## 4 Comparative Simulation Analysis
### Comparative Analysis with DLC
Similarly, as seen in Figure 11, the absolute values of the maximum body pitch angle velocity via the MPC and DLC strategies are 0.0105 and 0.0490 rad/s, respectively. Furthermore, when compared with the DLC strategy, the MPC strategy shows that the absolute value of the maximum body pitch angle velocity dropped by 78.57%. The MPC strategy reduces the pitch angle and pitch angle velocity of the body in most of the cases. The vertical movement of the vehicle body is also an important factor affecting the comfort of the vehicle. The changes in the vertical velocity and vertical acceleration of the vehicle body mass center are shown in Figure 12,b, respectively. It is evident from Figure 12 that the absolute values of the maximum body mass center velocity through the MPC and DLC strategies are 0.0057 and 0.0128 m/s, respectively. Furthermore, when compared with the DLC strategy, the MPC strategy shows that the absolute value of the maximum body mass center velocity dropped by 55.47%. From Figure 12, it can be seen that the absolute values of the body mass center accelera  
Figure 11: Body pitch angle and pitch angle velocity. (**a**) Body pitch angle; (**b**) Body pitch angle velocity. Figure 12: Body mass center velocity and acceleration. (**a**) Body mass center velocity; (**b**) Body mass center acceleration. tion obtained by the MPC strategy are lower than those obtained by the DLC strategy in most circumstances. During active suspension control, the maximum control force cannot exceed the maximum action force. The variations in the front and rear suspension control forces are shown in Figure 13a,b, respectively. Figure 13 indicates that under the MPC strategy, the absolute values of the maximum control forces of the front and rear suspensions are 936 and 1033 N, respectively, which do not exceed the constraint value (1500 N). Combining Figures 3 and 8, it can be seen that in order to reduce the vertical motion of the vehicle body caused by the braking intensity, the MPC strategy has greater control force than the DLC strategy for a long time. The root mean square (RMS) value is an important indicator of signal power. The RMS values of some indicators reflecting the comfort of the vehicle are shown in Table 2. Here, \(\omega\) = (RMS(DLC) \(-\) RMS(MPC))/RMS(DLC). From Table 2, it can be seen that the RMS values obtained by the MPC strategy are all smaller than those obtained by the DLC strategy. Compared with the DLC strategy, the RMS values of the front and rear body vertical velocity, body pitch angle and body pitch angle velocity under the MPC strategy are all reduced by more than 70%, further verifying that the MPC strategy improves the comfort of the vehicle. In summary, under the gradual braking condition, the robustness of the control system is discussed, and two control strategy simulations, namely the MPC and DLC strategies, were carried out. Figure 5 demonstrates that the control system has a certain anti-interference ability. Figures 6 and 7 reflect the influence of parameter mismatch on the control effect, indicating that the control system has a certain tolerance for parameter mismatch. The variations in the vertical velocity of the front and rear bodies are shown \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Category** & **MPC** & **DLC** & \(\omega\) \\ \hline Front body vertical velocity & 0.0107 & 0.0358 & 0.7011 \\ Rear body vertical velocity & 0.0065 & 0.0385 & 0.8312 \\ Body mass center velocity & 0.0032 & 0.0044 & 0.2727 \\ Body mass center acceleration & 0.0163 & 0.0282 & 0.4220 \\ Body pitch angle & 0.0063 & 0.0239 & 0.7364 \\ Body pitch angle velocity & 0.0058 & 0.0251 & 0.7689 \\ \hline \end{tabular}
\end{table} 
Table 2: Root mean square (RMS) of some parameters. Figure 13: Front and rear suspension control forces. (**a**) Front suspension control force; (**b**) Rear suspension control force. in Figure 8a,b, respectively.