Tuning rules for robust FOPID controllers based on multi-objective optimization with FOPDT models

• Published in: ISA transactions Vol. 66; pp. 344 - 361
• Main Authors: Sánchez, Helem Sabina, Padula, Fabrizio, Visioli, Antonio, Vilanova, Ramon
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.01.2017
• Subjects: Balanced tuning; Fractional-order PID controllers; Multi-objective optimization; Nash solution; Nash solution; Balanced tuning; Multi-objective optimization; Fractional-order PID controllers
• ISSN: 0019-0578; 1879-2022; 1879-2022
• DOI: 10.1016/j.isatra.2016.09.021

In this paper a set of optimally balanced tuning rules for fractional-order proportional-integral-derivative controllers is proposed. The control problem of minimizing at once the integrated absolute error for both the set-point and the load disturbance responses is addressed. The control problem is stated as a multi-objective optimization problem where a first-order-plus-dead-time process model subject to a robustness, maximum sensitivity based, constraint has been considered. A set of Pareto optimal solutions is obtained for different normalized dead times and then the optimal balance between the competing objectives is obtained by choosing the Nash solution among the Pareto-optimal ones. A curve fitting procedure has then been applied in order to generate suitable tuning rules. Several simulation results show the effectiveness of the proposed approach. •A set of optimally balanced tuning rules for fractional-order proportional-integral-derivative controllers is proposed.•The control problem of minimizing at once the integrated absolute error for both the set-point step response and the load disturbance step response is addressed. Further, the maximum sensitivity is considered as a constraint for the optimization problem.•The control problem is stated as a multi-objective optimization problem where a first-order-plus-dead-time process model has been considered. The Nash solution is chosen between the set of Pareto optimal solutions obtained for different normalized dead times.•A curve fitting procedure has then eventually been applied in order to generate suitable tuning rules.