Modeling and robust control of two flexible beams connected by a spring

In this paper, modeling and robust control of two flexible beams connected by a spring are discussed. We derive dynamic equations of the connected flexible beams with a spring by means of Hamilton's principle. As the obtained boundary conditions 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. As the original system is infinite dimensional and controller 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. The physical parameters of the system, for example a flexural rigidity, a damping coefficient and a spring constant, cannot be estimated correctly. In order to compensate the unmodeled dynamics and the parameter uncertainty, a robust controller should be constructed.