# Cooperative Control of Interconnected Air Suspension Based on Model Predictive Control
## 4 Simulation Analysis  
MATLAB/Simulink is usually used to simulate the designed controller. The simulation is conducted under the case of C-level and a driving velocity of 20 m/s to examine the effectiveness of the control algorithm. In this simulation, the suspension dynamic travels are set as \(\pm 60\) mm. Furthermore, the predict step size is set as 30, the control step size is set as 10, and the sampling time \(T_{\text{s}}\) is 0.01 s. To test the advantages of the proposed cooperative control strategy, the traditional controller is introduced for comparison. In the traditional controller, PID-PWM control strategy and imitated skyhook control strategy [20] are adopted, respectively, in the OMAs and IMAs. The model of imitated sky-hook inter connected mode control is shown in Figure 5. The rule of imitating sky-hook interconnected mode control is degenerated into [20]:  
\[\text{Interconnecting state}= \begin{cases}\text{Off}&\tau(\tau-\tau_{\text{t}})>0 \\ \text{On}&\tau(\tau-\tau_{\text{t}})\leq 0\end{cases}  \tag{25}\]  
In the current sampling time of vehicle state, the suspension forces generated by the OMAs and the IMAs are computed, respectively, combining with the above best suspension force and the method which computes activation actions in Section 3. The states of interconnected mode activation are illustrated in Figure 6. Pressure changes caused by interconnected mode activation in four air suspensions are shown in Figure 6a, best suspension forces generated by interconnected mode activation are illustrated in Figure 6b and solenoid valve actions in interconnected mode activation are shown in Figure 6c. Figure 5: The model of imitated sky-hook interconnected mode control. Figure 6: Interconnected mode activation state. (**a**) Pressure changes caused by IMA in four air suspensions. (**b**) Best suspension force generated by IMA. (**c**) Solenoid valve actions in IMA. As shown in Figure 6a,b, pressure changes and best suspension caused by interconnected mode activation in four air suspensions has relevance. When the force of one air spring decreases due to interconnection, the spring force of one air spring connected with it must increase. Figure 6c shows that the solenoid valves which were acted upon by cooperative controller works. The states of outsourced mode activation are illustrated in Figure 7. Solenoid valve actions during inflation in outsourced mode activation are shown in Figure 7a, solenoid valve actions during deflation in outsourced mode activation are illustrated in Figure 7b, and best suspension forces generated by outsourced mode activation are shown in Figure 7c. As shown in Figure 7a,b, solenoid valve actions during inflation and deflation in outsourced mode activation works well. Figure 7c shows that the best suspension caused by outsourced mode activation has no relevance because the outsourced mode connects to the atmosphere. It not only deflates but also inflates due to the forces have no relevance. It has been verified in Figures 6 and 7 that the proposed cooperative works effectively. To test ride comfort performance in the full-vehicle, simulation cases were designed ranged from A-level to E-level road in velocities of 30 m/s, respectively. The performances of cooperative control and traditional control in different cases are shown in Figure 8.  
Vehicle ride comfort is a significant index to evaluate vehicle performance [21]. The evaluation indices the root-mean-square value of the sprung mass acceleration (RMS\({}_{Ams}\)) and root-mean-square value of the tire dynamic (RMS\({}_{fmn}\)) are chosen to represent vehicle ride comfort. It is known that a lower value indicates better performance [21]. As shown in Figure 8a, RMS\({}_{Ams}\) reduced 21.18% under E-level road and at most 76.04% under A-level road. RMS\({}_{fmn}\) reduced 13.18% under E-level road and at most 65.73% under A-level road, as shown in Figure 8b. It is concluded that proposed cooperative control has higher improvement of performance in the better road condition in Figure 8c.