## 4 Numerical Simulation Results
The fuzzy-LQR controller requires less power, as seen in Figure 13 when looking at the change in the controller forces required by the motor over time. It can be seen that it ranges from about \(-520\) to \(250\) N for the PSO-based fuzzy-LQR controller. Similarly, it can be seen that the highest force requirement is for LQR control (about \(-1000\)-\(1000\) N). The previous graphs show that the fuzzy-LQR controller provides better control with less force requirement. Table 6 provides a comparison table for the body motion, car acceleration, suspension deflection, tire deflection, and required force parameters of the methods used in the study according to the performance index of the integral time-weighted absolute error (ITAE). \[ITAE=\int\textit{t}\textit{e}t \tag{14}\]  
In Table 6, the values that have the best error performance are shown in bold. According to the car body motion results obtained using the performance criteria in Table 4, the fuzzy-LQR control method has the lowest error performance with a value of \(0.00302\) m. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Performance Criteria (ITAE)** & **Passive** & **LQR** & **PSO-Based FLC** & **PSO-Based Fuzzy-LQR** \\ \hline Body travel \((X_{body})(\text{m})\) & 0.01914 & 0.00450 & 0.00380 & 0.00302 \\ \hline Body acceleration \((\tilde{X}_{body})\) \((\text{m}/\text{s}^{2})\) & 0.75410 & 0.14680 & 0.15020 & 0.07545 \\ \hline Suspension deflection \((X_{body}-X_{whel})(\text{m})\) & 0.01801 & 0.00430 & 0.00363 & 0.00280 \\ \hline Tire deflection \((X_{whel}-X_{road})(\text{m})\) & 0.00113 & 0.00046 & 0.00024 & 0.00015 \\ \hline Actuator \((F)(\text{N})\) & - & 67.16 & 68.46 & 59.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparisons of applied control methods using performance criteria. Figure 14: The response to the force using the methods described. The LQR control approach (0.00450 m) showed the worst error performance. According to the ITAE criteria, the error performance of the PSO-based FLC control method (0.00380 m) was relatively better than that of the LQR control method. For the results of the acceleration error of the car body, another parameter listed in the table, the PSO-based fuzzy-LQR control method, showed the lowest error performance with a value of 0.007545 m/s\({}^{2}\). The LQR control approach (0.14680 m/s\({}^{2}\)) showed the worst error performance. According to the ITAE criteria, the PSO-based FLC method performed relatively better than the LQR control method in the acceleration error of the car body (0.15020 m/s\({}^{2}\)). According to the results of suspension span error, another parameter listed in the table, the PSO-based fuzzy-LQR control method, showed the lowest error performance and was 0.00280 m. The LQR control approach (0.00430 m) showed the worst error performance. According to the ITAE criteria, the error performance of the PSO-based FLC method (0.00363 m) was relatively better than that of the LQR control method. According to the tire deflection error results, another parameter in the table, the PSO-based fuzzy-LQR control method, showed the lowest error performance and its value was 0.00015 m. The LQR control approach (0.00046 m) showed the worst error performance. According to the ITAE criteria, the error performance of the PSO-based FLC method in tire deformation (0.00024 m) was relatively better than that of the LQR control method. According to the error results of another given parameter, the force to be applied, the PSO-based fuzzy-LQR control method showed the lowest error performance, and its value was 59.29 N. The LQR control approach (67.16 N) showed the worst error performance. According to the ITAE criteria, the error performance of the PSO-based FLC method in tire deformation (68.46 N) was relatively better than that of the LQR control method. The percentage improvement performance of the applied methods compared to the passive system was determined using Equation (15). Figure 15 shows the percentage improvement graphs of the methods compared to the passive system.