## 4 Simulation and Experiment of Suspension System  
### Simulation of Suspension Control Unit  
To verify the effectiveness of the designed suspension controller, a simulation model of the suspension control unit is built in Matlab/Simulink. The parameter values of the suspension control unit system are shown in Table 2.  
Substitute the parameter values in Table 2 into Equation (8), and the state equation of suspension control unit can be expressed as:  
\[\left\{\begin{array}{l}\dot{X}=\left[ \begin{array}{cc}0&1\\ 331.13&0\\ Y=\left[\begin{array}{cc}1&0\\ \end{array}\right]X\\ \end{array} \right]X+\left[ \begin{array}{c}0\\ 0.12\\ \end{array} \right]u\right. \tag{18}\]  
The PID, LADRC and Fuzzy-LADRC controllers are compared and simulated from three aspects, which are adaptability, anti-interference ability and noise suppression performance, to verify the superiority of Fuzzy-LADRC method. See Table 3 for the simulation parameters of each controller. (1) Adaptability analysis  
With the control parameters unchanged, change the reference given signal into x = 16, 18, 20 and experiment with the adaptability of the controller. The response curves of PID, LADRC and Fuzzy-LADRC control methods are shown in Figure 7.  
It can be seen from Figure 7 that the three control methods of PID, LADRC and Fuzzy-LADRC can make the platform reach the given position and stably levitate, and the Fuzzy-LADRC method is superior to PID and LADRC methods in overshoot, adjustment time and other performance indicators. If using the curve response does not exceed 2% of the given value as the criterion for judging the stability of the system when the given signal x = 18 mm, the maximum overshoot of the system is 4 mm and the adjustment time is 0.26 s under the PID control, then the adjustment time of LADRC and Fuzzy-LADRC is almost synchronous: 0.049 s. The maximum overshoot of LADRC is 0.35 mm, while the maximum overshoot of Fuzzy-LADRC is 0.13 mm. On the basis of ensuring the adjustment time, the overshoot of the system is greatly reduced. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Nominal Value** \\ \hline Mass of the controlled unit & \(m\) & 200 kg \\ Cross-sectional area of magnetic conductivity & \(A\) & \(4.5\times 10^{-3}\) mm\({}^{2}\) \\ Vacuum permeability & \(u_{0}\) & 4 pi \(\times 10^{-7}\) H/m \\ Coil turns & \(N\) & 1000 Turns \\ Equilibrium position & \(x_{0}\) & 0.018 m \\ Balanced current & \(i_{0}\) & 2.79 A \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of suspension control unit. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Controller** & **Parameter** & **Value** & **Parameter** & **Value** \\ \hline PID & \(K_{\text{P}}\) & 50,000 & \(K_{\text{i}}\) & 200,000 \\  & \(K_{\text{d}}\) & 1200 & \(\backslash\) & \(\backslash\) \\ \hline \multirow{3}{*}{LADRC} & \(k_{\text{P}}\) & 85,000 & \(k_{\text{d}}\) & 1500 \\  & \(\beta_{1}\) & 600 & \(\beta_{2}\) & 120,000 \\  & \(\beta_{3}\) & 8,000,000 & \(b_{0}\) & 0.12 \\ \hline \multirow{3}{*}{Fuzzy-LADRC} & \(k_{\text{P}0}\) & 85,000 & \(k_{\text{d}0}\) & 1500 \\  & \(l_{\text{P}}\) & 9000 & \(l_{\text{d}}\) & 100 \\ \cline{1-1}  & \(\beta_{1}\) & 600 & \(\beta_{2}\) & 120,000 \\ \cline{1-1}  & \(\beta_{3}\) & 8,000,000 & \(b_{0}\) & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters of three controllers. 2. Anti-interference performance analysis On the basis of stable suspension at the given suspension air gap x = 18 mm, a 5 V step interference is applied to the controller at t = 2 s and the interference is removed at t = 4 s. The anti-interference performance of the controller was tested. The response curves of PID, LADRC, and Fuzzy-LADRC control methods are shown in Figure 8.  
Figure 8: Response curves of three control methods under step interference. Figure 7: Response curves of three control methods under different settings. It can be seen from Figure 8 that PID, LADRC and Fuzzy-LADRC have certain anti-interference ability.