## 4 Results and Discussion
### Bump Road Excitation  
To reveal the transient response characteristics of the electric vehicle and the IWM, the bumpy road excitation is introduced as follows:  
\[z_{g}=\left\{ \begin{array}{cc}\frac{a}{2}(1-\cos(\frac{2\pi v_{0}}{l}t)),&t_{0 }\leq t\leq\frac{l}{v_{0}}+t_{0}\\ 0,&t>l/v_{0}+t_{0}\end{array} \right. \tag{52}\]  
where \(a\) denotes the height of the bump; \(l\) denotes the length of the bump; \(v_{0}\) denotes vehicle forward velocity. Here we choose \(v_{0}\) = 25 km/h, \(l\) = 0.2 m and \(a\) = 0.1 m. Figure 8a,b show the road displacement excitation and speed excitation, respectively. Figure 9 shows the time-domain responses of passive suspension, \(\mathrm{K_{C}}\) and \(\mathrm{K_{P}}\). It can be observed that, compared with passive suspension, the body acceleration, tire dynamic force and suspension deflection of active suspension with \(\mathrm{K_{C}}\) and \(\mathrm{K_{P}}\) are obviously reduced. Furthermore, the periods of their transients become much shorter. These imply that the performance of the electric vehicle has been improved with active control system. In addition, it can be observed that the control effects of \(\mathrm{K_{C}}\) and \(\mathrm{K_{P}}\) are similar in time domain. Figure 8: Bump input from the ground: (**a**) displacement excitation; (**b**) speed excitation. Figure 7: Control structure of the active suspension system. Besides, the corresponding responses of the rotor eccentricity and the UEF of IWM are illustrated in Figure 10. It can be seen that the magnitudes of the eccentricity and the UEF under active suspension are significantly reduced in time domain, indicating that the active suspension greatly improve the performance of the IWM. The reason behind this is that active suspension inhibits the rotor eccentricity, restricting the magnetic force oscillation. Thus, the coupling effect in IWM is alleviated. Figure 11a,b show the frequency responses from the ground velocity to the body vertical acceleration for the open and closed-loop systems using the conventional robust controller and the parameter-dependent controller. It can be observed that the closed-loop system minimizes the acceleration of the sprung mass in the frequency range from 1 Hz to 8 Hz implying that the ride comfort of EV is enhanced. The parameter-dependent controller for active suspension systems achieve less value of sprung mass acceleration than the conventional robust controller. It means that the control effect of the parameter-dependent controller is slightly better. In addition, the second peak value of \(T_{\tilde{z}_{b}/\tilde{z}_{g}}\), which decreases with an increase in the sprung mass, is the fixed point for active suspension system. Figure 10: The motor responses under bump excitation: (**a**) the rotor eccentricity; (**b**) the UEF. Figure 9: Vehicle dynamic responses under bump excitation: (**a**) body acceleration; (**b**) suspension deflection; (**c**) tire dynamic force; (**d**) actuator force. Figure 11c,d demonstrate the frequency responses from the ground velocity to the rotor eccentricity for the open and closed-loop systems. It can be seen that the closed-loop system reduces the value of \(T_{(z_{\tau}-z_{g})/z_{g}}\) in the frequency range from 1 Hz to 4 Hz, implying that active suspension can suppress the interference from the ground to the IWM in the corresponding frequency range, alleviating the coupling effect in IWM. Figure 11e,f show the frequency responses from the \(F_{r}\) (UEF) to the body vertical acceleration for the open and closed-loop systems. One can observe that the closed-loop system can suppress the influence of the UEF on the body vertical acceleration, improving the ride comfort of EV. Compared with the conventional robust controller, the parameter-dependent controller performs better in frequency domain.