Dynamics and Robust Control of an Underactuated Torsional Vibratory Gyroscope Actuated by Electrostatic Actuator

It has been shown that the underactuated MEMS gyroscopes provide inherent robustness against structural and environmental parameter variations. To further improve the performance of the systems, the electrical and mechanical coupling dynamics of the underactuated torsional gyroscopes with double oscillators actuated by a single electrostatic actuator is investigated in this paper. It is shown that the highly nonlinear coupling dynamics of the underactuated gyroscope systems can be transformed into the fifth-order linear systems even though the electrical uncertainties of the systems are considered. For the purpose of simplifying the structures of the underactuated torsional MEMS gyroscopes, an observer-based robust controller with considering structural uncertainties is presented on the basis of linear matrix inequalities (LMIs). The robust stability of the presented controller is also demonstrated by some numerical simulations on a three-degree-of-freedom underactuated MEMS gyroscope. It is shown that the LMI-based robust controller can accommodate both large initial errors in the system state and bounded uncertainties in the structural parameters of the system.