# Hybrid Model Predictive Control of Semiactive Suspension in Electric Vehicle with Hub-Motor
## 6 Conclusions and Discussion  
In this paper, we proposed a semiactive suspension control method that can consider the nonlinear constraint of damping force to suppress the vibration of the sprung mass and motor in order to address the deterioration of the vertical performance of HM-EV. A state observer was designed based on the Kalman filter algorithm for HM-EV to meet the control needs of the controller. The main conclusions are as follows:  
(1) The state observer designed based on the Kalman filter algorithm can effectively accomplish the observation task. Simulations were performed to verify the observation effect under white noise random roads and bump roads, and the results show that the errors between the observed and actual values are small under both road excitations. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Road Excitation** & **Performance Index** & **Passive** & **COC** & **HMPC** \\ \hline \multirow{4}{*}{\(a=0.1\) m} & Vertical acceleration of sprung mass & 13.4729 & \begin{tabular}{c} 10.7764 \\ (\(\uparrow\)20.01\%) \\ \end{tabular} & \begin{tabular}{c} 8.9044 \\ (\(\uparrow\) 33.91\%) \\ \end{tabular} \\ \cline{2-4}  & Motor eccentricity & \(10\times 10^{-4}\) & \begin{tabular}{c} 8.0169 \(\times 10^{-4}\) \\ (\(\uparrow\) 19.83\%) \\ \end{tabular} & \begin{tabular}{c} 6.1764 \(\times 10^{-5}\) \\ (\(\uparrow\) 38.24\%) \\ \end{tabular} \\ \cline{2-4}  & Tire dynamic load & 6119.2 & \begin{tabular}{c} 4685.1 \\ (\(\uparrow\) 23.44\%) \\ \end{tabular} & \begin{tabular}{c} 3611.4 \\ (\(\uparrow\) 40.98\%) \\ \end{tabular} \\ \hline \multirow{4}{*}{\(a=0.02\) m} & Vertical acceleration of sprung mass & 2.6946 & \begin{tabular}{c} 2.1553 \\ (\(\uparrow\) 20.01\%) \\ \end{tabular} & \begin{tabular}{c} 1.8280 \\ (\(\uparrow\) 32.16\%) \\ \end{tabular} \\ \cline{2-4}  & Motor eccentricity & 2.0913 \(\times 10^{-4}\) & \begin{tabular}{c} 1.6034 \(\times 10^{-4}\) \\ (\(\uparrow\) 23.33\%) \\ \end{tabular} & \begin{tabular}{c} 1.2476 \(\times 10^{-4}\) \\ (\(\uparrow\) 40.35\%) \\ \end{tabular} \\ \cline{2-4}  & Tire dynamic load & 1223 & \
\begin{tabular}{c} 937 \\ (\(\uparrow\) 23.39\%) \\ \end{tabular} &
\begin{tabular}{c} 736 \\ (\(\uparrow\) 39.82\%) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The peak-to-peak (PTP) values of HM-EV evaluation indexes. Figure 23: Tire dynamic load. (2) The proposed control algorithm can effectively improve the vertical performance of the vehicle. Simulation analysis was carried out and compared with the COC control algorithm under different magnitudes of random road excitation and bump road excitation. The results show that the proposed control algorithm can effectively reduce the sprung mass and motor vibration regardless of the excitation magnitude and outperforms the COC control algorithm. The effectiveness of the proposed control algorithm was verified. The COC control method ignores the constraints in the optimization calculation and then feeds back to the system after limiting the calculated forces according to the current state, which destroys the optimality of the control. The HMPC control algorithm was able to consider the nonlinear constraints of the damping force directly in the controller, but this also greatly increased the computational effort of the controller and increased the computational time. The HMPC algorithm requires online optimization calculations which increases the actual workload and computation time of the control system and violates the real-time requirements of the control during the operation of the actual vehicle. In order to shorten the computation time, the online computation process of the control law can be transformed into a simple offline table look-up process using multiparameter planning techniques so that the proposed control algorithm can be applied to the real vehicle. This is one of the future research directions. Funding acquisition, Z.L. ; Methodology, H.J. ; Project administration, H.J. ; Software, C.W. ; Validation, H.J. ; Writing--original draft, C.W.