## 4 Random Pavement Excitation
To more clearly observe the dynamic performance of each HVS system at different vehicle speeds, Table 3 provides the root mean square (RMS) values of the seven evaluation indicators for the four HVS systems at vehicle speeds of 5, 10, 15, 20, 25 and 30 m/s, with the corresponding line graphs shown in Figure 6. It can be seen from Figures 5 and 6 that the RMS(\(z_{aa}\)), RMS(\(\varphi_{a}\)), RMS(\(z_{aa}\)), RMS(\(I_{sssf}\)), RMS(\(I_{sssf}\)), RMS(\(J_{DTL}\)) and RMS(\(J_{DTL}\)) for the HVS system coupled with NESIs are all lower than those of the original HVS system at different vehicle speeds, which shows the advantage of NESI. Figure 6a-e show that the RMS(\(z_{aa}\)), RMS(\(\varphi_{a}\)), RMS(\(z_{aa}\)), RMS(\(J_{sssf}\)) and RMS(\(I_{sssf}\)) for the active HVS system coupled with NESI using the MFAC method are significantly smaller than those of the original HVS system, the HVS system coupled with NESI, and the active HVS system coupled with NESI using the PID control method; Figure 6f,g show that the RMS(\(J_{DTL}\)) and RMS(\(J_{DTL}\)) are also slightly smaller than those of the other three HVS systems, which reflects the best dynamic performance among the four HVS systems and shows the effectiveness of the MFAC method. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Speed** & **Indictators** & **Original** & **NESI** & **PID** & **MFAC** \\ \hline \multirow{8}{*}{5 m/s} & RMS(\(z_{aa}\)) & 0.2668 m/s\({}^{2}\) & 0.2531 m/s\({}^{2}\) & 0.2157 m/s\({}^{2}\) & 0.1424 m/s\({}^{2}\) \\  & RMS(\(\varphi_{a}\)) & 0.2464 rad/s\({}^{2}\) & 0.2099 rad/s\({}^{2}\) & 0.1711 rad/s\({}^{2}\) & 0.1261 rad/s\({}^{2}\) \\  & RMS(\(z_{aa}\)) & 0.2977 m/s\({}^{2}\) & 0.2174 m/s\({}^{2}\) & 0.1252 m/s\({}^{2}\) & 0.0629 m/s\({}^{2}\) \\ \cline{1-1}  & RMS(\(J_{sssf}\)) & 0.0051 m & 0.0047 m & 0.0047 m & 0.0035 m \\ \cline{1-1}  & RMS(\(J_{sssf}\)) & 0.0048 m & 0.0043 m & 0.0042 m & 0.0037 m \\ \cline{1-1}  & RMS(\(J_{DTL}\)) & 320.0783 N & 265.4598 N & 263.0662 N & 253.0396 N \\ \cline{1-1}  & RMS(\(J_{DTL}\)) & 331.3083 N & 274.6861 N & 271.1194 N & 259.0869 N \\ \hline \multirow{8}{*}{10 m/s} & RMS(\(z_{aa}\)) & 0.4284 m/s\({}^{2}\) & 0.3658 m/s\({}^{2}\) & 0.3056 m/s\({}^{2}\) & 0.1925 m/s\({}^{2}\) \\  & RMS(\(\varphi_{a}\)) & 0.3246 rad/s\({}^{2}\) & 0.2951 rad/s\({}^{2}\) & 0.2512 rad/s\({}^{2}\) & 0.1831 rad/s\({}^{2}\) \\ \cline{1-1}  & RMS(\(z_{aa}\)) & 0.3844 m/s\({}^{2}\) & 0.2982 m/s\({}^{2}\) & 0.1732 m/s\({}^{2}\) & 0.0909 m/s\({}^{2}\) \\ \cline{1-1}  & RMS(\(J_{sssf}\)) & 0.0071 m & 0.0067 m & 0.0065 m & 0.0053 m \\ \cline{1-1}  & RMS(\(J_{sssf}\)) & 0.0071 m & 0.0058 m & 0.0085 m & 0.0044 m \\ \cline{1-1}  & RMS(\(J_{DTL}\)) & 452.0866 N & 378.6921 N & 373.8841 N & 354.6754 N \\ \cline{1-1}  & RMS(\(J_{DTL}\)) & 472.6359 N & 387.9935 N & 386.5476 N & 361.2199 N \\ \hline \multirow{8}{*}{15 m/s} & RMS(\(z_{aa}\)) & 0.5600 m/s\({}^{2}\) & 0.4765 m/s\({}^{2}\) & 0.3831 m/s\({}^{2}\) & 0.2425 m/s\({}^{2}\) \\ \cline{1-1}  & RMS(\(\varphi_{a}\)) & 0.3702 rad/s\({}^{2}\) & 0.3411 rad/s\({}^{2}\) & 0.2956 rad/s\({}^{2}\) & 0.2187 rad/s\({}^{2}\) \\ \cline{1-1}  & RMS(\(z_{aa}\)) & 0.4603 m/s\({}^{2}\) & 0.3588 m/s\({}^{2}\) & 0.2137 m/s\({}^{2}\) & 0.1071 m/s\({}^{2}\) \\ \cline{1-1}  & RMS(\(J_{sssf}\)) & 0.0088 m & 0.0083 m & 0.0080 m & 0.0069 m \\ \cline{1-1}  & RMS(\(J_{sssf}\)) & 0.0087 m & 0.0072 m & 0.0069 m & 0.0053 m \\ \cline{1-1}  & RMS(\(J_{DTL}\)) & 554.0991 N & 465.7717 N & 460.4525 N & 435.7612 N \\ \cline{1-1}  & RMS(\(J_{DTL}\)) & 552.5659 N & 478.8739 N & 475.7574 N & 441.6093 N \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMS values of dynamic performance evaluation indicators for different HVS systems under random pavement excitation at different vehicle speeds.