## 3 Regenerative Electronic Strategy and Stability Control Strategy  
The main objective of the yaw rate controller design was to compare the vehicle yaw rate and other stability-related states with the desired states obtained using drive commands of the autonomous vehicles. The desired state parameters -yaw rate and side slip angle- were calculated using a two-DoF vehicle single-track model. The two DoF equations of motion are expressed below.  
\[\dot{v}_{y_{d}}=\frac{1}{m_{t}}\big{[}\big{(}C_{f}+C_{r}\big{)}\frac{v_{y_{d}}} {v_{x_{d}}}+\big{(}1C_{f}-1C_{r}-m_{t}v_{x_{d}}^{2}\big{)}\frac{\gamma_{d}}{v_ {x_{d}}}-C_{f}\delta\big{]} \tag{13}\]  
\[\dot{\gamma}_{d}=\frac{1}{l_{zz}}\big{[}\big{(}2 lC_{f}-2 lC_{r}\big{)}\frac{v_ {y_{d}}}{v_{x_{d}}}+\big{(}(2l)^{2}C_{f}+(2l)^{2}C_{r}\big{)}\frac{\gamma_{d}} {v_{x_{d}}}-2 lC_{f}\delta\big{]} \tag{14}\]  
Here, \(\gamma_{d}\) desired yaw rate, \(\dot{v}_{y_{d}}\) desired lateral acceleration, \(\dot{v}_{x_{d}}\) desired longitudinal acceleration, \(C_{f}\) and \(C_{r}\) indicate the lateral stiffnesses of the front and rear wheels given as in Table 1, respectively, \(\delta\) denotes the steering angle of the front tire. Figure 4 shows the yaw rate controller scheme. In this scheme, input parameters such as the vehicle speed, steering angle, and brake situation are defined from the autonomous vehicle with reference to the drive cycle and road profile. The referenced model determined the desired yaw rate and slip angle based on the outlined input parameters. A PID controller calculated the desired moment around the z-axis, \(M_{z,des}\), with respect to the vehicle reference coordinate using the error value between the actual yaw rate, which was calculated using the detailed vehicle model, and the desired yaw rate. Additionally, the desired torque value, \(T_{si}\), for each tire was calculated using the value from the wheel slip controller. These value input parameters of the torque distribution algorithm produced values that were the same as those obtained using the desired wheel slip torque, which was calculated from the wheel slip PID controller and drive force at the x-axis defined from the vehicle based on the drive cycle. The torque distribution algorithm requires the input of the torque value for the control of the yaw rate of the vehicle. A parallel PID structure was chosen, as the parallel form allows the complete decoupling of proportional, integral, and derivative actions and also decreases the time for finding the optimum PID coefficients.  
In electric vehicles, three different regenerative braking strategies are used: series braking with an optimal feel, series braking with optimal energy recovery, and parallel braking [44]. It should be noted that the regenerative braking strategy of HFCEVs has to meet two main requirements. Firstly, the total required braking force has to be distributed  
Figure 4: Yaw rate controller scheme.  
and the kinetic energy of the vehicle has to be recovered as much as possible. Secondly, the total requiring braking force on the rear and front axles needs to be distributed to achieve steady-state braking performance. Based on these requirements, in this study, the method of series braking with optimal energy recovery was chosen as in [44]. The main working principle of this strategy is based on this approach: when the vehicle is braked with a deceleration rate which is smaller than road friction, the braking force can be varied within a certain range. In this scenario, the sum of the rear and front braking forces equals the inertia force of the vehicle, and it is assumed that this principle is satisfied in the referenced FTP75 and NEDC drive cycles.