# Hybrid Particle Swarm Optimization Genetic LQR Controller for Active Suspension
## 4 Simulation Analysis and Comparison  
The detailed simulations results are presented in this section to verify the efficacy of the proposed control method. To illustrate the performance of the controller proposed in this paper, the simulation is carried out based on passive suspension, active suspension with traditional LQR control, active suspension with optimization LQR control, and the full-order state observer under case 1 and case 2. To evaluate the performance of suspension systems, the sprung mass acceleration, sprung mass deflection, and tire dynamic load are selected as evaluation indicators. The smaller the value of sprung mass acceleration and deflection, the better the performance of the ride comfort of the suspension system. The lower the value of the tire dynamic load, the better the performance of the road holding. The closer to zero the value of the observer estimation error is, the better the observer. The vehicle parameters [36] used for simulation in this paper are shown in Table 1.  
The simulation results under case 1 are shown in Figures  
Figure 8: Tire Dynamic Load (case 1). Figure 10: Sprung Mass Deflection (case 2). Figure 9: Sprung Mass Acceleration (case 2). Figure 11: Tire Dynamic Load (case 2). Figure 12: RMS of Sprung Mass Acceleration. Figure 13: RMS of Sprung Mass Deflection. Figures 6a-8a demonstrate the sprung mass acceleration, deflection, tire dynamic load of passive suspension, active suspension with traditional LQR control, active suspension with optimization LQR, and the full-order state observer under case 1. Figures 6b-8b show the estimation error of the sprung mass acceleration, deflection, and tire dynamic load under case 1. Figures 9a-11a show the sprung mass acceleration, deflection, tire dynamic load of passive suspension, active suspension with traditional LQR control, active suspension with optimization LQR, and the full-order state observer under case 2. Figures 9b-11b show the estimation error of the sprung mass acceleration, deflection, and tire dynamic load under case 2. Figures 12-14 and Tables 2 and 3 show the statistical results of the RMS of the sprung mass acceleration, RMS of the sprung mass deflection, and RMS of the tire dynamic load under each state. Figures 6a and 9a show the sprung mass acceleration for passive suspension, active suspension with traditional LQR control, active suspension with optimization LQR control, and the full-order state observer under case 1 and case 2. It can be observed from Figures 6a and 9a that the curve of the sprung mass acceleration under active suspension with the optimization LQR control is smoother than the curve of the passive suspension, active suspension with traditional LQR control, and active suspension, indicating that the ride comfort under the active suspension with optimization LQR control is better than the other cases. In Figures 7a and 10a, the sprung mass deflection for passive suspension, active suspension with traditional LQR control, active suspension with optimization LQR control, and the full-order state observer under case 1 and case 2 are shown. It can be observed from \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicators** & **Acceleration** & **Deflection** & **Tire Dynamic Load** \\ \hline Passive & 0.554 & 0.0108 & 1505.4 \\ Traditional LQR & 0.1526 & 0.0043 & 93.45 \\ Optimization LQR & 0.1179 & 0.002 & 29.3 \\ Observer & 0.1204 & 0.0022 & 31.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of RMS values in case 1. Figure 14: RMS of Tire Dynamic Load. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicators** & **Acceleration** & **Deflection** & **Tire Dynamic Load** \\ \hline Passive & 1.1196 & 0.0218 & 1876.2 \\ Traditional LQR & 0.4708 & 0.0123 & 282.1 \\ Optimization LQR & 0.1221 & 0.0035 & 21.4 \\ Observer & 0.1226 & 0.0038 & 22.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of RMS values in case 2.