Fast attitude maneuver of a flexible spacecraft with passive vibration control using shunted piezoelectric transducers

Abstract

This paper is concerned with designing a bang-bang control input to perform a quick rotational maneuver of a rigid spacecraft hub connected with flexible appendages. The control design is based on only the rigid body mode making it very simple to design and at the same time achieve the quickest maneuver possible. The induced vibrations are suppressed using piezoelectric transducers bonded to the appendages and connected to an electric circuit with the objective of converting the vibrational energy to electrical energy and then dissipating it using passive electric elements, such as a resistance and an inductor. The proposed control design method is applied to a spacecraft containing a rigid hub and flexible appendages. The attitude control torque is produced using either the reaction wheels contained inside the rigid hub or jet thrusters mounted outside it. The control design process starts with deriving the nonlinear partial differential equations of motion for the spacecraft using Hamilton’s principle which accounts for the electromechanical coupling and the presence of resistive or resistive-inductive circuits. To simplify the analysis, the nonlinear ordinary differential equations of motion are then obtained using the assumed mode method. The effectiveness of the control design method is numerically tested on a spacecraft that is required to perform a quick attitude maneuver and, simultaneously, suppress the induced vibrations. The simulations show a quick and accurate maneuver has been achieved combined with very low levels of vibrations resulting from the reduced coupling between flexible and rigid motions as well as the damping added as a result of the passive shunt circuit. Furthermore, the resistance-inductance shunt circuit is shown to be more effective in damping the vibrations than the resistance shunt circuit.