# Sliding Mode Control of Laterally Interconnected Air Suspensions
## 4 Simulations and Analysis
### Simulation Results Under Varying Situations
This action is reasonable as it is aimed at minimizing the roll angle and the performance is the same as the \"OFF\" state. Thus, under the applied excitation, the sliding mode controller manages to drop 63% of the steady-state value of roll angle response compared with the \"ON\" state, while it raises 58% and 86% of the peak and RMS values of the acceleration response. Figure 4: \(Cont.\)  
Furthermore, simulations are conducted under varying road roughness levels and lateral accelerations to evaluate the performance of sliding mode controller on actual driving conditions. Road excitations are established with roughness levels varying from A to E. The lateral accelerations are also added, which vary from 0 m/s\({}^{2}\) to 3 m/s\({}^{2}\) and step 0.2 m/s. Under each condition, the responses of roll angle and acceleration of driver position are recorded. Then, the RMS values of those records are calculated. Finally, the RMS values of all the roll angle records are presented in ratios using the \"ON\" state performance as a baseline. Meanwhile, the RMS values of all the acceleration records are presented in ratios using the \"OFF\" state performance as a standard. Figure 5a,b show the results of the simulations. Figure 5a,b show that the interconnected air suspension performs better in reducing both roll angle and acceleration under straight driving condition no matter the road roughness levels, while the non-interconnected air suspension can reduce the roll angle notably when the lateral acceleration increases. The skyhook controller drops the roll angle under minor lateral acceleration excitations, but it is defeated by the \"OFF\" state when lateral acceleration increases. The RMS of roll angle responses remains the lowest under any conditions with the sliding mode controller, which declines 20% at least and 85% at most compared with the \"ON\" state. In Figure 5a, the curve shows that the sliding mode controller is always better at reducing the roll angle compared with the \"OFF\" state, but in Figure 4a, the roll angles are the same. This is because the road excitations are added in the simulations of Figure 5a. When the road excitations change the sign of the pressures' difference of two connected air springs, the sliding mode controller manages to turn on the interconnection, which changes the distributions of air mass in each spring and finally results in smaller RMS values. This phenomenon is illustrated in Figure 6 below. The vehicle drives in a straight line at time 0-10 and 60-70 seconds and in steady turning during 10-60 seconds. During this period, the sliding mode controller keeps the interconnection shut for most of the time, but turns the interconnection on several times and, each time, reduces the roll angle. Finally, the roll angle response of sliding mode controller reduces at a visible level compared with the \"OFF\" state. Figure 4: The response of the vehicle under lateral acceleration: (**a**) roll angles of sprung mass; (**b**) accelerations of driver position. Figure 5: The response of the vehicle under varying conditions: (**a**) ratio of root mean square (RMS) roll angle compared with the “ON” state; (**b**) ratio of RMS acceleration at driver position compared with the “OFF” state. Because of the aim of reducing the roll angle, the performance of sliding mode controller is limited at acceleration decreasing. Figure 5b shows that the sliding mode controller increases the driver position acceleration by 5% for the A level road and 0 m/s\({}^{2}\) lateral acceleration condition compared with the \"OFF\" state. However, the RMS values drops with the increase of road roughness levels and the lateral acceleration amplitudes. Finally, the RMS values are approximately the same with the \"OFF\" state. The skyhook controller performs better than the sliding mode controller when the lateral acceleration is small, but it fails when the lateral acceleration input grows.