Control of a class of microelectromechanical systems using finite-time stabilization approach

This thesis studies the control problem of a class of microelectromechanical systems (MEMS) by using a finite-time stabilization approach. This problem is addressed on a dynamic model which is widely used in the study of microelectromechanical systems, and it is complicated by a quadratic nonlinearity in this model. A constructive approach based on finite-time stabilization technique is used in this thesis to develop several state feedback controllers which can achieve finite-time stability for the microelectromechanical system model. First, for constant references, we design a controller to make the moveable electrode position be stabilized to the desired constant position. Second, for time-varying references, we first identify the class of time-varying references which can be tracked and then design a controller to make the moveable electrode position track the time-varying references. Finally, in the cases when there exists noise or some states of the system are not measurable, we use an Extended Kalman filter to estimate states for the controllers. Lyapunov stability theory is used to show that our state feedback controllers yield asymptotic stability and fast local convergence rate of the tracking error. The effectiveness of the approach and tracking performance of the proposed control are demonstrated via computer simulations.

Index Terms---MEMS, Finite-time stabilization, Lyapunov function, Tracking, Extended Kalman Filter.