Active vibration control of a large space telescope based on H∞ control with unilateral and constrained input

Abstract

The development of the telescope with large aperture is driven by the increasing demand for higher imaging resolution and imaging area. The large membrane diffraction space telescope is particularly attractive due to their lightweight nature, ease of folding and unfolding, and high precision imaging capabilities. However, the flexible and large structure of these telescope makes them prone to long-time, low-frequency vibrations in space. These vibrations can degrade the imaging quality and potentially cause damage to the instrument in the space telescope. Therefore, it is crucial to develop effective active vibration control methods to suppress these structural vibrations. This paper proposes a control method that utilizes cables as actuators. Since cables can only withstand tension and have limited output tension, this constraint is taken into account during the control design process. Firstly, a dynamics model of the membrane diffraction space telescope with hinge flexibility is developed by the beam theory and finite element method. Next, an active controller is designed by combining H∞ control theory and Linear Matrix Inequalities (LMI). Additionally, the optimal positions of cable actuators are determined using the Gram controllability criterion and a particle swarm algorithm. Finally, the effectiveness of the control method is verified through numerical simulations. The simulation results demonstrate that the hinge flexibility significantly influences the structural vibration behavior of the telescope. Furthermore, the proposed control method demonstrates the ability to effectively suppress the vibrations of the telescope while also exhibiting robustness to changes in natural frequencies of the structure.