A Quasi-Stationary Approach to Control Problems for Hybrid Flexible Systems

Abstract

A control problem for a string-type inhomogeneous system with boundary loads is considered. It is supposed that boundary and distributed control forces are applied to the plant. By using corresponding eigenproblems, the lumped dynamics of the hybrid system is considered. Based on an original numerical technique for eigenvalues computation, a combined approach to vibration control is proposed. At the first stage, the linear-quadratic regulator is used for suppression of some highest eigenmodes. After preliminary damping of the oscillations, an explicit quasi-stationary control law is applied to the main (lowest) eigenmode. The proposed quasi-stationary control affects only the main eigenmode and almost does not disturb the highest modes. A numerical example is given and discussed.