Robust Control of a Proportional Solenoid Valve

This paper considers the application of $H_{\infty}$ robust optimal control system for solenoid valves to control the position of the valve plunger with the aim of tracking a pre designed reference transfer function. Robustness analysis was conducted in order to evaluate the performance of tuned PID controllers applied to the uncertain model of the solenoid valve. Two PID controllers were designed; the first one involved the nominal parameters of the transfer function, while the second dealt with the uncertain model. Simulation results show an improvement on the robustness of the controller over the entire range of system uncertainty. An optimal $H_{\infty}$ controller was computed using loop shape technique, the obtained responses were found to be more robust to the changes in system parameters. It was found that the system is more sensitive to the changes in both the coil resistance and the return spring stiffness.