Research on Hierarchical Control Strategy of nonlinear Hydraulic Regenerative Braking System of Electric Vehicle*

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1 Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, 27 Research on Hierarchical Control Strategy o nonlinear Hydraulic Regenerative Braking System o Electric Vehicle* Ning Li,2, Qiucheng Wang, Xiaobin Ning,* School o Mechanical Engineering, Zhejiang University o Technology, Hangzhou 34, Zhejiang, China 2 School o Mechanical Engineering, Zhijiang College o Zhejiang University o Technology, Shaoxing 323, Zhejiang, China *Corresponding author(xiaobin Ning, nxb@zjut.edu.cn) Abstract In order to study the inluence o nonlinear deormation o suspension about electric vehicles on eiciency o braking energy regeneration, a simulation or electric vehicle s hydraulic regenerative braking system is established with nonlinear deormation o suspension, and validates it via bench test. The hierarchical control strategy is proposed to control the established nonlinear hydraulic regenerative system o electric vehicle. Wherein, the upper control strategy distributes the braking orce o ront and rear axles o hydraulic regenerative braking system o electric vehicle in braking according to ideal distribution principle o break orce, and distributes the driving torque o hydraulic regenerative braking system in driving according to acceleration signal. The lower control adopts the strategy o uzzy control to distribute the hydraulic regenerative braking orce and mechanical braking orce o ront axis according to hydraulic accumulator pressure, vehicle speed and severity o braking. Lastly, the linear and nonlinear hydraulic regenerative systems o electric vehicle adopting hierarchical control strategy are simulatively compared in UDDS condition to ind that the energy regeneration eiciency o nonlinear hydraulic regenerative braking system o electric vehicle is 7.25% higher than the linear system. Key words: Hydraulic Regenerative Braking, Energy Recovery, Nonlinear System, Hierarchical Control. INTRODUCTION Future development trend o automobile is pure electric vehicle without emission o o gas or noise(hedegaard and Ravn, 22; Bayar and McGee, 977). Currently in research on electric vehicles, some scholars proposed combined use o hydraulic regenerative braking system(hrbs) and lithium battery to drive and brake electric vehicle, which means that the braking energy o electric vehicle is regenerated via HRBS in braking and the energy is released by HRBS and lithium battery simultaneously to drive vehicles in driving, to avoid heavy load discharge o lithium battery to maximize the service lie o lithium battery(zhou and Ning, 23; Xu and Su, 27; Shi and Lv, 26; Guo and Ning, 24). In research on adoption o HRBS in electric vehicle, Jorge, L. adopted HRBS in heavy electric vehicle or energy regeneration and researched the energy regeneration eiciency o system(jorge and Jose, 26). Based on motor and HRBS, R.Ramakrishnan designed control strategy o cooperative working o motor/hydraulic system, and optimized each parameter o hydraulic regenerative system using multiobjective optimization method (Ramakrishnan and Hiremath, 24 ). Based on simulation o electric vehicle and HRBS, Li, Y. researched distribution o braking orce o ront and rear axles when the electric vehicle's composite system o motor/hydraulic system is regenerating braking energy(li and Zhang, 25). Fang, G. H. designed the scheme o HRBS applied to 4WD electric vehicle, and veriied it via simulation (Fang and Liang, 27). The above scholars all took the study on HRBS based on linear vehicle without considering the inluence o nonlinear deormation o suspension system on regeneration o braking energy, While when the real vehicle is braking, the nonlinear deormation o suspension inluences the distribution o braking orce and energy regeneration eiciency, leading to deviation o analytic result rom actuality. The paper researches the principle o work between electric vehicle and HRBS, considers the inluence o nonlinear deormation o suspension on regeneration eiciency o braking energy in braking, and builds a o nonlinear electric vehicle's HRBS in simulink. The hierarchical control strategy is proposed to control the current nonlinear regenerative braking system, i.e. The upper control distributes the braking orce o ront and rear axles o electric vehicle's system in braking according to ideal distribution principle o break orce, and distributes the driving moment o HRBS in driving according to acceleration signal. The lower control adopts uzzy control strategy to distribute hydraulic regenerative braking orce and mechanical braking orce according to accumulator pressure, vehicle speed and severity o braking. Lastly, the energy regeneration eiciency o established nonlinear and linear electric vehicle's hydraulic regeneration system is compared by simulating UDDS cyclic condition. 2. THE ESTABLISHMENT OF SIMULATION MODEL ABOUT HRBS FOR ELECTRIC VEHICLE 93

