Power-Law Compensator Design for Plants with Uncertainties: Experimental Verification

Costas Psychalinos,Mohammad Saleh Tavazoei,Stavroula Kapoulea,Ahmed S Elwakil

doi:10.3390/electronics10111305

Abstract

A power-law compensator scheme for achieving robust frequency compensation in control systems including plants with an uncertain pole, is introduced in this work. This is achieved through an appropriate selection of the compensator parameters, which guarantee that the Nyquist diagram of the open-loop system compensator-plant crosses a fixed point independent of the plant pole variations. The implementation of the fractional-order compensator is performed through the utilization of a curve-fitting-based technique and the derived rational integer-order transfer function is realized on a Field-Programmable Analog Array device. The experimental results confirm that the the phase margin is well preserved, even for ±40% variation in the pole location of the plant.

Highlights

Fractional-order controllers are useful building blocks for compensating the existence of uncertainty in the model of a plant, which occurs in real-world control systems, and many efforts towards the implementation of such blocks have been made [1,2,3]
Compared to time-domain approaches, frequency-domain methods provide a more powerful framework for optimal tuning of the tunable orders of the fractional operators in the structures of fractional controllers. Such controllers have been designed with the aim of offering flatness in the open-loop phase response around the gain crossover frequency [7,8,9,10,11,12,13,14,15] and have been introduced to ensure robustness against variations in the time constant of a plant
Field-Programmable Analog Arrays (FPAAs) are analog signal processors based on configurable analog blocks (CABs) that offer design programmability and versatility [26,27]

Summary

Introduction

Fractional-order controllers are useful building blocks for compensating the existence of uncertainty in the model of a plant, which occurs in real-world control systems, and many efforts towards the implementation of such blocks have been made [1,2,3]. Compared to time-domain approaches, frequency-domain methods provide a more powerful framework for optimal tuning of the tunable orders of the fractional operators in the structures of fractional controllers Such controllers have been designed with the aim of offering flatness in the open-loop phase response around the gain crossover frequency [7,8,9,10,11,12,13,14,15] and have been introduced to ensure robustness against variations in the time constant of a plant. The derived compensator transfer function is approximated through the utilization of a curve-fitting technique, resulting in a rational integer-order transfer function This transfer function is capable of fulfilling the robust compensation problem of control systems, including plants with an uncertain pole [18] and can be implemented using conventional filter design techniques. A design example and experimental results are presented in Section 3, certifying the validity of the presented concept

Theory

Design Example

Experimental Verification

Compensator-Plant System

Effect of the Plant Uncertainties

Conclusions