Method for Robust Tuning of Linear Quadratic Optimal Controllers

Abstract

A methodology for robust tuning of controllers designed according to linear quadratic (LQ) optimal control formulation is presented. It allows a direct approach to the problem when a low-order model and an uncertainty description are available for the system. As a preliminary step, a formal solution for the LQ controller, which depends explicitly on the model, input, and weight transfer functions, is presented. Analytical solutions for this formal expression are possible for common input and system models, including time delays and right-half-plane zeros. The controller tuning is accomplished thereafter by finding the value of the parameter of the weight function that guarantees the required robustness through an iterative numerical procedure. Application to cases of relevant interest in process control are illustrated, and guidelines for the selection of the input weight for the extreme cases of lag-dominant and delay dominant systems are given