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Optimal PID Controller Design for DC Motor Speed Control System with Tracking and Regulating Constrained Optimization via Cuckoo Search

  • Received : 2017.06.03
  • Accepted : 2017.08.14
  • Published : 2018.01.01

Abstract

Metaheuristic optimization approach has become the new framework for control synthesis. The main purposes of the control design are command (input) tracking and load (disturbance) regulating. This article proposes an optimal proportional-integral-derivative (PID) controller design for the DC motor speed control system with tracking and regulating constrained optimization by using the cuckoo search (CS), one of the most efficient population-based metaheuristic optimization techniques. The sum-squared error between the referent input and the controlled output is set as the objective function to be minimized. The rise time, the maximum overshoot, settling time and steady-state error are set as inequality constraints for tracking purpose, while the regulating time and the maximum overshoot of load regulation are set as inequality constraints for regulating purpose. Results obtained by the CS will be compared with those obtained by the conventional design method named Ziegler-Nichols (Z-N) tuning rules. From simulation results, it was found that the Z-N provides an impractical PID controller with very high gains, whereas the CS gives an optimal PID controller for DC motor speed control system satisfying the preset tracking and regulating constraints. In addition, the simulation results are confirmed by the experimental ones from the DC motor speed control system developed by analog technology.

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Fig. 1. Schematic diagram of DC motor

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Fig. 2. DC motor plant

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Fig. 3. DC motor plant testing rig

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Fig. 4. Plots of actual speed response and plant model

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Fig. 5. PID control loop

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Fig. 6. Tracking and regulating purposes

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Fig. 7. CS-based PID control design optimization

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Fig. 8. Flow diagram of CS algorithms

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Fig. 9. Convergent rates of objective function

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Fig. 10. Responses without and with PID designed by Z-N

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Fig. 11. Responses without and with PID designed by CS

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Fig. 12. DC motor speed control system testing rig

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Fig. 13. System responses (experimental results)

