Integrated control of anti-lock and regenerative braking for in-wheel-motor-driven electric vehicles

1. INTRODUCTION

Many studies imply that almost one-half of the driving energy is dissipated during braking, especially in urban driving circumstances with frequent acceleration and deceleration manipulations^[1,2]. The energy consumption during braking processes in different driving cycles is shown in Table 1^[3], where UDDS and ECE stand for urban dynamometer driving schedule and Economic Commission of Europe, respectively. Therefore, regenerative braking systems (RBS), which could recapture kinetic energy and greatly reduce power consumption^[5], are widely researched in electric or hybrid vehicles^[4–6], and brake-by-wire systems^[7,8] that support the application of regenerative braking (RB) are investigated as well^[7–10]. Xu et al. divided the braking into four different modes for hybrid electric vehicles, and a hierarchical controller is designed to switch the braking mode and to realize optimal efficiency control^[11]. Guo et al. presented a piecewise RB strategy for safety and energy-saving control of intelligent electric vehicles^[12]. However, the above strategies do not take the vehicle braking stability into consideration, which will cause the vehicle instability in limited conditions. Biao et al. proposed an optimization distribution algorithm-based RB strategy considering vehicle stability during braking situations^[13]. The torque distribution ratio is determined by the braking strength and related constraint conditions, and the energy recapture efficiency of the proposed strategy was raised by about fifty percent, but the stability effect of the vehicle was not reflected in the verification part.

The in-wheel motor, which is located directly in the wheels, will significantly enhance controllability and response speed by removing all the intermediate mechanical connections. Additionally, it acquires high efficiency both in motor and generator modes^[14]. Therefore, the control strategies for in-wheel motor-driven electric vehicles (IWMDEV) have been widely studied. Karabacak et al. designed a fuzzy logic controller in the motor mode and a pulse width modulation controller in the RB mode for two IWMDEV (2IWMDEV), and the algorithm is embedded in a DSP microcontroller^[15]. Gang and Zhi proposed an RB control method for four IWMDEV (4IWMDEV) under urban scenes using motor efficiency maps, and the simulation results validated the effectiveness of the proposed method under urban driving cycles^[16]. A feedback hierarchical controller for 4IWMDEV is presented by Chen et al. to control the vehicle to track the desired velocity and assign braking torque to increase energy recovery^[17]. However, in addition to improving recovery efficiency, the braking performance and stability should also be considered, especially under heavy braking strength request conditions, which will cause the braking torque distribution problem^[18–21].

Dadashnialehi et al. estimated wheel speed accurately based on the back electromotive force of the brushless DC (BLDC) motor, and proposed a sensorless anti-lock braking system (ABS) for IWMDEVs both theoretically and experimentally^[22]. Wang and He presented an improved linear quadratic Gaussian controller to derive braking torques for ABS control, and a varying charge voltage in steps control is designed to recover more energy^[23]. Yang et al. employed a combination method of logic threshold and phase plane theory to generate the braking torque for ABS control and then proposed a coordination strategy of RBS and ABS to increase recovery efficiency for ABS-triggered scenarios^[24]. Although these methods integrate the RBS and ABS control together to improve the braking performance and recover more energy, rarely do these methods address the stability problem during braking situations. He et al. took the braking stability into consideration and designed a combined sliding mode controller to realize ABS control^[25]. Tang et al. presented a comprehensive controller: the braking torque distribution strategy. This strategy considers safety and recovery efficiency optimization while also involving a coordinated strategy of RBS and ABS based on model predictive control^[26]. Pei et al. proposed a coordinated controller to realize optimal energy regeneration and braking stability for distributed electric vehicles by regulating hydraulic and RB torques^[27]. However, the braking intension is rarely considered during the coordinated control of energy recovery and braking stability.

The above studies indicate that the problem of how to simultaneously improve the braking stability and regeneration efficiency for 2IWMDEVs considering braking intension is still not resolved. This paper aims to present an integrated control method to combine ABS and RBS control, even in emergency braking situations, and synthetically improve braking performance, recovery efficiency, stability, and road adaptability of 2IWMDEVs. The main contributions of the paper include a robust SMC-based ABS controller to make full use of the road conditions under different adhesion coefficients and an RBS strategy to distribute the regenerative and hydraulic braking torques to recapture more energy.

