Gain scheduling controller tuning with multi-objective evolutionary algorithms

Gain scheduling is a simple technique that uses several linear partitions of a nonlinear process and tunes a simple controller for each one. When merged with simple techniques as PID control, this mechanism allows nonlinear control loops to achieve a reasonable trade-off between performance, robustness, and complexity. In such instances, multi-objective optimization offers a suitable strategy for controller tuning to achieve trade-offs. Despite the extensive application of multi-objective techniques for PID controller tuning, little has been said about using such techniques in a gain scheduling scenario. Therefore, this paper was motivated by the following question: How could multi-objective optimization techniques be merged with gain scheduling to address performance, simplicity in controller tuning, and the fixed structure of a given controller? In this paper, we propose a gain scheduling controller tuning method using the ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document}-gap technique to reduce the number of required controllers while maintaining a predetermined fixed low-order structure (in this research, a PI controller is considered), along with multi-objective optimization to find new control values for a nonlinear system. Simulation experiments using a Peltier cell benchmark process validate the proposal by significantly reducing the set of adjustable variables and maintaining the performance of the controller when compared to other tuning alternatives.