The solenoid valve system has strong nonlinear characteristics. In order to overcome the nonlinear characteristics, the controller is designed by linearization near the operating point. This is because there is a difficulty that the system mathematical model changes as the operating point changes and the control gain also changes. The controller of the solenoid valve system is constructed by using the back stepping control technique which can obtain the asymptotic stability of the system and can set the gain more simply than the gain of the general PID controller. In order to estimate the non-observable state of the controller configuration, it designed the Luenberger state observer and estimate the state simply. This system improves the tracking performance of the system and achieves asymptotic stability. Since the position error of the state estimator is within 0.1 [mm], the result of accurate state estimation can be obtained, and the back-stepping controller can obtain the result that the steady state position error is within 0.1 [%].
Jeon, Y., & Lee, S. (2019). Back-stepping controller design for stable solenoid valve system. International Journal of Innovative Technology and Exploring Engineering, 8(4S2), 5–8.