## 3 Controller Designs for the Suspension System
The particle swarm optimization flowchart (PSO-FLC) used to fit the membership functions of the FLC method proposed for suspension system control is shown in Figure 2.  
The controller uses the error (\(e\)) and the rate of change of the error (\(\dot{e}\)) as input values. The membership functions and the control table obtained using triangular membership functions and PSO-FLC are given below. Figures 3 and 4 show the membership functions defined for the system's input values \(e\) and \(\dot{e}\). Figure 5 shows the membership functions defined for the \(F\) (force) output value. Figure 2: Particle swarm optimization (PSO-based FLC) flowchart used to adjust the membership functions of the FLC method. The fuzzy linear quadratic regulator (fuzzy-LQR) control method, which is another recommended method for active control of the suspension system, is a control method that shares the advantageous aspects of the linear quadratic controller (LQR) and the fuzzy control method. Here, an attempt is made to utilize the advantages of the LQR and FLC methods by combining them. Obtaining the Q and R matrices that affect the performance of the LQR control method with fuzzy logic causes the proposed method (fuzzy-LQR) to become a dynamic structure that depends on variable road conditions, thus increasing passenger comfort and achieving a realistic performance of the method. The fuzzy-LQR controller, which takes the error and its derivative as input to the controller, uses the fuzzy controller rules to change the \(K=[k_{1},k_{2},k_{3}]\) expressions of the state feedback gain. The boundary values of the membership functions of the fuzzy-LQR control algorithm were obtained using particle swarm optimization (PSO), one of the swarm-based optimization algorithms. For the PSO algorithm, the mean square error (MSE) was set as the objective function to minimize the errors resulting from the system's operation. The controller uses the error (\(\mathbf{e}\)) and the rate of change of the error (\(\dot{\mathbf{e}}\)) as input values. The fuzzy-LQR control method uses the Mamdani method and triangular membership functions. The membership functions and the rule table created for fuzzy-LQR are given below. For the PSO algorithm, the number of particles is 75 and the number of iterations is 130. Figures 6 and 7 shows the membership functions and limits for the system's input values \(e\) and \(\dot{e}\). The membership functions and bounds for the \(F\) (force) output value is shown in Figure 8.  
Table 4 shows the boundary values of the membership functions used in the fuzzy-LQR control method and optimized with the PSO algorithm. Table 5 shows the rule table  
Figure 8: Fuzzy-LQR membership functions defined for the output value \(F\). Figure 6: Fuzzy-LQR membership functions defined for the input value \(\mathbf{e}\). Figure 7: Fuzzy-LQR membership functions defined for the input value \(\dot{\mathbf{e}}\). created for the fuzzy-LQR control method. In the table, the fuzzy control variables \(e,\ \dot{e},\ \ F,\) and \(F\) indicate the error, error variation, and power, respectively. The values given in the table, NB, NS, Z, PS, and PB, represent negative large, negative small, zero, positive small, and positive large, respectively.