Gain Scheduling Control of Control Moment Gyroscope

This paper presents gain scheduling (GS) control of a Variable Speed Control Moment Gyroscope (VSCMG) based on sum of squares (SOS). Nonlinear motion equations of the VSCMG are complicated because they contain sine and cosine of angles of gimbals. The dynamics varies depending on an attitude of a spacecraft. In this study, the difficulty of control design of the VSCMG is solved by two methods. First, the complex nonlinear model is transformed to the linear parameter varying (LPV) model, which the linear control method can be applied, to make prospect of control design easy by using a proposed approximation method. The highly accurate LPV model is reduced to polynomially parameterdependent linear matrix inequalities (PDLMIs). Second, GS controller whose gains are adjusted depending on the angles and the attitude is applied. The polynomially PDLMIs can be relaxed to finite design conditions based on matrix SOS polynomials. The GS controller is designed by solving the finite SOS conditions. By using those methods, GS controller which appropriately calculates gains depending on the nonlinearities is designed. The effectiveness of the proposed controller is illustrated by simulations and experiments.