A New Reduced-Order Implementation of Discrete-Time Fractional-Order PID Controller

Rafal Stanislawski,Zhixiong Li,Marek Rydel

doi:10.1109/access.2022.3150883

Abstract

This paper presents a new method for computationally effective implementation of a discrete-time fractional-order proportional–integral–derivative (FOPID) controller. The proposed method is based on a unique representation of the FOPID controller, where fractional properties are modeled by a specific finite impulse response (FIR) filter. The balanced truncation model order reduction method is applied in the proposed approach to obtain an effective, low-order model of the FOPID controller. The time-invariant FOPID controller implementation is presented first, and then the methodology is extended to the controller with time-varying gains. A comparative analysis shows that the proposed methodology leads to the effective modeling of discrete-time FOPID controllers. In addition to simulation runs, the effectiveness of the introduced methodology is confirmed in a real-life experiment involving the control of the DC motor servo system. The paper concludes with the implementation tools developed in the Matlab/Simulink environment.

Highlights

During the past two decades, the fractional-order generalizations of various control strategies have attracted considerable research attention in science and technology
The approach is based on a specific representation of the fractionalorder proportional-integral-differential (FOPID) controller, where fractional properties are modeled by the finite impulse response (FIR)-based filter, leading to the high FOPID modeling accuracy in the high-frequency range
In order to obtain an effective and low order model of FOPID controller, BT model order reduction using analytical solutions of the controllability and observability gramians is applied in the proposed approach

Summary

Introduction

During the past two decades, the fractional-order generalizations of various control strategies have attracted considerable research attention in science and technology. FOPID has two additional parameters compared to the classical PID controller, which are fractional orders of integrator and derivative Since these extra parameters are mutually influenced by the controller’s gains, tuning the parameters of the FOPID controller is much more challenging than for the classical integer-order case. To solve this problem, various optimization strategies have been applied, including particle swarm optimization [2]–[4], genetic algorithms [5], [6], differential evolution methods [5], chaotic firefly algorithms [7], extensions of classical tuning methods for PID controllers [8], [9], and other techniques [10]–[14]. Various variable-order FOPID controller implementations can be found in the literature [26]– [29]

Methods

Results

Conclusion