Practical hybrid model predictive control for electric pneumatic braking system with on-off solenoid valves

Accurate and rapid braking pressure regulation in electric pneumatic braking systems (EPBS) is vital to vehicle safety. Due to the switching behaviors of the on-off solenoid valves, the operation of the EPBS shows a hybrid nature with both continuous variables and discrete events, which raises the hybrid control problem. One of the possible solutions is to employ the hybrid model predictive controller with the mixed logical dynamical (MLD) model based on the linear approximation of the system dynamics. However, the nonlinearity and complexity of the EPBS make the MLD model obtained by linearizing the system equations directly require high storage and computing capacity. To address these issues, this article presents a practical hybrid model predictive controller based on the system dynamics simplified expressions considering the EPBS pressure variations caused by on-off solenoid valve states at the current sampling time and the last sampling time. The relationship between the pressure variations and the on-off solenoid valve states is first studied by the system mathematical model, followed by applying the mixed logic dynamical modeling approach to establish the hybrid model of the pressure continuous dynamics with discrete features of on-off solenoid valves. Based on these, a hybrid model predictive controller is formulated to solve the EPBS pressure control problem. The simulations and bench experiments are carried out to verify the controller. Besides, an existing model predictive control (MPC) controller is compared with the proposed controller. All the results demonstrate the effectiveness of the hybrid model predictive controller.