Brake-Blending Control of EVs

CHAPTER 8

Brake-Blending Control of EVs Chen Lv1, Hong Wang2 and Dongpu Cao1 1 Cranfield University, Bedford, United Kingdom University of Waterloo, Waterloo, ON, Canada

2

8.1 INTRODUCTION The ever-heavier burden on the environment and dwindling energy resources require automobiles to be cleaner and more efficient (Martinez et al., 2016). Studies show that in urban driving situations, about one-third to one-half of the energy of a powerplant is consumed during deceleration processes (Gao et al., 2001; Zhang et al., 2012; Lv et al., 2014a
c; Crolla and Cao, 2012). Among the key features of electrified vehicles, the regenerative braking system, which is capable of effectively improving the fuel economy by converting the vehicle’s kinetic energy into electric energy during braking procedures, has become a hot topic of research and development among automakers, parts manufacturers, and researchers worldwide (Sovran and Blaser, 2006; Lv et al., 2015a
c; Chiara and Canova, 2013; Kum et al., 2011, Von Albrichsfeld and Karner, 2009). Most manufactured electrified vehicles, including the Toyota Prius, Nissan Leaf, and Tesla Model S, are equipped with regenerative braking (Nakamura et al., 2002; Ohtani et al., 2011; Fleming, 2013). However, to guarantee the vehicle’s brake performance, a mechanical brake is still needed. Compared to a conventional friction brake, the regenerative brake has very different dynamic characteristics. For example, the motor’s brake torque responds quickly and accurately, whereas a regenerative brake is significantly affected by the operation conditions of the motor and battery. In addition, its transmission path, via a gear box, driving shaft, and half shaft to the wheel, is much longer than that of frictional brakes, which are mounted on the side of the wheel. These features not only provide great potential for improving the vehicle dynamics performance under normal and critical driving conditions, but also present tremendous challenges to existing brake theories and control methods. Therefore researching the mechanism and control method for regenerative and friction brake blending is of great importance. Modeling, Dynamics, and Control of Electrified Vehicles DOI: http://dx.doi.org/10.1016/B978-0-12-812786-5.00008-2

Copyright © 2018 Elsevier Inc. All rights reserved.

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For blending control of regenerative braking and hydraulic braking, the existing research has mainly focused on two aspects: the energymanagement strategy and dynamic blending control.

8.1.1 Blended-Braking Energy Management The task of braking energy management is to explore the potential of using regenerative braking to the maximum extent by reasonably allocating the regenerative braking force and friction braking force, improving the energy efficiency of an electric vehicle (EV) as much as possible. In regenerative braking control, currently available research mainly concentrates on a normal deceleration process with the aim of improving the regeneration efficiency and coordinated control between the regenerative brake and the frictional brake. Gao et al. (2001) put forward two regenerative braking strategies. In existing studies, automakers, parts manufacturers, and researchers worldwide have carried out research and development in system design and control. Toyota developed an electrohydraulic brake system successfully implemented in a commercialized hybrid electric vehicle (HEV) (Nakamura et al., 2002). The electrically driven intelligent brake system, which features an electrically driven motor and a ball screw, was developed by Hitachi and applied in the Nissan Leaf electric car (Aoki et al., 2007). A powertrain equipped with an energy-regeneration system was designed (Paladini et al., 2007). The ultracapacitor can recover the regenerative energy. In regenerativebraking control, the present research mainly concentrates on the cooperation between regenerative braking and friction braking (Uzunoglu and Alam, 2007). A new regenerative-braking control strategy for rear-driven electrified minivans was designed (Zhang et al., 2014a,b). A control strategy coordinating the regenerative brake and the pneumatic brake was proposed in order to recapture the braking energy and improve the fuel economy of a fuel-cell city bus (Zhang et al., 2013). To improve the blended brake control performance further, a novel control method based on on-off solenoid valves was proposed (Lv et al., 2014a
c).

8.1.2 Dynamic Blending Control Dynamic blending control targets dynamic processes. In contrast to a conventional internal combustion engine (ICE) vehicle, an EV equipped with a regenerative brake has three different braking states: friction braking, regenerative braking, and blended braking. These three braking states

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may occur independently or switch between each other frequently during one braking process. In particular, because the dynamics of an electrified powertrain is quite different from that of a conventional friction brake, the introduction of the electric motor torque during deceleration may make it a new source of vibration and jerk on the system and vehicle levels. In addition, the dynamic modulation of the frictional braking force may also cause pressure fluctuations in the brake circuits, resulting in negative impacts on brake performance, brake comfort, and even the energy efficiency of the vehicle (Lv et al., 2014a
c). Thus determining the electrified powertrain dynamics and its impact on blended brake control have become significant aspects of regenerative braking control. It is also important to determine how to dynamically couple the two different braking forces and coordinate the three different deceleration states to simultaneously ensure braking performance and improve energy efficiency. A cooperative control algorithm for an electronic brake and regenerative braking for an automatic-transmission (AT)-based HEV was proposed to maintain the demanded braking force and driving comfort during a downshift with regenerative braking (Jo et al., 2012). A differential braking and driving vehicle stability control strategy was developed for a hybrid electric sport utility vehicle equipped with axle motors (Bayar et al., 2012). Several critical techniques that are suitable for the development and examination of HEVs with regenerative braking capability have been proposed. A hybrid antilock break system (ABS) for EVs and hybrid vehicles, endowed with in-wheelmotors (IWMs) and friction brakes, has also been designed (de Castro et al., 2012). However, electrified powertrain dynamics and its impact on regenerative braking control performance are rarely seen in the existing research. Although some researchers have studied the powertrain system dynamics of EVs, they targeted the traction control under critical driving conditions or focused on the NVH (noise, vibration, and harshness) performance of the vehicles (Amann et al., 2004; Yin et al., 2009). In this chapter, with the aim of cooperative optimization of regeneration efficiency and ride comfort, brake-blending control strategies are investigated for electrified passenger cars. The models of blended brakes, including a nonlinear electric powertrain model and a hydraulic brake system model, are developed in MATLAB/Simulink. The control effects and regeneration efficiencies of the control strategies in a typical deceleration process are studied and analyzed via simulation and vehicle testing.

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Moreover, since the regenerative braking provided by an electric powertrain is far different from conventional friction braking with respect to system dynamics, the effects of the powertrain nonlinearities, i.e., the backlash and flexibility on vehicle drivability during regenerative deceleration, are analyzed. To further improve brake-blending control performance, a mode-switching-based active control algorithm with a hierarchical architecture is developed for the backlash and flexibility compensation. The proposed control algorithms are compared with the baseline strategy under the regeneration-braking process. Some simulation and experimental results are also given.

8.2 BRAKE-BLENDING SYSTEM MODELING 8.2.1 System Outline Fig. 8.1 shows the overall structure of the regenerative and hydraulic blended-braking system considered in this study. A central electric motor is installed at the front axle of the vehicle. During deceleration, regenerative braking torque, which is transmitted by the driveline, is exerted on the axle. In the meantime, friction braking torque is modulated by the hydraulic modulator. The blended-braking torque produces the overall braking operation.

Figure 8.1 Overall structure of the regenerative and hydraulic blended-braking system.

