basis of he new measuremens, his procedure is repeaed a nex sampling ime in opimizaion process 12, 13. A. Conroller design model According o he vehicle dynamics model, he sae equaion for hydraulic and elecric braking disribuion can be esablished. The sae and conrol variables are defined as follows, X U x1 x 2 u1 u 2 ωmf ω mr, Tm T h. Then based on equaion (2), (3), (1), he sae equaions can be described as follows, ẋ 1 g 2J µ f F zf R e K 1 + K (g u 1 + u 2 ), (15a) ẋ 2 g 2J µ rf zr R e K (g u 1 + u 2 ). (15b) Noe ha, brake orque T m and T h are boh defined posiive. K is he raio of fron wheel brake orque o rear wheel brake orque, which is defined in he above secion. B. Cos funcion

4 brake pedal posiion desired brake orque calculaion T ref MPC conroller Thf, Thr Tmf, Tmr hydraulic unie moor conroller brake wheel cylinder moors vehicle F, va, zi x ω SOC baery uni Fig. 3: Srucure of regeneraive braking conrol sysem Due o he goal ha recovering as much energy as possible by disribuing he brake orque beween hydraulic and elecric brake, several cos funcion erms are need o be esablished. Acually, he braking mode swiching is deermined by he characerisics and consrains of he elecric moor. Firs, in order o meeing he demand of oal required brake orque and maximizing energy recovery, he elecric moor braking mode is implemened as far as possible. If moors have achieved he maximum orque corresponding he curren moor speed, hen hydraulic braking mode compensae he remaining par of oal required braking demand. Secondly, as he vehicle velociy decreases, energy recovery power of elecric moors would be lower han is inernal copper loss power, hen he moors can no produce regeneraive curren. Therefor, he elecric moor braking mode is compleely convered ino hydraulic braking mode while he moor speed achieve he cerain value. There are hree cos funcion erms considered here, he unified objecive of hem are o be minimum in he curren predicive horizon. Firs, he sum of moor brake orque and hydraulic brake orque is demanded o rack he desired oal brake orque T ref, which is given from he diver o ensure he safey. We assumed ha he required brake orque is calculaed in advance and precisely. The form of his cos erm J 1 is described as equaion (16), in which e is he brake orque error. The objecive of his erm is o make he sum of he oal brake orque error square from curren ime o + pt s as small as possible, p represens he predicive horizon and T s represens he sampling ime. J 1 e 2 d (g T m + T h T ref ) 2 d. (16) Secondly, for he purpose of energy opimizaion, we should maximizing he energy recovery and reducing he energy consumpion as far as possible. Then based on he moor and baery model equaions (8), (11), (12), as given in he second secion, he second cos funcion J 2 is defined as equaion (17), which represens he sum of charging power P c. I is equal o he difference of copper loss power P loss and energy recovery power P m. Acually, wha his cos funcion implies is he energy condiion of elecric moor braking mode. The ideal work mode swiching of hybrid braking mode during braking process is ha, if he energy recovery power is lager han he copper loss power, hen implemen he moor braking mode. Conversely, implemen he hydraulic braking mode. J 2 P c d (P loss P m )d α 2 RT 2 m η( Kω mf T m K ω mrt m K + 1 )d. (17) Furhermore, in order o achieve he aims of saving energy and proecing he environmen, he less energy consumpion from hydraulic braking mode, he beer. As a resul, he hird cos funcion J 3 is defined in equaion (18), in which P h represens he hydraulic braking power. This cos funcion represens he sum of hydraulic braking power, i implies he energy consumpion of hydraulic braking mode a four ires. J 3 P h d Kω mf T h g (K + 1) + ω mrt h g (K + 1) d. (18) Due o he conrol requiremens of vehicle safey and maximizing energy recovery, he hree cos funcions for he overall performance are demanded coordinae. So, according o he previously menioned cos funcions, he inegral cos funcion is defined as follows, min Ju( ) pj 1 + qj 2 + sj 3 q(g u 1 + u 2 T ref ) 2 + p(α 2 Ru 2 1 ηu 1(Kx 1 + x 2 ) ) K su 2(Kx 1 + x 2 u 2 ) d, g (K + 1) (19) where q, p, s represen he weighing coefficiens ha deermine he significance of each cos erms.

