Abstract: The surface precision of the space-borne antenna reflector is the main influence factor of its electromagnetic performance. The active shape control methodology is an effective way to guarantee the surface precision of space-borne antenna reflectors in orbit. Considering the uncertain material properties of the space-borne antenna reflectors in orbit, a robust shape control method based on P-CS (Probability-Convex Set) model and digital twin is proposed in this paper. The uncertain material properties are quantified in a uniform model (P-CS model), and the P-CS model can be updated driven by displacement monitoring data based on Bayesian theory. According to the P-CS model, a voltage layout optimization model is proposed to achieve optimal robustness of the surface precision under uncertainties. To solve such voltage layout optimization problem with multiple local optimal solutions and large scale of discrete variables, the voltage layout is described by a bounded field with space correlation based on the continuous representation a dimensionality reduction method, and then the design space is discretized and sequential sub-optimization problems are formed. The optimal solution can be achieved by solving sub-optimization problems one by one. At last, the proposed method is used to an active shape control problem for a regular hexagon space-borne antenna reflector. Two cases with the constraints of applying one kind of voltage and four kinds of voltage are proposed to demonstrate the validity and applicability of the proposed method.

Key words: Space-borne antenna reflector, active shape control method, Robustness layout optimization, Digital twin