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Mathematical Problems in Engineering
Volume 2018, Article ID 5478781, 9 pages
https://doi.org/10.1155/2018/5478781
Research Article

Fuzzy Fractional-Order PID Controller for Fractional Model of Pneumatic Pressure System

1Electrical Engineering Department, College of Engineering at Wadi Addawasir, Prince Sattam Bin Abdulaziz University, Wadi Addawasir, Saudi Arabia
2Systems Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
3Department of Mathematics, College of Arts & Science at Wadi Addawasir, Prince Sattam Bin Abdulaziz University, AlKharj, Saudi Arabia

Correspondence should be addressed to K. S. Nisar; moc.liamg@1rasinsk

Received 22 June 2017; Revised 8 January 2018; Accepted 30 January 2018; Published 28 February 2018

Academic Editor: Hung-Yuan Chung

Copyright © 2018 M. Al-Dhaifallah et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. B. Oldham and J. Spanier, Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press, New York, NY, USA, 1974.
  2. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1993. View at MathSciNet
  3. A. Atangana and D. Baleanu, “New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model,” THERMAL SCIENCE, vol. 20, no. 2, pp. 763–769, 2016. View at Publisher · View at Google Scholar · View at Scopus
  4. I. Petras, L. Dorcak, and I. Kostial, “Control quality enhancement by fractional order controllers,” Acta Montanistica Slovaca, vol. 3, pp. 143–148, 1998. View at Google Scholar
  5. N. M. F. Ferreira and J. A. T. Machado, “Fractional-order hybrid control of robotic manipulators,” in Proceedings of the 11th International Conference on Advanced Robotics, pp. 393–398, Coimbra, June 2003.
  6. A. Kailil, N. Mrani, M. M. Touati, S. Choukri, and N. Elalami, “Low Earth-orbit satellite attitude stabilization with fractional regulators,” International Journal of Systems Science, vol. 35, no. 10, pp. 559–568, 2004. View at Publisher · View at Google Scholar · View at Scopus
  7. C. Ma and Y. Hori, “The application of fractional order control to backlash vibration suppression,” in Proceedings of the 2004 American Control Conference (AAC), pp. 2901–2906, usa, July 2004. View at Publisher · View at Google Scholar · View at Scopus
  8. D. Xue, C. Zhao, and Y. Chen, “Fractional order PID control of A DC-motor with elastic shaft: A Case Study,” in Proceedings of the American Control Conference, pp. 3182–3187, Minneapolis, Minn, USA, June 2006. View at Scopus
  9. K. Erenturk, “Fractional-order PIλDμ and active disturbance rejection control of nonlinear two-mass drive system,” IEEE Transactions on Industrial Electronics, vol. 60, no. 9, pp. 3806–3813, 2013. View at Publisher · View at Google Scholar · View at Scopus
  10. P. Rastogi, S. Chatterji, and D. S. Karanjkar, “Performance analysis of fractional-order controller for pH neutralization process,” in Proceedings of the 2012 2nd International Conference on Power, Control and Embedded Systems, ICPCES 2012, India, December 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. K. M. Passino and S. Yurkovich, Fuzzy-Control, Wesley Longman, California, USA, 1998.
  12. M. Vahedpour, A. R. Noei, and H. A. Kholerdi, “Comparison between performance of conventional, fuzzy and fractional order PID controllers in practical speed control of induction motor,” in Proceedings of the 2nd International Conference on Knowledge-Based Engineering and Innovation, KBEI 2015, pp. 912–916, Iran, November 2015. View at Publisher · View at Google Scholar · View at Scopus
  13. N. Bouarroudj, B. Djamel, and F. Boudjema, “Tuning fuzzy fractional order PID sliding-mode controller using PSO algorithm for nonlinear systems,” in Proceedings of the 2013 3rd International Conference on Systems and Control, ICSC 2013, pp. 797–803, Algeria, October 2013. View at Publisher · View at Google Scholar · View at Scopus
  14. G. Mann, B. Hu, and R. Gosine, “Analysis and performance evaluation of linear-like fuzzy PI and PID controllers,” in Proceedings of the 6th International Fuzzy Systems Conference, pp. 383–390, Barcelona, Spain, 1997. View at Publisher · View at Google Scholar
  15. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  16. Y. Q. Chen, I. Petráš, and D. Y. Xue, “Fractional order control—a tutorial,” in Proceedings of the American Control Conference (ACC '09), pp. 1397–1411, June 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. R. E. Gutiérrez, J. M. Rosário, and J. T. MacHado, “Fractional order calculus: basic concepts and engineering applications,” Mathematical Problems in Engineering, vol. 2010, Article ID 375858, 19 pages, 2010. View at Publisher · View at Google Scholar
  18. I. Petráš, Stability of Fractional-Order Systems with Rational Orders: A Survey Fractional Calculus Applied Analysis12, 2009, pp. 269-298.
  19. I. Petráš, “Tuning and implementation methods for fractional-order controllers,” Fractional Calculus and Applied Analysis, vol. 15, no. 2, pp. 282–303, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. L. Ljung, System Identification Toolbox TM Users Guide, MathWorks Co. Ltd, 2015.
  21. A. Tepljakov, E. Petlenkov, and J. Belikov, “FOMCON: a MATLAB toolbox for fractional-order system identification and control,” International Journal of Microelectronics and Computer Science, vol. 2, no. 2, pp. 51–62, 2011. View at Google Scholar
  22. A. T. Azar, S. Vaidyanathan, and A. Ouannas, Fractional Order Control and Synchronization of Chaotic Systems, Springer, 2017.
  23. S. Ahmed, “Parameter and delay estimation of fractional order models from step response,” in Proceedings of the IFAC 9th International Symposium on Advanced Control of Chemical Processes, vol. 48, pp. 942–947, Whistler, British Columbia, Canada, June 7-10, 2015. View at Publisher · View at Google Scholar
  24. J. G. Ziegler and N. B. Nichols, “Optimum settings for automatic controllers,” Transactions of the ASME, vol. 64, pp. 759–768, 1942. View at Google Scholar
  25. C. Y. Quan, “Applied Fractional Calculus,” in Proceedings of the American Control Conference-ACC2009, St. Louis, Missouri, USA, 2009.
  26. C. Junyi and C. Binggang, “Fractional-order control of pneumatic position servosystems,” Mathematical Problems in Engineering, vol. 2011, Article ID 287565, 14 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  27. S. Manabe, “The non-integer integral and its application to control systems,” JIEE (Japanese Institute of Electrical Engineers) Journal, vol. 6, pp. 83–87, 1961. View at Google Scholar
  28. A. Oustaloup, F. Levron, B. Mathieu, and F. M. Nanot, “Frequency-band complex noninteger differentiator: characterization and synthesis,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 47, no. 1, pp. 25–39, 2000. View at Publisher · View at Google Scholar · View at Scopus
  29. M. A. Luersen and R. le Riche, “Globalized nelder-mead method for engineering optimization,” Computers & Structures, vol. 82, no. 23–26, pp. 2251–2260, 2004. View at Publisher · View at Google Scholar · View at Scopus
  30. R. K. Mudi and N. R. Pal, “A robust self-tuning scheme for PI- and PD-type fuzzy controllers,” IEEE Transactions on Fuzzy Systems, vol. 7, no. 1, pp. 2–16, 1999. View at Publisher · View at Google Scholar · View at Scopus