As the core component of the hydrodynamic retarder braking system, pneumatic proportional solenoid valve plays an important role in the process of braking torque control. However, the hysteresis characteristic caused by friction and air compressibility will lead to the deviation of braking torque. In order to solve this problem, the hysteresis characteristic of pneumatic proportional solenoid valve is experimentally studied, and the causes of hysteresis phenomenon are analyzed through mathematical modeling of the valve core. Then, a high-precision prediction model of braking torque is obtained by combining Computational Fluid Dynamics (CFD) and response surface method, which is used to construct the mapping relationship between control air pressure and braking torque. Furthermore, a feedforward controller based on Prandtl–Ishlinskii inverse model is designed to compensate the hysteresis characteristics. On this basis, a compound hysteresis characteristics compensation control strategy combined with Proportional Integral Derivative (PID) feedback control is proposed to realize the accurate control of braking torque. Finally, the test verification of braking torque control is carried out. The average error of compound control, feedforward control, and PID control under torque step working condition is 3.16%, 5.97%, and 6.23%, and the response time is 3.75, 8.75, and 3.2 s, respectively. The compound control strategy also has smaller torque error and shorter response time under both ramp torque tracking and constant torque conditions. To sum up, this compound control strategy can effectively compensate the hysteresis characteristics of the pneumatic hydrodynamic retarder and ensure the driving safety by improving the control accuracy and response speed of braking torque.
