Active Shape Adjustment of Large Cable-Mesh Reflectors Using Novel Fast Model Predictive Control

Abstract

Active shape adjustment of a cable-mesh reflector is a significant procedure to compensate the effects of a complicated space environment in orbit. In this paper, the active shape adjustment of a large cable-mesh reflector with actuators is addressed, and the dynamic input voltage profiles of actuators are estimated using a novel fast model predictive control method. The electromechanical coupling dynamic model of the cable-mesh reflector with piezoceramic (PZT) actuators is first established by using piezoelectric constitutive equations and Hamilton’s principle. For a certain shape distortion, the dynamic control voltage profiles are then obtained via the novel fast model predictive control method in which the structural dynamics model is reformulated as a novel explicit repression form to avoid the computations of matrix exponential. Additionally, some fast computation strategies based on the Newmark-β method are used to increase computational efficiency. Finally, a 3-meter diameter cable-mesh reflector is chosen as a numerical example, and the simulation results demonstrate that the proposed control algorithm provides a valid and efficient solution for the shape control of large cable-mesh reflectors.