Simple adaptive control for vibration suppression of space structures using control moment gyroscopes as actuators

This paper presents an adaptive control strategy for vibration suppression of cantilevered flexible space structures with collocated control moment gyroscopes and angular rate sensors. Equations of motion capturing the detailed dynamics of the control moment gyroscopes and their interactions with the small-scale flexible motion of the structures are linearized to a state-space form. Modal analysis is then performed based on the linearized equations to transform the dynamic model into a bicoupled form. It shows that the skew-symmetric gyricity terms produced by using control moment gyroscopes as actuators make the dynamic characteristics of the structures much different from those of the traditional structures. The strictly positive realness of the system, which could guarantee the stability of the proposed adaptive controller, is proved both in the frequency-domain condition and the time-domain condition. It is found that any small damping could make the system strictly positive real. An adaptive controller is designed, and then its Lyapunov stability is analyzed. The controller is synthesized only by using the angular rates of the locations where the actuators are mounted. Numerical examples of cantilevered gyroelastic beam and plate structures demonstrate the efficacy of the proposed method.