### Fractional Order PID Controller Design for DC Motor Speed Control System via Flower Pollination Algorithm

#### Abstract

Over two decades, the fractional (non-integer) order PID (FOPID or PI* ^{l}*D

*) controller was introduced and demonstrated to perform the better responses in comparison with the conventional integer order PID (IOPID). In this paper, the design of an optimal FOPID controller for the DC motor speed control system by the flower pollination algorithm (FPA), one of the most efficient population-based metaheuristic optimization searching techniques, is proposed. Based on the modern optimization framework, five parameters of the FOPID controller are optimized by the FPA to meet the response specifications of the DC motor speed control system defined as particularly constraint functions. Results obtained by the FOPID controller are compared with those obtained by the IOPID designed by the FPA. As simulation results, the FOPID can provide superior speed responses to the IOPID, significantly.*

^{m}#### Full Text:

PDF#### References

Y. Q. Chen, I. Petráš and X. Dingyü, “Fractional Order Control - a Tutorial,” Proceeding of the American Control Conference, pp.1397-1411, 2009.

P. Shah and A. Agashe, “Review of Fractional PID Controller,” Mechatronics, Vol. 38, pp.29-41, 2016.

I. Podlubny, “Fractional-Order Systems and PI𝜆D𝜇 Controllers,” IEEE Transactions on Automatic Control, Vol. 44, No. 1, pp.208-214, 1999.

C. A. Monje, B. M. Vinagre, V. Feliu and Y. Chen, “Tuning and Auto-Tuning of Fractional Order Controllers for Industry Applications,” Control Engineering Practice, Vol. 16, pp.798-812, 2008.

M. Zamani, M. Karimi-Ghartemani, N. Sadati and M. Parniani, “Design of a Fractional Order PID Controller for an AVR using Particle Swarm Optimization,” Control Engineering Practice, Vol. 17, pp.1380-1387, 2009.

D. Xue, C. Zhao and Y. Q. Chen, “Fractional Order PID Control of A DC-Motor with Elastic Shaft: A Case Study,” Proceedings of the 2006 American Control Conference, pp.3182-3187, 2006.

A. J. Calderón, B. M. Vinagre and V. Feliu, “Fractional Order Control Strategies for Power Electronic Buck Converters,” Signal Processing, Vol. 86, No. 10, pp.2803-2819, 2006.

S. K. Mishra and D. Chandra, “Stabilization and Tracking Control of Inverted Pendulum using Fractional Order PID Controllers,” Journal of Engineering, Vol. 2014, pp.1-9, 2014.

Q. Gao, J. Chen, L. Wang, S. Xu and Y. Hou, “Multiobjective Optimization Design of a Fractional Order PID Controller for a Gun Control System,” The Scientific World Journal, Vol. 2013, pp.1-8, 2013.

D. Valério and J. C. Sáda, “Tuning of Fractional PID Controllers with Ziegler-Nichols Type Rules,” Signal Processing, Vol. 86, No. 10, pp.2771-2784, 2006.

Y. Chen, T. Bhaskaran and D. Xue, “Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers,” Journal of Computational and Nonlinear Dynamics, Vol. 3, 2008.

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

C. Zhao, D. Xue and Y. Chen, “A Fractional Order PID Tuning Algorithm for a Class of Fractional Order Plants,” Proceedings of the International Conference on Mechatronics & Automation, Niagara Falls, 2005.

V. Zakian, Control Systems Design: A New Framework, Springer-Verlag, 2005.

V. Zakian and U. Al-Naib, “Design of Dynamical and Control Systems by the Method of Inequalities,” Proceedings of the IEE International Conference, Vol. 120, pp.1421-1427, 1973.

X. S. Yang, “Flower Pollination Algorithm for Global Optimization,” Unconventional Computation and Natural Computation, Lecture Notes in Computer Science, Vol. 7445, pp.240-249, 2012.

X. S. Yang, M. Karamanoglu and X. He, “Multi-Objective Flower Algorithm for Optimization,” Procedia Computer Science, Vol. 18, pp.861-868, 2013.

X. He, X. S. Yang, M. Karamanoglu and Y. Zhao, “Global Convergence Analysis of the Flower Pollination Algorithm: A Discrete-Time Markov Chain Approach,” Procedia Computer Science, Vol. 108C, pp.1354-1363, 2017.

A. Abdelaziz, E. Ali and S. A. Elazim, “Combined Economic and Emission Dispatch Solution using Flower Pollination Algorithm,” International Journal Electrical Power Energy Systems, Vol. 80, pp. 264-274, 2016.

S. Ouadfel and A. Taleb-Ahmed, “Social Spiders Optimization and Flower Pollination Algorithm for Multilevel Image Thresholding: A Performance Study,” Expert Systems, Vol. 55, pp. 566-584, 2016.

