*3.1. Sinusoidal Road Input*

In the sinusoidal road input simulation process, the parameters are set as follows. The vehicle height was adjusted under a vertical input of *zr* = 0.01 sin 2*πt*, the initial height of air sprung *za*<sup>0</sup> = 0.03 m, the uncertain outer boundary perturbation input *F*1(*t*) = *F*2(*t*) = 0.01, *x*<sup>1</sup> is initialized as 0.2 m, and other states are initialized to 0. The sampling time is 0.001 s and the simulation results are shown in Figures 2–7.

Figure 2 shows the tracing effect of the car body height on the reference trajectory in the process of vehicle height adjustment. Under control of the controller, the tracing curve of the car body height almost coincides with reference trajectory. As *z*<sup>1</sup> = *x*<sup>1</sup> − *x*1*<sup>r</sup>* , *z*<sup>1</sup> = 0 can be inferred. Figure 3 is the curve of *z*1, which confirms *z*<sup>1</sup> = 0. Compared with the PID controller, the designed controller can not only track the reference curve more accurately, but also make the error more inclined to 0.

**Figure 2.** Tracing curve of vertical displacement of sprung mass.

Figure 4 is the state curve of car body speed. Compared with the design controller, the PID controller has greater fluctuation of the speed curve. The corresponding system state error under the proposed control algorithm is shown in Figure 5. Combining Figure 4 and Figure 5, the car body completes the car body height adjustment with a smooth curve under the proposed control algorithm. The value of the system state error *z*<sup>2</sup> approaches 0 after a very short period of fluctuation.

**Figure 3.** Tracing error curve of vertical displacement of sprung mass.

**Figure 4.** State curve of car body speed.

**Figure 5.** State curve of *z*2.

Figure 6 is the state curve of car body acceleration. As shown in the picture, the value of *x*<sup>6</sup> approaches 0 and the fluctuation is small. Figure 7 is the state curve of the controller. However, in both figures, the PID controller takes longer to stabilize and has a larger fluctuation range. The simulation confirms that the controller can keep stable.

**Figure 6.** State curve of car body acceleration.

**Figure 7.** State curve of controller.

From Figures 2–7, the system remains stable under the control of the controller, which shows that the control algorithm is effective. Compared with the PID controller, the designed controller achieves better control effects.
