This paper presents a control-oriented LPV (Linear Parameter-Varying) model for commercial vehicle air brake systems, where a pneumatic valve actuator is used to control the brake chamber pressure. To improve the brake system response time and reduce the vehicle stopping distance, the traditional treadle valves used in the air brake system are replaced by electro-pneumatic valves. Also, to develop the model-based brake control strategy, a nonlinear mathematical model is developed based on Newton’s second law, fluid dynamics of the orifice, force balance of spool, and solenoid dynamic characteristics. The brake chamber dynamics is also considered during the charging and discharging processes. The developed nonlinear model is calibrated based on both valve actuator geometry and test bench experimental results. It is proposed to model the nonlinear system in the LPV form so that gain-scheduling controllers can be developed. To obtain the LPV model, system identification is conducted using the calibrated nonlinear model to obtain a set of linearized models under different brake chamber pressure levels, and the resulting identified linear models are assembled to form the LPV model with brake chamber pressure as the varying parameters. A linear infinite-horizon continuous-time LQR (Linear Quadratic Regulator) controller was designed for the braking system based on the developed LPV model with the fixed parameter to demonstrate the effectiveness of the developed LPV model.
Power sources coordination through multivariable linear parameter-varying/ H ∞ control with application to multi-source electric vehicles
