Utilization of numerical optimization techniques in the design of robust multi-input, multi-output control systems

Abstract

A direct design method for solving the problem of robustness to cross-coupling perturbations in mulltivariable control systems is presented. The method uses numerical optimization procedures to manipulate the system feedback gains as direct design variables. The manipulation is accom­plished in a manner that produces desired performance by pole placement and robustness by modification of the minimum singular values of the system return difference matrix. Channels affected by cross-coupling perturbation may be recognized by the character of their transfer function plot. The mechanism used by the pole placement and robustness routine in obtaining a robust design is evident from the gain changes associated with the transfer and the zero shifts shown on pole-zero function diagram plots. The pole placement and robustness routine uses gain equalization and zero assignment to modify the characteristics of the system in the areas of low singular values, producing a robust design. A modification of the pole placement and robustness routine uses gain equalization and zero assignment to modify the characteristics of the system in the areas of low singular values, producing a robust design. A modification of the pole placement that may be applied to the design routine observers is also presented. Using feedback and filter gains as direct design variables a practical design procedure for robustness recovery in observer based systems is obtained.