Tracking and robustness analysis for controlled microelectromechanical relays

Abstract

AbstractThe feedback control problem for microelectromechanical (MEM) relays is complicated by a quadratic nonlinearity in the dynamic model. We show that this nonlinearity imposes constraints on the reference trajectories that can be tracked and on the global convergence rate of the tracking error. Using a dynamic model that is applicable to both electrostatic and electromagnetic MEM relays, we introduce a new class of nonlinear tracking controls. In particular, we use Lyapunov theory to construct a state feedback that yields uniform global asymptotic stability and arbitrarily fast local exponential convergence of the tracking error. We then show how our control can be redesigned with partial‐state feedback under the assumption that only the movable electrode position and the electrical state (i.e. charge or flux) are fed back. Finally, we utilize input‐to‐state stability theory to quantify the robustness of our state feedback controller to parametric uncertainties. Our simulation results illustrate the good stability and tracking performance of the proposed control. They also illustrate how to craft a reference trajectory that satisfies the aforementioned constraints while being compatible with a typical relay operation. Copyright © 2007 John Wiley & Sons, Ltd.