# Cooperative Control of Interconnected Air Suspension Based on Model Predictive Control
###### Abstract  
The suspension system is a significant part of a vehicle because it transmits the torque and force between the wheels and the frame, meeting the requirements of ride comfort. In this paper, a novel interconnected air suspension was introduced and a cooperative control between interconnected mode activation (IMA) and outsourced mode activation (OMA) was designed. To improve ride comfort in a bus at a minimal energy consumption, this cooperative control based on model predictive control (MPC) for computing the best force and the rule was defined to distribute the best suspension force generated by IMA and OMA. The simulation and experimental results showed that the proposed control strategy significantly improved ride comfort in different conditions. Compared with traditional control in the test vehicle, the RMS of the front-left sprung mass and unsprung vertical acceleration decreased by 24.2% and 14.5%, respectively, under a straight condition; the RMS of the sprung (unsprung) mass vertical acceleration reduced by 22.38% and 15.43%, respectively, under a bump condition.  
interconnected air suspension; model predictive control; cooperative control; ride comfort; interconnected mode +
Footnote †: journal: Applied  
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Footnote 1: School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China 1  
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Footnote 2: School of Vehicle and Mobility, Tsinghua University, Beijing 100084, China 2  
It is difficult to define an effective rule to avoid charging and discharging gas at the same in one spring when the OMA and IMA work at the same time.  
Compared with the above control strategies, MPC has advantages against the limitation from the process dead-time, nonminimum phase, and process dynamic due to the predictions over the future horizon [12]. When it comes to activation saturation control problems, MPC allows explicit taking into account of the effect of input and state constraints in the control design step [13]. MPC has been successfully implemented on a large number of industrial processes [14; 15]. Some scholars designed an MPC approach for semi-active suspension systems. [PERSON] et al. [16] proposed MPC, which gave a trade-off between ride comfort and road holding while guaranteeing physical constraints of the semi-active dampers in the suspension system. Simulation results showed the effectiveness of the proposed approach. [PERSON] et al. [17] multiplexed an MPC controller integrated with soft constraints, and a Kalman filter is proposed based on a full-car model. The results show that the overall performance of ride comfort and roadholding could be improved significantly. [PERSON] et al. [18] presented MPC of a new semiactive hydro-pneumatic inerter-based suspension system. The results of the numerical simulations and experiments verify the effectiveness of the control method.  
To further improve IAS performance, the cooperative between OMA and IMA was designed. A controller based on MPC theory was designed to compute the best suspension. Simultaneously, the rule is defined to distribute the best suspension force between IMA and OMA. The effectiveness of the proposed cooperative control strategy is examined through simulation and vehicle tests.  
The remainder of the paper is organized as follows. In Section 2, the model of the system is introduced. The controller based on MPC theory is designed, and the simulation results are presented in Section 3. The vehicle test results are discussed in Section 4 before the paper is concluded in Section 5.