2 Hydraulic pump/motor Hydraulic accumulator Battery Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, The working principles o HRBS or electric vehicles In this paper, the HRBS and motor adopts the parallel structure (Li and Ning, 27), which is composed o a hydraulic pump/motor, hydraulic accumulator and tank, realizes the recycling o braking energy o the ront wheel when braking, and drives the vehicle by releasing stored energy when starting and accelerating, the parallel HRBS or electric vehicles as shown in Fig.. Rear wheel Electric motor Front wheel rear axle Coupler Transmission Front axle Tank Figure.The structural diagram o HRBS or electric vehicles The working principle as ollows: when vehicle brake, wheel drives hydraulic pump/motor rotation, the oil o the tank is transmitted to the high pressure accumulator, at the moment, the hydraulic pump/motor works under the condition o the pump, the kinetic energy o the vehicle is recovered and stored in a high pressure accumulator in the orm o hydraulic energy. When the wheels are in the driving mode, the electric motor and the hydraulic motor can independently provide power to the vehicle and also can work together. At the moment, stored in the high pressure accumulator oil is released via the hydraulic pump/motor to tank, the hydraulic pump/motor works under the condition o the motor and drives the wheel to rotate, and realizes accelerating and driving o the wheels Hydraulic pump/motor mathematical During the process o vehicle braking/driving, the pump/motor torque is pq Tp 6 2 Where, T p is the hydraulic pump/motor torque while braking or driving the vehicle, N m; p is the pressure at the hydraulic pump/motor outlet, MPa; η m is the mechanical eiciency o the hydraulic pump/motor; and q is the hydraulic pump/motor displacement, ml/r. The hydraulic pump/motor torque is transmitted to the wheels through a torque coupler, vehicle-bridge dierential and reduction gears. Ultimately, the speed and torque o the wheels are T T i i (2) reb np nw ii (3) Where, T reb is the wheel torque supplied by the hydraulic pump/motor, N m; i is the transmission ratio o the torque coupler;i is the transmission ratio o the vehicle-bridge dierential; n p is the hydraulic pump/motor speed, r/min; and n w is the wheel speed, r/min Hydraulic accumulator mathematical According to Boyle s law, the relationship between the hydraulic accumulator volume and pressure is n n pv p2v 2 cons tant (4) In the process o brake energy regeneration, the amount o energy that an accumulator stores can be obtained by n pv n p Eacc (5) n p 2 m p () 94

3 Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, 27 Where, p is the initial pressure o the hydraulic accumulator, Pa; p 2 is the maximum working pressure o the hydraulic accumulator, Pa;V is the initial volume o the hydraulic accumulator, m 3 ;n=.4, treatment by adiabatic processes; and E acc is the stored energy o the hydraulic accumulator The ull vehicle o a HRBS This section considers the eects o suspension nonlinear deormation on the energy recovery eiciency o a HRBS when studying the recovery o braking energy. A hal-vehicle considering the nonlinear deormation o the suspension was established, as shown in Fig.2. The rectangular coordinate OXYZ is the vehicle coordinate system, the X-axis is parallel to the ground and pointing orward, the Z-axis is perpendicular to the ground and the Y-axis is perpendicular to the OXZ plane. The vehicle moves orward in the OX direction, vertical motion is in the OZ direction and the sprung mass rotates about the OY axis or pitching motion. a Z b X θ mc O yc k c kr cr m y mr yr kt ktr Figure 2. Nonlinear hal-vehicle. According to reerences (Gao and Fan, 25), the nonlinear spring s resilience-displacement is expressed as shown in Eq. (6): 3 F k ( x x2) k( x x2) (6) Where, ε is the spring s nonlinear parameter. The orce equation o nonlinear suspension when braking is F k ( y 3 asin y ) k ( y asin y ) c ( y asin y ) (7) s c c c 3 Fsr kr ( yc bsin yr ) kr ( yc bsin yr ) cr ( yc bsin yr ) (8) The sprung mass equations o motion are m y F F (9) c c s sr J m h x F bcos F a cos () c c g sr s The unsprung mass equations o motion are m y r r ktryr Fsr () m y k y F (2) t The equations o motion or the wheels are J F R T (3) r r s x T reb J F R T (4) Wheel orce and the equations o the wheel orces on the ground are F m gb/ L m g k y (5) z F zr c c xr r r r t tr m ga / L m g k y (6) Longitudinal dynamic equations o vehicle. The longitudinal dynamic equations or nonlinear ull vehicle and linear ull vehicle are roughly the same, with dierence in that the nonlinear ull vehicle considers the inluence o nonlinear deormation o suspension in moving process, as shown in equation 7. dx m Fx Fxr F Fw dt (7) r 95

