Variable Structure Control of a Mass Spring Damper Subjected to a Unilateral Constraint: Application to Radio-Frequency MEMS Switches

Abstract

A feedback control strategy is presented for improving the transient response of the ubiquitous mass-spring-damper (MSD) system; the closed-loop system has a small settling time with no overshoot for a step input. This type of response is ideal for MSD systems subjected to a unilateral constraint such as radio-frequency micro-electro-mechanical-system (RF MEMS) switches, which are required to close in a short period of time without bouncing. The control strategy switches the stiffness of the MSD between its nominal value and a negative value, resulting in a hybrid dynamical system. A phase portrait analysis of the hybrid system is carried out to establish the asymptotic stability property of the equilibrium and quantify the transient response. Simulation results are presented using parameter values of a real RF MEMS switch from the literature. As compared to open-loop strategies that are currently used, the proposed feedback control strategy promises to provide comparable switch-closing times with robust performance and eliminate bouncing.