Research On Vibration Control Of Large Space Flexible Structure Based On Precise Integration Method

Space truss structure and plate structure are important structure forms in space engineering. They have received extensive attention for their structural simplicity and the ability of folding and deploying. However, their drawbacks are also obvious, like large size and weak damping characteristics. Thus, when being hit by a mass or something, they will inevitably experience long period and large amplitude vibration, which will strongly affect the normal work of the space structure. So active control must be applied to suppress the vibration.In this paper, firstly, the precise integration method is used to solve the dynamics differential equation, so the precision and speed of the algorithm are guaranteed. Secondly, on the basis of the discrete algebraic equation, and combined with the decentralized control theory, the solving method of the control force that based on the LQ (Linear Quadratic) optimal control theory has been improved. Thirdly, a new control method, the eigenvalue control method is proposed in this paper, and its relationship with the LQ optimal control method is discussed. Finally, these two control methods are applied on two actual structures to analysis their effects on vibration suppression. This paper takes the flexible space structure as the research object, focusing on the vibration control on the structure. The main work is as follows:(1) Selecting the T-shaped truss structure and plate structure as the research objects, using finite element method to establish the simplified math model, then we can establish the dynamics model.(2) Exerting a transient impact on a given node, using the precise integration method to solve the dynamics equation to get the displacement and velocity responses and the changing curve of the total system energy, then we can establish the discrete time model.(3) The solving method of the control force that based on the LQ optimal control theory has been improved. Since the dimensions of the model is very large, the decentralized control theory is involved to divide the model into several blocks to obtain the node controlling solution. Based on the discrete algebraic equation, the control solution is finally obtained by using the pole assignment method.(4) A new control method, the eigenvalue control method is proposed in this paper. It is also based on the discrete algebraic equation. This control method does not need to solve the Riccati equation, but its effectiveness is equivalent to the one of the LQ optimal control method when the LQ optimal control method requires the displacement and velocity responses to be minimized in each step. And the relationship between the two methods has been proved in both theory and numerical simulation ways.(5) The above two control methods are applied on truss structure and plate structure, and the control effects have been compared. By applying the genetic algorithm, the number of the actuators are reduced, and the location of the actuators are optimized.Active control research of flexible structure is a challenging research topic, many aspects need further study and discussion. Thus, at the end of this paper, the research work and achievements are comprehensively summarized, and the problems of the research in the future are prospected.