Robust PID controller tuning based on the heuristic Kalman algorithm

• Published in: Automatica (Oxford) Vol. 45; no. 9; pp. 2099 - 2106
• Main Authors: Toscano, Rosario, Lyonnet, Patrick
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.09.2009; Elsevier
• Subjects: [formula omitted] control; Algorithms; Applied sciences; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Exact sciences and technology; Heuristic; Heuristic Kalman algorithm; Mathematical models; Non-convex optimization problems; Optimization; PID controller; Proportional integral derivative; Robustness; Strategy; Tuning; Non-convex optimization problems; PID controller; Robustness; H ∞ control; Heuristic Kalman algorithm; Selftuning control; Non convex programming; Multicriteria analysis; Kalman filter; H infinite control; Control synthesis; H; control; Constrained optimization; Robust control; Heuristic method; Convexity; Differential integral proportional control
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2009.05.007

This paper presents a simple but effective tuning strategy for robust PID controllers satisfying multiple H ∞ performance criteria. Finding such a controller is known to be computationally intractable via the conventional techniques. This is mainly due to the non-convexity of the resulting control problem which is of the fixed order/structure type. To solve this kind of control problem easily and directly, without using any complicated mathematical manipulations and without using too many “user defined” parameters, we utilize the heuristic Kalman algorithm (HKA) for the resolution of the underlying constrained non-convex optimization problem. The resulting tuning strategy is applicable both to stable and unstable systems, without any limitation concerning the order of the process to be controlled. Various numerical studies are conducted to demonstrate the validity of the proposed tuning procedure. Comparisons with previously published works are also given.