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

Tufan Doğruer; Nusret Tan

EN

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

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.

Keywords

Controller design,fractional control systems,phase lead and lag controller

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.

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

Tufan Doğruer

Nusret Tan

Publication Date

November 7, 2016

Submission Date

November 14, 2016

Acceptance Date

-

Published in Issue

Year 2016 Volume: 5

IZ

https://izlik.org/JA65UF36HU

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. https://izlik.org/JA65UF36HU

AMA

1.Doğruer T, Tan N. Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty. JNRS. 2016;5:96-110. https://izlik.org/JA65UF36HU

Chicago

Doğruer, Tufan, and Nusret Tan. 2016. “Design of Lag Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty”. Journal of New Results in Science 5 (November): 96-110. https://izlik.org/JA65UF36HU.

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

[1]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, Nov. 2016, [Online]. Available: https://izlik.org/JA65UF36HU

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 1, 2016): 96-110. https://izlik.org/JA65UF36HU.

JAMA

1.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, Nov. 2016, pp. 96-110, https://izlik.org/JA65UF36HU.

Vancouver

1.Tufan Doğruer, Nusret Tan. Design of Lag/Lead Controller for Fractional Order Systems Containing Time-Delay and Uncertainty. JNRS [Internet]. 2016 Nov. 1;5:96-110. Available from: https://izlik.org/JA65UF36HU