DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM

Djalil Boudjehem; Badreddine Boudjehem; Belgacem Mecherı

doi:10.1501/Commua1_0000000840

DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM

Year 2018, Volume: 67 Issue: 1, 168 - 178, 01.02.2018

Djalil Boudjehem Badreddine Boudjehem Belgacem Mecherı

https://doi.org/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

Keywords

Fractional system, fractional controller, diğusive representation, optimal control, Adaptive partitioning Algorithm

References

I. S. Jesus, J. A. T. Machado, “Fractional control of heat diğusion systems”. Nonlinear Dynamics, 54 (3), 263–282, 2008.
D. Boudjehem, B. Boudjehem, “A fractional model for robust fractional order Smith predic- tor”. Nonlinear Dynamics, 73 (3), 1557–1563, 2013.
B. Boudjehem, D. Boudjehem, “Fractional order controller design for desired response”. Pro- ceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 227 (12), 243–251, 2013.
G. Montseny. “Simple Approach to Approximation and Dynamical Realization of Pseudo- diğerential Time Operators such as Fractional ones”, IEEE Transactions on Circuits and Systems II, 51 (11), 613–618.
G. Montseny, Diğ usive representation of pseudo-diğ erential time-operators. LAAS, 1998.
G. Montseny, “Diğusive wave-absorbing control: Example of the boundary stabilization of a thin *exible beam”. Journal of Vibration and Control, 18 (11), 1708–1721, 2012.
L. Laudebat, P. Bidan, G. Montseny, “Modeling and Optimal Identi…cation of Pseudodif- ferential Electrical Dynamics by Means of Diğusive Representation”, IEEE Transactions on Circuits and Systems I, 51 (9), 1801–1813, 2004.
C. Casenave, G. Montseny, “Identi…cation and state realisation of non-rational convolution models by means of diğusive representation”, Control Theory and Applications, IET, 5 (07), 934–942, 2011.
Oustaloup, A. La commande CRONE: commande robuste d´ ordre non entier 1991, Hermès, Paris.
Audounet, J., Devy-Vareta, F., and Montseny, G. Pseudo-invariant diğusive control. In 14th Symosium of mathematical theory of networks and systems, perpignan, France, 2000.
Devy-Vareta, F., Audounet, J., Matignon, D., and Montseny, G. Pseudo invariant by matched scaling: application to robust control of *exible beam. In 2nd European conference on struc- tural control, France, 2000.
D. Boudjehem, B. Boudjehem, A. Boukaache. “Reducing dimension in global optimization”. International Journal of Computational Methods, 8 (03), 535–544, 2011.

Year 2018, Volume: 67 Issue: 1, 168 - 178, 01.02.2018

Djalil Boudjehem Badreddine Boudjehem Belgacem Mecherı

https://doi.org/10.1501/Commua1_0000000840

Abstract

References

I. S. Jesus, J. A. T. Machado, “Fractional control of heat diğusion systems”. Nonlinear Dynamics, 54 (3), 263–282, 2008.
D. Boudjehem, B. Boudjehem, “A fractional model for robust fractional order Smith predic- tor”. Nonlinear Dynamics, 73 (3), 1557–1563, 2013.
B. Boudjehem, D. Boudjehem, “Fractional order controller design for desired response”. Pro- ceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 227 (12), 243–251, 2013.
G. Montseny. “Simple Approach to Approximation and Dynamical Realization of Pseudo- diğerential Time Operators such as Fractional ones”, IEEE Transactions on Circuits and Systems II, 51 (11), 613–618.
G. Montseny, Diğ usive representation of pseudo-diğ erential time-operators. LAAS, 1998.
G. Montseny, “Diğusive wave-absorbing control: Example of the boundary stabilization of a thin *exible beam”. Journal of Vibration and Control, 18 (11), 1708–1721, 2012.
L. Laudebat, P. Bidan, G. Montseny, “Modeling and Optimal Identi…cation of Pseudodif- ferential Electrical Dynamics by Means of Diğusive Representation”, IEEE Transactions on Circuits and Systems I, 51 (9), 1801–1813, 2004.
C. Casenave, G. Montseny, “Identi…cation and state realisation of non-rational convolution models by means of diğusive representation”, Control Theory and Applications, IET, 5 (07), 934–942, 2011.
Oustaloup, A. La commande CRONE: commande robuste d´ ordre non entier 1991, Hermès, Paris.
Audounet, J., Devy-Vareta, F., and Montseny, G. Pseudo-invariant diğusive control. In 14th Symosium of mathematical theory of networks and systems, perpignan, France, 2000.
Devy-Vareta, F., Audounet, J., Matignon, D., and Montseny, G. Pseudo invariant by matched scaling: application to robust control of *exible beam. In 2nd European conference on struc- tural control, France, 2000.
D. Boudjehem, B. Boudjehem, A. Boukaache. “Reducing dimension in global optimization”. International Journal of Computational Methods, 8 (03), 535–544, 2011.

There are 12 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	Djalil Boudjehem This is me Badreddine Boudjehem This is me Belgacem Mecherı This is me
Publication Date	February 1, 2018
Published in Issue	Year 2018 Volume: 67 Issue: 1

Cite

APA	Boudjehem, D., Boudjehem, B., & Mecherı, B. (2018). DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1), 168-178. https://doi.org/10.1501/Commua1_0000000840
AMA	Boudjehem D, Boudjehem B, Mecherı B. DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2018;67(1):168-178. doi:10.1501/Commua1_0000000840
Chicago	Boudjehem, Djalil, Badreddine Boudjehem, and Belgacem Mecherı. “DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, no. 1 (February 2018): 168-78. https://doi.org/10.1501/Commua1_0000000840.
EndNote	Boudjehem D, Boudjehem B, Mecherı B (February 1, 2018) DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 1 168–178.
IEEE	D. Boudjehem, B. Boudjehem, and B. Mecherı, “DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 67, no. 1, pp. 168–178, 2018, doi: 10.1501/Commua1_0000000840.
ISNAD	Boudjehem, Djalil et al. “DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (February 2018), 168-178. https://doi.org/10.1501/Commua1_0000000840.
JAMA	Boudjehem D, Boudjehem B, Mecherı B. DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:168–178.
MLA	Boudjehem, Djalil et al. “DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 67, no. 1, 2018, pp. 168-7, doi:10.1501/Commua1_0000000840.
Vancouver	Boudjehem D, Boudjehem B, Mecherı B. DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL USING ADAPTIVE PARTITIONING ALGORITHM. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(1):168-7.