Modeling and robust control of connected two flexible beams

Summary form only given. In this paper, modeling and robust control of a flexible structure with a closed-loop mechanism are discussed. It is important to derive a mathematical model and construct a controller for such complicated space structures. We consider two connected flexible beams as a simple model of the space structures with the closed-loop mechanism. This structure can be regarded as an element of the truss structure. We derive dynamic equations of the connected flexible beams by means of Hamilton´s principle. As the obtained boundary conditions of the distributed parameter system are nonhomogeneous, we introduce a change of variables to derive homogeneous boundary conditions. The solution of an eigenvalue problem related to the distributed parameter system yields eigenvalues and corresponding eigenfunctions. On the basis of the truncated eigenfunction expansion, an approximated finite-dimensional modal model are derived. As the original system is infinite dimensional and controllers should be designed on the basis of an approximated finite dimensional model, it is necessary to compensate the spillover instability caused by the residual modes which are neglected at the controller design phase. It is difficult to estimate the physical parameters of the system, for example a flexural rigidity, a damping coefficient, etc., correctly. In order to compensate the unmodeled dynamics and the parameter uncertainty, a robust controller should be constructed. In the paper, an optimal controller with low-pass property and a robust H/sub /spl infin// controller are designed. Simulations have been carried out and responses for the controllers are compared.