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Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty

Year 2016, Volume: 5 , 96 - 110, 07.11.2016

Abstract

This paper presents a methodology to design a phase-lead and phase-lag controllers for a fractional order system with time-delay and parameter uncertainty. The method that was used in the study is a classic design method used by D. P. Atherton. The method has been shown to be successful by adding time-delay and parameter uncertainty to this classic design method. The controllers are obtained by the implementation of individual design steps for the phase-lead and phase-lag controller. The unit-step responses and Bode diagrams of the systems with controllers are plotted. Considering the results obtained, it is observed that the method gave successful results for a fractional order plant with time-delay and parameter uncertainty.

References

  • K. Ogata, Modern control engineering, University of Minnesota, 5th edition, 2002.
  • F. Golnaraghi, B. C. Kuo, Automatic control systems, 9th edition, 2009.
  • C. Yeroğlu, N. Tan, Classical controller design techniques for fractional order case, ISA Transactions, Volume:50, Issue:3, pp:461-472, July 2011.
  • H. Özbay, C. Bonnet, A. R. Fioravanti, PID controller design for fractional-order systems with time delays, Systems & Control Letters, Volume:61, Issue:1, pp:18-23, Jan 2012.
  • D. J. Wang, X. Chen, Turning of fractional order phase lead compensators: a graphical approach, Proceedings of the 29th Chinese Control Conference, July 2010.
  • C. A. Monje, A. J. Calderon, B. M. Vinagre, V. Feliu, The fractional order lead compensator, Computational Cybernetics Second IEEE International Conference on, Sept 2004.
  • D. Valerio, J. S. Costa, Tuning of fractional PID controllers with Ziegler-Nichols-type rules, Signal Processing, Volume:86, Issue:10, pp:2771-2784, Oct 2006.
  • R. Singhal, S. Padhee, G. Kaur, Design of fractional order PID controller for speed control of DC motor, International Journal of Scientific and Research Publications, Volume:2, Issue:6, June 2012.
  • A. Tustin, J. T. Allanson, J. M Layton, J. Jakeways, The design of systems for automatic control of the position massive control, Proceedings of the IEE, Volume:25, Issue:1, 1958.
  • M. M. Özyetkin, Robust analysis and design of fractional order control systems, PhD Thesis, İnönü University Graduate School of Natural and Applied Sciences, 2013.
  • C. Yeroğlu, Frequency response analysis and design of the fractional order control systems, PhD Thesis, İnönü University Graduate School of Natural and Applied Sciences, 2011.
  • M. R. Faieghi, A. Nemati, On fractional order PID design, Applications of MATLAB in Science and Engineering, Prof. Tadeusz Michalowski (Ed.), ISBN: 978-953-307-708-6, InTech, 2011.
  • I. Petras, The fractional-order controllers: methods for their synthesis and application, J. Of Elect. Eng., pp:284-288, 1999.
  • R. Matusu, Application of fractional order calculus to control theory, International Journal of Mathematical Models and Methods in Applied Sciences, Volume:5, Issue:7, pp:1162-1169, 2011.
  • S. Manabe, The non-integer integral and its application to control systems, ETJ of Japan , 6/3-4, 83-87, 1961.
  • S. Manabe, The system design by the use of a model consisting of a saturation and noninteger integral, ETJ of Japan , 8/3-4, 47-150, 1963.
  • Y. Sarı, A. F. Boz, Autotuning of second order plus dead time systems using standard forms and PID-PD, 5th International Advanced Technologies Symposium (IATS’09), Karabük, 2009.
  • I. Podlubny, Fractional order systems and PID controllers, IEEE Transaction on Automatic Control, Volume:44, Issue:1, 1999.
  • C. Zhao, D. Xue, Y. Chen, A fractional order PI^λ D^μ tuning algorithm for a class of fractional order plants, Proceedings of the IEEE International Conference on Mechatronics and Automation, Canada, 2005.
  • D. P. Atherton, Control engineering, Brighton, 2009.
  • D. P. Atherton, Control engineering problems with solutions, Brighton, 2013.
  • D. Xue, Y. Chen, D. P. Atherton, Linear feedback control analysis and design with MATLAB, Philadelphia, 2007.
  • Y. Chen, I. Petras, D. Xue, Fractional order control - A tutorial, USA, 2009.
  • T. Doğruer, N. Tan, Zaman gecikmesine sahip kesirli dereceli belirsiz sistemler için kontrolör tasarımı, Elektrik-Elektronik ve Bilgisayar Sempozyumu, Tokat, pp:163-167, Mayıs 2016.
Year 2016, Volume: 5 , 96 - 110, 07.11.2016