4 Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, 27 F mg ) (8) ( 2u 2 Fw CD Au / 2.5 (9) Where, F s and F sr are the orces on the ront and rear suspensions, respectively, N; y c is the displacement o the sprung mass, m; L is the wheelbase, m; a is the distance rom the centre o mass to the ront axle, m; b is the distance rom the centre o mass to the rear axle, m;θ is the pitch angle o the vehicle when braking, deg; k and k r are the spring stinesses o the ront and rear suspensions, N/m; c and c r are the damping coeicients o the ront and rear suspensions, N/m/s; y and y r are the unsprung mass displacements o the ront and rear suspensions, m; mc is the sprung mass, kg; J c is the pitching moment o inertia o the sprung mass, kg m2; x is the longitudinal displacement, m; h g is the height o the vehicle s centre o mass, m; m and m r are the unsprung masses o the ront and rear suspensions, respectively, kg; J and J r are the moments o inertia o the ront and rear wheels, respectively, kg m 2 ; ω and ω r are the angular velocities o the ront and rear wheels, rad/s; T and T r are the braking torques acting on the ront and rear wheels o the braking system while braking, N m; and T reb is the wheel torque supplied by the motor, N m; R and R r are the rolling radii o the ront and rear wheels, rad/s; k t and k tr are the vertical stiness o the ront and rear tyres, N/m; F z and F zr are the normal applied orces o the ront and rear wheels on the ground, respectively, N; m is the overall mass o the vehicle, kg; u is the vehicle speed, m/s; F x and F xr are the braking orces on the ront and rear wheels rom the ground, N; F is the tire rolling resistance orce, N; F w is the air resistance, N; and 2 are the rollingresistance coeicients; C D is the airresistance coeicient; A is the vehicle s rontal area, m Veriication o simulation o HRBS To veriy the correctness o established or HRBS, the lywheel is adopted to simulate kinetic energy o the vehicle in braking to simulate regeneration o braking energy, as shown in Fig.3, and HRBS testbed is used or experimental veriication, as shown in Fig.4. The testbed working principle is: when the electromagnetic clutch No. (2) close, the motor() drives the lywheel(4) to rotate, which is used to simulate the kinetic energy o the automobile brake; when the lywheel reaches a certain speed, the electromagnetic clutch(2) disconnect, and electromagnetic clutch No.2(7) close, lywheel(4) drives the pump/motor(8) to rotate, and the accumulator start illing, the oil lows to the hydraulic accumulator(2) via the uel tank(9), at this moment, simulating vehicle braking condition, the pump/motor will be to work under the condition o the pump, the lywheel(4) s kinetic energy transorms to the hydraulic potential energy which stored in the accumulator(2). When simulating the vehicle acceleration condition, the regenerative braking system releases energy, oil drain valve(5) opens, the accumulator(2) drives the pump/motor(8) to rotate, now the pump/motor works under the condition o the motor and drives the lywheel(4) to rotate, the oil lows to the tank(9) via a hydraulic accumulator(2), the hydraulic potential energy translate into kinetic energy to release. Figure 3. Hydraulic regenerative braking simulation 96

5 Hydraulic accumulator pressure / MPa Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, 27 -Motor, 2-Electromagneticclutch No., 3-Magnetic powder brake, 4-Flywheel, 5-Revolutionspeedtransducer, 6-Commutator, 7-Electromagneticclutch No.2, 8-Hydraulic pump/motor, 9-Tank, -Relievalve, -Hydraulicpressure sensor, 2-Hydraulicaccumulator, 3-Hub motor, 4-Proportional ampliier, 5-Oil discharge valve. Figure 4.The hydraulic regenerative braking testbed The related parameters in testbed are as ollows: lywheel mass is 46.2kg, the hydraulic pump in pump/motor is variable displacement pump, with adjustable range o displacement rom 38ml/r to 7ml/r; initial volume o hydraulic accumulator V is 7L, initial pressure P is MPa, and maximum pressure P is 3.5MPa. With rotation rate o lywheel being 3r/min, and displacement o variable displacement pump being 4ml/r, 5ml/r, 6ml/r, 7ml/r, 8ml/r, 9ml/r, ml/rrespectively, the braking energy is regenerated. Fig.5 and Fig.6 respectively show the curves o change o accumulator pressure and braking time with displacement o variable