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

Helem Sabina Sánchez¹, Fabrizio Padula², Antonio Visioli³

¹Departament de Telecomunicació i Enginyeria de Sistemes, ETSE, Universitat Autònoma de Barcelona, Carrer de es Sitges, 08193 Bellaterra, Barcelona, Spain.

ISA Transactions

|December 19, 2016

Summary

This study proposes new tuning rules for fractional-order controllers to minimize errors in set-point and disturbance responses. The method balances competing objectives using multi-objective optimization and Nash solutions for robust control.

Keywords:

Balanced tuning Fractional-order PID controllers Multi-objective optimization Nash solution

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The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

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Published on: October 14, 2017

Area of Science:

Control Engineering
Optimization Theory
Process Control

Background:

Fractional-order controllers offer enhanced performance over integer-order counterparts.
Tuning rules are crucial for practical implementation of advanced control strategies.
Minimizing integrated absolute error for both set-point and load disturbance responses is a key control objective.

Purpose of the Study:

To propose optimally balanced tuning rules for fractional-order proportional-integral-derivative (FOPID) controllers.
To address the multi-objective optimization problem of minimizing integrated absolute error for set-point and load disturbance responses simultaneously.
To develop robust tuning rules considering a first-order-plus-dead-time (FOPDT) process model with a maximum sensitivity constraint.

Main Methods:

Formulating the control problem as a multi-objective optimization task.
Considering a first-order-plus-dead-time (FOPDT) process model with a maximum sensitivity constraint.
Obtaining Pareto optimal solutions for various normalized dead times.
Selecting the Nash solution from the Pareto set to achieve optimal balance.
Applying a curve fitting procedure to derive tuning rules.

Main Results:

A set of Pareto optimal solutions was generated for different normalized dead times.
The Nash solution effectively balanced the competing objectives of minimizing integrated absolute error.
The proposed curve fitting procedure yielded suitable tuning rules.
Simulation results demonstrated the effectiveness of the developed FOPID tuning approach.

Conclusions:

The proposed method provides a systematic way to derive optimally balanced tuning rules for FOPID controllers.
The approach effectively handles the trade-offs in multi-objective control problems for FOPDT systems.
The derived tuning rules offer a practical solution for improving control performance in terms of integrated absolute error minimization and robustness.