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8.2.2 Electrified Powertrain Model The electric powertrain is comprised of an electric motor, gearbox, final drive, differential, and half shafts. Fig. 8.2 shows a simplified powertrain model, whereas a two-inertia model is used in this study. One inertia indicates the electric motor, and the other corresponds to the contribution of the wheel. The gearbox, consisting of the transmission, final drive, differential, and inner and outer constant-velocity (CV) joints, is located close to the motor inertia. The backlash contributions throughout the powertrain are lumped together into one single backlash angle 2α. The main flexibility of the driveline is assumed to be in the half shafts, represented by the stiffness and damping properties. Assuming that the half shafts are of the same length, the motor output torque is considered to be equally distributed to the left and right half-shafts. Considering the effect of the electrical system dynamics, the motor torque is modeled as a first-order reaction with a small time constant τ m taken into consideration (Lv et al., 2015a
c), as shown below. τ m T_ m 1 Tm 5 Tm;ref

(8.1)

where Tm is the real value of motor torque and Tm;ref is the reference value. The dynamic equation for the transmitted torque from the motor output shaft to the half-shafts is as follows: Jm θ€m 1 bm θ_ m 5 Tm 2

1 U2Ths i0 ig

(8.2)

where Jm is the motor inertia, bm is the viscous friction of the motor, i0 is the final drive ratio, ig is the transmission ratio, and Ths is the half-shaft torque. A flexible half shaft with nonlinear backlash connects the gearbox and the wheel inertia. The nonlinear model for the half-shaft torque can be given by (Lv et al., 2015a
c):

Figure 8.2 Simplified two-inertia model of the electrified powertrain.

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Modeling, Dynamics, and Control of Electrified Vehicles

Ths 5 khs θs 1 chs θ_ s

(8.3)

θs 5 θd 2 θb

(8.4)

θd 5 θ1 2 θ3 ; θb 5 θ2 2 θ3

(8.5)

where khs and chs are the stiffness and damping coefficients, respectively, of the half-shaft; θd is the shaft twist angle; θb is the position in the backlash; θ1 , θ2 , and θ3 are the angles at the indicated positions on the shaft, as shown in Fig. 8.2, where θ1 5 θm =i0 ig and θ3 5 θw . The nonlinear model for the backlash position is described by Lagerberg and Egardt (2007): ! 8 > k hs > > ðθd 2 θb Þ ; θb 5 2 α > max 0; θ_ d 1 > chs > > > > < khs _θb 5 θ_ d 1 ðθd 2 θb Þ ; jθb j , α (8.6) chs > > ! > > > > khs > _ > ; θb 5 α > : min 0; θd 1 chs ðθd 2 θb Þ where 2α is the backlash gap size. The above Eq. (8.6) indicates that θb can only change within the backlash gap and not beyond the boundaries. When stuck at a boundary, the shaft-displacement rate θ_ d must be large enough in relation to the shaft twist in order for θb to start moving into the gap. The dynamic equation for a driven wheel is as follows: Jw θ€w 1 bw θ_ w 5 Ths 2 Thb 2 Tbx

(8.7)

where Jw is the wheel inertia and the road load is divided into a friction term bw and an exogenous tire longitudinal force Tbx. The friction braking torque Thb generated by mechanical hydraulic brake devices can be considered as a disturbance to the wheel.

8.2.3 Hydraulic Brake System To simulate and analyze the brake-blending performance, the hydraulic brake system models, including valve dynamics and wheel brake pressure, were developed. The schematic diagram of the hydraulic brake system is shown in Fig. 8.3.

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8.2.3.1 Valve Dynamics During the brake pressure build-up process, the hydraulic fluid flows through the normally open inlet valve from the master cylinder to the wheel cylinder. Therefore the inlet valve model is of great importance for the simulation of hydraulic brake pressure modulation. Detailed descriptions of valve structure and models have been reported (Lv et al., 2014a
c, 2016, 2017; Zhang et al., 2014a,b). The schematic diagram of the inlet valve with a coordinate system is presented in the right plot of Fig. 8.3. The axial dynamic equation for the position of valve core can be expressed as: mv x€ v 5 Fe 2 Fs 2 Fh 2 FB

(8.8)

where mv is the mass of the valve core, xv is the displacement of the valve core, Fe is the electromagnetic force, Fs is the spring force, Fh is the hydraulic force, and FB is the viscous force. The electromagnetic force, acting on the valve core, can be expressed by the following relation: Fe 5

ðIN Þ2 2Rg l

(8.9)

where I is the coil current, N is the number of turns, l is the air gap length, and Rg is the magnetic reluctance of the air gap. The spring force can be given by the following relation: Fs 5 ks ðxv 1 x0 Þ

Figure 8.3 Schematic diagram of the hydraulic brake system.

(8.10)

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Modeling, Dynamics, and Control of Electrified Vehicles

where ks is the stiffness coefficient of the return spring and x0 is the preload displacement of the spring. The viscous force is affected by the viscosity of the fluid and the movement velocity of the valve core, as shown in Eq. (8.11). FB 5 Bx_ v

(8.11)

where B is the viscous damping coefficient. The hydraulic force, exerted on the valve core by the fluid, can be calculated as (Lv et al., 2014a
c): Fh 5 πRv2 ðcosαÞ2 UΔp 2 2ΔpCd2 Av cosα 2 ρfluid L q_v πdm Av 5 Rv

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d2 Rv2 2 m Uxv 4

(8.12)

(8.13)

where Cd is the flow coefficient of the inlet of the valve, ρfluid is the density of the hydraulic fluid, Rv is the spherical radius of the valve core, L is the damping length, qv is the fluid flow of valve, Δp is the pressure difference across the valve, and dm is the average diameter of the valve seat. 8.2.3.2 Hydraulic Brake Pressure The structure of the wheel cylinder is simplified to a piston and a spring. Based on the valve dynamics analyzed above, the wheel-cylinder pressure can be represented as (Lv et al., 2014a
c): sffiffiffiffiffiffiffiffiffiffiffi kFW 2UΔp (8.14) p_FW 5 2 4 Cd Av ρfluid π rFW where kFW is the spring stiffness of the wheel cylinder and rFW is the piston radius of the wheel cylinder.

8.2.4 Vehicle and Tire A model of vehicle dynamics with eight degrees of freedom has been built in MATLAB/Simulink by the present authors (Zhang et al., 2012). The tire model, which is of great importance for research on braking, should be able to simulate the real tire in both adhesion and sliding. In this chapter, the well-known Pacejka magic formula model is adopted (Pacejka and Bakker, 1992). The tire behavior can be accurately described under a combined longitudinal and lateral slip condition.

Brake-Blending Control of EVs

Table 8.1 Key parameters of the electrified powertrain and vehicle Parameter Value

Electric motor Battery pack Vehicle

Peak power Maximum torque Voltage Capacity Total mass (m) Wheel base (L) Coefficient of air resistance (CD) Nominal radius of tire (r) Gear ratio

45 144 326 66 1360 2.50 0.32 0.295 7.881

283

Unit

kW Nm V Ah kg m — m —

The detailed vehicle and tire models developed have been described (Lv et al., 2014a
c; Zhang et al., 2012). The feasibility and the effectiveness of the models have been validated via hardware-in-the-loop tests and vehicle tests. Key parameters of the electrified powertrain and vehicle are listed in Table 8.1.