The rest of the paper is organized as follows: In the second section, a SMC-based ABS controller is proposed for 2IWMDEVs, including wheel dynamics models, slip ratio models, ABS controllers, and stability and robustness analysis of the controller. The distribution method of regenerative and frictional braking torques is designed in the third section. In the fourth section, the RB efficiency map is generated through bench experiments. Hardware-in-the-loop (HIL) simulations are conducted in the fifth section to validate the proposed algorithm. Finally, within the same section, conclusions are made, and a future work outlook is provided.

2. SMC-BASED ABS CONTROLLER

2.1. Wheel dynamics

An electric vehicle equipped with two front in-wheel motors and RBSs is applied in the paper, and the two rear wheels are driven by a traction motor. Figure 1 shows rotational dynamics of single wheels, where $$ T_{di} $$ and $$ T_{bi} $$ represent drive and brake torques on the i-th wheel, respectively, $$ F_{mi} $$, $$ F_{xi} $$, and $$ F_{zi} $$ denote gravity, longitudinal force, and vertical force on the tire, respectively. $$ \omega_i $$ stands for velocity of the i-th wheel, and v is vehicle velocity.

Figure 1. Wheel dynamic.

The following assumptions are made.

● The tire rolling resistance and vehicle aerodynamics are negligible during braking processes.

● Tire self-aligning torque is negligible.

● The chamber angle of each wheel is zero.

The dynamic equations are as follows.

(1) $$ m_i \dot{v}=F_{x i}$$

(2) $$ J_{\omega i} \dot{\omega}_i=-T_{b i}+r F_{x i} $$

(3) $$ F_{xi}=\mu_i\left(\lambda_i\right) F_{z i} $$

where $$ J_{\omega i} $$ represents the rotational inertia of the $$ i $$-th in-wheel motor, $$ m_i $$ is the total mass distributed on the $$ i $$-th wheel, $$ r $$ is the effective wheel rolling radius, and $$ \mu_i $$ and $$ \lambda_i $$ present longitudinal utilized friction coefficient and the slip ratio of the $$ i $$-th wheel, respectively.

Combining Equations (1), (2), and (3) yields

(4) $$ \begin{equation} \left\{\begin{array}{c} \dot{\omega}_i=\frac{-T_{b i}+r \mu_i\left(\lambda_i\right) F_{z i}}{J_{\omega i}} \\ \dot{v}=\frac{-\sum \mu_i\left(\lambda_i\right) F_{z i}}{m_i} \end{array}\right. \end{equation} $$

where the slip ratio could be expressed as follows during braking situations

(5) $$ \lambda_i=\frac{v-r \cdot \omega_i}{v} $$

Taking the derivative of Equation (5) with respect to time and substituting Equation (4) into it, we have

(6) $$\dot{\lambda}_i=\frac{r}{J_{\omega i} v} T_{b i}-\frac{r^2}{J_{\omega i} v} \mu_i\left(\lambda_i\right) F_{z i}-\frac{r \omega_i}{m_i v^2} \sum \mu_i\left(\lambda_i\right) F_{z i} $$

Figure 2 represents experimental results based on JAC iEV7S, a four-wheel double-drive electric vehicle; it shows the relationship between slip ratios and longitudinal utilized friction coefficients, and the curve could be simplified with two lines intersecting at the peak utilized friction coefficient point. The longitudinal utilized friction coefficient can be described as follows

(7) $$ \begin{equation} \mu_i\left(\lambda_i\right)= \begin{cases}k_{\mu i t} \lambda_i, & \lambda_i \leq \lambda_{d i} \\ \mu_{\text {imax }}-k_{\mu i h}\left(\lambda_i-\lambda_{d i}\right), & \lambda_i>\lambda_{d i}\end{cases} \end{equation} $$

Figure 2. The curve of $$ \mu_i $$ and $$ \lambda_i $$.

where $$ k_{uit} $$ and $$ k_{uih} $$ denote the slope of lines corresponding to linear and nonlinear areas, respectively, $$ \lambda_{di} $$ stands for reference slip ratios for the $$ i $$-th wheel, and $$ \mu_{imax} $$ represents peak longitudinal utilized friction coefficients of the $$ i $$-th wheel.