5 C. Consrains Due o he limiaion of he in-wheel moors, he maximum absolue value of he brake orque for each wheel T b,max is 118Nm, which can be described as follows. T mi 2T b,max. (2) D. Model predicive conrol law Due o he difficuly o ge an analyical expression for he opimizaion problem, numerical soluion approaches are applied for solving opimizaion issue online. In his research, fmincon funcion in Malab opimizaion ool box is used o solve he above cos funcion. 4 Simulaions and Analysis In his secion, he above proposed regeneraive braking conrol sraegy is verified hrough he combined simulaion on a elecric vehicle model wih four in-wheel moors based on Malab/Simulink and AMESim sofware. The elecric vehicle model parameers are lised in Table 1. Table 1: Main parameers of elecric vehicle Definiion Symbol Value Vehicle mass M 15kg Heigh of vehicle c.g. h.474m Axle disance d 1.45m Disance from c.g. o fron axle l f 1.2m Disance from c.g. o rear axle l r 1.2m Effecive radius of he ire R e.29m Maximum orque of moor T m,max 118Nm Maximum power of moor P m,max 26W Reducer raio g 5 Flux of moor φ.8wb In order o illusrae he efficiency of he presened regeneraive braking conrol sraegy, he off-line simulaions based on Malab/Simulink and AMESim sofware are conduced in NEDC (New European Driving Cycle). In his research, a deailed elecric vehicle model for he simulaions is esablished in AMESim sofware. I mainly includes vehicle dynamics module, suspension sysem module, Magic Formula ire module, in-wheel moors module, a high power dynamic baery pack module, and a diver module, which provides he desired driving and brake orque. he mechanical seering sysem module,ec. The simulaion ime in his driving cycle is 12 s, and he sampling ime T s is se o.1 s, boh of he conrol horizon and predicive horizon of he model predicive conrol mehod for allocaion of hybrid braking mode is se o 3. Resuls of he simulaion are shown as follows. Vehicle speed racking curve is shown in Fig. 4. I can be easily seen from he simulaion resuls ha, he acual vehicle speed can well rack he conrolled vehicle speed, and he average error beween he wo is.3 m/s. This indicaes ha he proposed regeneraive braking conroller can ensure vehicle in a sable sae corresponding o he driver expecaion, no only he driving performance, as well as he braking performance. Fig. 5 and Fig. 6 are respecively represens he brake orque on a single fron and rear wheel of elecric and hydraulic braking mode. Torque disribuion during 37 s o Speed (m/s) Speed (m/s) Vehicle speed conroled speed acual speed Fig. 4: Vehicle speed racking graph Single wheel elecric brake orque fron wheel orque rear wheel orque Fig. 5: Single wheel elecric brake orque graph Single wheel hydraulic brake orque fron wheel orque rear wheel orque Fig. 6: Single wheel hydraulic brake orque graph 1 Vehicle speed conroled speed acual speed Single wheel elecric brake orque fron wheel orque 1 rear wheel orque Single wheel hydraulic brake orque 1 fron wheel orque rear wheel orque Fig. 7: Torque disribuion during braking period 385 s is given in Fig. 7. Noe ha he brake orque of lef and righ wheels in his research are he same. i can be seen from hese simulaion resuls ha, elecric moor braking plays a major role in each braking process. Hydraulic braking mode works only when he vehicle speed below a cerain value,

