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A Novel Fractional-Order PIλDμAν Controller and Its Design Optimization Based on Spiritual Search


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DOI: https://doi.org/10.15866/ireaco.v12i6.17456

Abstract


A novel fractional-order PIλDμAν controller involving fractional-order integrator, fractional-order differentiator and fractional-order accelerator is proposed for higher-order systems. The proposed PIλDμAν controller is a successor of the fractional-order PIλDμ and the integer-order PIDA controllers. In this paper, time-domain and frequency-domain responses of the PIλDμAν controller are characterized. With the design optimization framework, seven parameters of the PIλDμAν controller, i.e. proportional gain, integral gain, derivative gain, accelerated gain, fractional order of integrator, fractional order of differentiator and fractional order of accelerator, are optimized by the spiritual search (SS), one of the most efficient hybrid metaheuristic optimizers. To perform its benefits and effectiveness, the PIλDμAν controller and its SS-based design optimization are applied to three real-world higher-order control systems. Results obtained by the PIλDμAν controller are compared with those obtained by the PIDA and PIλDμA controllers. As results, it was found that the proposed PIλDμAν controller exhibits very satisfactory responses superior to the PIDA and PIλDμA controllers, significantly.
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Keywords


Fractional-Order PIλDμAν Controller; Spiritual Search; Metaheuristic Optimizer

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References


S. Bennett, A History of Control Engineering 1930-1955, IEE Control Engineering Series 47, 1993.

S. Bennett, Nicolas Minorsky and the Automatic Steering of Ships, IEEE Control Systems, vol. 4, pp.10-15, 1984.

S. Bennett, A Brief History of Automatic Control, IEEE Control Systems Magazine, vol. 16, pp.17-25, 1996.

O. Mayr, The Origins of Feedback Control (Cambridge, MA: M.I.T. Press, 1970).

J. F. Coales, Historical and Scientific Background of Automation, Engineering, vol. 182, pp. 363-370, 1956.

N. Minorsky, Directional Stability of Automatically Steered Bodies, Journal of the American Society of Naval Engineering, vol. 34, no. 2, pp. 280-309, 1922.
https://doi.org/10.1111/j.1559-3584.1922.tb04958.x

N. Minorsky, Automatic Steering Tests, Journal of the American Society of Naval Engineering, vol. 42, pp. 285-310, 1930.
https://doi.org/10.1111/j.1559-3584.1930.tb05036.x

K. J. Åström, T. Hägglund, PID Controllers: Theory, Design, and Tuning (Instrument Society of America, Research Triangle Park, North Carolina, 1995).

A. Dwyer, Handbook of PI and PID Controller Tuning Rules (Imperial College Press, London, U.K., 2003).

J. G. Ziegler, N. B. Nichols, Optimum Settings for Automatic Controllers, Transactions on ASME, vol. 64, pp. 759-768, 1942.

J. G. Ziegler, N. B. Nichols, Process Lags in Automatic Control Circuits, Transactions on ASME, vol. 65, pp. 433-444, 1943.

G. H. Cohen, G. A. Coon, Theoretical Consideration of Retarded Control, Transactions on ASME, vol. 75, pp. 827-834, 1953.

K. L. Chien, J. A. Hrones, J. B. Reswick, On the Automatic Control of Generalized Passive Systems, Transactions on ASME, vol. 74, pp. 175-185, 1952.

K. Ogata, Modern Control Engineering (Prentice Hall, 2010)

B. C. Kuo, F. Golnaraghi, Automatic Control Systems (John Wiley & Sons, 2010).

C. L. Phillips, R. D. Harbor, Feedback Control Systems (Prentice Hall, 2000).

R. C. Dorf, R. H. Bishop, Modern Control Systems (Pearson Prentice Hall, 2017).

I. Podlubny, Fractional-Order Systems and Fractional-Order Controllers (UEF-03-94, Slovak Academy of Sciences, Kosice, 1994).

I. Podlubny, Fractional-Order Systems and PIlDm-Controllers, IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 208-214, 1999.
https://doi.org/10.1109/9.739144

D. Valério, J. C. Sáda, Tuning of Fractional PID Controllers with Ziegler-Nichols Type Rules, Signal Processing, Vol. 86, No. 10, pp.2771-2784, 2006.
https://doi.org/10.1016/j.sigpro.2006.02.020

Y. Chen, T. Bhaskaran, D. Xue, Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers, Journal of Computational and Nonlinear Dynamics, Vol. 3, 2008.
https://doi.org/10.1115/1.2833934

R. Caponetto, L. Fortuna, D. Porto, A New Tuning Strategy for a Non Integer Order PID Controller, Fractional Differentiation and its Applications, Bordeaux, 2004.

