Robust proportional–integral–derivative design for processes with interval parametric uncertainty

• Published in: IET control theory & applications Vol. 11; no. 7; pp. 1016 - 1023
• Main Authors: Mercader, Pedro, Baños, Alfonso, Vilanova, Ramón
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 25.04.2017
• Subjects: Categories; control system synthesis; Design optimization; fractional‐order loop transfer function; instrumental fractional‐order plant; interval parametric uncertainty; interval process; Intervals; optimisation; Optimization; performance maximisation; Proportional integral derivative; Research Article; RO problems; robust control; robust optimisation problems; robust proportional–integral–derivative design; Robustness; Simplification; Smith‐predictor‐based dead‐time compensator; stability margins; three‐term control; transfer functions; uncertain process; uncertain systems; Uncertainty; three-term control; fractional-order loop transfer function; Smith-predictor-based dead-time compensator; performance maximisation; uncertain systems; control system synthesis; robust optimisation problems; interval process; robust proportional–integral–derivative design; optimisation; RO problems; robust control; stability margins; transfer functions; instrumental fractional-order plant; uncertain process; interval parametric uncertainty
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2016.1239

A novel method for designing proportional–integral–derivative controllers for processes containing interval parametric uncertainty is presented. The control design problem is posed as an optimisation problem where performance is maximised subject to some stability margins over a family of transfer functions. The resulting problem falls within the category of robust optimisation (RO) problems. The authors derive conditions that allow to obtain a solution to the RO problem by solving a nominal optimisation problem (in some cases at the expense of introducing some conservatism). This simplification is made by introducing an instrumental fractional-order plant that characterises the uncertain (interval) process and stating certain conditions over the fractional-order loop transfer function. The design approach is also applied to a Smith-predictor-based dead-time compensator. Some examples are given throughout this study to illustrate the proposed design method.