8.3 REGENERATIVE BRAKING ENERGY-MANAGEMENT STRATEGY 8.3.1 Braking-Force Distribution Strategy In a conventional vehicle, since the brake pedal is mechanically connected to the downstream of the brake circuits, the front-rear brake force distribution (BFD) is not regulated during braking processes and is set as a fixed value, which is determined by parameters of the installed brake devices, to prevent the brake pedal feel from being affected by the modulation of hydraulic pressure. However, for an EV equipped with a brakeblending system, the brake pedal is mechanically decoupled from the mechanical brake actuators, and the ideal braking distribution can be achieved by the bywire brake system via modulating the braking forces between the front and rear wheels. Thus to achieve high regeneration efficiency and guarantee the brake safety in the meantime, the front-rear BFD needs to be reconsidered. 8.3.1.1 Front- and Rear-Braking Force Allocation For a front-wheel-drive car, the motor’s braking torque can be only exerted on the front axle. To reach the maximum regeneration efficiency, the front-axle regenerative braking torque needs to be fully utilized,

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Modeling, Dynamics, and Control of Electrified Vehicles

Figure 8.4 Diagram of the front- and rear-braking force allocation.

leading to the BFD being close to the x axis in Fig. 8.4. But to guarantee stability during braking processes, a vehicle should have enough rear-braking force, which is required by the regulation of ECE-R13, as Eqs. (8.15) and (8.16) show (Gao et al., 1999). z $ 0:1 1 0:85ðϕ 2 0:2Þ z5

du 1 U dt g

(8.15)

(8.16)

where zindicates the brake intensity, ϕ is the adhesion coefficient of the road, and u is the longitudinal velocity of the vehicle. However, if desirable braking performance is expected, the BFD should be set close to the ideal BFD, which is far from the x axis. As the ideal braking force allocation is required, the front/rear braking forces can be expressed as (Lv et al., 2014a
c): Fμ1 1 Fμ2 5 ϕUG

(8.17)

b 1 ϕUhg Fμ1 5 Fμ2 a 2 ϕUhg

(8.18)

Eliminating the variable ϕ, the relationship between front-wheel braking force and rear-wheel braking force can be given as Eq. (8.19). The ideal BFDs (laden and unladen) are shown in Fig. 8.4.

Brake-Blending Control of EVs

" rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  # 4h L 1 G Gb g Fμ2 5 1 2Fμ1 b2 1 Fμ1 2 2 hg hg G

285

(8.19)

where Fμ1 is the front-wheel braking force, Fμ2 is the rear-wheel braking force, G is the gravity of the vehicle, a is the longitudinal distance from the center of gravity of the vehicle to the front axle, b is the longitudinal distance from the center of gravity to the rear axle and L is the axle base, and hg is the height of the gravity center. Therefore, according to the analysis above, we can see that there exists a contradiction between regeneration efficiency and brake performance in designing the front/rear BFD for a front-wheel-drive EV. The BFD for maximizing regeneration is required to be far from the one demanded by maximizing braking performance. For the original strategy, the BFD is set as a fixed value (Zhang et al., 2012), i.e., the front brake force is linearly correlated with the rear one, as shown by the red dotted line shown in Fig. 8.4. By doing this, however, the regeneration capability cannot be fully utilized. To tackle this issue, coordinating the regeneration efficiency and braking performance, a BFD for an EV is worthwhile to explore. During the daily operating conditions of an EV, the regenerative braking usually needs to be activated under normal braking procedures, which corresponds to the deceleration of the vehicle at 0.1
0.3 g. Once entering critical braking situations (deceleration of the vehicle usually greater than 0.5 g), good braking performance is required for a vehicle to ensure short braking distance. Based on these practical requirements, targeting a front-wheel-drive electric car, a braking-force distribution strategy is proposed as follows: 1. As shown in Fig. 8.4, under small brake intensity, only front-wheel regenerative braking force is applied, and no friction brake on the rear axle is exerted (O to A); 2. To fully guarantee the rear-braking force is within the limits set by the ECE regulation, the rear-wheel friction force is added and modulated by the bywire brake system from point A, before reaching the limitation required by the ECE regulation; 3. When the deceleration is beyond 0.3 g, the designed line of BFD gets close to the ideal BFD (B to C) gradually, to make the vehicle obtain better braking performance under heavier brake intensity; 4. Once the deceleration reaches 0.6 g (C point), the vehicle enters the emergency driving condition, and the bywire brake system will

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Modeling, Dynamics, and Control of Electrified Vehicles

regulate the hydraulic forces in the front and rear wheels, making the designed BFD go complying with the ideal one, guaranteeing the best dynamic braking performance of the vehicle. The designed BFD is illustrated in Fig. 8.4, as the black dotted line shows. Based on the regenerative braking-control strategy described above, the target EV can be expected to achieve the high regeneration efficiency under normal deceleration processes, and ensure good braking stability under emergency braking situations. 8.3.1.2 Regenerative and Hydraulic Brakes Distribution As shown in Fig. 8.5, during deceleration, the overall braking force of the vehicle is supplied by the regenerative- and friction-blending brakes. The overall brake force is controlled and is consistent with the brake intention of the driver, as Eq. (8.20) shows. Tb

need

5 Treg 1 Tfric

(8.20)

where Tb need is the total braking demand of the vehicle, Treg is the regenerative-braking torque generated by the electric motor, and Tfric indicates the friction braking torque provided by the mechanical braking system. To maximize the regeneration efficiency, during brake blending, the regenerative-braking torque is fully used on the front axle. As shown in Fig. 8.5, only the regenerative brake is exerted on the front axle at first. Based on the control algorithm, once the brake request cannot be met solely by the electric brake, the rear-wheel brake will be supplemented by the hydraulic brake system. And with the increase of the driver’s brake demand, the hydraulic braking force on the front axle will then be

Figure 8.5 Diagram of the distribution between the regenerative brake and hydraulic brake.

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applied gradually. In addition, when the car enters any critical driving situations, such as when the ABS or the traction control system (TCS) activates, the regenerative-braking torque will be removed gradually, i.e., only the hydraulic brake takes over all the braking operation under emergency braking conditions.

8.3.2 Cooperative Control Algorithm of Blended Brakes Fig. 8.6 illustrates the control block diagram of the cooperative regenerative braking. When the driver presses the brake pedal, the total brake demand (Tb need ) can be detected via pressure sensor in the pedal unit, as Eq. (8.21) shows. need 5

Tb

4πUμb rf2 Re β

f

Upm

(8.21)

where pm is the hydraulic cylinder pressure of the pedal unit, μb is the friction coefficient of the brake disc, rf is the radius of the piston of the front wheel cylinder, Re f is the effective friction radius of the brake disc, and β is the real-time front-rear braking force distribution coefficient. Based on the brake demand of the vehicle and the designed brakingforce distribution strategy, the front-axle braking torque (Tb f ) and rear-axle braking torque (Tb r ) can be calculated as follows: Tb Tb

f

5 4πUμb rf2 Re f Upm r

5 Tb

need

2 Tb

f

Figure 8.6 Cooperative control block diagram of the brake-blending system.

