Dynamic analysis and deploying process control of large parabolic cylinder antennas

Abstract. The deployable parabolic cylindrical antenna, due to its large structural scale, complex transmission linkages, and multiple closed-loop constraints, endures significant differential loads on its structural components during the deployment process. This leads to substantial deformations or even damage to the structure. To enhance the reliability of the antenna's deployment and the load-bearing safety of its components, it is imperative to comprehensively identify the dynamic characteristics inherent in the control of the antenna deployment process. In this paper, a fast dynamic modeling method for large-scale, module-assembled, space deployable supporting structures is proposed. Based on this, an algorithm for solving high-dimensional differential equations which features polycondensation and recursion module by module is proposed. First, the dynamic and constraint equations are established for a large-scale deployable supporting structure with parabolic cylindrical surfaces which is divided into 25 sub-modules. Then, sub-modules are assembled to realize the fast dynamic modeling of the large-scale supporting structure. Further, an efficient recursive algorithm, which is solved module by module, is presented according to the concept of building dynamic equations in modularization. Finally, a nonlinear deployment control strategy based on velocity feedback is introduced to ensure stable deployment control over strongly nonlinear systems, such as the deployable supporting structure with parabolic cylindrical surfaces; moreover, ideal deployment control effects are achieved for such systems. The results indicate that the control method can reduce the peak velocity of the supporting structure during the deployment process from 5.508 to 0.0323 m s−1 and that it improves the synchronicity of the antenna's supporting structure deployment by 69.49 %. This study provides a feasible implementation scheme for the dynamic characteristic analysis and deployable process control of back-shell truss antennas.