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.

In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range.