(8.22) (8.23)

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Modeling, Dynamics, and Control of Electrified Vehicles

As Eq. (8.24) shows, according to the SoC of the battery pack, the speed of the motor, and the torque demand of the front axle, brake control unit (BCU) calculates the command value of the regenerative braking torque (Treg cmd ) and sends it to the motor control unit (MCU) via the Controller Area Network (CAN) bus. Treg

cmd

5 minðTreg

lim ; Tb f Þ

(8.24)

where Treg lim is the braking torque limit the electrified powertrain can provide. Meanwhile, based on the feedback signal of the real value of the regenerative-braking torque, the target values of the front-wheel cylinder pressure (pf tgt ) and the rear-wheel cylinder pressure (pr tgt ) can be figured out, respectively, as Eqs. (8.25) and (8.26): pf

tgt

pr

5

tgt

Tb f 2 Treg 4πμb rf2 Re

f

Tb r 4πμb rr2 Re

r

5

real

(8.25)

(8.26)

where rr is the radius of the piston of the rear-wheel cylinder and Re r is the effective friction radius of the rear brake disc. Thus the hydraulic brake system can modulate the front- and rearwheel cylinder pressures to the target values separately based on the above calculation results. Finally, the regenerative-braking torque provided by the electrified powertrain and the friction-braking force generated by the hydraulic brake will meet the total brake request of the vehicle.

8.3.3 Hardware-in-the-Loop Simulation of the Braking Energy-Management Strategy Fig. 8.7 illustrates the configuration of the hardware-in-the-loop simulation system for the regenerative-braking control system. The entire system is comprised of a real-time simulation system and a real brakecontrol unit. The real-time simulation system is the AutoBox from dSPACE. Virtual models, including vehicle dynamics, the battery, the tire, and the electric motor are embedded in the AutoBox. The brake-control unit is a real controller, which is identical to the one installed on a vehicle.

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Figure 8.7 Configuration of the hardware-in-the-loop simulation system.

8.3.3.1 HiL Simulation Scenario Setup The simulations are carried out during scenarios of normal deceleration processes. In simulation, the initial braking speed is set at 30 km/h, the braking pressure of the master cylinder is taken as a ramp input stabilizing at 3 MPa, and the road is assumed to have a dry surface with a high adhesion coefficient. Taking the original BFD allocation as a baseline strategy, the regeneration efficiencies of the baseline strategy and the newly proposed regenerative-braking control algorithm are compared during the normal braking processes. 8.3.3.2 HiL Simulation Results and Analysis The simulation results of the two different regenerative-braking control strategies, namely the baseline strategy and the proposed strategy, are shown in Fig. 8.8. For an EV with the original regenerative-braking control strategy, as shown in Fig. 8.8A, since the front-rear braking force distribution is set as a fixed value, the rear-wheel braking pressure keeps the same

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Modeling, Dynamics, and Control of Electrified Vehicles

Figure 8.8 (A) Simulation results of the baseline regenerative-braking control strategy; (B) simulation results of the proposed regenerative-braking control algorithm.

value with the master cylinder pressure without any modulation during the whole braking process. Under the proposed regenerative-braking control strategy, the simulation results are shown in Fig. 8.8B. At the beginning of the deceleration procedure, the regenerative-braking torque of the electric motor is exerted gradually on the front axle, and the front-wheel brake pressure is regulated by the bywire brake system based on the proposed braking force allocation, while the rear-wheel brake is not applied. After 0.35 s, the master cylinder pressure reaches 3 MPa, leading to the brake demand of the vehicle increasing accordingly. The regenerative brake and the mechanical brake couple in the front axle. In the meantime, the rearwheel brake force starts to be applied and dynamically modulated by the bywire brake modulator, and its pressure is much lower than the master cylinder pressure, which is due to the defined control strategy. At about 2.4 s, the vehicle speed decreases to a relatively low value. Limited by its full-load characteristics, the regenerative-braking torque drops significantly. Thus the front hydraulic pressure increases correspondingly to supplement the vehicle’s brake request. The front and rear hydraulic pressures are still modulated by the brake modulator based on the proposed distribution strategy. During the whole deceleration, the regenerative brake and the frictional brake cooperate

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well and the braking deceleration changes smoothly, guaranteeing the braking performance of the vehicle. To evaluate the energy-regeneration performance by the proposed control algorithm during regenerative braking, the regeneration efficiency ηreg is adopted as an evaluation parameter, expressed as: ηreg 5

Ereg 3 100% Erecoverable

(8.27)

where Ereg is the energy regenerated by the regenerative-braking system and Erecoverable is the maximum value of the recoverable energy, i.e., the kinetic energy left after subtracting all the energy that would be dissipated by road drag and air resistance. The regenerated energy is expressed by: Ereg 5

ð t1 UIdt

(8.28)

t0

The recoverable energy by: 1 Erecoverable 5 mv2 2 2

ð t1

fmgvdt 2

t0

ð t1

CD UA Uð3:6vÞ2 Uvdt 21:15 t0

(8.29)

where t0 is the initial braking time, t1 is the final braking time, U is the output voltage of battery pack, and I is the charging current of battery. The regeneration results in a normal braking process are shown in Table 8.2. According to the data, the regeneration efficiency of the original control strategy is 64.94%, while the regeneration efficiency of the proposed control algorithm is 80.10%. The improvement of the regeneration efficiency by the proposed control algorithm based on the brake-blending system is above 23%.

Table 8.2 Regeneration results under normal braking process Regeneration Regenerated Control Recoverable efficiency energy strategy energy (%) (kWh) (kWh)

Efficiency improvement (%)

Baseline Proposed


23.36

39.84 39.98

25.87 32.02

64.94 80.10

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8.4 DYNAMIC BRAKE-BLENDING CONTROL ALGORITHM The introduction of regenerative braking into deceleration operations not only provides great potential for improving vehicle-energy efficiency but also poses tremendous challenges to existing brake theories and control methods. It is of great importance to take the dynamic behavior of the powertrain system into consideration when developing an advanced blended-braking control system for EVs. There are mainly two aspects of a powertrain that greatly affect the dynamic performance of a vehicle: backlash and flexibility. They introduce hard nonlinearities into the powertrain control loop for torque generation and transmission, causing unexpected driveline oscillations (referred to as shuffle; Templin, 2008). Therefore powertrain backlash and flexibility compensation are important for improving vehicle drivability and control performance during regenerative deceleration and are worth researching.

