Optimal controller with prescribed dominant energy eigenvalues

An optimal controller with prescribed dominant energy eigenvalues is proposed. The closed-loop control system preserves some of the eigenvalues of the original system. The eigenvalues selected to shift into the desired region are determined using the concept of dominant energy modes. A systematic design method, for sequentially finding the weighting matrix elements and the feedback gains of the controller corresponding to the given eigenvalues, is developed. The proposed method can also be used for efficiently tuning the weighting matrix of an already optimal feedback system so that the dominant eigenvalues of the resulting system are located in the desired region. It follows that, by shifting only the dominant eigenvalues of the proposed controller, simple and efficient control of the dynamic system can be obtained. An illustrative example is provided to demonstrate the effectiveness of the proposed method