displacement pump. The black curve represents simulation result, and red curve represents test result on testbed. It is observed that the simulation result roughly coincides with the test result, indicating the simulation o hydraulic regenerative system is correct. Wherein, in Fig.5, when the variable displacement pump brakes with dierent displacements, the test value or maximum pressure o accumulator is all smaller than the simulation value. The analysis shows the reason is that the connection between connectors o uel pipeline is not entirely sealed in experiment, leading to leakage o uel. In Fig.6, when variable displacement pump/motor brakes with dierent displacements, the test value o braking stop time o lywheel is smaller than the simulation value. The analysis shows that the reason is due to inhibition o rotation o lywheel by air drag when the lywheel is rotating, which, however, is not considered in simulation simulation -----test Displacement o variable pump / ml Figure 5. Comparison o simulation and test value o accumulator pressure 97

6 Fxr / N Braking time / s Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, simulation -----test Displacement o variable pump / ml Figure 6. Comparison o simulation and test value o braking time o lywheel 3. HIERARCHICAL CONTROL STRATEGY The paper adopts hierarchical control strategy or electric vehicle's hydraulic regeneration braking system. Wherein, the upper control distributes the braking orce o ront and rear axles in braking according to ideal distribution principle o break orce, and distributes the driving moment o HRBS in driving according to acceleration signal. The lower control strategy distributes the regenerative braking orce and mechanical braking orce o ront axis according to SOC (state o charge, as shown in equation.2) o accumulator pressure, vehicle speed and severity o braking. The SOC o accumulator pressure is calculated as ollows: P P SOC (2) P 2 P Where, P is current pressure o hydraulic accumulator, Pa. 3.. Upper control strategy The upper control strategy mainly distributes braking orce o ront and rear axles in braking, and distributes driving moment o HRBS in driving r curve I curve.6.7 curve B..2 O A Fx / N Figure 7.Optimized curve o ideal braking orce distribution The distribution curve o braking orce o ront and rear axles in braking is as shown in Fig.7. This principle o braking orce distribution is the optimized ideal distribution principle o braking orce, and divides the braking process into three processes, being respectively OA section(z<.), AB section ( z =.) and behind point B ( z>.). For OA section, the severity o braking is low, and motor can provide all the braking orce needed. Besides, the low severity o braking now leads to higher security. Thereore, to maximize regeneration o braking energy entails distributing all braking orce to the ront axis. F zg x Fxr (2) (22) 98

7 Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, 27 For AB section, the severity o braking is relatively higher and motor cannot provide all braking orce, so braking orce needs to be provided by the two axles together. Fx.G (23) Fxr zg.g (24) For BC section, in consideration o braking stability o vehicle, the distribution is according to ideal braking power distribution curve I. As or the nonlinear vehicle, which is aected by the deormation o the suspension during braking, the ront and rear wheel load transer is nonlinear or braking deceleration. Furthermore, it cannot be in accordance with the linear ormula o ideal braking orce distribution principle to distribute the braking orce required by the ront and rear wheels,which needs to be allocated according to the current loads o the ront and rear wheels (Li and Ning, 27) : F F zg (25) x Fx Fz (26) Fxr Fzr Where, z is braking intensity; G is Vehicle weight, N. In driving, the upper control strategy directly converts acceleration signal into hydraulic pump/motor displacement signal to control driving moment by adjusting the displacement o hydraulic pump/motor. In this paper, the acceleration signal and displacement ratio are in a proportional linear relationship: When the acceleration signal is, the displacement ratio signal controlling secondary component is zero, and now the actual displacement o secondary component is zero, low is zero, and moment is not output. When the acceleration signal is the maximal, the displacement ratio signal controlling secondary component is, and now the secondary component runs with the maximum discharge and outputs the maximum torque able to be output currently Lower control strategy Principle o lower control strategy: The lower control strategy is just to distribute the braking orce o ront