8.4.1 Effects of Powertrain Backlash and Flexibility on Brake-Blending Control In existing studies on blended braking, the powertrain is usually modeled as a rigid system, with nonlinear backlash and flexibility neglected, to simplify control design modeling. Thus the half-shaft torque is regarded as an amplification of the motor’s output torque, multiplied by the gear ratio, whereas the motor torque is open-loop controlled. However, it is obvious that backlash nonlinearity and flexibility exist in the real world. Their impacts on vehicle drivability and regenerativebraking performance are discussed below. 8.4.1.1 Effect of Powertrain Backlash on Vehicle Drivability During Regenerative Deceleration For an EV, if we define the contact as being positive when a half-shaft is transmitting a driving torque, then the contact during regenerative deceleration is negative. Once the EV goes from driving mode to regenerative braking, the backlash is traversed, exciting the nonlinearity. In backlash (noncontact) mode, the system, which is described by Eqs. (8.1)
(8.7), can be implemented in a state-space formulation, as shown in Eq. (8.30), indicating that no torque is transmitted through the half-shaft in backlash gap and that the motor and the load are decoupled:

Brake-Blending Control of EVs

0 B B B 1 B 0 B T_ m B B_ C B B θs C B C B B B θ€m C 5 B C B B B € C B @ θw A B B B _θb B B B B @

2

1

1 τm

0

0

0

khs chs

0

0

2

0

bm Jm

1 Jm

0

2

0

0

0

0

khs chs

1 i0 ig

0

1 B τm B B B 0 B 1B B 0 B B 0 B @ 0

293

0

0

0

0

0

0

2

1 Jw

0

2

1 Jw

0

0 2

bw Jw

21

0

C C C C0 1 0C C Tm CB CB θs C C CB C _ 0C B θ CB m C C CB C@ θ_ w C A C 0C C θb C C C 0A

(8.30)

1 0C C0 T m;ref C 0 CB CB Thb 0C CB C@ Tbx 0C C Tl A

1 C C C A

0

Fig. 8.9A illustrates regenerative braking of the simulated EV. During the first second, the vehicle is operating in drive mode, with the backlash in positive contact. At 1 s, the driver depresses the brake pedal, requesting a deceleration operation, so that a transition from positive to negative motor torque occurs. At approximately 1 s, an unexpected torque oscillation occurs on the half-shaft during the transition, resulting in an uncomfortable jerk in the vehicle’s deceleration. Focusing on the torque transition procedure shown in Fig. 8.9B, the backlash traverse happens at approximately 1.1 s, and the contact is changed from the positive side (CO 1 ) to the negative side (CO 2 ) for 40 ms. Because the motor is decoupled from the load, i.e., the half-shaft torque Ths is zero. Based on Eq. (8.2), within the backlash gap, all the motor output torque is applied to its own inertia, Jm θ€m 5 Tm , which accelerates the motor greatly. Therefore when the negative contact occurs, the speed difference between the motor and the load exceeds 22 rad/s. This speed difference results in a great impact (shunt), which causes torque oscillations (shuffle) on the half-shaft and an unexpected jerk in vehicle deceleration, which indicates the drivability, as the subplots

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Modeling, Dynamics, and Control of Electrified Vehicles

Figure 8.9 (A) Simulation results of regenerative braking under nonactive powertrain control; (B) transition procedure of vehicle going from driving mode to regenerative braking.

in Fig. 8.9B show. Thus a controller that does not take traversing of the backlash into account will have a very difficult time damping the torque oscillations. 8.4.1.2 Effect of Powertrain Flexibility on Brake-Blending Performance The flexibility is mainly contributed by the damping and elastic characteristics of the driveline, especially the half-shaft. Unlike backlash traverse, which only occurs during transitions between driving and braking modes, flexibility exists throughout the overall operating process, including traction and deceleration. As Fig. 8.9 shows, during blended braking, after negative contact is established (i.e., in the contact mode), because of the drivetrain flexibility, the half-shaft torque oscillations last for approximately 1 s and then gradually decrease. Moreover, the torque is consumed by the flexibility characteristics of the driveline during its transmission.

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Compared to the target value, the torque consumed in drivetrain reaches 80 Nm on the half-shaft in the static state. Motivated by observation of the above phenomena in the time domain, the effect of half-shaft stiffness and damping on powertrain dynamics in contact mode is analyzed in the frequency domain. In contact mode, the system state-space formulation is reformulated as shown in Eq. (8.31). The state vectors indicate that the torque transmission is recovered on the shaft and the connection between the motor and the load is reestablished. 0 B B B B T_ m B B_ C B B θs C B C B B B θ€m C 5 B C B B B € C B @ θw A B B B θ_ b B B @ 0

2

1

1

1 τm

0

0

0

0

khs chs

0

0

2

bm Jm

1 Jm

0

2

0

0

0

2

0

0

0 0 1 0 B τm B B B 1 B 0 B chs B B 1B B 0 2 2 B i0 ig Jm B B B B 0 0 B @ 0

0

0

0 0 0 2

1 Jw

0

0 bw Jw

0

C C C0 1 C Tm C 0 CB C CB θs C CB C CB θ_ m C C C B 0 CB C _ θ C@ w A C C θb 0C C A 0 1

(8.31)

0

C C C C0 1 C T m;ref chs C CB CB Thb 2 C CB 2 @ Tbx i0 ig Jm C C C Tl C 1 C Jw C A

1 C C C A

0

Based on the above state-space formulation, the transfer function from the motor torque to the half-shaft torque can be expressed as: Ths Jw s2 1 ðJw chs 1 bw khs Þs 1 bw chs 5 Tm a1 s3 1 a2 s2 1 a3 s 1 a4

(8.32)

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Modeling, Dynamics, and Control of Electrified Vehicles

1 Jm Jw ; i0 ig 1 1 a2 5 Jm ðbw 1 khs Þ 1 Jw bm 1 2Jw khs ; i0 ig i0 ig 1 1 a3 5 Jm chs 1 bm ðbw 1 khs Þ 1 2ðJw chs 1 bw khs Þ; i0 ig i0 ig chs ðbm 1 2bw Þ a4 5 i0 ig

where a1 5

Fig. 8.10 shows the Bode plots of the half-shaft torque to an input motor torque, based on the above transfer function. In the low-frequency range, the driveline can be regarded as rigid. When the frequency exceeds 30 rad/s, the response of the load torque is characterized by a resonance peak. When the damping coefficient chs decreases (c0 , c1 , c2 , c3 , 1 N), both the magnitude and phase responses are subject to amplitude growth at approximately the resonance point. As the frequency increases beyond

Figure 8.10 Bode plot of the half-shaft torque responses to an input motor torque.

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297

50 rad/s, the gradient of the magnitude response gradually decreases from 0 to 220 dB, whereas the phase value converges to 290 degrees, reflecting the elastic and damping characteristics of the system. Therefore because of its elastic and damping properties, the electrified powertrain cannot be regarded as simply rigid. Moreover, the open-loop dynamic response of the electric powertrain is not satisfied for advanced control of EVs.

8.4.2 Active Powertrain Control Algorithm Design To further enhance the drivability of the EV during blended braking, an active control algorithm that considers powertrain backlash nonlinearity and flexibility compensation was developed, as described in this section. 8.4.2.1 Hierarchical Control Architecture Based on the analysis presented above, the obvious goal of backlash control is to reduce the impact force of the motor on the load when contact is reestablished, realizing a “soft landing” that avoids chatter. This can be accomplished by requiring the speed difference ðθ_ w ðtÞ 2 θ_ m ðtÞ=i0 ig Þ to be small. We also desire a fast traverse with a short time delay, because the waiting time limits the torque-tracking performance. Thus the backlash compensation can be seen as a speed-tracking problem. The control objective is to track the reference speed θ_ ref ðtÞ, which is the wheel speed θ_ w ðtÞ in this study, with the motor speed θ_ m ðtÞ=i0 ig . In contact mode, active control for flexibility compensation can be seen as a torque- tracking problem, rather than speed tracking as in backlash control. The control objective is therefore to track the target torque Tm;tgt ðtÞ with the half-shaft torque 2Ths ðtÞ=i0 ig . Based on the considerations discussed above, an overall control protocol was developed. The control protocol has a hierarchical architecture consisting of a high-level mode-switching supervisor and a low-level active controller, as shown in Fig. 8.11. 8.4.2.2 Sliding-Mode-Based Controller for Powertrain-Backlash Compensation Because of its ability to address nonlinearity and achieve good performance and fast response, a sliding-mode control (SMC) scheme is adopted. As discussed above, the objective in backlash mode is to track the reference speed with the motor speed, which is set by the high-level supervisory controller. Thus the error term is defined as:

