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Research Papers

Model Predictive Control of Fractional Order Systems

[+] Author and Article Information
Aymen Rhouma

Université de Tunis El Manar,
Ecole Nationale d'Ingénieurs de Tunis,
LR11ES20 Laboratoire Analyse,
Conception et Commande des Systèmes,
Tunis 1002, Tunisia
Faculté des Sciences de Tunis,
Tunis 2092, Tunisia
e-mail: aymenrh@yahoo.fr

Faouzi Bouani

Université de Tunis El Manar,
Ecole Nationale d'Ingénieurs de Tunis,
LR11ES20 Laboratoire Analyse,
Conception et Commande des Systèmes,
Tunis 1002, Tunisia
e-mail: faouzi.bouani@enit.rnu.tn

Badreddine Bouzouita

Université de Tunis El Manar,
Ecole Nationale d'Ingénieurs de Tunis,
LR11ES20 Laboratoire Analyse,
Conception et Commande des Systèmes,
Tunis 1002, Tunisia
Université de Sousse,
Ecole Nationale d'Ingénieurs de Sousse,
Sousse 4054, Tunisia
e-mail: badreddine.bouzouita@enit.rnu.tn

Mekki Ksouri

Université de Tunis El Manar,
Ecole Nationale d'Ingénieurs de Tunis,
LR11ES20 Laboratoire Analyse,
Conception et Commande des Systèmes,
Tunis 1002, Tunisia
e-mail: mekki.ksouri@enit.rnu.tn

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 25, 2013; final manuscript received January 10, 2014; published online February 13, 2014. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 9(3), 031011 (Feb 13, 2014) (7 pages) Paper No: CND-13-1188; doi: 10.1115/1.4026493 History: Received July 25, 2013; Revised January 10, 2014

This paper provides the model predictive control (MPC) of fractional order systems. The direct method will be used as internal model to predict the future dynamic behavior of the process, which is used to achieve the control law. This method is based on the Grünwald–Letnikov's definition that consists of replacing the noninteger derivation operator of the adopted system representation by a discrete approximation. The performances and the efficiency of this approach are illustrated with practical results on a thermal system and compared to the MPC based on the integer ARX model.

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References

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Figures

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Fig. 2

Errors for two methods

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Fig. 3

Closed-loop responses

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Fig. 5

Open loop step responses

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Fig. 6

Identification data

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Fig. 8

Closed-loop results with Hp = 8

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Fig. 9

Closed-loop results with Hp = 12

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Fig. 10

Closed-loop results with fractional model

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Fig. 11

Closed-loop results with integer model

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