M. Sharawi, E. Emary, I. A. Saroit and H. El-Mahdy, “Flower Pollination Optimization Algorithm for Wireless Sensor Network Lifetime Global Optimization,” International Journal of Soft Computing Engineering, Vol. 4, No. 3, pp. 54-59, 2014.

P. Agarwal and S. Mehta, “Enhanced Flower Pollination Algorithm on Data Clustering,” International Journal of Computer Applications, Vol. 38, No. 2-3, pp. 144-155, 2016.

E. Nabil, “A Modified Flower Pollination Algorithm for Global Optimization,” Expert System Application, Vol. 57, pp. 192-203, 2016.

O. Abdel-Raouf, I. El-Henawy and M. Abdel-Baset, “A Novel Hybrid Flower Pollination Algorithm with Chaotic Harmony Search for Solving Sudoku Puzzles,” International Journal of Modern Education and Computer Science, Vol. 6, No. 3, pp.38, 2014.

S. M. Nigdeli, G. Bekdaş and X. S. Yang, “Application of the Flower Pollination Algorithm in Structural Engineering,” Metaheuristics and Optimization in Civil Engineering, Springer, pp.25-42, 2016.

D. Puangdownreong, “Optimal State-Feedback Design for Inverted Pendulum System by Flower Pollination Algorithm,” International Review of Automatic Control (IREACO), Vol. 9, No. 5, pp.289-297, 2016.

S. Hlungnamtip, C. Thammarat and D. Puangdownreong, “Obtaining Optimal PID Controller for DC Motor Speed Control System via Flower Pollination Algorithm,” Proceedings of the 9th International Conference on Sciences, Technology and Innovation for Sustainable Well-Being (STIWB), pp.52-56, 2017.

C. Thammarat, A. Nawikavatan and D. Puangdownreong, “Application of Flower Pollination Algorithm to PID Controller Design for Three-Tank Liquid-Level Control System,” Proceedings of the 9th International Conference on Sciences, Technology and Innovation for Sustainable Well-Being (STIWB), pp.42-46, 2017.

S. Hlungnamthip, N. Pringsakul, A. Nawikavatan and D. Puangdownreong, “FPA-Based PID Controller Design for Temperature Control of Electric Furnace System,” Proceedings of the 2018 International Conference on Engineering and Natural Science (ICENS 2018), pp.60-68, 2018.

D. Puangdownreong, C. Thammarat, S. Hlungnamtip and A. Nawikavatan, “Application of Flower Pollination Algorithm to Parameter Identification of DC Motor Model,” Proceedings of the 2017 International Electrical Engineering Congress (iEECON–2017), Vol. 2, pp.711-714, 2017.

Z. A. A. Alyasseri, A. T. Khader, M. A. Al-Betar, M. A. Awadallah and X. S. Yang, “Variants of the Flower Pollination Algorithm: A Review,” Nature-Inspired Algorithms and Applied Optimization, Studies in Computational Intelligence, Vol. 744, pp.91-118, 2018.

C. A. Monje, Y. Q. Chen, B. M. Vinagre, D. Xue and V. Feliu, Fractional-order Systems and Controls Fundamentals and Applications, Springer-Verlag, 2010.

D. Matignon, “Generalized Fractional Differential and Difference Equations: Stability Properties and Modelling Issues,” Proceedings of the Math. Theory of Networks and Systems Symposium, 1998.

K. Ogata, Modern Control Engineering, 5th edition, Prentice Hall, 2010.

D. Puangdownreong, “Optimal PID Controller Design for DC Motor Speed Control System with Tracking and Regulating Constrained Optimization via Cuckoo Search,” Journal of Electrical Engineering & Technology, Vol. 13, No. 1, pp.460-467, 2018.

MathWorks, System Identification Toolbox™, MATLAB-R2017b, 2017.

B. J. Glover, Understanding Flowers and Flowering: An Integrated Approach, Oxford University Press, 2007.

P. Willmer, Pollination and Floral Ecology, Princeton University Press, 2011.

K. Balasubramani and K. Marcus, “A Study on Flower Pollination Algorithm and Its Applications,” International Journal of Application or Innovation in Engineering & Management (IJAIEM), Vol. 3, pp.320-325, 2014.

I. Pavlyukevich, “Lévy Flights, Non-Local Search and Simulated Annealing,” Journal of Computational Physics, Vol. 226, pp.1830-1844, 2007.

A. Tepljakov, E. Petlenkov and J. Belikov, “FOMCON: Fractional-Order Modeling and Control Toolbox for MATLAB,” Proceedings of the 18th International Conference on Mixed Design of Integrated Circuits and Systems (MIXDES ’11), pp.684-689, 2011.

A. Tepljakov, E. Petlenkov and 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.

A. Tepljakov, E. Petlenkov and J. Belikov, FOMCON toolbox, [Available Online: http://www. fomcon.net], 2011.

### Refbacks

- There are currently no refbacks.

E-Journal © ECTI Asscoiation, Thailand, Contact Us.

Web: http://ecti-eec.org/