Tuning PID and FOPID Controllers using the Integral Time Absolute Error Criterion

TL;DR

This paper presents a PSO-based method for designing fractional-order PID controllers optimized using the ITAE criterion, demonstrating improved performance over traditional PID controllers especially for fractional-order plants.

Contribution

It introduces a novel PSO-based design approach for FOPID controllers with five parameters, optimized via ITAE, and compares their effectiveness to integer-order PID controllers.

Findings

FOPID controllers outperform PID controllers in fractional-order plant control.

The proposed method effectively optimizes five parameters of FOPID.

Simulation results confirm the superiority of FOPID over PID.

Abstract

Particle swarm optimization (PSO) is extensively used for real parameter optimization in diverse fields of study. This paper describes an application of PSO to the problem of designing a fractional-order proportional-integral-derivative (FOPID) controller whose parameters comprise proportionality constant, integral constant, derivative constant, integral order (lambda) and derivative order (delta). The presence of five optimizable parameters makes the task of designing a FOPID controller more challenging than conventional PID controller design. Our design method focuses on minimizing the Integral Time Absolute Error (ITAE) criterion. The digital realization of the deigned system utilizes the Tustin operator-based continued fraction expansion scheme. We carry out a simulation that illustrates the effectiveness of the proposed approach especially for realizing fractional-order plants. This paper also attempts to study the behavior of fractional PID controller vis-a-vis that of its integer order counterpart and demonstrates the superiority of the former to the latter.