ИСТИНА

A control problem for a string-type inhomogeneous system with boundary loads is consid- ered. It is supposed that boundary and distributed controls are applied to the plant. By using corresponding eigenproblems, the lumped dynamics of a hybrid system is consid- ered. Based on an original numerical technique for eigenvalues computation, a combined approach to vibration control is proposed. At the first stage, the linear-quadratic reg- ulator 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.