## 8 Simulation  
To perform the simulations, the MATLAB/Simulink software was used. To approximate and simulate speed, the \(\
u=d/t\) formula was used. Then, if the vehicle speed were 5 km/h (1.38 m/s) and the wheelbase were 2.99 m, the rear suspension would pass the bump approximately 2.2 s after the front suspension does. That is why the control action is on two seconds before the car arrives at the hump. The moment at which the vehicle meets the hump is at second 6. The latter is registered by a proximity sensor (see Section 9). Although the following experiments were developed to contrast four ways to lift the chassis of the car, for the sake of exposition, the first case (passive suspension action) and the last one (the proposed design) are illustrated:  
* Passive suspension. In Figure 8, oscillations are observed when the car reaches the obstacle and remains this way until the chassis goes down until reaching zero (normal body level). It is to be expected that the car has this behavior since the springs are oscillating and dissipating energy;
* Passive suspension plus actuators. In this case, many ripples showed up, negatively impacting the stable behavior of the structure;
* MR damper suspension. This case did not show many oscillations, but (as in the other) the suspension system just waited to reach the obstacle exactly at Second 6; the structure was elevated (then ripples appeared) and finally came down;
* MR damper+actuators. This case permits providing an in-advance action to lift the chassis at Second 2, but at this moment, a high overshoot of approximately 4 cm harmed the performance;
* Proposed system. MR dampers + actuators + Skyhook control action. This event is plotted in Figure 9. First, the speed bump is illustrated there to show the moment at which the car arrives at it. The proposed performance is provided also there, and it can be noticed because it has a big overshoot at Second 6 and many undesirable oscillations when the chassis leaves the obstacle. Although this performance was demonstrated to be better than the others cited above, it was afterwards improved by adding a smoother linear dynamics plus a PID controller. This fact definitely ameliorated the latter behavior, as can be observed there. Figure 7: Real closed-loop system. The case shown in Figure 9 uses a sinusoidal model for the speed-calming device. According to the figure, it is a speed bump. The system reacts differently if the vehicle meets a Gaussian bump. As shown in Figure 1 and Table 2, the way a bump and a hump force cars to slow down changes. Humps can be higher than humps (remember Figure 2). If the height of a Gaussian hump is increased, the controller performs well, as illustrated in Figure 10. Observe that the chassis was elevated beforehand, and once on top of the speed hump, the control produced an even higher vertical displacement to avoid the bump crest. The return to the original level of the chassis was also smooth. Figure 8: Passive actuation to elevate the structure of the vehicle when it meets a speed bump/hump. Although the goal was accomplished, there were undesirable ripples, and the motion of the chassis was abrupt. Figure 9: The proposed solution (red) and an ulterior version of it (yellow) could accomplish the task of lifting the car in advance (at Second 2, i.e., 4 s before reaching the bump). Besides, from Seconds 9–16, the car remains up for safety, and the return to its original height transits softly during all the vertical displacement. Notice that the return to its original position (zero level) was performed gently, and the hump was sinusoidal. An additional example is offered, modifying the smoother dynamics used for the case shown in Figure 9. It was also possible to elevate the car when encountering a pothole, and this situation is illustrated in Figure 11. As indicated before, the control action actuated 2 s in advance.