Substituting Equation (7) into Equation (6), after some manipulations, we have

(8) $$ \begin{equation} \dot{\lambda}_i= \begin{cases}\frac{r}{J_{\omega i} v} T_{b i}-\frac{r^2}{J_{\omega i} v} \lambda_i k_{u i t} F_{z i}-\frac{r \cdot \omega_i}{m_i v^2} \sum k_{\mu i t} \lambda_i F_{z i}, & \lambda_i \leq \lambda_{d i} \\ \frac{r}{J_{\omega i} v} T_{b i}-\frac{r^2}{J_{\omega i} v}\left(\mu_{i m a x}-k_{\mu i h}\left(\lambda_i-\lambda_{d i}\right)\right) F_{z i}-\frac{r \cdot \omega_i}{m_i v^2} \sum\left(\mu_{i m a x}-k_{\mu i h}\left(\lambda_i-\lambda_{d i}\right)\right) F_{z i}, & \lambda_i>\lambda_{d i}\end{cases} \end{equation} $$

3. DISTRIBUTION OF REGENERATIVE AND FRICTIONAL BRAKING TORQUES

With two front in-wheel motors, the regenerative and frictional blending brake is related, and the optimal objective is to improve energy recovery efficiency and braking stability. To this end, the distribution of the regenerative and frictional braking torques should be first discussed. As shown in Figure 3, the requested braking pressure of the driver is calculated according to brake pedal stroke and the characteristics of brake pressure $$ vs $$. pedal stroke (P-S curve) shown in reference^[7], and then the requested braking force $$ F_b $$ and torque $$ T_b $$ are estimated. A braking torque distribution controller is designed to generate the desired regenerative and frictional braking torques according to the braking strength. The RB torque is executed by the in-wheel motors, while the frictional braking torque is realized by a novel electro-hydraulic actuator illustrated in reference^[28], and the novel electro-hydraulic actuator generates braking force fast and has a fast and good pressure-tracking performance.

Figure 3. Braking torque control schematic.

To improve tire-road friction coefficient (TRFC) utilization efficiency and directional stability during braking situations, both the front and rear wheels should be locked simultaneously, and the desired braking forces of the front and rear axles are expressed as follows

where $$ F_{\mu 1} $$ and $$ F_{\mu 2} $$ denote the desired braking forces of the front and rear axles, respectively, G stands for the weight of vehicles, L represents wheelbase, b is the horizontal distance between the rear axle and center of gravity, and $$ h_g $$ indicates the height of the center of gravity with respect to the ground.

With manipulations of Equation (23), we have

As shown in Figure 3, the braking strength z is achieved according to the requested braking force and $$ F_b $$-$$ z $$ lookup table. The braking mode is divided into three levels: mild ($$ z \leq 0.1 $$), moderate ($$ 0.1 < z \leq 0.7 $$), and emergency ($$ z>0.7 $$), and the braking torque distribution strategy is discussed based on different modes.

(A) When $$ z\leq 0.1 $$, the requested braking torque of the front axle will be offered only by the two front regenerative motors; the braking torque distribution of axles and blended braking system are derived

where $$ T_{bfr} $$ and $$ T_{bfh} $$ represent regenerative and hydraulic braking torques of the front axle, respectively, and the braking torque of the left and right wheels of the front axle is allocated averagely; $$ T_{br} $$ denotes the braking torque of the rear axle.

(B) When $$ 0.1<z \leq 0.7 $$, the RB torque may not meet the request one, and the braking torques are distributed as follows

where $$ T_{bf} = (F_b^2h_g+F_bGb)r/GL $$ is the braking torque calculated by Equation (24), $$ T_{bfrmax} $$ stands for the maximum RB torque that both the left and right motors could be applied for at the same time.

