Angular Displacement Control for Timoshenko Beam by Optimized Traveling Wave Method

Abstract

The vibration of flexible structures in spacecraft, such as large space deployable reflectors, solar panels and large antenna structure, has a great impact on the normal operation of spacecraft. Accurate vibration control is necessary, and the control of angular displacement is a difficulty of accurate control. In the traditional control method, the mode space control has a good effect on suppressing low-order modes, but there is control overflow. The effect of traveling wave control on low-order modes is worse than the former, but it has the characteristics of broadband control. It can better control high-order modes and reduce control overflow. In view of the advantages and disadvantages of the two control methods, based on Timoshenko beam theory, this paper uses vector mode function to analyze the modal of spacecraft cantilever beam structure, establishes the system dynamic equation, and puts forward an optimized traveling wave control method. As a numerical example, three strategies of independent mode space control, traditional traveling wave control and optimized traveling wave control are used to control the active vibration of beam angle. By comparing the numerical results of the three methods, it can be seen that the optimal control method proposed in this paper not only effectively suppresses the vibration, but also improves the robustness of the system, reflecting good control performance. An innovation of this paper is that the Timoshenko beam model is adopted, which considers the influence of transverse shear deformation and moment of inertia on displacement and improves the accuracy of calculation, which is important for spacecraft accessory structures with high requirements for angle control. Another innovation is that the optimized traveling wave control method is exquisite in mathematical processing and has good results in global and local vibration control, which is not available in other methods.

Keywords

• Timoshenko beam
• modal space control
• optimized traveling wave method
• angular displacement control