Passive vibration control of flexible spacecraft using shunted piezoelectric transducers

This paper is devoted to the attitude and vibration control of spacecraft containing flexible appendages. It entails an investigation of a passive control strategy which consists in connecting piezoelectric transducers bonded to the flexible elements to electric circuits in such a way that the vibration energy, once converted into electrical energy, is transferred and partially dissipated into the electric circuit. This strategy enables to circumvent some difficulties involved in active control such as instability and the necessity of a large amount of hardware, which can be critical in space applications. One considers an artificial satellite model composed of a hub, a reaction wheel used for angular position control and two identical flexible panels, which contain piezoelectric patches symmetrically bonded to their surfaces. The equations of motion are derived based on the Assumed Modes approach, accounting for the electromechanical coupling and the presence of two types of circuits (resistive, and resistive-inductive). The effectiveness of the control strategy suggested is assessed by means of numerical simulations of a satellite undergoing an angular position correction commanded by proportional-derivative torque applied by the reaction wheel. The results demonstrate that the panel vibrations levels and coupling between flexible and rigid-body motions are significantly reduced for both types of circuits considered, such effectiveness being greater for resistive-inductive shunt circuits.