Modeling and Control of a Thermally Driven MEMS Actuator for RF Applications

Abstract

Thermally driven V-shaped microelectromechanical systems (MEMS) actuators have been used extensively in different fields of MEMS including RF MEMS applications. For this reason, developing a dynamic model is of importance for understanding the MEMS actuator dynamic behavior and for improving its transient response. Obtaining such a model is challenging as multi-physics phenomena are involved in the actuation mechanism. The complexities involved in modeling can be reduced by using macromodeling approaches. As such, a new mixed-level nonlinear electro-thermo-mechanical dynamic macromodel for a thermally driven V-shaped MEMS actuator is proposed. The proposed reduced-order macromodel is composed of a nonlinear circuit-level electrothermal macromodel and a nonlinear system-level thermo-mechanical macromodel obtained by the application of the Galerkin method. The system dynamic behavior is successfully reproduced using the proposed macromodel. The results obtained by the macromodels are in good agreement with the finite element ANSYS simulations and are computationally less expensive by far. Furthermore, the experimental static tip displacements of the actuator for different actuation voltages are in very good agreement with steady-state values of the actuator's tip displacements obtained by the proposed macromodel, and the maximum error obtained is less than 9%. Furthermore, a first-order dynamic model, based on the ANSYS input voltage and output displacement data, is developed in order to describe the displacement transient response of the MEMS actuator. The results obtained from the first-order and the ANSYS models are in very good agreement. The electro-thermo-mechanical macromodel and the first-order model are then used in closed-loop form with conventional and adaptive proportional-integralderivative (PID) algorithms to speed up the displacement transient response of the thermal MEMS actuator. Using SIMULINK, it is shown that the adaptive PID controller outperforms the conventional PID controller by meeting all the design requirements.