Output Stabilization of Flexible Spacecraft with Active Vibration Suppression

A desired characteristic of future spacecraft and space structures is the possibility of reducing the costs inherent with their transport in the space. Hence, it is necessary to decrease their weight; the main drawback consists of the decreased rigidity of the structure. Therefore, the elimination of vibrations becomes an important issue in spacecraft maneuvers. Another issue, related to the previous one, is the reduction of the number of sensors necessary to implement a control strategy. This is an interesting aspect in case of sensor failures and for the reduction of the structure and control system design costs. In this case the main problem is the measure of the variables describing the flexible motion, the modal position, and velocity. Additional problems arise when one measures only the output, namely some variables are not available for measuring, such as the spacecraft angular velocity. The effects of the flexible dynamics, affecting the rigid motion, and the absence of measurements of the corresponding modal variables and of the angular velocity, render the controller task more severe. In fact, the reduced accuracy in the control action, due to the use of estimates, may impair the stability of the overall control scheme. An interesting solution for the attenuation of the flexible oscillations induced by spacecraft maneuvers is given by piezoelectric actuators [1–6]. These actuators consist of films of piezoelectric material placed along the flexible elements of the structure. Due to their inherent distributed nature, the piezoelectric actuators are natural candidates for damping out undesirable vibrations. The techniques present in the literature, among which the nonlinear input-output decoupling and linearization [7–14], fail to give an appropriate answer to the active control problem from output measurements, since they need the knowledge of the entire state of the system. Hence, for solving this problem, in this work a dynamic controlled is proposed, based on the Lyapunov technique (see for instance [15] for its application in the design of spacecraft control systems). The controller derived uses estimates of the modal variables and of the angular velocity. Since the total angular momentum remains constant when external torques are absent, the estimate of the spacecraft angular velocity is easily determined; a similar approach can be used when the external torque depends on known variables. When disturbances are absent, see also [16] for a recent result on attitude control from quaternion measures. In the presence of disturbance torques and when we deal with system parameter variations, the same control scheme fails to solve exactly the posed control problem. In this case and under appropriate conditions on the disturbances and parameter variations, it is possible to show that