Differential Flatness Applications to Industrial Machine Control

Ejike C. Anene; Ganesh K. Venayagamoorthy

doi:doi:10.11648/j.acis.20140204.11

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Differential Flatness Applications to Industrial Machine Control

Ejike C. Anene, Ganesh K. Venayagamoorthy

Published in Automation, Control and Intelligent Systems (Volume 2, Issue 4)

Received: 2 August 2014 Accepted: 19 August 2014 Published: 10 September 2014

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Abstract

In this article the applications of differential flatness to some industrial systems are presented. Computational methods of obtaining the flat output and the straight forward method of constructing the corresponding control law are given. Some theoretical and industrial systems are used as illustration including the third order synchronous machine model and the one degree of freedom magnetic levitation system model. Computations of the flat output are done using various approaches. The Levine’s approach is presented in such detail as to facilitate quick understanding. Computations for the synchronous machine model yielded a flat output that is a function of the load angle while the magnetic levitation model yielded a flat output that is a function of the objects’ position. Results showing the stabilization of the applied systems in fault and uncertain situations are discussed.

Published in	Automation, Control and Intelligent Systems (Volume 2, Issue 4)
DOI	10.11648/j.acis.20140204.11
Page(s)	42-52
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Magnetic Levitation, Flatness, Feedback Linearization, Synchronous Machine

References

[1]	Fliess M., Lévine J., Martin Ph., and Rouchon P. (1999) “A Lie-Bäcklund approach to equivalent and flatness of nonlinear systems”, IEEE Transactions on Automatic Control, 38: 700-716.
[2]	Fliess M., Lévine J., Martin Ph., and Rouchon P. (1993) “Flatness and defect of nonlinear systems: introductory theory and examples”, Int. J. of Control, 61(6): 1327-1361.
[3]	Lévine J. (2003) Revised (2006) “On the necessary and sufficient conditions for differential flatness” Electronic Print, Digital Library for Physics and Astronomy, Harvard-Smithsonian center for Astrophysics, (arXiv: math/0605405v).
[4]	Hebertt Sira-Ramirez, and Sunil K. Agrawal (2004) Differentially flat systems, Marcel Dekker, Inc, New York
[5]	Fliess M., Lévine J., Martin Ph., and Rouchon P. (1993) “Flatness and defect of nonlinear systems: introductory theory and examples”, Int. J. of Control, 61(6): 1327-1361.
[6]	Rouchon P., Fliess M, Lévine J., and Martin Ph. (1993) “Flatness and motion planning: the car with n-trailers”. In Proc. ECC’ 93, Groningen, Pages 1518-1522.
[7]	Lévine J. (1999) Are there new industrial perspectives in the control of mechanical systems? In Paul M. Frank, editor, Advances in Control, pages 195–226. Springer-Verlag, London.
[8]	Kiss B., Lévine J., and Mullhaupt Ph. (2000) Control of a reduced size model of us navy crane using only motor position sensors. In A. Isidori, F. Lamnabhi-Lagarrigue, and W. Respondek, editors, Nonlinear Control in the Year 2000, volume 2, pages 1–12. Springer.
[9]	Charlet B., Lévine J., and Marino R. (1991) “Sufficient conditions for dynamic state feedback linearization”, SIAM J. of Control and Optimization, 29(1):38-57.
[10]	Anderson P.M and Fouad A.A (1994) Power system control and stability, IEEE series on Power Systems.
[11]	E. C. Anene, J. T. Agee, U. O. Aliyu and J. Levine, (2006) “A new technique for feedback linearisation and an application in power system stabilisation”. IASTED International Conference on POWER, ENERGY and APPLICATIONS Gaborone Botswana, September.11-13, Pages 90-95.
[12]	Ejike Anene, Ganesh K. Venayagamoorthy (2010), Senior Member, IEEE “PSO tuned flatness based control of a magnetic levitation system”, 45th IEEE Industrial Automation and Control Annual Conference, 3rd – 7th October, Houston Texas.

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APA Style

Ejike C. Anene, Ganesh K. Venayagamoorthy. (2014). Differential Flatness Applications to Industrial Machine Control. Automation, Control and Intelligent Systems, 2(4), 42-52. https://doi.org/10.11648/j.acis.20140204.11

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ACS Style

Ejike C. Anene; Ganesh K. Venayagamoorthy. Differential Flatness Applications to Industrial Machine Control. Autom. Control Intell. Syst. 2014, 2(4), 42-52. doi: 10.11648/j.acis.20140204.11

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AMA Style

Ejike C. Anene, Ganesh K. Venayagamoorthy. Differential Flatness Applications to Industrial Machine Control. Autom Control Intell Syst. 2014;2(4):42-52. doi: 10.11648/j.acis.20140204.11

