Robust control of Control Moment Gyroscope with friction disturbance - Using polytopic representation

Abstract

This paper presents robust control design for Control Moment Gyroscope (CMG). There are practical difficulties in the control design of CMG. First, friction occurs on the rotation axis of CMG. Second, CMG is a nonlinear system. Third, there are uncertainties in the mathematical model of CMG. In this study, those practical difficulties are solved. The controller is designed to compensate the friction. The controller has the integrator for the error between state and reference to eliminate steady-state error. There are trigonometric functions of a state variable in the mathematical model of CMG. In this study, the trigonometric function is approximated more exactly by not first-order but third-order Taylor series expansion. The mathematical model involving those high order terms is represented as the equivalent first-order system by using descriptor representation and linear fractional transformation (LFT). The robust stability for the system with those trigonometric functions is guaranteed by using polytopic representation based on Linear Matrix Inequalities (LMIs). The moment of inertia has one of the uncertainties in the mathematical model. It is treated as the uncertain parameter in this study. The robust stability for the system with the uncertainty is guaranteed by using polytopic representation based on LMIs. The effectiveness of the proposed controller is illustrated by simulations.