Nonlinear parameter‐varying state‐feedback design for a gyroscope using virtual control contraction metrics

Abstract

In this article, we present a virtual control contraction metric (VCCM) based nonlinear parameter-varying approach to design a state-feedback controller for a control moment gyroscope (CMG) to track a user-defined trajectory set. This VCCM based nonlinear (NL) stabilization and performance synthesis approach, which is similar to linear parameter-varying (LPV) control approaches, allows to achieve exact guarantees of exponential stability and (Formula presented.) -gain performance on NL systems with respect to all trajectories from the predetermined set, which is not the case with the conventional LPV methods. Simulation and experimental studies conducted in both fully- and under-actuated operating modes of the CMG show effectiveness of this approach compared with standard LPV control methods