Abstract
A synthesis method of linear optimal regulators for multivarible systems is presented using singular values of the loop transfer function evaluated at the input point. To this objective, performance specification and condition of stability robustness are first examined to obtain magnitude constraints of the singular values. The weighting matrices of a quadratic performance index are then tuned iteratively so that the resulting loop shape may satisfy these constratints. This tuning is done by the quasi-Newton method so as to minimize the criterion which consists of a weighted sum of the differences between desired and actual singular values at some discrete frequencies. To avoid numerical difficulties, the weighting matrices are assumed to be diagonal, which leads to a nonsingular matrix in terms of directional derivatives. Two numerical examples are given to illustrate and to substantiate the proposed method. The resulting optimal requlators are shown to improve the characteristics of the controlled system effectively while keeping their inherent stability property.