References

  1. C. L. Phillips and R. D. Harbor, Feedback Control Systems, Prentice-Hall, 1991.
  2. B. C. Kuo, Automatic control systems, John Wiley & Sons, 2003.
  3. R. C. Dorf and R. H. Bishop, Modern Control Systems, Prentice-Hall, 2005.
  4. K. Ogata, Modern Control Engineering, Prentice-Hall, 2010.
  5. J. J. Rubio, "Hybrid controller with observer for the estimation and rejection of disturbances," ISA Transactions, vol. 65, pp.445-455, 2016. https://doi.org/10.1016/j.isatra.2016.08.026
  6. A-I. Carlos, S-R. Hebertt and S. S-C. Miguel, "A linear active disturbance rejection control for a ball and rigid triangle system," Mathematical Problems in Engineering, vol. 2016, pp. 1-11, 2016.
  7. J. J. Rubio, "Sliding mode control of robotic arms with deadzone," IET Control, Theory and Applications, vol. 11, no. 8, pp. 1214-1221, 2017. https://doi.org/10.1049/iet-cta.2016.0306
  8. N. Minorsky, "Directional stability of automatically steered bodies," American Society of Naval Engineering, vol. 34, pp. 284, 1922.
  9. A. Dwyer, Handbook of PI and PID Controller Tuning Rules, Imperial College Press, 2003.
  10. J. J. Rubio, P. Cruz, L. A. Paramo, J. A. Meda, D. Mujica and R. S. Ortigoza, "PID anti-vibation control of a robotic arm," IEEE Latin America Transactions, vol. 14, no. 7, pp. 3144-3150, 2016. https://doi.org/10.1109/TLA.2016.7587614
  11. P. T. Garran and G. Garcia, "Design of a PID controller for a coupled tanks system employing ADRC," IEEE Latin America Transactions, vol. 15, no. 2, pp. 189-196, 2017. https://doi.org/10.1109/TLA.2017.7854611
  12. J. G. Ziegler and N. B. Nichols, "Optimum settings for automatic controllers," Trans. ASME, vol. 64, pp. 759-768, 1942.
  13. G. H. Cohen and G. A. Coon, "Theoretical consideration of retarded control," Trans. ASME, vol. 75, pp. 827-834, 1953.
  14. V. Zakian, Control Systems Design: A New Framework, Springer-Verlag, 2005.
  15. V. Zakian and U. Al-Naib, "Design of dynamical and control systems by the method of inequalities," in Proc. of the IEE International Conference, vol. 120, pp. 1421-1427, 1973.
  16. S. Mehrdad and C. Greg, "An adaptive PID controller based on genetic algorithm processor," in Proc. of the International Conference on Genetic Algorithm in Engineering System, pp. 88-93, 1995.
  17. Y. Mitsukura, T. Yamamoto and M. Kaneda, "A design of self-tuning PID controller using a genetic algorithm," in Proc. of the International Conference on American Control Conference, pp. 1361-1365, 1999.
  18. J. F. Whidborne, "A genetic algorithm approach to design finite-precision PID controller structures," in Proc. of the International Conference on American Control Conference, pp.4338-4342, 1999.
  19. R. Bindu, K. Mini and K. Namboothiripad, "Tuning of PID controller for DC servo motor using genetic algorithm," in Proc. of the International Journal of Emerging Technology and Advanced Engineering (IJETAE), vol. 2, no. 3, pp. 310-314, 2012.
  20. S. Srikanth and G. R. Chandra, "Modeling and PID control of the brushless DC motor with the help of genetic algorithm," in Proc. of the IEEE International Conference on Advances in Engineering, Science and Management (ICAESM-2012), pp. 639-644, 2012.
  21. N. P. Adhikari, M. Choubey and R. Singh, "DC motor control using Ziegler Nichols and genetic algorithm technique," Int. J. Electr. Electron. Comput. Eng., 2012.
  22. Y. Arturo, J. C. Ren, J. R. Troncoso, L. M. Velazquez and R. A. Osornio-Rios, "PID-controller tuning optimization with genetic algorithms in servo systems," International Journal of Advanced Robotic Systems, vol.10, pp. 324, 2013. https://doi.org/10.5772/56697
  23. A. T. El-Deen, A. A. H. Mahmoud and A. R. El-Sawi, "Optimal PID tuning for DC motor speed controller based on genetic algorithm," International Review of Automatic Control (IREACO), vol. 8, no. 1, pp. 80-85, 2015. https://doi.org/10.15866/ireaco.v8i1.4839
  24. A. J. Mohammed, "A particle swarm optimization (PSO) based optimum of tuning PID controller for a separately excited DC motor (SEDM)," Eng. & Tech. Journal, vol. 29, no. 16, pp. 3322- 3323, 2011.
  25. H. E. A. Ibrahim and M. A. Elnady, "A comparative study of PID, fuzzy, fuzzy-PID, PSO-PID, PSO-fuzzy, and PSO-fuzzy-PID controllers for speed control of DC motor drive," International Review of Automatic Control (IREACO), vol. 6, no. 4, pp. 393-403, 2013.
