Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty
Year 2016,
Volume: 5 , 96 - 110, 07.11.2016
Tufan Doğruer
,
Nusret Tan
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
Tufan Doğruer
,
Nusret Tan
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.