Closed-loop active shape control of radial rib in umbrella antenna based on fiber-optic shape sensing

Radial ribs are important supporting parts of umbrella antenna, and its shape is a crucial factor affecting the overall reflector accuracy. Considering the difficulty of in-orbit shape sensing, a fiber-optic shape sensing (FOSS) method for the radial rib is presented in this paper, then on the basis of FOSS a shape active control method for the radial rib driven by Macro-Fiber Composite actuators is proposed. Firstly, combining the deformation characteristics of the radial rib structure, an improved Ko displacement algorithm is proposed for its shape sensing using distributed fiber-optic. Then, establish the shape active control model with the Influence-Coefficient-Matrix method, and propose a closed-loop shape active control method with FOSS as feedback for the radial rib. In this paper, the optimization problem of solving control voltage is established by using the Least-Square method, and Root-Mean-Square error is taken as the convergence condition. Finally, numerical simulation and experiment show that the relative error of the shape sensing with fiber-optic is less than 5%, and the shape accuracy of radial rib after control is improved by more than 90% to reach submillimeter level, which verifies the effectiveness of the radial rib shape active control method based on FOSS.