axis distributed in the upper control strategy. The uzzy control strategy is adopted, with three variables o vehicle speed v, severity o braking z and accumulator pressure SOC as input variables o uzzy controller and expected regenerative braking orce as output variable to distribute regenerative braking orce and mechanical braking orce. The schematic diagram o lower control strategy is as shown in Fig.8. xr Braking intensity z Upper-layer control strategy Fb Fbr - Fm Mechanical braking orce Wheels Speed v Hydraulic accumulator SOC Fuzzy controller K Fre Regenerative braking orce Pump/motor control module Hydraulic accumulator Figure 8.Schematic diagram o lower control strategy The braking orce o ront and rear axles distributed according to upper control strategy is F b and F br respectively. Wherein, the braking orce F b distributed to ront wheel is resultant orce o regenerative braking orce and mechanical braking orce, and F br to rear wheel is pure mechanical braking power. The lower control strategy begins to distribute regenerative braking orce and mechanical braking orce or the braking orce o ront axis.firstly, uzzy controller calculated the braking orce coeicient K according to the input o the braking intensity z, vehicle speed v and accumulator pressure SOC, and with the ront axle total braking orce F b to do product operation; then, we obtain the ront wheel s regeneration braking orce F reb. The ront wheel s total braking orce F b minus the regenerative braking orce F reb yields the ront wheel s mechanical braking orcef m,the mechanical braking orce F m and F br are the current state o the ront and rear wheels that is required to be applied to the mechanical braking orce, F reb is the current state o the ront wheel that needs to be applied the regenerative braking orce. The variable displacement pump/ motor control module according to the distribution o braking orce F reb, Adjustment the swashplate angle o the variable displacement pump so that the 99

8 Degree o membership u Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, 27 regenerative orce produced by the variable displacement pump/motor is consistent with the regenerative braking orce required by the rontaxle. Then began working, and the oil in the oil cylinder is introduced into the hydraulic accumulator through the variable displacement pump/motor, so as to realize the recovery o braking energy. The design o the uzzy controller: Largely inluenced by pavement state, driver's intent and state o motor and accumulator pressure, the vehicle state is uncertain and nonlinear, and diicult to be expressed by equation, entailing application o uzzy control technology to design o braking orce distribution. The uzzy technology can conveniently express the inluence o dierent actors on regenerative braking and the control law that is hard to be quantiied (Whang and Li, 24). In this paper, a Mamdani-type uzzycontroller is used to control the regenerative and machinerybraking orces using the brake intensityz,the hydraulic accumulator s SOC and speed v as input variables. The regenerative braking orce coeicient K is an output variable. The structure o the controller is shown as Fig.9. Figure 9. Schematic diagram o the structure o a uzzy controller The symbol z indicates the input variable braking intensity, which is subjected to a uzzy transormation to allow it to be described in the uzzy language. Finally, with uzzy variables having values o very low(vl), low(l), middle(m), high(h), very high(vh), the corresponding uzzy subsets are set as {VL, L, M, H, VH}, the domain range is [, ] and the membership unctions are as shown in Fig.. The symbol SOC indicates the input variable pressure o hydraulic accumulator, which is subjected to a uzzy transormation to allow it to be described in the uzzy language. Finally, with uzzy variables having values o very low(vl), low(l), middle(m), high(h), very high(vh), the corresponding uzzy subsets are set as {VL, L, M, H, VH}, the domain range is [, ] and the membership unctions are as shown in Fig.. The symbol v indicates the input variable speed, which is subjected to a uzzy transormation to allow it to be described in the uzzy language. Finally, with uzzy variables having values o very low (VL), low(l), middle(m), high (H), very high(vh), the corresponding uzzy subsets are set as {VL, L, M, H, VH}, the domain range is [,2] and the membership unctions are as shown in Fig.2. The symbol K indicates the output variable regenerative braking orce coeicient o ront axle total braking orce. which is subjected to a uzzy transormation to allow it to be described in the uzzy language. Finally, with uzzy variables having values o very low (VL), low(l), middle(m), high (H), very high(vh), corresponding uzzy subsets areset as {VL, L, M, B, H,VH}, the domain range is [, ] and the membership unctions are as shown in Fig.3. VL L M H VH Braking intensity z Figure.The membership unctions o braking intensity z