  26. A. Jalilvand, A. Kimiyaghalam and A. H. Kord, "Optimal tuning of PID controller parameters on a DC motor based on advanced particle swarm optimization algorithm," International Journal on Technical and Physical Problems of Engineering (IJTPE), vol. 3, no. 4, pp. 10-17, 2011.
  27. A. Jalilvand, R. Aghmasheh and E. Khalkhali, "Optimal design of PID power system stabilizer in multi-machine power system using PSO and genetic algorithm," International Review of Electrical Engineering (IREE), vol. 6, no. 2, pp. 907-912, 2011.
  28. M. I. Solihin, L. F. Tack and M. L. Kean, "Tuning of PID controller using particle swarm optimization (PSO)," in Proc. of the International Conference on Advanced Science, Engineering and Information Technology (ICASEIT2011), 2011.
  29. S. Bouallegue, J. Haggege, M. Ayadin and M. Benrejeb, "PID-type fuzzy logic controller tuning based on particle swarm optimization," Elsevier journal on Engineering Applications of Artificial Intelligence, vol. 25, no. 3, pp. 484-493, 2012. https://doi.org/10.1016/j.engappai.2011.09.018
  30. H. T. Dorrah, A. M. El-Garhy and M. E. El-Shimy, "Design of PSO-based optimal fuzzy PID controllers for the two-coupled distillation column process," in Proc. of the International Middle East Power Systems Conference (MEPCON2010), 2010.
  31. M. Nasri, N. P. Hossein and M. Maghfoori, "A PSObased optimum design of PID controller for a linear brushless DC motor," World Academy of Science, Engineering and Technology, vol. 20, pp. 211-215, 2007.
  32. C. Kiree, D. Kumpanya, S. Tunyasrirut and D. Puangdownreong, "PSO-Based Optimal PI(D) Controller Design for Brushless DC Motor," Journal of Electrical Engineering & Technology, vol. 11, no. 3, pp. 715-723, 2016. https://doi.org/10.5370/JEET.2016.11.3.715
  33. M. Unal, A. V. Topuz and H. Erdal, "Optimization of PID controllers using ant colony and genetic algorithms," Springer, 2013.
  34. H. E. A. Ibrahim and A. A. H. Mahmoud, "DC motor control using PID controller based on improved ant colony algorithm," International Review of Automatic Control (IREACO), vol. 7, no. 1, pp. 1-6, 2014. https://doi.org/10.15866/ireaco.v7i1.1283
  35. M. J. Blondin and P. Sicard, "PID controllers and anti-windup systems tuning using ant colony optimization," Journal of Power Electronics and Applications (EPE), pp. 1-10, 2013.
  36. I. Chiha, H. Liouane and N. Liouane, "A hybrid method based on multi-objective ant colony optimization and differential evolution to design PID DC motor speed controller," International Review on Modelling and Simulations (IREMOS), vol. 5, no. 2, pp. 905-912, 2012.
  37. X. S. Yang and S. Deb, "Cuckoo search via Lévy flights," in Proc. of the World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), pp. 210-214, 2009.
  38. X. S. Yang, "Cuckoo search and firefly algorithm: overview and analysis," Studied in Computational Intelligence: Cuckoo search and Firefly Algorithm Theory and Applications, Springer, pp. 1-26, 2014.
  39. X. S. Yang and S. Deb, "Engineering optimisation by cuckoo search," Mathematical Modelling and Numerical Optimisation, vol. 1, no. 4, pp. 330-343, 2010. https://doi.org/10.1504/IJMMNO.2010.035430
  40. X.S. Yang and S. Deb, "Multiobjective cuckoo search for design optimization," Computers and Operations Research, vol. 40, no. 6, pp. 1616-1624, 2013. https://doi.org/10.1016/j.cor.2011.09.026
  41. M. Kishnani, S. Pareek and R. Gupta, "Optimal tuning of PID controller by cuckoo search via Levy flights," in Proc. of the International Conference on Advances in Engineering and Technology Research (ICAETR), 2014.
  42. R. Sethi, S. Panda and B. P. Sahoo, "Cuckoo search algorithm based optimal tuning of PID structured TCSC controller," Computational Intelligence in Data Mining, vol. 1, pp. 251-263, 2014.
  43. D. Puangdownreong, C. Kiree, D. Kumpanya and S. Tunyasrirut, "Application of cuckoo search to design optimal PID/PI controllers of BLDC motor speed control system," in Proc. of the Global Engineering & Applied Science Conference, pp. 99-106, 2015.
  44. P. C. Krause, Analysis of Electric Machinery, McGraw- Hill Book Company, 1983.
  45. P. C. Krause, O. Wasynczuk, S. D. Sudhoff, Analysis of Electric Machinery and Drive Systems, IEEE Press, Piscataway, NJ, 2002.