## 2 Design of the Revised Braking Regenerative Control Strategy
### Braking Work-Point Switching Logic of RRBCS  
The objective of the regenerative braking control strategy for R-EEV is to guarantee the comprehensive regenerative braking performance during operation. The allocation logic of the  
Figure 4: Diagram of the optimal slip ratio control process by the double fuzzy logic controller (DFLC). braking work-point is crucial to the efficiency of RRBCS [20]. In this paper, the braking work-point in RRBCS was divided into five types, as shown in Figure 5a,b. Allocation logic of the braking work-point in RRBCS is as follows: (1) If \(Z_{req\_I}<Z_{a\_J}\) and \(\mu_{max}<\mu_{\mu\_J}\), the braking work-point should follow the \(I\) curve on work-point 1 (\(W_{\rm C1}\)) to protect the wheel from locking and slipping. (2) If \(Z_{req\_I}<Z_{a\_J}\) and \(\mu_{max}>\mu_{\mu\_J}\), the braking work-point should follow the \"\(OA\)\" curve on work-point 2 (\(W_{\rm C2}\)) to protect the wheel from locking and slipping. Regenerative braking torque provides sufficient braking torque at the front wheel and the rear wheel hydraulic force is 0. (3) If \(Z_{b\_I}>Z_{req\_m}>Z_{a\_J}\) and \(\mu_{max}<\mu_{\mu\_J}\), the braking work-point should follow the \(I\) curve on work-point 3 (\(W_{\rm C3}\)) to protect the wheel from locking and slipping due to the fact that larger \(Z_{req\_m}\) exists. (4) If \(Z_{b\_I}>Z_{req\_m}>Z_{a\_J}\) and \(\mu_{max}>\mu_{\mu\_J}\), the braking work-point should follow the \"\(AB\)\" curve on work-point 4 (\(W_{\rm C4}\)). The motor will provide its maximum regenerative torque applied at the front wheels, and the insufficient part of the driving braking torque would be compensated by the hydraulic braking system. (5) If \(Z_{req\_I}>Z_{b\_I}\), the braking work-point should follow the \(I\) curve on work-point 5 (\(W_{\rm C5}\)). In order to control the fluctuation range of the battery SoC and prevent the RCC from being too large to affect the battery life, the regenerative charging work-point of the control logic is referenced in the battery SoC characteristics for conservative adjustments. The strategy makes the SoC close to the pre-set value, which not only protects the battery state of health, but also fully uses the battery pack power. The \"conservative braking mode\" is a conservative adjustment of the original braking work-point of RBCS. In order to meet the above performance requirements, the braking work-point switching logic needs to be adjusted in real time according to the vehicle status. With SoC characteristics as the switching limit, the braking work-point switching logic is shown in Figure 6.  
The battery SoC value at the \(k\) instant \(SoC^{(k)}\) and the \(k+1\) instant \(SoC^{(k+1)}\) were detected, respectively. The SoC change rate \(k_{SoC}\) and change rate discrimination value \(k_{\sigma}\) were calculated as follows:  
\[k_{SoC}=(SoC^{(k+1)}-SoC^{(k)})\Delta t^{-1} \tag{7}\]  
Figure 5: Allocation logic of five braking work-points in RRBCS: (**a**) area schematic; (**b**) logic schematic; and (**c**) switching logic schematic. Figure 6: Schematic diagram of the braking work-point switching logic: (**a**) charge depletion (CD) and (**b**) charge sustaining (CS). \[k_{\sigma}=\xi_{0}k_{0}=\xi_{0}(SoC_{0}^{(k+1)}-SoC_{0}^{(k)})\Delta t^{-1} \tag{8}\]  
where \(SoC_{0}\) is the \(SoC\) control target value; \(k_{0}\) is the SoC control target change rate on drop stage; the \(k_{0\_CD}\) is a preset value in charge depletion; the \(k_{0\_CS}=0\) in charge sustaining; and \(\zeta_{0}\) is a correction coefficient with a value of 0.5. As depicted in Figures 5c and 6, the braking work-point is changed to follow the \(I\) curve, that is, \(W_{C1}\) is switched to \(W_{C2}\), and the \(W_{C4}\) is switched to the \(W_{C3}\). The \"conservative braking mode\" is realized in three cases and the details are explained as follows: (1) In CD, if \(k_{soc}>|k_{cr}|>0\), the \"conservative braking mode\" should be used to prevent SoC from deviating too much from \(SoC_{0}\), which can reduce the adverse impact of RCC on the battery.