Output feedback control of piezoelectrically actuated non-classical micro-beams using T-S fuzzy model

This paper proposes a Takagi-Sugeno (T-S) model based fuzzy control design approach for nonlinear strain gradient micro-beams with the constraints on the control input. The nonlinearity of the system is because of the mean axial extension of the clamped-clamped micro-beam known as the mid-plane stretching effect. In this work, the governing partial differential equation of motion of the nonlinear micro-beam with piezoelectric actuator is derived employing a combination of the strain gradient theory and the Hamilton׳s principle and then is reduced to ordinary differential form using the Galerkin projection method. A new observer-based controller with saturated input is designed to suppress the unwanted vibration of the system. The structure of the proposed controller is based on the T-S fuzzy systems with saturated input. Asymptotic stabilization of the closed-loop system is investigated via the Lyapunov direct method. A numerical example is provided to show the effectiveness of the proposed method.