Lyapunov-Based Stabilization of MEMS Relays

In this paper, nonlinear stabilizers are introduced for voltage-controlled microelectromechanical system (MEMS) relays. The control constructions follow a Lyapunov approach and are based on a nonlinear dynamic model applicable to the two types of MEMS relays-electrostatic and electromagnetic. Two control schemes are presented with the objectives of avoiding pull-in during the microrelay closing and improving the transient response during the microrelay opening. First, an adaptive state feedback stabilizer is proposed to compensate for parametric uncertainty in all mechanical parameters and selected electrical parameters while ensuring asymptotic regulation of the electrode opening and closing. Next, a model-based observer/stabilizer is proposed to account for the lack of velocity measurements. Simulations demonstrate the performance of the two control schemes in comparison to the typical open-loop operation of the MEMS relay.