Robust PI Control of Interval Plants With Gain and Phase Margin Specifications: Application to a Continuous Stirred Tank Reactor

Radek Matusu,Bilal Senol,Libor Pekar

doi:10.1109/access.2020.3014684

Radek Matusu, Bilal Senol + Show 1 more

Open Access

https://doi.org/10.1109/access.2020.3014684

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Journal: IEEE Access	Publication Date: Jan 1, 2020
Citations: 14	License type: CC BY 4.0

Affiliation: Inonu University, Tomas Bata University in Zlín

Abstract

The paper is focused on robust Proportional-Integral (PI) control of interval plants with gain and phase margin specifications and on the application of this approach to a Continuous Stirred Tank Reactor (CSTR). More specifically, the work aims at the determination of PI controller parameter regions, for which not only robust stability but also some level of robust performance of the closed-loop control system is guaranteed, and this robust performance is represented by the required gain and phase margin that has to be ensured for all potential members of the interval family of controlled plants, even for the worst case. The applied technique is based on the combination of the previously published generalization of stability boundary locus method (for specified gain and phase margin under the assumption of fixed-parameter plants) with the sixteen plant theorem. This extension enables the direct application of the method to design the robustly performing PI controllers for interval plants. The effectiveness of the improved method is demonstrated on a CSTR, modeled as the interval plant, for which the robust stability and robust performance regions are obtained.

Highlights

The controlled plants that are burden with nonlinear, highorder, or other complex behavior, imprecise knowledge of their physical properties, or changeability of parameters are commonly modeled in a simplified way as the linear timeinvariant (LTI) systems with interval uncertainty, in short, as the interval plants
The application of the improved method is demonstrated on a Continuous Stirred Tank Reactor (CSTR), which is described by the linearized mathematical model with interval uncertainty, i.e., the robust performance region of PI controller parameters for given gain and phase margin specifications is obtained
Note that the same interval plant model was robustly stabilized by PI controllers using various methods in [38], [39], but the present paper addresses robust stability and robust performance problem

Summary

INTRODUCTION

The controlled plants that are burden with nonlinear, highorder, or other complex behavior, imprecise knowledge of their physical properties, or changeability of parameters are commonly modeled in a simplified way as the linear timeinvariant (LTI) systems with interval uncertainty, in short, as the interval plants. R. Matušů et al.: Robust PI Control of Interval Plants With Gain and Phase Margin Specifications: Application to a CSTR. This work intends to extend the interesting results published previously in the papers [9], [31], where the generalization of stability boundary locus method for specified gain and phase margins is introduced and further discussed, but where the presented applications are limited to the controlled plants with fixed parameters. The application of the improved method is demonstrated on a CSTR, which is described by the linearized mathematical model with interval uncertainty, i.e., the robust performance region of PI controller parameters for given gain and phase margin specifications is obtained.

ROBUST STABILIZATION OF INTERVAL PLANTS VIA PI CONTROLLERS

CONCLUSION