Sequential design of linear quadratic state regulators via the optimal root-locus techniques

Abstract

The paper considers the use of well known root-locus techniques for sequentially finding the weighting matrices and the linear quadratic state regulators of multivariable control systems in the frequency domain. The proposed sequential design method enables the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system, and it allows some optimal closed-loop poles to be placed in a specific region of the complex plane, by sequentially assigning some virtual finite openloop zeros (which are finite asymptotic poles of a virtual closed loop system as the scalar gain factor goes to infinity). Moreover, it provides a design procedure for determining the weighting matrices and linear quadratic state regulators for optimal control of multivariable systems in the frequency domain. The selection of the state weightingmatrix, via the proposed method, places emphasis on specific linear combinations of the states (of the designers choice), rather than prespecified linear combinations of the states (output) which often arise in practical applications. An illustrative example is provided to demonstrate the effectiveness of the proposed method.