# Cooperative Control of Interconnected Air Suspension Based on Model Predictive Control
## 5 Vehicle Test  
To examine the proposed cooperative control strategy, experiments are performed with a test vehicle shown in Figure 9. The test vehicle is a medium-sized bus produced by Nanjing Golden Dragon Bus Co., Ltd. (Nanjing, China). The specification of acceleration sensor is shown in Table 3. The sprung mass acceleration sensors are installed near the upper cover plates of the four air springs, respectively, and unsprung mass acceleration sensors are set at the lower cover plates of the four air springs, respectively. In the MPC controller solution process, the controller requires the values of all state variables of the current system to make predictions. In this paper, a Kalman observer cited by [22] is designed to estimate the state variables of the system. Raspberry Pi (RPi) 3B+ is used as the controller hardware of the vehicle test, which is connected to MATLAB/Simulink through the hardware support package. The designed cooperative control designed in Section 3 is stored in MATLAB/Simulink. The signal of sensors uploads to computer for saving in real-time. The test procedure follows the national test standard in China [23] and the velocity is 30 km/h.  
The sprung mass acceleration and unsprung mass acceleration of cooperative and traditional control under straight working condition are illustrated in Figure 10. As illustrated in Figure 10, the RMS of the sprung mass vertical acceleration of cooperative control reduced by 24.2% compared with the traditional control (0.4661 m/s\({}^{2}\) and 0.7086 m/s\({}^{2}\), respectively). The RMS of the unsprung mass vertical acceleration reduced by 14.5% (1.8928 m/s\({}^{2}\) and 2.2127 m/s\({}^{2}\), respectively).  
Figure 8: Performance comparisons between traditional and cooperative control at 30 m\(\cdot\)s\({}^{-1}\). (**a**) Comparison of RMS\({}_{Ams}\) between traditional control and cooperative control. (**b**) Comparison of RMS\({}_{\mathit{rms}}\) between traditional control and cooperative control. (**c**) Improvement rate of RMS\({}_{Ams}\) and RMS\({}_{\mathit{rms}}\) under different road level.  
The sprung mass acceleration and unsprung mass acceleration of cooperative and traditional control under bump working condition are illustrated in Figure 11.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Specification** & **Value** \\ \hline Product type & MMA8451Q \\ Working voltage & 1.95 v\textasci{-}3.6 v \\ Output frequency & 1.65–800 Hz \\ Maximum operating temperature & +85C \\ Protocol & l\({}^{2}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 3: Specification of acceleration sensor.  
Figure 10: Comparison of cooperative control and traditional control under straight condition. (**a**) Front-left sprung mass vertical acceleration. (**b**) Front-left unsprung mass vertical acceleration.  
Figure 9: Schematic diagram of the test system.  
As shown in Figure 11, the RMS of the sprung (unsprung) mass acceleration are 1.1694 m/s\({}^{2}\) (3.9133 m/s\({}^{2}\)) and 1.4311 m/s\({}^{2}\) (4.6275 m/s\({}^{2}\)), respectively, in the cooperative controller and non-cooperative controller. These indexes reduced by 22.38% and 15.43%, respectively.