An LPV Design Approach for Voltage Control of an Electrostatic MEMS Actuator

This paper examines the stabilization and deflection control of an electrostatic microelectromechanical-system (MEMS) actuator using linear parameter-varying (LPV) control methodology. As a case study, a 1-DOF model of an electrostatic MEMS actuator is considered, and its static and dynamic characteristics are discussed. The presented model captures the significant characteristics of the actuator such as the pull-in effect and bifurcation instability. Designed and compared in this paper are control strategies for set-point tracking of the MEMS device deflection, namely: 1) an LPV output-feedback H_∞ controller; 2) an LPV state-feedback H_∞ controller integrated with an observer; and 3) a time-invariant H_∞ controller. To design the LPV controllers, the system dynamics is first reformulated in a quasi-LPV form, considering the actuation charge as the scheduling parameter. We subsequently provide a reduced-order parameter-dependent proportional-integral (PI) controller from the full-order LPV controller for ease of practical implementation. The time-invariant H_∞ controller is provided for comparison purposes. The design of the dynamic output-feedback controllers uses a mixed-sensitivity loop shaping, where the weighting selection is discussed. Step reference tracking results are presented and compared for the three control-design approaches. The simulation results illustrate the following: 1) the asymptotic stability and desired performance satisfaction for the controllers against the pull-in effect and random vibration disturbances and 2) the improved performance achieved using the output-feedback LPV controller in terms of the transient tracking response, tracking bandwidth, and control effort over the full range of the device operation.