9 Degree o membership u Degree o membership u Degree o membership u Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, 27 VL L M H VH Hydraulic accumulator SOC Figure.The membership unctions oaccumulator pressure VL L M H VH Velocity V Figure 2.The membership unctions ovehicle speed v VL L M H VH Regenerative braking orce coeicient K Figure 3.The membership unctions o regenerative braking orce coeicient K The uzzy controller is designed according to severity o braking z, accumulator pressure SOC, vehicle speed v and regenerative braking orce coeicient K. The main principle o design or the controller is as ollows: () When the severity o braking is too high, the energy is not regenerated or the sake o braking saety. When the severity o braking is low, the energy is regenerated as much as possible. (2) When SOC value is too high, the hydraulic accumulator tends to saturation point, and braking energy is regenerated as little as possible. When the SOC value is too low, the energy is regenerated as much as possible. (3)When the vehicle speed is too high, the braking energy is not regenerated or the sake o braking saety. When the vehicle speed is too low, the energy regenerative eiciency is too low, the braking energy is not regenerated. Table shows the inal design o the uzzy-rules. Table.. Fuzzy-rule table or the braking orce distribution SOC K z VL L M H VH VL VL VL VL VL VL VL L VH VH VH H VL L M VH VH H M VL M H VH H M L VL H V

10 Actual speed Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, SIMULATIVE ANALYSIS AND COMPARISON VH VL VL VL VL VL VH The simulation o driving cycles in this section adopts backward ing, with the expected vehicle speed o driving cycles o cities and actual vehicle speed ed back by the system as input to translate the speed deviation into moment demand via driver to be input into o vehicle controller. The o vehicle controller makes judgment according to moment demand to igure out moment signal needed by each system, which is output to braking or driving. Then the braking or driving transmits the moment to vehicle. In the meanwhile, the hydraulic pump/motor calculate displacement demand according to current moment signal and transmit it to the hydraulic accumulator. Finally the actual vehicle speed is calculated and output via vehicle dynamic beore ed back to driver to orm a closed loop system, thereby simulating the running o vehicle in driving cycles. The low chart o simulation o driving cycles is as shown in Fig.4. Hydraulic accumulator Hydraulic pump/ motor Drive cycle Desired speed Driver Vehicle controller Driving Braking Vehicle motion Hydraulic accumulator Hydraulic pump/ motor Figure 4.The low chart o simulation o driving cycles To compare the energy regeneration eiciency or linear and nonlinear hydraulic regenerative system o electric vehicle, the UDDS condition promulgated by American Environmental Protection Agency or urban road test o passenger vehicles is adopted or simulative analysis. This condition simulates the condition o common urban road, including requent start and stop as well as acceleration and deceleration, etc. The simulation o cyclic condition is as shown in Fig.5. Fig.5.The simulation o cyclic condition Fig.6 shows the comparison between the expected vehicle speed obtained via PID control o driver and actual vehicle speed ater simulation ends. It is observed that the actual vehicle speed roughly coincides with expected vehicle speed indicating the PID parameters in driver are reasonably set. Fig.7 shows the change o SOC o hydraulic accumulator with time in simulation process. Fig.8 shows the change o hydraulic accumulator volume with time, wherein, the black curve represents the linear electric vehicle's HRBS, and red curve represents the nonlinear electric vehicle's HRBS. It is observed that the accumulator SOC in nonlinear system o electric vehicle drops more slowly than the linear system in simulation process, and accumulator volume increases more slowly than the linear system, indicating the braking energy regeneration eiciency o nonlinear system o electric vehicle is higher than that o linear system in UDDS condition. 2

