Control Techniques for a Class of Fractional Order Systems

Mircea Ivanescu,Ioan Dumitrache,Nirvana Popescu,Decebal Popescu

doi:10.3390/math9192357

Mircea Ivanescu, Ioan Dumitrache + Show 2 more

Open Access

https://doi.org/10.3390/math9192357

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Abstract

The paper discusses several control techniques for a class of systems described by fractional order equations. The paper presents the unit frequency criteria that ensure the closed loop control for: Fractional Order Linear Systems, Fractional Order Linear Systems with nonlinear components, Time Delay Fractional Order Linear Systems, Time Delay Fractional Order Linear Systems with nonlinear components. The stability criterion is proposed for the systems composed of fractional order subsystems. These techniques are used in two applications: Soft Exoskeleton Glove Control, studied as a nonlinear model with time delay and Disabled Man-Wheelchair model, analysed as a fractional-order multi-system.

Highlights

The extension of the applications of the fractional order systems (FOS) has determined a corresponding increase of the control techniques, of the methods of investigation of the special requirements imposed by these systems
Stability criteria are formulated in the form of algebraic criteria [22,23,24] or are derived by analytical techniques derived from the Lyapunov method [25,26,27,28]
Motivated by the above discussion, our main objective in this paper is to develop new stability criteria for FOS models via the approach in which the control laws are defined by frequency criteria

Summary

Introduction

The extension of the applications of the fractional order systems (FOS) has determined a corresponding increase of the control techniques, of the methods of investigation of the special requirements imposed by these systems. Motivated by the above discussion, our main objective in this paper is to develop new stability criteria for FOS models via the approach in which the control laws are defined by frequency criteria. Exoskeleton Glove Control that is studied as a nonlinear FOS model with time delay and Disabled Man-Wheelchair system that is studied as a fractional-order multi- system. The paper is structured as follows: Section 2 presents mathematical preliminaries, and the control techniques proposed in this paper, Section 3 treats two applications: Soft Exoskeleton Glove Control and Disabled Man-Wheelchair system control, Section 4 is dedicated to Discussion and Section 5 presents Conclusions

Control Techniques

Mathematical Preliminaries