C. Zhao, D. Xue, Y. Chen, A Fractional Order PID Tuning Algorithm for a Class of Fractional Order Plants, The International Conference on Mechatronics & Automation, Niagara Falls, 2005.
https://doi.org/10.1109/icma.2005.1626550

Y. Q. Chen, I. Petráš, X. Dingyü, Fractional Order Control - a Tutorial, The American Control Conference, pp.1397-1411, 2009.

P. Shah, A. Agashe, Review of Fractional PID Controller, Mechatronics, Vol. 38, pp.29-41, 2016.
https://doi.org/10.1016/j.mechatronics.2016.06.005

S. Jung, R. C. Dorf, Analytic PIDA Controller Design Technique for a Third Order System, The 35th IEEE Conference on Decision and Control, pp. 2513-2518, 1996.
https://doi.org/10.1109/cdc.1996.573472

S. Jung, R. C. Dorf, Novel Analytic Technique for PID and PIDA Controller Design, The 13th Triennial World Congress, pp. 1146-1151, 1996.
https://doi.org/10.1016/s1474-6670(17)57819-2

P. Ukakimaparn, P. Pannil, P. Boonchuay, T. Trisuwannawat, PIDA Controller Designed by Kitti’s Method, The ICCAS-SICE2009, pp. 1547-1550, 2009.
https://doi.org/10.23919/sice.2017.8105730

D. K. Sambariya, D. Paliwal, Comparative Design and Analysis of PIDA Controller using Kitti’s and Jung-Dorf Approach for Third Order Practical Systems, British Journal of Mathematics & Computer Science, vol. 16, no. 5, pp. 1-16, 2016.
https://doi.org/10.9734/bjmcs/2016/26223

K. Bettou, A. Charef, Optimal Tuning of Fractional Order PIlDmA Controller using Particle Swarm Optimization Algorithm, The 20th World Congress of the International Federation of Automatic Control (IFAC PaperOnLine), vol. 50-1, pp. 8084-8089, 2017.
https://doi.org/10.1109/icosc.2017.7958652

K. Bettou, A. Charef, Optimal Fractional Order PIlDmA Controller Design for Bioreactor Control using Particle Swarm Optimization, The 6th International Conference on Systems and Control (ICSC), pp. 481-486, 2017.
https://doi.org/10.1109/icosc.2017.7958652

C. A. Monje, Y. Q. Chen, B. M. Vinagre, D. Xue, V. Feliu, Fractional-order Systems and Controls Fundamentals and Applications (Springer-Verlag, 2010).
https://doi.org/10.1007/978-1-84996-335-0

K. J. Åström, T. Hägglund, Benchmark Systems for PID Control, The IFAC Digital Control: Past, Present and Future of PID Control, pp. 165-166, 2000.
https://doi.org/10.1016/s1474-6670(17)38238-1

Puangdownreong, D., Spiritual Search: a Novel Metaheuristic Algorithm for Control Engineering Optimization, (2018) International Review of Automatic Control (IREACO), 11 (2), pp. 86-97.
https://doi.org/10.15866/ireaco.v11i2.13897

P. Harvey, An Introduction to Buddhism: Teachings, History and Practices (Cambridge University Press, 2013).

W. Rahula, What the Buddha Taught (Grove Press, New York, 1974).

A. Nawikavatan, C. Thammarat, D. Puangdownreong, Application of Spiritual Search to Optimal PIDA Controller Design for Cardiac Pacemaker, The 4th International Conference on Digital Arts, Media and Technology (ECTI-DAMT) and The 2nd ECTI Northern Section Conference on Electrical, Electronics, Computer and Telecommunications Engineering (ECTI-NCON), pp. 286-289, 2019.
https://doi.org/10.1109/ecti-ncon.2019.8692275

A. Tepljakov, E. Petlenkov, J. Belikov, FOMCON: Fractional-Order Modeling and Control Toolbox for MATLAB, The 18th International Conference on Mixed Design of Integrated Circuits and Systems (MIXDES ’11), pp.684-689, 2011.
https://doi.org/10.1515/9783110571745-010

A. Tepljakov, E. Petlenkov, 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.
https://doi.org/10.1109/bec.2014.7320594

P. Khluabwannarat, A. Nawikavatan, D. Puangdownreong, Fractional-Order Model Parameter Identification of BLDC Motor by Flower Pollination Algorithm, WSEAS Transaction on Systems and Control, pp. 573-579, 2018.
https://doi.org/10.1109/ieecon.2017.8075889


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