11 Volume o the hydraulic accumulator / L Hydraulic accumulator SOC Speed / Km/h Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, The desired Speed The actual speed Time / s Figure 6.Comparison o desired speed and actual.85.8 The linear The nonlinear Time / s Figure 7.The change o SOC o hydraulic accumulator with The linear The nonlinear Time / s Figure 8.The change o hydraulic accumulator volume with time Table shows the changes in accumulator pressure, volume and SOC in UDDS condition in simulation process o linear and nonlinear electric vehicle's HRBS. Comparison shows that in simulation process o UDDS cyclic condition, the accumulator pressure o linear electric vehicle's hydraulic regenerative system drops 4.8MPa, volume increases 4.87L, SOC o accumulator pressure decreases.92, and the accumulator pressure o nonlinear hydraulic regenerative system o electric vehicle drops 2.886MPa, volume increases 3.26L, SOC o accumulator pressure decreases.34, indicating the energy regeneration eiciency o nonlinear HRBS o electric vehicle is 7.25% higher than that o the linear system. Table.2.Parameter change o hydraulic accumulator Accumulator Pressure(MPa) Volume (L) SOC Item Linear Nonlinear Initial Final Change Initial Final Change

12 Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 2, pp. 93-4, 27 Deviation 4.53% -4.% 7.25% 5. CONCLUSIONS The paper researches the work principle o electric vehicle's hydraulic energy regenerative braking system, considers the inluence o nonlinear deormation o suspension on eiciency o braking energy regeneration, establishes simulation or electric vehicle's HRBS that considers nonlinear deormation o suspension, and lastly veriies the established HRBS via bench test. The paper proposes hierarchical control strategy to control the electric vehicle's HRBS. Wherein, the upper control strategy mainly realizes distribution o braking orce o ront and rear axle in braking according to ideal distribution principle o braking orce and distributes driving moment o HRBS in driving. The lower control strategy is based on the uzzy control strategy to distribute regenerative braking orce and mechanical braking orce or the distributed braking orce according to current vehicle speed, accumulator SOC and severity o braking. Lastly the simulative comparison between the established linear and nonlinear electric vehicle's HRBS is conducted in UDDS condition to ind that the braking energy regeneration eiciency o nonlinear in UDDS condition is 7.25% higher than that o the linear. Acknowledgements This work was supported by the National Natural Science Foundation o China (No ) and by the und o Zhijiang College o Zhejiang University o Technology (No.442). Reerences Bayar, K., McGee, R. et al. (23) Regenerative Braking Control Enhancement or the Power Split Hybrid Architecture with the Utilization o Hardware in the Loop Simulations, SAE International Journal o Alternative Powertrains, 2(), pp Fang, G. H., Liang, Y.L., Chang, F. (27) Analysis o Four-Wheel Drive Electric Vehicle Regenerative Braking Power System Based on AMESim, Machinery Design & Manuacture, 6, pp Gao, Y., Fan, J.W., Pan, S.H., Li, S., Kong, F. (25) Fractional-order Fuzzy Control Method or Vehicle Nonlinear Active Suspension, China Mechanical Engineering, 26(), pp Guo, Y. Y., Ning, X.B., Xie, W.D. (24) Analysis on energy recovery eiciency o hydraulic regenerative braking system, Journal o Mechanical&Electrical Engineering, 6(3), pp Hedegaard, K., Ravn, H., Juul, N, Meibom, P. (22) Eects o electric vehicles on power systems in northern Europe, Int J Energy, 48, pp Jorge, L., Jose, M.G., Mario, J.A. (26) Case Study o an Electric-Hydraulic Hybrid Propulsion System or a Heavy Duty Electric Vehicle, SAE Papers, Li, N., Ning, X.B., Wang, W.Q. (27) Genetic Algorithm Optimization o Hydraulic Regenerative Braking System or Electric Vehicles, BoletínTécnico, 6(55), pp Li, N., Ning, X.B., Wang, W.Q., Li, J.L. (27) Hydraulic regenerative braking system studies based on a nonlinear dynamic o a ull vehicle, Journal o Mechanical Science and Technology, 3(6), pp Li, Y., Zhang, J.W., Guo, K.H., Wu, D.M.. (25) Driving and braking orce distribution between ront and rear axles or 4WD electric vehicle, Journal o Jilin University, 45(3), pp Ramakrishnan, R., Hiremath, S.S.., Singaperumal, M.. (24) Design strategy or improving the energy eiciency in series hydraulic/electric synergy system, Energy, 67(4), pp Shi, M. S., Lv, Y.S. (26) Study on Stability o Generative Braking or Electric Vehicle, Machine Tool& Hydraulics,4(44), pp Whang, G. J., Li, X.P., Sui, X.L. (24) Universal Approximation and ItsRealization o Generalized MamdaniFuzzy System Based on K-integral Norms, Jacta Automatica Sinica, (4), pp Xu, D, Su, S.Q., Liang, Y.L. (27) Research on Fuzzy Control Strategy or Electric Vehicle, Machine Tool& Hydraulics, 2(45), pp Zhou, L. X., Ning, X.B., Xie, W.D. (23) Hydraulic regenerative braking system in electrical vehicle, Journal o Mechanical &Electrical Engineering, 6(3), pp