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@article{10.11648/j.acis.20140204.11,
  author = {Ejike C. Anene and Ganesh K. Venayagamoorthy},
  title = {Differential Flatness Applications to Industrial Machine Control},
  journal = {Automation, Control and Intelligent Systems},
  volume = {2},
  number = {4},
  pages = {42-52},
  doi = {10.11648/j.acis.20140204.11},
  url = {https://doi.org/10.11648/j.acis.20140204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20140204.11},
  abstract = {In this article the applications of differential flatness to some industrial systems are presented. Computational methods of obtaining the flat output and the straight forward method of constructing the corresponding control law are given. Some theoretical and industrial systems are used as illustration including the third order synchronous machine model and the one degree of freedom magnetic levitation system model. Computations of the flat output are done using various approaches. The Levine’s approach is presented in such detail as to facilitate quick understanding. Computations for the synchronous machine model yielded a flat output that is a function of the load angle while the magnetic levitation model yielded a flat output that is a function of the objects’ position. Results showing the stabilization of the applied systems in fault and uncertain situations are discussed.},
 year = {2014}
}

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TY  - JOUR
T1  - Differential Flatness Applications to Industrial Machine Control
AU  - Ejike C. Anene
AU  - Ganesh K. Venayagamoorthy
Y1  - 2014/09/10
PY  - 2014
N1  - https://doi.org/10.11648/j.acis.20140204.11
DO  - 10.11648/j.acis.20140204.11
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 42
EP  - 52
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20140204.11
AB  - In this article the applications of differential flatness to some industrial systems are presented. Computational methods of obtaining the flat output and the straight forward method of constructing the corresponding control law are given. Some theoretical and industrial systems are used as illustration including the third order synchronous machine model and the one degree of freedom magnetic levitation system model. Computations of the flat output are done using various approaches. The Levine’s approach is presented in such detail as to facilitate quick understanding. Computations for the synchronous machine model yielded a flat output that is a function of the load angle while the magnetic levitation model yielded a flat output that is a function of the objects’ position. Results showing the stabilization of the applied systems in fault and uncertain situations are discussed.
VL  - 2
IS  - 4
ER  -

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Author Information

Ejike C. Anene

Electrical Engineering Programme, Abubakar Tafawa Balewa University, PMB 0248, Bauchi, Nigeria
Ganesh K. Venayagamoorthy

Real-Time Power and Intelligent Systems Laboratory, Clemson University, Clemson, USA

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APA Style

Ejike C. Anene, Ganesh K. Venayagamoorthy. (2014). Differential Flatness Applications to Industrial Machine Control. Automation, Control and Intelligent Systems, 2(4), 42-52. https://doi.org/10.11648/j.acis.20140204.11

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ACS Style

Ejike C. Anene; Ganesh K. Venayagamoorthy. Differential Flatness Applications to Industrial Machine Control. Autom. Control Intell. Syst. 2014, 2(4), 42-52. doi: 10.11648/j.acis.20140204.11

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AMA Style

Ejike C. Anene, Ganesh K. Venayagamoorthy. Differential Flatness Applications to Industrial Machine Control. Autom Control Intell Syst. 2014;2(4):42-52. doi: 10.11648/j.acis.20140204.11

Copy | Download

@article{10.11648/j.acis.20140204.11,
  author = {Ejike C. Anene and Ganesh K. Venayagamoorthy},
  title = {Differential Flatness Applications to Industrial Machine Control},
  journal = {Automation, Control and Intelligent Systems},
  volume = {2},
  number = {4},
  pages = {42-52},
  doi = {10.11648/j.acis.20140204.11},
  url = {https://doi.org/10.11648/j.acis.20140204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20140204.11},
  abstract = {In this article the applications of differential flatness to some industrial systems are presented. Computational methods of obtaining the flat output and the straight forward method of constructing the corresponding control law are given. Some theoretical and industrial systems are used as illustration including the third order synchronous machine model and the one degree of freedom magnetic levitation system model. Computations of the flat output are done using various approaches. The Levine’s approach is presented in such detail as to facilitate quick understanding. Computations for the synchronous machine model yielded a flat output that is a function of the load angle while the magnetic levitation model yielded a flat output that is a function of the objects’ position. Results showing the stabilization of the applied systems in fault and uncertain situations are discussed.},
 year = {2014}
}

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TY  - JOUR
T1  - Differential Flatness Applications to Industrial Machine Control
AU  - Ejike C. Anene
AU  - Ganesh K. Venayagamoorthy
Y1  - 2014/09/10
PY  - 2014
N1  - https://doi.org/10.11648/j.acis.20140204.11
DO  - 10.11648/j.acis.20140204.11
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 42
EP  - 52
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20140204.11
AB  - In this article the applications of differential flatness to some industrial systems are presented. Computational methods of obtaining the flat output and the straight forward method of constructing the corresponding control law are given. Some theoretical and industrial systems are used as illustration including the third order synchronous machine model and the one degree of freedom magnetic levitation system model. Computations of the flat output are done using various approaches. The Levine’s approach is presented in such detail as to facilitate quick understanding. Computations for the synchronous machine model yielded a flat output that is a function of the load angle while the magnetic levitation model yielded a flat output that is a function of the objects’ position. Results showing the stabilization of the applied systems in fault and uncertain situations are discussed.
VL  - 2
IS  - 4
ER  -

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