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Modeling, Dynamics, and Control of Electrified Vehicles

Figure 8.11 Hierarchical architecture of the control algorithm.

eBL 5 θ_ m =i0 ig 2 θ_ w

(8.33)

The first step in designing the SMC is to define the sliding surface. To guarantee zero steady error, an integral-type sliding surface was chosen (Song and Hedrick, 2011), as shown in Eq. (8.34):  n ð d 1λ eBL dt 5 0 S5 (8.34) dt where n is the order of the system and λ is the positive gain. Based on Eq. (8.2), the order of the system is one. Therefore the sliding surface can be defined as follows:

Brake-Blending Control of EVs

299

ð S 5 eBL 1 λ eBL dt

(8.35)

One method for designing a control law that derives the system trajectories to the sliding surface is the Lyapunov direct method. The following Lyapunov function is used for the single-input, single-output system: 1 V 5 SS 2

(8.36)

To ensure the stability of the system, the derivative of the Lyapunov function should satisfy the following condition: V_ 5 SS_ # 0

(8.37)

If SS_ 5 2 SKS, where K is a positive control gain, then the above inequality can be satisfied. Hence, SS_ 5 2 SKS.SðS_ 1 KSÞ 5 0

(8.38)

Based on Eq. (8.35), the derivative of S can be expressed as: S_ 5 θ€m =i0 ig 2 θ€w 1 λe

(8.39)

To guarantee the stability and reachability of the SMC system, the positive control gain K can be chosen as (Khalil, 2001; Lv et al., 2016, 2017): K # θ€w 2 θ€m =i0 ig 1 λðθ_ w 2 θ_ m =i0 ig Þ

(8.40)

Combining Eqs. (8.2) and (8.39), neglecting the electric motor’s dynamics, and plugging S_ into S_ 1 KS 5 0, the following expression is obtained: 1 θ€w 2 Tm;ref 1 λeBL 1 KS 5 0 i0 ig Jm

(8.41)

Thus, the control input in backlash mode can be written as: Tm;ref 5 Tref ;BL 5 i0 ig Jm ðθ€w 1 λeBL 1 KSÞ

(8.42)

A block diagram of the backlash mode active controller is shown in Fig. 8.12.

300

Modeling, Dynamics, and Control of Electrified Vehicles

Figure 8.12 Block diagram of the backlash mode active controller.

In fact, the standard SMC law for this system should be defined as: 0 Tref ;BL 5 i0 ig Jm ðθ€w 1 λeBL 1 KsgnðSÞÞ

8 < 1 ;S.0 sgnðSÞ 5 0 ;S50 : 21 ; S , 0

(8.43)

(8.44)

However, it is well known that in standard SMC, the discontinuous signum function, sgn(S), may cause chatter when the state trajectories are closing to the sliding surfaces. To avoid this phenomenon, the above discontinuous term is replaced by the continuous function KS in Eq. (8.42), which removes the chatter from the control input (Fazeli et al., 2012). During the blended-braking process, the hydraulic brake, whose behavior exerts a strong influence on backlash control performance, also needs to be considered. Because the half-shaft torque in the backlash phase is zero, based on Eq. (8.7), given a stable operating point ðTbx;0 ; θ_ w;0 Þ, the wheel dynamics can be represented by: 1 1 θ€w ðtÞ 5 2 Thb ðtÞ 2 ðTbx;0 1 bw θ_ w;0 Þ Jw Jw

(8.45)

According to Eq. (8.45), if jT_ hb ðtÞj , 0, i.e., if the hydraulic braking torque is decreased, the wheel deceleration will increase, which will make the speed difference become larger. Therefore greater control effort will   be required for the motor to traverse the gap. If T_ hb ðtÞ . 0, i.e., if the friction braking torque is increased, even though the relative speed will become smaller, the regeneration efficiency will be weakened. Considering a worst case, if the frictional brake is overapplied, the contact

Brake-Blending Control of EVs

301

might be reestablished on the opposite side. To simplify the implementation, the friction-braking torque, i.e., the wheel-cylinder pressure, can be maintained during the backlash phase, as shown in Eq. (8.46). p_FW ;ref ðtÞ 5 0

(8.46)

8.4.2.3 Torque-Tracking Controller for Powertrain Flexibility Compensation As described above, in contact mode, powertrain flexibility compensation can be seen as a torque-tracking problem. The control objective is to track the target torque Tm;tgt with 2Ths =i0 ig . A combined feed-forward and feedback control structure was adopted (Lv et al., 2015a
c): Tm;ref 5 Tff 1 Tfb

(8.47)

where Tff is the feed-forward input term required for tracking and Tfb is the feedback component designed to reduce the control error. Based on the control objective, the feed-forward term can be determined by: Tff 5 Tm;tgt

(8.48)

      Tm;tgt  5 min Tb;f ; 1 Tm;lim  (8.49) i0 ig where Tm;tgt is the target value of the motor torque, Tb;f is the total brake demand of the front wheels, and Tm;lim is the torque limit of the electric motor, calculated on the basis of the battery state of charge and the motor speed. Since the value of half-shaft torque is unable to be measured by a sensor in vehicle implementation, the estimation techniques have been studied by some researchers (Bottiglione et al., 2012; Amann et al., 2004). Assuming that the value of the half-shaft torque is available, the error term between the target and the real value of half-shaft torque can be represented by: eCO 5 Tm;tgt 2 2Ths =i0 ig For the feedback term, a linear PID control law is adopted: ð d Tfb 5 KP eCO 1 KI eCO dt 1 KD eCO dt where the feedback gains KP , KI , and KD are tuning parameters.

(8.50)

(8.51)

302

Modeling, Dynamics, and Control of Electrified Vehicles

Figure 8.13 Block diagram of the contact-mode controller.

Therefore, in contact mode, the control input can be written as: ð d Tm;ref 5 Tref ;CO 5 Tm;tgt 1 KP eCO 1 KI eCO dt 1 KD eCO (8.52) dt A block diagram of the torque-tracking controller for flexibility compensation in contact mode is shown in Fig. 8.13. To meet the overall braking demand of the vehicle in contact mode, the reference value of the hydraulic brake pressure was calculated based on the total brake demand of the front wheels, Tb;f , and the value of the half-shaft torque, Ths , as shown in Eq. (8.53): pFW ;ref 5 k0 ðTb;f 2 2Ths Þ

(8.53)

where k0 is the conversion coefficient of the wheel cylinder pressure and braking torque, determined by the parameters of the mechanical brake devices.

