In the paper, the authors describe and solve the problem of optimum control of selected vibration forms in mechanical systems. Two illustrative examples have been used to present the procedure for determination of the optimum controller coefficients.

In the first example, a simplified mechanical system is considered, while in the second one – a rotor with magnetic bearing. In both cases, the integral performance indices have been defined in order to minimize the vibration level at selected points of the structures.

The system with the magnetic bearing is structurally unstable. For this reason, the authors present the way of finding the weight coefficients of integral performance index for unstable, multi-degrees-of-freedom system. In that way, the selected modal forms attain the previously assumed dynamic properties and the performance index takes the minimum value. The results of numerical analysis show that the proposed way is efficient and makes it possible to control selected forms of vibration in the system.