Skip to main content
Log in

The Use of a Heuristic Optimization Method to Improve the Design of a Discrete-time Gain Scheduling Control

  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This undertaking delves into the designing of a based nonlinear discrete-time control scheme. The control input exploits the feedback linearization technique, the gain scheduling control approach, and genetic algorithms to develop an optimization method, for achieving trajectory tracking objectives. In order to demonstrate the effectiveness of the proposed scheme, the results from this investigation was compared with those attained using the fuzzy control method. The simulation results from the application of the designed approach to a continuous stirred tank reactor (CSTR) temperature control problem, revealed the efficiency of this scheme, and its satisfactory overall performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Cannon, Dynamics of Physical Systems, McGraw-Hill, Dover, New York, 2003.

    Google Scholar 

  2. J. H. Moon, S. C. I. Jee, and H. J. Lee, “Output-feedback control of underwater gliders by buoyancy and pitching moment control: Feedback linearization approach,” International Journal of Control, Automation and Systems, vol. 14, no. 4, pp. 255–262, February 2016.

    Article  Google Scholar 

  3. H. Wang and X. Liu, “Permanent magnet synchronous motor feedback linearization vector control,” Mechatronics and Automatic Control Systems, vol. 237, pp. 601–608, 2013.

    Article  Google Scholar 

  4. Z. Wan and M. V. Kothare, “Efficient scheduled stabilizing model predictive control for constrained nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 13, no. 3, pp. 331–346, February 2003.

    Article  MathSciNet  Google Scholar 

  5. H. Chaouech, S. Charfeddine, K. Ouni, H. Jerbi, and L. Nabli, “Intelligent supervision approach based on multi-layer neural PCA and nonlinear gain scheduling,” Neural Computing and Applications, vol. 31, no. 4, pp. 1–11, April 2019.

    Google Scholar 

  6. S. Charfeddine and H. Jerbi, “A Survey on nonlinear gain scheduling design control for continuous and discrete time,” International Journal Modeling, Identification and Control, vol. 19, no. 3, pp. 203–216, January 2013.

    Article  Google Scholar 

  7. M. S. Koo, H. L. Choi, and J. T. Lim, “Approximate feed-back linearization of a class of nonlinear systems with time-varying delays in states via matrix inequality,” International Journal of Control, Automation and Systems, vol. 12, no. 4, pp. 742–748, July 2014.

    Article  Google Scholar 

  8. S. Charfeddine and H. Jerbi, “Synthesis of a nonlinear control system for disturbance rejection in a periodic process,” Proc. of the 9th International Multi-Conference on Systems, Signals and Devices, pp. 1–6, 2012.

  9. L. Ozkan and M. V. Kothare, “Stability analysis of a multi-model predictive control algorithm with application to control of chemical reactors,” Journal Process Control, vol. 16, no. 2, pp. 81–90, February 2006.

    Article  Google Scholar 

  10. J. Q. Deng, H. B. Li, C. Hao, and Z. Q. Sun, “Research on gain scheduling control of the networked control system with long delay,” International Journal of Control, Automation and Systems, vol. 13, no. 1, pp. 33–38, December 2014.

    Article  Google Scholar 

  11. W. J. Rugh and J. S. Shamma, “Research on gain scheduling,” Automatica, vol. 36, no. 10, pp. 1401–1425, October 2000.

    Article  MathSciNet  Google Scholar 

  12. S. Charfeddine and H. Jerbi, “Trajectory tracking and disturbance rejection for nonlinear periodic process: A gain scheduling design,” International Review on Modeling and Simulations, vol. 5, no. 2, pp. 1075–1083, January 2012.

    Google Scholar 

  13. S. Vimal, “Improved state-space criterion for global asymptotic stability of fixed-point state-space digital filters with saturation arithmetic,” Arabian Journal Science Engineering, vol. 32, no. 2b, pp. 317–326, October 2007.

    Google Scholar 

  14. J. S. Shamma and M. Athans, “Guaranteed properties of gain scheduled control for linear parameter-varying plants,” Automatica, vol. 27, no. 3, pp. 559–564, May 1991.

    Article  MathSciNet  Google Scholar 

  15. S. Dubljevic and N. Kazantsis, “A new Lyapunov design approach for nonlinear systems based on Zubov’s method,” Automatica, vol. 38, no. 11, pp. 1999–2007, November 2007.

    Article  MathSciNet  Google Scholar 

  16. R. Genesio, M. Tartaglia, and A. Vicino, “On the estimation of asymptotic stability regions: state of art and new proposals,” IEEE Trans. on Automatic Control, vol. 30, no. 8, pp.747–755, August 1985.

    Article  MathSciNet  Google Scholar 

  17. H. Jerbi, N. Ben Hadj Braiek, and A. Belhadj Brahim Bacha, “A method of estimating the domain of attraction for nonlinear discrete-time systems,” Arabian Journal Science Engineering, vol. 39, no. 5, pp. 3841–3849, February 2014.

    Article  MathSciNet  Google Scholar 

  18. H. Jerbi, “Estimations of the domains of attraction for classes of nonlinear continuous polynomial systems,” Arabian Journal for Science and Engineering, vol. 42, no. 7, pp. 2829–2837, March 2017.

    Article  MathSciNet  Google Scholar 

  19. W. Jebri, H. Jerbi, and M. N. Abdelkarim, “Synthesis of an approximate feedback nonlinear control based on optimization methods,” WSEAS Trans. on Systems and Control, vol. 5, no. 8, pp. 646–655, August 2010.