8.4.3 Simulation Verification of the Dynamic Brake-Blending Control To evaluate the control performance of the proposed algorithm during normal deceleration processes, simulations were carried out in MATLAB/ Simulink using the models described in Section 8.2. In the simulations, the initial braking speed was set to 40 km/h. The vehicle is powered during the first second, and then brake torque is requested by the driver at 1 s. The transition of contact occurs from the CO 1 to the CO 2, and the backlash is traversed. The master cylinder pressure was taken as a ramp input stabilizing at 3 MPa. The road was assumed to have no slope and to have a dry surface with a high adhesion coefficient of 0.8. Conventional open-loop nonactive control was used as a baseline. The simulation results for this baseline control are shown in Fig. 8.9.

Brake-Blending Control of EVs

303

To demonstrate the importance of the active control system developed and its effectiveness in improving control performance, contact-mode active control (“contact active”) for flexibility compensation alone and active control in combined contact and backlash modes (“combined active”) for both flexibility and backlash compensation were simulated. The value of longitudinal acceleration was selected as a parameter to evaluate the vehicle’s drivability. Some results are described below. 8.4.3.1 Simulation Results of Contact-Mode Active Control Fig. 8.14 shows the simulation results of contact-mode active control for flexibility compensation, neglecting the effect of the backlash gap. According to Fig. 8.14, to compensate for the power loss during regenerative-brake torque transmission in the driveline, the motor torque

Figure 8.14 (A) Simulation results of contact-mode active control; (B) simulation results of combined contact and backlash modes active control.

304

Modeling, Dynamics, and Control of Electrified Vehicles

is increased and ensures that the actual half-shaft torque reaches the target quickly, beginning at 1.4 s. However, because backlash compensation is not involved in this control, the speed difference between the motor and the wheel is greatly increased to almost 23 rad/s, during the backlash traverse. Although the waiting time for the gap traverse is shortened to 38 ms, this effort results in a drastic oscillation in the half-shaft torque, leading to unexpected jerks occurring at the beginning of reoccurrence of negative contact. Because the hydraulic brake pressure is regulated based on the motor’s brake torque, it also experiences an undesired frequency modulation during the period between 1.1 and 1.4 s. These results indicate that active control for backlash compensation is worth implementing in an advanced electric powertrain control system. 8.4.3.2 Simulation Results of Active Control in Combined Contact and Backlash Modes Fig. 8.14A shows the simulation results of active control for both flexibility and backlash compensation. As with the contact-mode active control discussed above, this strategy also ensures that the half-shaft torque remains consistent with the target value to compensate for the torque loss in the driveline. Furthermore, during backlash mode, the active slidingmode controller reduces the motor torque effort, which reduces the speed difference between the motor and the wheel. Hydraulic brake pressure is maintained during backlash control, as seen in the third subplot of Fig. 8.14B. Although the waiting time for the backlash traverse increases slightly to 46 ms, the half-shaft torque oscillation is significantly reduced. The motor’s regenerative-brake torque is smoothly applied during the transition, ensuring comfortable deceleration. 8.4.3.3 Comparisons of the Three Control Algorithms Fig. 8.15A shows that both of the two active control algorithms ensure good torque-tracking performance while compensating for the powertrain flexibility. The combined active control strategy is more advantageous than the other two with respect to the backlash compensation achieved during the transition process, which further improves the vehicle drivability, as shown in Fig. 8.15B. The performance and regeneration efficiencies of the three control strategies are also compared quantitatively below. To compare the control performance of each strategy, the tracking errors et of the half-shaft torque from t 5 1 to 2.5 s were examined by various means. The average

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tracking error jet j and the standard deviation of the errors σet were selected as evaluation parameters. As Table 8.3 shows, the combined active control strategy yields the best tracking performance of the three strategies, as indicated by the values jet j 5 21.05 Nm and σet 5 55.31 Nm, respectively. The control performance of the three control strategies was also compared at the vehicle level, as shown in Table 8.4. The two active control algorithms developed are more advantageous than the conventional one with respect to deceleration and regeneration efficiency. Although the two improved control algorithms perform almost the same in deceleration, the combined active control algorithm performs better with respect

Figure 8.15 (A) Simulation results of half-shaft torque under three different control algorithms; (B) simulation results of vehicle drivability under three different control algorithms. Table 8.3 Simulation results of torque-tracking performance jet j (Nm) Control algorithm σet (Nm) Backlash traverse time (ms)

Baseline Contact active Combined active

64.82 25.50 21.05

85.69 60.25 55.31

40 38 46

Table 8.4 Simulation results of driveability and regeneration efficiency Control Mean deceleration Root mean square of Regeneration algorithm (m/s2) jerk (m/s3) efficiency (%)

Baseline Contact active Combined active

2.75 2.96

10.35 3.46

64.68 67.52

2.96

3.38

67.71

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Modeling, Dynamics, and Control of Electrified Vehicles

to the variation in vehicle jerk, which confirms the validity and effectiveness of the active control algorithm for backlash compensation.

8.5 CONCLUSION In order to further explore the potential of the braking-energy regeneration and brake performance of EVs, brake-blending control algorithms were investigated. The layout of the adopted system was introduced. The models of the main components related to the regenerative brake and the frictional brake of the target electric passenger car were built in MATLAB/ Simulink. The proposed regenerative-braking control algorithm was illustrated. The control effects and regeneration efficiencies of the proposed control strategy were hardware-in-the-loop simulated and compared with the original strategy. The hardware-in-the-loop (HiL) simulation results showed that the proposed regenerative-braking control algorithm is advantageous with respect to the regeneration efficiency. The regeneration efficiency of the original control strategy is 64.94%, while the regeneration efficiency of the proposed control algorithm reaches 80.10%. The improvement of the regeneration efficiency by the proposed control algorithm based on the bywire brake system is above 23%. In order to improve vehicle drivability during regenerative decelerations, the active control of the powertrain for backlash and flexibility compensation were discussed. The effects of nonlinear backlash and powertrain flexibility on vehicle drivability during regenerative deceleration were analyzed. To further improve the drivability and blendedbraking performance, a mode-switching-based active control algorithm was developed and simulated under normal deceleration processes. The simulation results showed that under combined active control, the average tracking error of the half-shaft torque and the root mean square of the vehicle jerk were 21.05 Nm and 3.38 m/s3, respectively, demonstrating the feasibility and the effectiveness of the proposed algorithm.

REFERENCES Amann, N., Bocker, J., Prenner, F., 2004. Active damping of drive train oscillations for an electrically driven vehicle. IEEE/ASME Trans. Mechatron. 9 (4), 697
700. Aoki, Y., Suzuki, K., Nakano, H., Akamine, K., Shirase, T., Sakai, K., 2007. Development of hydraulic servo brake system for cooperative control with regenerative brake (No. 2007-01-0868). SAE Technical Paper.

