Diffusive representation of a fractional control using adaptive partitioning algorithm

Boudjehem Djalil; Boudjehem

doi:10.1501/commua1_0000000840

Abstract

This article presents optimal fractional control. This control is based on the property of the invariance of a fractional order differential equation. The problem formulation of the used control is expressed by diffusivere presentation. The fractional control problem is described in a minimization form, where the global optimum represents the diffusive realization of the controller. To determine the optimal fractional diffusive control, an adaptive partitioning algorithm is used. As an application, we have chosen the control of a DC motor with uncertain parameters

Highlights

The fractional operators become an interesting tool in the systems mathematical modeling and design, their use appeared strongly in di¤erent disciplines
In controlling uncertain dynamic systems, the use of robust control laws that are able to ensure the best compromise between performances and Robustness is highly required
In order to satisfy this requirement researchers used the fractional control as an alternative choice, where the concept of the robustness is based on the property of the invariance of the fractional di¤erential equation

Summary

Introduction

The fractional operators become an interesting tool in the systems mathematical modeling and design, their use appeared strongly in di¤erent disciplines. Their convenient interest has been proved in the last decade. The use of fractional operators leads to some di¢ culties and problems, which come mainly from the fact that these operators are hereditary with singular kernels, and the numerical approximation becomes very di¢ cult and requires large memory storage capacities To remedy these problems, the fractional control will be achieved by Received by the editors: December 20, 2016, Accepted: May 16, 2017. This representation allows the realization of the fractional operators in non-hereditary way using linear dynamical systems of di¤usive nature.[9] We apply this concept to the control of a DC motor of which the transfer function is uncertain.

Fractional Calculus

Fractional Control

The optimization algorithm

Application to a dc motor control