6 which in his simulaion is abou 1 m/s. Energy (J) Power 8 x 16 Energy recovery and consumpion energy recovery energy consumpion Fig. 8: Energy recovery and consumpion graph Energy recovery power Fig. 9: Energy recovery power graph The energy consumpion and recovery sae are simulaneously represened in Fig. 8. I can be seen ha energy consumed during he driving process and hydraulic braking process, and recovered during elecric moor braking process. The oal energy consumpion during his driving cycle is abou J, and he oal energy recovery is abou J. In his paper, he energy recovery efficiency is defined as he raio beween energy recovery and energy consumpion, ζ Energy recover Energy consumpion, (21) and he energy recovery efficiency rend is shown in Fig. 9, i can be seen ha he energy recovery efficiency changes wih vehicle speed. The oal energy recovery efficiency a he end is abou 17.2%. In summary, he simulaion resuls indicae ha he regeneraive braking conrol sraegy proposed can mee he driver s expecaion as well as recovering energy as far as possible. 5 Conclusion In his research, a regeneraive braking conrol sysem of elecric vehicle wih four in-wheel moors for energy conservaion and environmenal proecion is proposed. The research is developed from wo aspecs. Firs, in order o ensure he adhesion beween ire and road during braking process, a sraegy allocaing braking orques on fron and rear axis respecively is proposed based on fron and rear muaive ire load raio. Second, for he purpose of maximizing he energy recovery, a conroller is designed based on model predicive conrol mehod o disribue he braking orques beween he hydraulic braking mode and he elecric moor braking mode. In he end, he simulaion resuls of he elecric vehicle model wih four individually driven in-wheel moors based on Malab/Simulink and AMESim sofware illusrae ha he presened regeneraive braking conrol approach has a good effeciveness on boh racking driver s expecaion and energy recovery. The nex work is o design an inegraed conroller which akes he safey consrain of ire slip raio ino accoun. References 1 K. Maeda, H. Fujimoo, and Y. Hori, Four-wheel drivingforce disribuion mehod for insananeous or spli slippery roads for elecric vehicle, Auomaika-Journal for Conrol, Measuremen, Elecronics, Compuing and Communicaions, vol. 54, no. 1, p. 13C113, B. Wang, J. Xu, and B. Cao, A novel mulimode hybrid energy sorage sysem and is energy managemen sraegy for elecric vehicles, Journal of Power Sources, vol. 281, pp , G. Xu, K. Xu, C. Zheng, X. Zhang, and T. Zahid, Fully elecrified regeneraive braking conrol for deep energy recovery and safey mainaining of elecric vehicles, IEEE Transacions on Vehicular Technology, pp. 1 13, S. Kanarachos, M. Alirezaei, S. Jansen, and J. P. Maurice, Conrol allocaion for regeneraive braking of elecric vehicles wih an elecric moor a he fron axle using he saedependen riccai equaion conrol echnique, Journal of Auomobile Engineering, vol. 228, no. 2, pp , X. Nian, F. Peng, and H. Zhang, Regeneraive braking sysem of elecric vehicle driven by brushless DC moor, IEEE Transacions on Indusrial Elecronics, vol. 61, no. 1, pp , X. Huang and J. Wang, Model predicive regeneraive braking conrol for lighweigh elecric vehicles wih in-wheel moors, Journal of Auomobile Engineering, vol. 226, no. 9, pp , H. Chen, Model Predicive Conrol, 1s ed., ser. Sysem and Conrol Series. Beijing, China: Science Press, B. Ren, H. Chen, H. Zhao, and L. Yuan, MPC-based yaw sabiliy conrol in in-wheel-moored ev via acive fron seering and moor orque disribuion, Mecharonics, 215(online). 9 R. de Casro, R. E. Araujo, and D. Freias, Wheel slip conrol of evs based on sliding mode echnique wih condiional inegraors, IEEE Transacions on Indusrial Elecronics, vol. 6, no. 8, pp , H. B. Pacejka, Tyre and Vehicle Dynamics, second ediion ed. London, UK: Elsevier, W. Liu, H. He, and J. Peng, Driving conrol research for longiudinal dynamics of elecric vehicles wih independenly driven fron and rear wheels, Mahemaical Problems in Engineering, H. Zhao, B. Ren, H. Chen, and W. Deng, Model predicive conrol allocaion for sabiliy improvemen of four-wheel drive elecric vehicles in criical driving condiion, Conrol Theory and Applicaions, IET, vol. 9, no. 18, pp , V. S. L. Efsahios, S. Efsahios, Rear wheel orque vecoring model predicive conrol wih velociy regulaion for elecric vehicles, Vehicle Sysem Dynamics: Inernaional Journal of Vehicle Mechanics and Mobiliy, vol. 53, no. 11, pp , 215.