*3.2. Random Road Input*

In the process of the random input of pavement simulation, the vertical input of the pavement is filtered white noise (Figure 8)

$$z\_{\mathbf{r}}(t) = -2\pi n\_1 v z\_{\mathbf{r}}(t) + 2\pi n\_0 \sqrt{\mathcal{G}\_{\mathbf{q}}(n\_0) v w(t)}\tag{21}$$

The parameters are set as follows. *n*<sup>1</sup> is the lower cutoff frequency, *v* is speed of the car, *n*<sup>0</sup> is the spatial reference frequency, and *Gq*(*n*0) is the coefficient of road roughness. Class A uneven pavement is used in the simulation, where *n*<sup>0</sup> = 0.1 m<sup>−</sup>1, *Gq*(*n*0) = <sup>16</sup> × <sup>10</sup>−<sup>6</sup> <sup>m</sup>3, *<sup>n</sup>*<sup>1</sup> = 0.01 m<sup>−</sup>1, and *<sup>v</sup>* = 10 m/*s*.

**Figure 8.** Vertical input for Class A uneven road surface.

The vehicle height was adjusted under a vertical input of *zr* = 0.01 sin 2*πt* and an 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, all states are initialized to 0, and the sampling time is 0.001 s.

The simulation results are shown in Figures 9–13. Figure 9 presents the difference between the state curves for the vehicle body height with and without the controller. Under the control of the controller, the state curves for the vehicle body height still have a certain level of fluctuation, but it is too small to be seen. Figure 10 shows the state curves for the vehicle body height tracking error. Combining the two figures, it can be seen that the controller can effectively reduce the variation range of the process of the car body height adjustment, which means that the controller reduces the car body vibration created by the road input.

**Figure 9.** State curves for the vehicle body height.

Figure 11 shows the state curves for vehicle body velocity. During the process of car body height adjustment, the value of the vehicle body velocity increases and changes greatly. In contrast, the state curves for the vehicle body velocity keep stable under the control of the controller. However, like *x*1, *x*<sup>2</sup> has small fluctuations but they are too small to be seen.

Figure 12 shows the state curves for the vehicle body acceleration. With the designed controller, the vertical acceleration of the body is reduced and thus, the comfort is improved. Under the condition of no controller, the fluctuation of the vehicle body acceleration state curve is large. The PID controller cannot reduce the fluctuation amplitude of the

body acceleration curve. Compared with the PID controller, the designed controller is more efficient.

**Figure 10.** State curves for the vehicle body height tracking error.

**Figure 11.** State curves for the vehicle body velocity.

**Figure 12.** State curves for the vehicle body acceleration.

In the process of the vehicle body height adjustment, the state curves of the controller are shown in Figure 13. Compared with the PID controller, the designed controller has a shorter settling time and faster stabilization.

**Figure 13.** State curves of the controller.
