Analytical Design of a Wide Class of Controllers with Two Tunable Parameters Based on H∞ Specifications

Abstract

First, the paper introduces a specific class of controllers with two tunable parameters called affine controllers, which includes almost all controllers with a fixed structure commonly used in industrial practice, including PI(D) controllers. The main result of this paper presents a new analytical method for the design of the H∞ affine controller based on a description of the boundary of the H∞ region in the parametric plane of the controller. A user-friendly interactive implementation of this method, supporting multiple system models, is available at www.pidlab.com. The use of this tool is also illustrated by an example.