Robust Stability Analysis of Unstable Second Order Plus Time-Delay (SOPTD) Plant by Fractional-Order Proportional Integral (FOPI) Controllers

Marzieh Asadi,Guillaume Crevecoeur,Arash Farnam,Hamed Nazifi,Sam Roozbehani

doi:10.3390/math10040567

Abstract

This study investigates the robust stability analysis of an unstable second order plus time-delay (SOPTD) plant by using Fractional-Order Proportional Integral (FOPI) controllers. We assume that there are simultaneous uncertainties in gain, time-constants, and time-delay of the plant. At first, a graphical method is provided for a robust stability analysis of the closed-loop system. Then, a robust stability checking function is introduced to facilitate the robust stability analysis. Additionally, new bounds are presented to reduce the computational burden for the robust stability analysis. Finally, two examples are provided to show the correctness of the proposed method.

Highlights

Integral (FOPI) Controllers.Generally, many real-world systems can be modeled by time-delay transfer functions because the dead time is inevitable and appears in real systems [1]
In [25,26], some auxiliary functions have been presented for robust stability analysis of interval fractional order systems having time-delay
This study develops the robust stability analysis of an unstable Second Order Plus timedelay (SOPTD) plant by Fractional-Order Proportional Integral (FOPI) controllers

Summary

Introduction

In [17,18], the value set approach has been provided for robust stability analysis of LTI fractional-order systems having time delay. In [25,26], some auxiliary functions have been presented for robust stability analysis of interval fractional order systems having time-delay. The methods presented in [30,31,32] cannot ensure the robust stability of the closed-loop system in the presence of plant uncertainties in time-delay, gain, and time constants This issue has prompted the authors of this paper to present a simple method to analyze the robust stability of a closed-loop system consisting of unstable SOPTD plants and FOPI controllers.

Background and Preliminaries

Main Results

Illustrative Examples

Conclusions