Modelling and Simulation of LQR and LFSV Controllers in the Magnetic Levitation System (MLS)

Authors

  • Alvaro Romero Acero Universidad Nacional de Colombia, Facultad de Minas, Grupo de Investigación: Inteligencia Artificial en Educación
  • Julian Andrés Orozco Quiceno Universidad Nacional de Colombia, Facultad de Minas
  • Jovani Alberto Jiménez Bulies Universidad Nacional de Colombia, Facultad de Minas, Grupo de Investigación: Inteligencia Artificial en Educación

DOI:

https://doi.org/10.15665/rp.v14i1.637

Keywords:

Linearization, Stability, State observer, Controllers LQR and LSFV

Abstract

In this article a control analysis in state variables is presented, applied to the nonlinear Magnetic Levitation system (MLS), which consists in keeping objects suspended in the air without any mechanical contact through the interaction of magnetic force. The design of Linear Quadratic Regulator (LQR) and Linear Feedback in State Variables (LFSV) controllers is implemented with the aim of comparing the results which guarantee a better stability performance in the system. The mathematical representation of the nonlinear and linearized model of the MLS plant is examined through the design of algorithms and simulation in Simulink-Matlad. In this way, the behavior of the system when there are perturbations and input changes is contrasted, with the priority of exerting a low control action as parameter of the system to be optimized.

References

S. Kumar, R. Singh, "Nonlinear Control of a Magnetic Levitation System using Feedback Linearization," Advanced Communication Control and Computing Technologies (ICACCCT), 2014 International Conference on., 152-156, 2014.

R. Morales, V. Feliu, H. Sira-Ramírez, "Nonlinear Control for Magnetic Levitation Systems Based on Fast Online Algebraic Identification of the Input Gain," Control Systems Technology, IEEE Transactions on., 19(4), 757-771, 2011.

P. Suster, A. Jadlovska, "Modeling and control design of Magnetic levitation system," Applied Machine Intelligence and Informatics (SAMI), 2012 IEEE 10th International Symposium on., 295-299, 2012.

E. Kofman, F. Fontenla, H. Haimovich, M. Seron, “Control design with guaranteed ultimate bound for feedback linearizable systems,” Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul, Korea, 242-247, 2008.

P. Suster and A. Jadlovska, "Modeling and Control Design of Magnetic Levitation System," Applied Machine Intelligence and Informatics (SAMI), 2012 IEEE 10th International Symposium on., 295-299, 2012.

R. Uswarman, A. Cahyadi, O. Wahyunggoro, "Control of a magnetic levitation system using feedback linearization," Computer, Control, Informatics and Its Applications (IC3INA), 2013 International Conference on., 95-98, 2013.

M. Seron, (2001) Nonlinear Systems - Laboratory of Dynamical Systems and Signal Processing (LSD), [Internet], National University of Rosario. Disponible desde: <http://www.fceia.unr.edu.ar/control/snl/Apunte.pdf> [Acceso 1 de agosto 2014].

R. Dorf, R. Bishop, "Modelos en variables de estado". En: Sistemas de Control Moderno, ed.; Prentice Hall, New Jersey, p.79–129.

P. Shiakolas, S.Van-Schenck, D. Piyabongkarn, I. Frangeskou, "Magnetic levitation hardware-in-the-loop and MATLAB-based experiments for reinforcement of neural network control concepts," Education, IEEE Transactions on., 47(1), 33-41, 2004.

T. Kumar, S. Shimi, D. Karanjkar, S. Rana, "Modeling, simulation and control of single actuator magnetic levitation system," Engineering and Computational Sciences (RAECS), 2014 Recent Advances in., 1-6, 2014.

K. Ogata, Modern control engineering 5th edition. Upper Saddle River, New Jersey: Prentice Hall, 2010, pp. 912.

Oishi, (2010) State Feedback - Ackermann’s Formula, [Internet], University of British Columbia. Disponible desde: <http://doctord.dyndns.org/courses/bei/mc300/oishi/lecture28.pdf> [Acceso 1 de junio 2015].

E. Kumar, J. Jerome, K. Srikanth, "Algebraic approach for selecting the weighting matrices of linear quadratic regulator," Green Computing Communication and Electrical Engineering (ICGCCEE), 2014 International Conference on., 1-6, 2014.

A. Romero, A. Marín, A. Jiménez, “Modelado, simulación e implementación de controladores LQR y RLVE al sistema péndulo invertido rotacional usando la plataforma NI ELVIS II,” Revista Científica Guillermo de Ockham, 11(1), 67-78, 2013.

P. Yadav, R. Mitra, "Real time implementation of hybrid fuzzy logic controller with linear quadratic regulator on magnetic levitation," Computational Intelligence and Computing Research (ICCIC), 2013 IEEE International Conference on., 1-4, 2013.

C. Chen, Linear system theory and design 4th edition. Oxford University Press, 2012, pp. 400.

Downloads

Published

2016-02-26

Issue

Vol. 14 No. 1 (2016)

Section

Articles

License

The authors to publish in this journal agree to the following conditions:

  1. The authors transfer the copyright and give the the journal first publication right of the work registered with Creative Commons Attribution License, which allows third parties to use the published work on the condition of always mentioning the authorship and first publication in this journal.
  2. The authors may perform other independent and additional contractual arrangements for the non-exclusive distribution of the version of the article published in this issue (E.g., Inclusion in an institutional repository or publication in a book), it must be indicated clearly that the work was first published in this journal.
  3. It allows and encourages the authors to publish their work online (eg institutional or personal pages) before and during the review and publication process. It can lead to productive exchanges and greater and faster dissemination of the published work (see The Effect of Open Access)

Instructions to fill out Certificate of Originality and Copyright Assignment

  1. Click here and get the forms of Certificate of Originality and Copyright Assignment  .
  2. In each field to fill out, click and complete the corresponding information.
  1. Once the fields are filled out, at the end of the form copy your scanned signature or digital signature. Please adjust the size of the signature on the form.
  2. Finally, you can save them as pdf files and send them through the OJS platform as an attachment.