Suppression of the noise-induced effects in an electrostatic micro-plate using an adaptive back-stepping sliding mode control

In this work, an adaptive backstepping sliding mode control approach is applied through the piezoelectric layer in order to control and to stabilize an electrostatic micro-plate. The mathematical model of the system by taking into account the small fluctuations in the gap considered as bounded noise is carried out. The accuracy of the proposed modal equation is proven using the method of lines. By using both approaches, the effects of noise are presented. It is found that they lead to pull-in instability as well as to random chaos. A suitable backstepping approach to improve the tracking performance is integrated to the adaptive sliding mode control in order to eliminate chattering phenomena and reinforce the robustness of the system in presence of uncertainties and external random disturbances. It is proved that all the variables of the closed-loop system are bounded and the system can follow the given reference signals as close as possible. Numerical simulations are provided to show the effectiveness of proposed controller.