Design of optimal systems by a frequency-domain technique

It is shown, by an extension of the optimality condition in the frequency domain, that certain relationships exist between the response of optimal system, the elements of the weighting matrices of the performance index and the optimal feedback matrix. On the basis of these relationships, and using a root-locus procedure, weighting matrices can be chosen which give a desired optimal response, and the corresponding optimal feedback can be calculated. Though general in its nature, as a computational technique it is at present limited to single-input systems. For single-input systems, a relationship between the performance index and the optimal feedback is also established. For the special case of single-input systems, a direct relationship is obtained between the closed-loop poles and the feedback matrix. Although the resulting system may, or may not, be optimal, this relationship constitutes a useful design procedure. An example is given illustrating the technique.