Fractional Model Reference Adaptive PIλDμ Control

Year 2016, Volume: 5 Issue: 11, 102 - 117, 31.12.2016

Hüseyin Arpacı Ömerül Faruk Özgüven , Mehmet Serhat Can

Abstract

This study explains the auto-adjustable fractional order the proportional–integral–derivative (PID) controller design methodology by using the technique of fractional model reference adaptive control (fractional MRAC). This method purposes a fractional order model reference adaptive PID (fractional MRAPI^λD^μ) control structure by applying the MIT rule to an adaptive control system which is including fractional order PID controller. This structure uses fractional order derivative, integral operators and fractional order reference model. Through this method, fractional order PID controller will be faster and more robustness.

 

Respectively using integer PID and fractional order PID, the coefficients of them are determined with Zeigler-Nichols technique, simulation applications of the fractional MRAPI^λD^μ control and the model reference adaptive PID (MRAPID) control performed. By means of the results obtained from simulation applications, fractional MRAPI^λD^μ control is compared to integer MRAPID control in terms of performance, speed and robustness.

Keywords

Fractional calculus, fractional PID (PIλDμ); Model Reference Adaptive Control; Fractional Model Reference Adaptive Control; Zeigler-Nichols; Performance and Robustness Comparison

References

• I. Petras, B. M Vinagre, Practical application of digital fractional-order controller to temperature control, Acta Montanistica Slovaca. 7(2), pp. 131-137, 2002.
• A. J. Caldero´n, B. M. Vinagre, V. Feliu, Fractional order control strategies for power electronic buck converters, Signal Processing 86, pp. 2803–2819, 2006.
• V. Feliu-Batlle, R. R Pe´rez, L.S Rodrı´guez, Fractional robust control of main irrigation canals with variable dynamic parameters, Control Engineering Practice, Volume 15, Issue 6, pp. 673-686, 2007.
• W. Li, Y. H. Fellow, Vibration suppression using single neuron-based PI fuzzy controller and fractional-order disturbance observe”, IEEE Transactions on Industrial Electronics, Vol. 54, No.1, pp. 117-126, February 2007.
• R. S. Barbosa, J. A. T. Machado, I. S. Jesus, On the fractional PID control of a Laboratory servo system, Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-11, pp. 15273-15278, 2008.
• I. Podlubny, Fractional order systems and controllers, IEEE Transactions on Automatic Control, Vol. 44, No. 1, pp. 208-214, January 1999.
• I. Petras, B. N. Vinagre, L. Dorcak, V. Feliu, Fractional digital control of a heat solid: experimental results, In Proc. International Carpathian Control Conference ICCC’2002 Malenovice, Czech Republic, pp. 27-30, May 2002.
• R. S. Barbosa, J. A. T. Machado, , I. M. Ferreira, A Fractional calculus perspective of PID tuning, In Proc. DETC’03, ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference Chicago, Illinois USA, 2003.
• R. S. Barbosa, J. A. T. Machado, I. M. Ferreira, Tuning of PID based on bode’s ideal transfer function, Nonlinear Dynamics 38, pp. 305–321, 2004.
• C. A. Monje, A. J. Calderon, B. M.Vinagre, Y. Q. Chen, V. Feliu, “On fractional PID controller some tuning rules for robustness to plant uncertainties”, Nonlinear Dynamics, 38, pp. 369–381, 2004.
• C. Zhao, D. Xue, Y. Q Chen, A fractional order PID tuning algorithm for a class of fractional order plants, Mechatronics and Automation, 2005 IEEE International Conference Vol. 1, pp. 216 – 221, 2005.
• D. Vale´rio, J. S. Costa, Tuning of fractional PID controllers with Ziegler–Nichols type rules”, Signal Processing, 86, pp. 2771–2784, 2006.
• D. Vale´rio, J. S. Costa, Tuning-rules for fractional PID controllers, Second IFAC Workshop on Fractional Differentiation and its Applications, Fractional Differentiation and its Applications, Volume 2, Part 1, 2006.
• J. Cervera, A. Baños, C. A. Monje, B. M. Vinagre, Tuning of fractional PID controllers by using QFT, IEEE Industrial Electronics, IECON 2006 - 32nd Annual Conference on, pp. 5402 – 5407, 6-10 Nov. 2006.
• S. E. Hamamci, An Algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers, IEEE Transactions on Automatic Control, Vol. 52, No. 10, pp. 1964-1969, October 2007.
• V. V. Chalam, Adaptive control systems techniques and applications, Marcel Dekker Inc., 1987.
• K. J. Astrom, B. Wittenmark, Adaptive control, Addison-Wesley Publishing Company, 1989.
