The surface precision of an antenna reflector can be improved using the actuation of piezoelectric materials to obtain a high-performance space antenna. In this study, the active shape control of a reflector with piezoceramic (lead zirconate titanate) actuators assembled on ribs is proposed by theoretical and experimental approaches. A finite element model of the integrated reflector–actuator system is established using piezoelectric constitutive equations and the virtual work’s principle. For a desired shape, a closed-loop iterative shape control method based on the influence coefficient matrix model is developed, which resolves the issue of high-precision shape control of the antenna reflector in the presence of model errors. The shape controller based on the proposed closed-loop shape control method is implemented on a planar hexagonal reflector with 30 lead zirconate titanate actuators. Experimental results demonstrate that the closed-loop control is an effective way to improve the surface precision of the reflector considering uncertainties.
Active shape control for an antenna reflector is a significant procedure used to compensate the impacts for a complicated space environment. In this paper, a physics-guided distributed model predictive control (DMPC) framework for reflector shape control with input saturation is proposed. First, guided by the actual physical characteristics, an overall structural system is decomposed into multilevel subsystems with the help of a so-called substructuring technique. For each subsystem, a prediction model with information interaction is discretized by an explicit Newmark-β method. Then, to improve the systemwide control performance, a coordinator among all the subsystems is designed in an iterative fashion. The input saturation constraints are addressed by transforming the original problem into a linear complementarity problem (LCP). Finally, by solving the LCP, the input trajectory can be obtained. The performance of the proposed DMPC algorithm is validated through an experiment on the shape control of an antenna reflector structure.
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