Robust Fuzzy Nonlinear Control of Microbeams Vibration with Piezoelectric Actuator and Electrostatic Force

In this paper, transverse vibration control of a microbeam with nonlinear governing equations is investigated. The non-classical modified strain gradient theory is used to derive the governing differential equations of motion. The dynamic model considers the electrostatic force and the nonlinear effect of mid-plane stretching. Piezoelectric layers are laminated on the beam and the piezoelectric voltage is defined as the actuating control signal. Because of the existence of nonlinear terms due to mid-plane stretching and electrostatic force, the governing partial differential equation is nonlinear. The control aim is to stabilize microbeam's transverse vibrations. In the present study, the governing partial differential equations are simplified using the Galerkin method. A robust nonlinear sliding mode controller is designed and implemented to compensate for the effects of higher modes in the closed-loop system. To prevent the chattering phenomenon near the sliding surface, a fuzzy logic controller is mixed with the sliding mode controller. The closed-loop response of the system is investigated in the presence of disturbances and uncertainties through numerical simulations. The innovations in this research include using the effect of electrostatic force, mid-plane stretch and the effect of piezoelectric all together in a model, providing exact mode shapes for Galerkin method, using Taylor's third-order expansion for electrostatic force that improves accuracy and designing terminal sliding mode and fuzzy-terminal sliding mode controller.