• P. V. Osburn, H. P. Whitaker, A. Kezer, Comparative studies of model reference adaptive control systems, Institute of Aeronautical Sciences, Paper No. 61–39, 1961.
• J. Xie, J. Zhao, Model reference adaptive control for switched LPV systems and its application, IET Control Theory & Applications, Vol. 10, Issue 17, pp. 2204 – 2212, 2016, DOI: 10.1049/iet-cta.2015.1332
• N. A. Bakshi, R. Ramachandran, Indirect model reference adaptive control of quadrotor UAVs using neural networks, Intelligent Systems and Control (ISCO), 2016 10th International Conference on, 7-8 Jan. 2016, DOI: 10.1109/ISCO.2016.7727123
• C. Hu, Z. Qi, Q. Ma, Factional order model reference adaptive control based on Lyapunov stability theory, Control Conference (CCC), 2016 35th Chinese, 27-29 July 2016, DOI: 10.1109/ChiCC.2016.7555021
• N. Aguila-Camacho, M. A. Duarte-mermoud, Improving the control energy in model reference adaptive controllers using fractional adaptive laws, IEEE/CAA Journal of Automatica Sinica, Vol. 3, Issue 3, pp. 332 – 337, 2016, DOI: 10.1109/JAS.2016.7508809
• R. Kumar, S. Das, A. K. Chattopadhyay, Comparative assessment of two different model reference adaptive system schemes for speed-sensorless control of induction motor drives, IET Electric Power Applications, Vol. 10, Issue 2, pp. 141 – 154, 2016, DOI: 10.1049/iet-epa.2015.0121
• H. Wu, M. Deng, Robust adaptive control scheme for uncertain non-linear model reference adaptive control systems with time-varying delays, IET Control Theory & Applications, Vol. 9, Issue 8, pp. 1181 – 1189, 2015
• R. Khanna, Q. Zhang, W. E. Stanchina, Maximum Power Point Tracking Using Model Reference Adaptive Control, IEEE Transactions on power electronics, Vol. 29, No. 3, 2014
• R. Ghanadan, Adaptive PID control of nonlinear systems, University of Maryland, Master of Secience Thesis, 1990.
• E. Poulin, A. Pomerleau, A. Desbiens, D. Hodouin, Development and evaulation of an auto-tuning and adaptive PID controller, Automatica, Vol. 32, No.1, pp. 71-82, 1996.
• M. Jun, M. G. Safonov, Automatic PID tuning: An application of unfalsified control, Proceedings of the IEEE International Symposium on Computer Aided Control System Design, pp. 328 – 333, 1999.
• P. Boonsrimuang, A. Numsomran, S. Kangwanrat, Design of PI controller using MRAC techniques for couple-tanks process, World Academy of Science, Engineering and Technology, 59, pp. 67-72, 2009.
• S. Ladaci, An adaptive fractional PIλDμ controller, Proceedings of TMCE 2006, Ljubljana, Slovenia, pp. 1533-1539, 2006.
• W. Li, Design and Implement of Neural Network Based Fractional-Order Controller, Robotic Welding, Intelligence and Automation, Lecture Notes in Control and Information Sciences, Volume 362, pp. 471-479, 2007.
• B. M. Vinagre, I. Petras, I. Podlubny, Y. Q. Chen, Using fractional order adjustment rules and fractional order reference models in model reference adaptive control, Nonlinear Dynamics, 29, pp. 269–279, 2002.
• S. Ladaci, A. Charef, On fractional adaptive control, Nonlinear Dynamics, 43, pp. 365–378, 2006.
• J. Ma, Y. Yao, D. Liu, Fractional order model reference adaptive control for a hydraulic driven flight motion simulator, 41st Southeastern Symposium on System Theory, University of Tennessee Space Institute, Tullahoma, TN, USA, March 15-17, pp. 340-343, 2009.
• R. Caponetto, G. Dongola, L. Fortuna, I. Petráš, Fractional order systems modeling and control applications, World Scientific Series on Nonlinear Science, Series A — Vol. 72.
• S. Das, Functional fractional calculus for system identification and controls, Springer-Verlag, Berlin, Heildelberg, 2008.
• R. Caponetto, L. Fortuna, D. Porto, Parameter tuning of a non integer order PID controller, in Proceedings of the Fifteenth International Symposium on Mathematical Theory of Networks and Systems, Notre Dame, Indiana, 2002.
• Y. D. Landau, Adaptive control: The model reference approach, Marcel Dekker, New York, 1979.
• K. S. Narendra, Y. H. Lin, Design of stable modern reference adaptive controllers, in Applications of Adaptive Control, Academic Press, 1980.
• S. Sastry , M. Bodson, Adaptive control, stability, convergence and robustness, Prentice-Hall, Inc., 1989.
• A. Oustaloup, La commande CRONE (in French), Herm`es. Paris, 1991.
• D. Xue, Y.Q. Chen, Sub-Optimum H2 rational approximations to fractional order linear systems, Procedings ASME 2005 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, pp. 24-28, September 2005.