    Google Scholar 

  20. Y. Wang, H. R. Karimi, H. Lam, and H. Yan, “Fuzzy output tracking control and filtering for nonlinear discrete-time descriptor systems under unreliable communication links,” IEEE Trans. on Cybernetics, vol. 50, no. 6, pp. 2369–2379, June 2020.

    Article  Google Scholar 

  21. Y. Wang X. Yang, and H. Yan, “Reliable fuzzy tracking control of near-space hypersonic vehicle using aperiodic measurement information,” IEEE Trans. on Industrial Electronics, vol. 66, no. 12, pp. 9439–9447, December 2019.

    Article  Google Scholar 

  22. X. Zhao, X. Wang, L. MA, and G. Zong, “Fuzzy approximation based asymptotic tracking control for a class of uncertain switched nonlinear systems,” IEEE Trans. On Fuzzy Systems, vol. 28, no. 4, pp. 632–644, April 2020.

    Article  Google Scholar 

  23. L. Ma, X. Huo, X. Zhao, and G. Zong, “Adaptive fuzzy tracking control for a class of uncertain switched nonlinear systems with multiple constraints: A small-gain approach,” International Journal of Fuzzy Systems, vol. 21, no. 9, pp. 2609–2624, October 2019.

    Article  MathSciNet  Google Scholar 

  24. L. K. Wong, H. F. Leung, and K. S. Tam, “Lyapunov-function-based design of fuzzy logic controllers and its application on combining controllers,” IEEE Trans. on Industrial Electronics, vol. 45, no. 3, pp. 502–509, June 1998.

    Article  Google Scholar 

  25. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, June 1965.

    Article  MathSciNet  Google Scholar 

  26. A. Hazzab, I. K. Bousserhane, M. Zerbo, and P. Sicard, “Real time implementation of fuzzy gain scheduling of PI controller for induction motor machine control,” Journal Neural Processing Letters, vol. 24, no. 3, pp. 203–215, October 2006.

    Article  Google Scholar 

  27. J. Garcia-Sandoval, V. Gonzalez-Alvarez, B. Castillo-Toledo, and C. Pelayo-Ortiz, “Robust discrete control of nonlinear processes: Application to chemical reactors,” Computers and Chemical Engineering, vol. 32, no. 12, pp. 3246–3253, December 2008.

    Article  Google Scholar 

  28. F. Hamidi, H. Jerbi, W. Aggoune, M. Djemai, and M. N. Abdelkrim, “Enlarging the domain of attraction in nonlinear polynomial systems,” International Journal Computer Communications and Control, vol. 8, no. 4, pp. 538–547, August 2013.

    Article  Google Scholar 

  29. M. Bauer and I. K. Craig, “Economic assessment of advanced process control-A survey and framework,” Journal of Process Control, vol. 18, no. 1, pp. 2–18, January 2008.

    Article  Google Scholar 

  30. L. Feng, J. L. Wang, and E. K. Poh, “Improved robust model predictive control with structured uncertainty,” Journal of Process Control, vol. 17, no. 8, pp. 683–688, September 2007.

    Article  Google Scholar 

  31. M. A. Kurtz and M. A. Henson, “Input-output linearizing control of constrained nonlinear processes,” Journal of Process Control, vol. 7, no. 1, pp. 3–17, February 1997.

    Article  Google Scholar 

  32. L. Magni, G. de Nicolao, L. Magnani, and R. Scattolini, “A stabilizing model-based predictive control algorithm for nonlinear systems,” Automatica, vol. 37, no. 9, pp. 1351–1362, March 2001.

    Article  MathSciNet  Google Scholar 

  33. W. H. Ray, Advanced Process Control, McGraw-Hill, New York, pp. 58–59, January 1981.

    Google Scholar 

  34. R. Vinodha, S. Abraham, and J. Prakash, “Design and implementation of simple adaptive control schemes on simulated model of CSTR process,” International Journal of Modeling, Identification and Control, vol. 14, no. 3, pp. 159–169, September 2011.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Charfeddine Samia.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Huanqing Wang under the direction of Editor Euntai Kim.

The authors would like acknowledge the support of the Deanship of Scientific Research at Hail University-KSA under the research project (RG-0191315).

Charfeddine Samia was born in Tunisia on June 14, 1983. She received her Ph.D. degree in electrical engineering from the ENIG University of Gabes, Tunisia, in 2013. From 2008 to 2015, she was an Assistant Professor in the College of Science of Gafsa, Tunisia.

Jerbi Houssem was born in Tunisia on October 20, 1971. He received his Ph.D. degree in electrical engineering from the ENIT University of Al Manar, Tunis, TUNISIA, in 2000. He is currently an Associate Professor in the Department of Industrial Engineering, College of Engineering, of the University of Hail- KSA and has been the main consultant of the GDPMO- UOH since 2014. From 2000 to 2010, he was an Assistant Professor in the College of Science of Sfax Tunisia. Since 2010, he has been a faculty member at the University of HAIL-KSA. He has published more than 100 scientific papers and book chapters in the field of nonlinear control and systems. His research interests include stability analysis, advanced control, big data control system engineering and fault tolerant control.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Samia, C., Houssem, J. The Use of a Heuristic Optimization Method to Improve the Design of a Discrete-time Gain Scheduling Control. Int. J. Control Autom. Syst. 19, 1836–1846 (2021). https://doi.org/10.1007/s12555-019-0774-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-019-0774-1

Keywords

Navigation