(C) When $$ z>0.7 $$, the braking torque distribution is the same as Equation (26) if the wheels are not locked. However, the ABS will probably be triggered in this large deceleration request situation, and the braking torques of the front and rear axles will not be decided by Equation (24) but rather by the results generated from ABS controllers. In this case, the torque distribution is determined by

where $$ T_{bfiA} $$ and $$ T_{briA} $$ stand for desired braking torques of the four wheels generated by the ABS controller, $$ T_{bfir} $$ and $$ T_{bfih} $$ represent distributed regenerative and hydraulic braking torques of the front two wheels, and $$ T_{bri} $$ is braking torque of two rear wheels.

4. EFFICIENCY MAP OF THE RB SYSTEM

An optimal energy recovery method should be designed based on an efficiency map by minimizing the transfer loss during blending brake, and the motor-to-battery efficiency is calculated by the following expression.

where $$ U_C $$ and $$ I_C $$ are the measured battery charging voltage and current during RB, respectively.

Figure 4 shows the test bench; a motor with the same characteristics is used instead of the in-wheel one, and a magnetic powder brake is adopted to simulate the vehicle rolling resistance to prevent the motor from moving or to supply kinetic energy during braking. Batteries and sensors are installed to collect energy recapture information. With Equation (28), the RB efficiency map is generated from bench tests under different braking torques and wheel velocities and is fitted, as shown in Figure 5, based on the experimental data.

Figure 4. Test bench.

Figure 5. RB efficiency map.

5. HIL SIMULATION AND RESULTS ANALYSIS

A HIL simulation system equipped with vehicle-manipulator systems, steering systems, and hydraulic braking system is developed to evaluate the performance of the proposed integrated algorithm. Figure 6 displays the system composition. Figure 7 illustrates the algorithm block diagram. In this diagram, the steering angle and braking torque are requested by the driver. The vehicle model is then simulated using the CarSim software. The torque distribution and ABS algorithm code are generated using MATLAB/Simulink and downloaded to the dSPACE/SCALEXIO for execution. Finally, the recaptured energy is stored in the battery pack.The vehicle model and controller parameters are listed in Table 2.

Figure 6. HIL simulation system.

Figure 7. Algorithm block diagram.

5.1. Results on homogeneous surface

A steering-braking maneuver with a 75 km/h initial forward velocity is performed on a high-mu homogeneous surface to verify the proposed algorithm, and a Proportional, Integral, and Derivative (PID) controller is also simulated to compare with the proposed one. Figure 8 shows the time histories of vehicle and wheel velocities derived from the two controllers under the specified simulation maneuver. At the end of the simulation, the four wheels of the PID controller are locked, while those of the SMC controller are not during the whole simulation, which indicates that the proposed SMC controller achieves better anti-lock performance than the PID controller. As shown in Figure 8A and B, compared with PID controllers, the regulation frequency of the front wheels of SMC controllers is lower, which will improve the vehicle stability and comfort.

Figure 8. Velocities of vehicles and wheels. (A) Front left wheel; (B) Front right wheel; (C) Rear left wheel; (D) Rear right wheel.

Figure 9 depicts the comparison of wheel slip ratios derived from the two controllers. Slip ratios of all the wheels of both the controllers are within a reasonable range near the optimal value in the beginning, and then, the fluctuation of the PID controller dramatically rises to approximately one while that of the SMC controller is still reasonable. The high braking torque regulation frequency of front wheels leads to frequent and dramatic chattering of the slip ratio. The results illustrate that the SMC controller acquires a significantly better tracking performance of the optimal slip ratio.

Figure 9. Slip ratio of the wheels.(A) Front left wheel; (B) Front right wheel; (C) Rear left wheel; (D) Rear right wheel.

