Robust Control Design of the Structural Vibration System via Eigenstructure Assignment

The robust control design in a class of structural vibration systems is considered in this paper. The aim is to design a state feedback controller such that the closed-loop system has the desired eigenvalues with minimum sensitivities with respect to system parameter perturbations. By utilizing a result of parametric eigenstructure assignment via state feedback, this robust control problem is changed into an optimal problem with some constraints and an algorithm for this optimization problem is established. This algorithm offers a parametric expression for the eigenvalue sensitivity index and utilizes directly the data of the original system, thus it is convenient to use in engineering applications. An example about three degrees of freedom shear structure system under vibration excitation is analyzed by using the proposed algorithm and the corresponding simulation results show the effectiveness of this algorithm.