Robust output regulation of a triaxial MEMS gyroscope via nonlinear active disturbance rejection

This paper presents a nonlinear disturbance rejection–based controller for the robust output regulation of a triaxial microelectromechanical system (MEMS) vibratory gyroscope. In a MEMS gyroscope, parameter variations, mechanical couplings, suspension system nonlinearities, thermal noise, and centripetal/Coriolis forces are the main uncertainty sources. In the dynamical equations of the gyroscope, these uncertainties appear as a matched total disturbance, which does not coincide with the required structure of a standard output regulation problem. More specifically, the total disturbance is not guaranteed to belong to the solution space of a fixed dynamical system. Therefore, we propose a control system that comprises a nominal output regulator equipped with a disturbance rejection loop. On the basis of a suitable reference dynamics of the gyroscope, the control system is developed as the stabilization of a zero‐error invariant manifold in the tracking error space. In the disturbance rejection loop, a nonlinear extended state observer (ESO) is designed to estimate the total disturbance. The convergence of the ESO is analyzed in a Lyapunov‐Lurie framework by linear matrix inequalities (LMIs). In the nominal output regulation loop, the stabilization problem of the desired manifold is tackled by introducing a suitable distance coordinate. Next, to achieve guaranteed attenuation of the ESO estimation errors, an energy‐to‐peak design is pursued. On the basis of the center manifold theory, the stability of the overall closed‐loop system is guaranteed. The efficacy of the proposed control method is assessed through software simulations.