## 4 Comparative Simulation Analysis
### Robustness Analysis of MPC System  
The stability and robustness of control systems are both research hotspots [39; 40]. The stability of the control system has been discussed in Section 3, and the robustness of the control system will be discussed in this section. The robustness of a control system includes its anti-interference ability and the influence of model errors on the performance of the control system [41]. The front body and the rear body vertical velocities are the control targets of this study. When these two state variables interfere, they will have an important influence on the control effect. Therefore, Gaussian noise with a mean value of zero is injected into these two state quantities to verify the anti-interference ability of the control system under the gradual braking condition. The front body and rear body vertical velocity noises are shown in Figure 4a,b, respectively. Figure 4: Body vertical velocity noises. (**a**) Front body vertical velocity noise; (**b**) Rear body vertical velocity noise. Figure 3: Vehicle braking condition. The vertical velocity changes of the front and rear bodies are shown in Figure 5a,b, respectively (no noise and with noise). It can be seen from Figure 5 that although the vertical velocities of the front and rear bodies are inconsistent after the noise is injected, the vertical velocities of the body always fluctuate near the no-noise curves. This verifies that the MPC system has a certain anti-interference ability. It should be noted that the rear body vertical velocity, for example, presents an amplitude of around 0.015 m/s, while the maximum value of noise reaches 0.0033 m/s. In other words, the maximum noise (i.e., the level of ambient disturbances) accounts for about 22% of the actual velocity signal, which proves that the proposed control system is able to work under such a challenging working condition. Stiffness and damping are important parameters of the suspension system. Therefore, the influence of model errors on the performance of the control system is discussed by changing the stiffness and damping of the suspension system in the equivalent half-vehicle model under the gradual braking condition. What needs to be explained here is that the control system still adopts the parameters in Table 1. The influence of the front and rear stiffness mismatch of the suspension on the control effect is shown in Figure 6a,b, respectively. Figure 5: Body vertical velocity changes. (**a**) Front body vertical velocity; (**b**) Rear body vertical velocity. Figure 6: Suspension stiffness mismatch effect. (**a**) Front suspension stiffness mismatch effect; (**b**) Rear suspension stiffness mismatch effect. The front suspension stiffness mismatch has an obvious impact on the vertical velocity of the front body, and the rear suspension stiffness mismatch has a remarkable impact on the rear body vertical velocity. Therefore, the vertical velocities of the front and rear bodies are selected to reflect the influence of stiffness parameters' mismatch. The Ksfp and Ksrp in Figure 6 represent the ratios of the actual values in the equivalent half-vehicle model to the corresponding parameters in Table 1. From Figure 6, although simulation results are different for inconsistent model parameters, the trend of change is the same and they all fluctuate around the target value (i.e., zero). Specifically, when Ksfp or Ksrp is less than 1, it has a greater impact on the control effect and the front suspension stiffness has a greater impact on the control effect. The influence of the front and rear damping mismatch of the suspension on the control effect is shown in Figure 7a,b, respectively. For reasons similar to stiffness, the vertical velocities of the front and rear bodies are selected to reflect the influence of damping parameters' mismatch.