Robust compensator control of a non-resonant MEMS gyroscope with linear quadratic regulator

This paper presents a controller design for a four degrees-of-freedom (4-DOF) non-resonant gyroscope via the linear quadratic regulator (LQR) technique. Compared to conventional MEMS gyroscopes, non-resonant gyroscopes are less vulnerable to fabrication perturbations. However, closed-loop performance of non-resonant gyroscopes has not been investigated previously. The control of non-resonant gyroscopes involves consideration of high order systems. LQR, which achieves balances between a fast response and a low control effort, has proven to be effective for high order systems. Our simulation results show that the closed-loop 4-DOF non-resonant gyroscope presented in this paper is able to achieve faster response and higher robustness to parameter uncertainties than the open-loop device. Under the sinusoidal input, compared to an error of 11.06% for the open-loop system, the closed-loop scale factor uniformity error is reduced to 0.014% under ±10% parameter perturbations. The device performance is analyzed by the behavior modeling approach in CoventorWare. The results show that the closed-loop non-resonant gyroscope achieves better performance through the LQR. The method reported here is proven to be effective and can be used in a wide range of applications.