Figure 10 presents the time histories of sideslip angular velocities and yaw rates. In Figure 10A, although the fluctuations of both two controllers are large in the beginning because of the steering input, the sideslip angular velocity derived from the SMC controller is constrained within a very small boundary in the remaining simulation process, while that of the PID method is still variate intensive. As shown in Figure 10B, the magnitude of the yaw rate of the PID controller is much larger than that of the SMC controller, especially at the end of the simulation. The results indicate that the proposed method achieves a better handling and stability performance than that of the PID controller.

Figure 10. Vehicle sideslip angular velocity and yaw rate. (A) Sideslip angular velocity; (B) Yaw rate.

Figure 11 and Figure 12 reveal the comparison of energy recovery between the SMC and PID controllers. Since the braking torque generated by the SMC controller is much bigger than that of the PID controller before about 1.5 s, the recapture energy of the SMC controller is larger during the beginning period. After about 2.4 s, the braking torque derived from PID is larger than SMC, which causes a greater wheel velocity variation even to lock, as shown in Figure 8. However, the recaptured energy by SMC grows faster than by PID due to the distribution of braking torques, and the main growth of recovery energy by SMC lies in this period. Overall, the SMC-based energy recovery efficiency is significantly higher than that of PID-based, and the efficiency increases by 52.9%.

Figure 11. Distribution of the regenerative braking energy.

Figure 12. Comparison of total recaptured energy.

5.2. Results on the split surface

A driver-in-the-loop simulation on the split surface with a 70 km/h initial forward velocity is conducted to evaluate the effectiveness of the proposed algorithm in non-ideal scenarios, and the TRFCs of the left and right sides are 0.3 and 0.8, respectively. Figure 13A shows the master cylinder pressure applied by the driver and the wheel cylinder pressures generated by the ABS controller. The applied pressure (about 8 MPa) is too big to anti-lock the wheels, and the ABS is triggered to regulate the wheel pressures. Furthermore, the generated pressures of the left wheels change more frequently than the right wheels due to the lower TRFC, and the pressure increasement times of the front left (FL) and rear left (RL) wheels are 25 and 26 in approximately eight seconds, whereas that of the front right (FR) and rear right (RR) are two and 24 times, respectively. Although the left wheels are easier to lock up due to their huge fluctuations of slip ratios, the frequent regulation of braking pressures keeps the wheels in anti-lock status, as shown in Figure 13B. The maximum equivalent braking pressure generated by the RB motor is calculated by the following expression.

(29) $$ P_{m r}=\frac{F_{b f r \max } r}{2 \pi r_w^2 \mu r_b} $$

Figure 13. Simulation results on the split surface. (A) Braking pressure; (B) Velocities; (C) Regenerative braking; (D) Hydraulic braking.

With the parameter values listed in Table 2, the value of $$ P_{mr} $$ is calculated as 2 MPa. Figure 13C and D indicates the braking distribution results of the front wheels derived from the proposed algorithm; only RB is applied if the pressure generated by the ABS controller is less than 2 MPa, and the residual pressure is generated by the hydraulic braking system.

6. CONCLUSIONS AND FUTURE WORK

An integrated algorithm is proposed for ABS and RBS coordinated control of 2IWMDEVs to improve vehicle braking stability and energy recovery efficiency, including both RB control on the front two wheels and anti-lock braking control on all four wheels. HIL simulations are carried out to verify the effectiveness of the integrated algorithm, and the results show that the ABS controller can prevent wheels from being locked to ensure braking performance and vehicle stability. With the distribution strategy of braking torques among in-wheel motors and friction brakes considering the required braking torque and strength, the recovered energy of the proposed strategy under ABS-triggered maneuver is increased by 52.9% than that of the PID controller. Therefore, the presented integrated algorithm can not only maintain the slip ratio within the desired range and braking stability but also achieve excellent energy recapture efficiency, which is significant to ensure safety and economy of the 2IWMDEVs.

Our future work will concentrate on adaptive threshold value design for braking modes division, experimental validation of the proposed algorithm through in-vehicle field and road tests with the consideration of uncertainties, and modification of the proposed algorithm to adapt to 4IWMDEVs.

DECLARATIONS