Controlling and Synchronizing of Fractional- Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Soukkou, Ammar; Leulmi, Salah

doi:10.5815/ijisa.2016.06.07

Cited by 7 publications

(3 citation statements)

References 20 publications

(31 reference statements)

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“…A review of physicalfractional and biological-genetic operators for modeling and control of industrial process by using multi objective genetic algorithm to optimize the parameters of the FOPID is analyzed in [39]. In [40], authors have presented fractional-order feedback controller for control and synchronization of fractional-order chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

A Genetic Algorithm based Fractional Fuzzy PID Controller for Integer and Fractional order Systems

Kumar¹,

Sharma²

2018

IJISA

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This work aims at designing a fractional Proportional-Integral-Derivative controller wherein we hybridize a genetic algorithm based fractional Proportional-Integral-Derivative controller with a fuzzy logic Proportional-Integral-Derivative controller. We attempt at optimizing the fractional order Proportional-Integral-Derivative controller parameters by incorporating a Genetic Algorithm based mechanism. Thereafter, the optimized genetic algorithm based fractional Proportional-Integral-Derivative control is further fine tuned and hybridized to a fuzzy Proportional-Integral-Derivative control. Here, fuzzy logic based inference mechanism is used to tackle system uncertainties and use of rule firing strengths produces an adaptive control. Genetic Algorithm has been used to generate the most optimal controller by a natural selection of the fittest. Amalgamating Genetic Algorithm and fuzzy control approaches on fractional order systems produces a highly efficient and noise tolerant control regime. We give simulation results and compare our hybrid approach against conventional and fractional Proportional-Integral-Derivative approaches on various integer and fractional order systems (with dead time) to elucidate its superiority and effectiveness.

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Section: Introductionmentioning

confidence: 99%

A Genetic Algorithm based Fractional Fuzzy PID Controller for Integer and Fractional order Systems

Kumar¹,

Sharma²

2018

IJISA

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“…In the paper [6], a simple and optimal form of fractional-order feedback approach assigned for the control and synchronization of a class of fractional-order chaotic systems is proposed. In the paper [7] introduce the classical EOQ model with a linear trend of timedependent demand having no shortages using the concept of fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Mathematical Models of Visco-Elastic Deformation Using a Fractional Differentiation Apparatus

Sokolovskyy¹,

Levkovych²

2018

IJMECS

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In this paper, using fractional differential and integral operators, constructed are two-dimensional mathematical models of viscoelastic deformation, which are characterized by memory effects, spatial non-locality, and self-organization. The fractal rheological models by Maxwell, Kelvin and Voigt, their structural properties and the influence of the fractional integro-differential operator on the process of viscoelasticity are investigated. Using the Laplace transform method and taking into account the properties of the fractional differential apparatus, analytical relations are obtained in the integral form for describing the stresses of generalized twodimensional fractional-differential rheological models by Maxwell, Kelvin, and Voigt. Since the fractionaldifferential parameters of fractal models allow describing deformation-relaxation processes more perfectly than traditional methods, algorithmic aspects of identification of structural and fractal parameters of models are presented in the work. Explicit expressions have been obtained to describe the deformation process for one-dimensional fractionaldifferential models by Voigt, Kelvin, and Maxwell. The results of identification of structural and fractal parameters of the Maxwell and Voigt models are presented. The estimates of the accuracy of the obtained identification results were found using the statistical criterion based on the correlation coefficient. The influence of fractional-differential parameters on deformation-relaxation processes is investigated.

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“…In recent years researches have been able to explore many potential applications of fractional calculus in science, engineering and management / business administration particularly in physical chemistry [1,2], biomedical engineering [3], control system [4][5][6][7], signal processing [8] and inventory management [9]. Fractional differentiators and integrators are an integral part of fractional filter based signal processing and fractional feedback control of complex systems and chaotic systems [10]. A fractional order system is an infinite dimensional filter having irrational continuous time transfer function in the s-domain.…”

Section: Introductionmentioning

confidence: 99%

Implementation of Carlson based Fractional Differentiators in Control of Fractional Order Plants

Shrivastava¹,

Varshney²

2018

IJISA

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This paper presents reduced integer order models of fractional differentiators. A two step procedure is followed. Using the Carlson method of approximation, approximated second iteration models of fractional differentiators are obtained. This method yields transfer function of high orders, which increase the complexity of the system and pose difficulty in realization. Hence, three reduction techniques, Balanced Truncation method, Matched DC gain method and Pade Approximation method are applied and reduced order models developed. With these models, fractional Proportional-Derivative and fractional Proportional-Integral-Derivative controllers are implemented on a fractional order plant and closed loop responses obtained. The authors have tried to reflect that the Carlson method in combination with reduction techniques can be used for development of good lower order models of fractional differentiators. The frequency responses of the models obtained using the different reduction techniques are compared with the original model and with each other. Three illustrative examples have been considered and their performance compared with existing systems.

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Controlling and Synchronizing of Fractional- Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Cited by 7 publications

References 20 publications

A Genetic Algorithm based Fractional Fuzzy PID Controller for Integer and Fractional order Systems

A Genetic Algorithm based Fractional Fuzzy PID Controller for Integer and Fractional order Systems

Two-Dimensional Mathematical Models of Visco-Elastic Deformation Using a Fractional Differentiation Apparatus

Implementation of Carlson based Fractional Differentiators in Control of Fractional Order Plants

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