Abstract

References

  • K. Ogata, Modern control engineering, University of Minnesota, 5th edition, 2002.
  • F. Golnaraghi, B. C. Kuo, Automatic control systems, 9th edition, 2009.
  • C. Yeroğlu, N. Tan, Classical controller design techniques for fractional order case, ISA Transactions, Volume:50, Issue:3, pp:461-472, July 2011.
  • H. Özbay, C. Bonnet, A. R. Fioravanti, PID controller design for fractional-order systems with time delays, Systems & Control Letters, Volume:61, Issue:1, pp:18-23, Jan 2012.
  • D. J. Wang, X. Chen, Turning of fractional order phase lead compensators: a graphical approach, Proceedings of the 29th Chinese Control Conference, July 2010.
  • C. A. Monje, A. J. Calderon, B. M. Vinagre, V. Feliu, The fractional order lead compensator, Computational Cybernetics Second IEEE International Conference on, Sept 2004.
  • D. Valerio, J. S. Costa, Tuning of fractional PID controllers with Ziegler-Nichols-type rules, Signal Processing, Volume:86, Issue:10, pp:2771-2784, Oct 2006.
  • R. Singhal, S. Padhee, G. Kaur, Design of fractional order PID controller for speed control of DC motor, International Journal of Scientific and Research Publications, Volume:2, Issue:6, June 2012.
  • A. Tustin, J. T. Allanson, J. M Layton, J. Jakeways, The design of systems for automatic control of the position massive control, Proceedings of the IEE, Volume:25, Issue:1, 1958.
  • M. M. Özyetkin, Robust analysis and design of fractional order control systems, PhD Thesis, İnönü University Graduate School of Natural and Applied Sciences, 2013.
  • C. Yeroğlu, Frequency response analysis and design of the fractional order control systems, PhD Thesis, İnönü University Graduate School of Natural and Applied Sciences, 2011.
  • M. R. Faieghi, A. Nemati, On fractional order PID design, Applications of MATLAB in Science and Engineering, Prof. Tadeusz Michalowski (Ed.), ISBN: 978-953-307-708-6, InTech, 2011.
  • I. Petras, The fractional-order controllers: methods for their synthesis and application, J. Of Elect. Eng., pp:284-288, 1999.
  • R. Matusu, Application of fractional order calculus to control theory, International Journal of Mathematical Models and Methods in Applied Sciences, Volume:5, Issue:7, pp:1162-1169, 2011.
  • S. Manabe, The non-integer integral and its application to control systems, ETJ of Japan , 6/3-4, 83-87, 1961.
  • S. Manabe, The system design by the use of a model consisting of a saturation and noninteger integral, ETJ of Japan , 8/3-4, 47-150, 1963.
  • Y. Sarı, A. F. Boz, Autotuning of second order plus dead time systems using standard forms and PID-PD, 5th International Advanced Technologies Symposium (IATS’09), Karabük, 2009.
  • I. Podlubny, Fractional order systems and PID controllers, IEEE Transaction on Automatic Control, Volume:44, Issue:1, 1999.
  • C. Zhao, D. Xue, Y. Chen, A fractional order PI^λ D^μ tuning algorithm for a class of fractional order plants, Proceedings of the IEEE International Conference on Mechatronics and Automation, Canada, 2005.
  • D. P. Atherton, Control engineering, Brighton, 2009.
  • D. P. Atherton, Control engineering problems with solutions, Brighton, 2013.
  • D. Xue, Y. Chen, D. P. Atherton, Linear feedback control analysis and design with MATLAB, Philadelphia, 2007.
  • Y. Chen, I. Petras, D. Xue, Fractional order control - A tutorial, USA, 2009.
  • T. Doğruer, N. Tan, Zaman gecikmesine sahip kesirli dereceli belirsiz sistemler için kontrolör tasarımı, Elektrik-Elektronik ve Bilgisayar Sempozyumu, Tokat, pp:163-167, Mayıs 2016.
There are 24 citations in total.

Details

Journal Section Articles
Authors

Tufan Doğruer

Nusret Tan

Publication Date November 7, 2016
Published in Issue Year 2016 Volume: 5

Cite

APA Doğruer, T., & Tan, N. (2016). Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty. Journal of New Results in Science, 5, 96-110.
AMA Doğruer T, Tan N. Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty. JNRS. November 2016;5:96-110.
Chicago Doğruer, Tufan, and Nusret Tan. “Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty”. Journal of New Results in Science 5, November (November 2016): 96-110.
EndNote Doğruer T, Tan N (November 1, 2016) Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty. Journal of New Results in Science 5 96–110.
IEEE T. Doğruer and N. Tan, “Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty”, JNRS, vol. 5, pp. 96–110, 2016.
ISNAD Doğruer, Tufan - Tan, Nusret. “Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty”. Journal of New Results in Science 5 (November 2016), 96-110.
JAMA Doğruer T, Tan N. Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty. JNRS. 2016;5:96–110.
MLA Doğruer, Tufan and Nusret Tan. “Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty”. Journal of New Results in Science, vol. 5, 2016, pp. 96-110.
Vancouver Doğruer T, Tan N. Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty. JNRS. 2016;5:96-110.


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