Brake-Blending Control of EVs

307

Bayar, K., Wang, J., Rizzoni, G., 2012. Development of a vehicle stability control strategy for a hybrid electric vehicle equipped with axle motors. Proc. Inst. Mech. Eng., Part D 226 (6), 795
814. Bottiglione, F., Sorniotti, A., Shead, L., 2012. The effect of half-shaft torsion dynamics on the performance of a traction control system for electric vehicles. Proc. Inst. Mech. Eng., Part D 226 (9), 1145
1159. Chiara, F., Canova, M., 2013. A review of energy consumption, management, and recovery in automotive systems, with considerations of future trends. Proc. Inst. Mech. Eng., Part D 227 (6), 914
936. Crolla, D.A., Cao, D., 2012. The impact of hybrid and electric powertrains on vehicle dynamics, control systems and energy regeneration. Veh. Syst. Dyn. 50 (Sup 1), 95
109. de Castro, R., Arau´jo, R.E., Tanelli, M., Savaresi, S.M., Freitas, D., 2012. Torque blending and wheel slip control in EVs with in-wheel motors. Veh. Syst. Dyn. 50 (Sup 1), 71
94. Fazeli, A., Zeinali, M., Khajepour, A., 2012. Application of adaptive sliding mode control for regenerative braking torque control. IEEE/ASME Trans. Mechatron. 17 (4), 745
755. Fleming, B., 2013. Electric vehicle collaboration-Toyota Motor Corporation and Tesla Motors [automotive electronics]. IEEE Veh. Technol. Mag. 8, 4
9. Gao, H., Gao, Y., Ehsani, M., 2001. A neural network based SRM drive control strategy for regenerative braking in EV and HEV. In: Electric Machines and Drives Conference, 2001. IEMDC 2001. IEEE International. IEEE, pp. 571
575. Gao, Y., Chen, L., Ehsani, M., 1999. Investigation of the effectiveness of regenerative braking for EV and HEV (No. 1999-01-2910). SAE Technical Paper. Jo, C., Ko, J., Yeo, H., Yeo, T., Hwang, S., Kim, H., 2012. Cooperative regenerative braking control algorithm for an automatic-transmission-based hybrid electric vehicle during a downshift. Proc. Inst. Mech. Eng., Part D 226 (4), 457
467. Khalil, H.K., 2001. Nonlinear Systems, third ed. Prentice Hall, Upper Saddle River, NJ. Kum, D., Peng, H., Bucknor, N.K., 2011. Supervisory control of parallel hybrid electric vehicles for fuel and emission reduction. J. Dyn. Syst. Meas. Control 133 (6), 061010. Lagerberg, A., Egardt, B., 2007. Backlash estimation with application to automotive powertrains. IEEE Trans. Control Syst. Technol. 15 (3), 483
493. Lv, C., Zhang, J., Li, Y., 2014a. Extended-Kalman-filter-based regenerative and friction blended braking control for electric vehicle equipped with axle motor considering damping and elastic properties of electric powertrain. Veh. Syst. Dyn. 52 (11), 1372
1388. Lv, C., Zhang, J., Li, Y., Sun, D., Yuan, Y., 2014b. Hardware-in-the-loop simulation of pressure-difference-limiting modulation of the hydraulic brake for regenerative braking control of electric vehicles. Proc. Inst. Mech. Eng., Part D 228 (6), 649
662. Lv, C., Zhang, J., Li, Y., Yuan, Y., 2014c. Regenerative braking control algorithm for an electrified vehicle equipped with a bywire brake system (No. 2014-01-1791). SAE Technical Paper. Lv, C., Zhang, J., Li, Y., Yuan, Y., 2015a. Mechanism analysis and evaluation methodology of regenerative braking contribution to energy efficiency improvement of electrified vehicles. Energy Convers. Manage. 92, 469
482. Lv, C., Zhang, J., Li, Y., Yuan, Y., 2015b. Synthesis of a hybrid-observer-based active controller for compensating powetrain backlash nonlinearity of an electric vehicle during regenerative braking. SAE Int. J. Alt. Power. 4 (1), 190
198. Lv, C., Zhang, J., Li, Y., Yuan, Y., 2015c. Mode-switching-based active control of a powertrain system with non-linear backlash and flexibility for an electric vehicle during regenerative deceleration. Proc. Inst. Mech. Eng., Part D 229 (11), 1429
1442.

308

Modeling, Dynamics, and Control of Electrified Vehicles

Lv, C., Hong, W., Cao, D., 2017. High-precision hydraulic pressure control based on linear pressure-drop modulation in valve critical equilibrium state. IEEE Trans. Ind. Electron. in press, online. Lv, C., Zhang, J., Li, Y., Yuan, Y., 2016. Directional-stability-aware brake blending control synthesis for over-actuated electric vehicles during straight-line deceleration. Mechatronics 38, 121
131. Martinez, C.M., Hu, X., Cao, D., Velenis, E., Gao, B., Wellers, M., 2016. Energy management in plug-in hybrid electric vehicles: recent progress and a connected vehicles perspective. IEEE Trans. Veh. Technol. in press, online. Nakamura, E., Soga, M., Sakai, A., Otomo, A., Kobayashi, T., 2002. Development of electronically controlled brake system for hybrid vehicle (No. 2002-01-0300). SAE Technical Paper. Ohtani, Y., Innami, T., Obata, T., Yamaguchi, T., Kimura, T., Oshima, T., 2011. Development of an electrically-driven intelligent brake unit (No. 2011-01-0572). SAE Technical Paper. Pacejka, H.B., Bakker, E., 1992. The magic formula tyre model. Veh. Syst. Dyn. 21 (S1), 1
18. Paladini, V., Donateo, T., De Risi, A., Laforgia, D., 2007. Super-capacitors fuel-cell hybrid electric vehicle optimization and control strategy development. Energy Convers. Manage. 48 (11), 3001
3008. Song, B., Hedrick, J.K., 2011. Dynamic Surface Control of Uncertain Nonlinear Systems: An LMI Approach. Springer Science & Business Media, London and New York. Sovran, G., Blaser, D., 2006. Quantifying the potential impacts of regenerative braking on a vehicle’s tractive-fuel consumption for the US, European, and Japanese driving schedules (No. 2006-01-0664). SAE Technical Paper. Templin, P., 2008. Simultaneous estimation of driveline dynamics and backlash size for control design. In: IEEE International Conference on Control Applications. CCA 2008. Uzunoglu, M., Alam, M.S., 2007. Dynamic modeling, design and simulation of a PEM fuel cell/ultra-capacitor hybrid system for vehicular applications. Energy Convers. Manage. 48 (5), 1544
1553. von Albrichsfeld, C., Karner, J., 2009. Brake system for hybrid and electric vehicles (No. 2009-01-1217). SAE Technical Paper. Yin, D., Oh, S., Hori, Y., 2009. A novel traction control for EV based on maximum transmissible torque estimation. IEEE Trans. Ind. Electron. 56 (6), 2086
2094. Zhang, J., Lv, C., Gou, J., Kong, D., 2012. Cooperative control of regenerative braking and hydraulic braking of an electrified passenger car. Proc. Inst. Mech. Eng., Part D 226 (10), 1289
1302. Zhang, J., Lv, C., Qiu, M., Li, Y., Sun, D., 2013. Braking energy regeneration control of a fuel cell hybrid electric bus. Energy Convers. Manage. 76, 1117
1124. Zhang, J., Li, Y., Lv, C., Yuan, Y., 2014a. New regenerative braking control strategy for rear-driven electrified minivans. Energy Convers. Manage. 82, 135
145. Zhang, J., Lv, C., Yue, X., Li, Y., Yuan, Y., 2014b. Study on a linear relationship between limited pressure difference and coil current of on/off valve and its influential factors. ISA Trans. 53 (1), 150
161.

FURTHER READING Gao, Y., Ehsani, M., 2001. Electronic braking system of EV and HEV—integration of regenerative braking, automatic braking force control and ABS (No. 2001-01-2478). SAE Technical Paper.