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Design of the PID Controller for Hydro-turbines Based on Optimization Algorithms

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  • Control Theory and Applications
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Abstract

In this study, multiple objective particle swarm optimization (MOPSO), genetic algorithm, bees, and reinforcement learning (RL) are used to calculate the rise time (tr), integral square-error, integral of time-multiplied-squared-error, integral absolute error, and integral of time multiplied by absolute error of the system transfer function and then we use a fuzzy algorithm on MOPSO, GA, bees, and RL based on the frequency sensitivity margin of a water turbine governor to optimize the proportional gain (kp) and integral gain (ki) and calculate the relative collapsing frequency response values. The MOPSO algorithm returned the optimal result. The radial basis function (RBF) neural network curve is obtained from the MOPSO algorithm with three variables (i.e., kp, ki, kd = 0.6 and grid frequency deviations values), and finally we identify and predict three variable values near the RBF neural network curve through deep learning. The result of the grid frequency deviation is close to 0, and the gain response time is better for damping the frequency oscillations in different operating conditions.

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References

  1. N. Minorsky, “Directional stability of automatically steered bodies,” J. Am. Soc. Nav. Eng., vol. 34, no. 2, pp. 280–309, May 1922.

    Article  Google Scholar 

  2. A. Callender, D. R. Hartree, and A. Porter, “Time-lag in a control system”, Phil. Trans. Royal Soc. London, vol. 235, no. 756, pp. 415–444, July 1936.

    MATH  Google Scholar 

  3. J. G. Ziegler and N. B. Nichols, “Optimum settings for automatic controllers,” Trans. ASME, vol. 64, pp. 759–768, November 1942.

    Google Scholar 

  4. R. A. Krohling, H. Jaschek, and J. P. Rey, “Designing PI/PID controllers for a motion control system based on genetic algorithms,” Proc. of the 12th IEEE International Symposium on Intelligent Control, Istanbul, pp. 125–130, July 1997.

    Chapter  Google Scholar 

  5. R. A. Krohling and J. P. Rey, “Design of optimal disturbance rejection PID controllers using genetic algorithms,” IEEE Trans. on Evol. Comput., vol. 5, no. 1, pp. 78–82, February 2001.

    Article  Google Scholar 

  6. Y. Mitsukura, T. Yamamoto, and M. Kaneda, “A design of self-tuning PID controllers using a genetic algorithm,” Proc. of the 1999 American Control Conference, San Diego, pp. 1361–1365, June 1999.

    Google Scholar 

  7. Y. Mitsukura, T. Yamamoto, and M. Kaneda, “Genetic tuning algorithm of PID parameters,” Proc. of IEEE Int. Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation, Orlando, pp. 923–928, October 1997.

    Google Scholar 

  8. P. Hušek, “PID controller design for hydraulic turbine based on sensitivity margin specifications,” Int. J. Electr. Power Energy Syst., vol. 55, pp. 460–466, February 2014.

    Article  Google Scholar 

  9. D. Pršíc, N. Nedíc, and V. Stojanovíc, “A nature inspired optimal control of pneumatic-driven parallel robot platform”, P. I. Mech. Eng. C-J. MEC., vol. 231, no. 1, pp. 59–71, January 2017.

    Article  Google Scholar 

  10. A. Younesi and H. Shayeghi, “Q-learning based supervisory PID controller for damping frequency oscillations in a hybrid mini/micro-grid,” Iran. J. Electr. Electron. Eng., vol. 15, no. 1, pp. 125–141, March 2019.

    Google Scholar 

  11. D. H. Thorne and E. F. Hill, “Field testing and simulation of hydraulic turbine governor performance,” IEEE Trans. Power App. Syst., vol. PAS-93, no. 4, pp. 1183–1191, July 1974.

    Article  Google Scholar 

  12. N. Nedíc, D. Pršíc, C. Fragassa, V. Stojanovíc, and A. Pavlovic, “Simulation of hydraulic check valve for forestry equipment”, Int. J. Heavy Veh. Syst., vol. 24, no. 3, pp. 260–276, June 2017.

    Article  Google Scholar 

  13. V. Stojanovic, N. Nedic, D. Prsic, and L. Dubonjic, “Optimal experiment design for identification of ARX models with constrained output in non-Gaussian noise,” Appl. Math. Model., vol. 40, no. 13–14, pp. 6676–6689, July 2016.

    Article  MathSciNet  Google Scholar 

  14. V. Stojanovic and V. Filipovic, “Adaptive input design for identification of output error model with constrained output”, Circ. Syst. Signal Pr., vol. 33, no. 1, pp. 97–113, January 2014.

    Article  MathSciNet  Google Scholar 

  15. J.-W. Perng, Y.-C. Kuo, and S.-P. Lu, “Grounding system cost analysis using optimization algorithms,” Energies, vol. 11, no. 12, pp. 3484, December 2018.

    Article  Google Scholar 

  16. J. Holland, Adaptation in Natural and Artificial System, University of Michigan Press, 1975.

    Google Scholar 

  17. Y. Shi and R. C. Eberhart, “A modified particle swarm optimizer,” Proc. of IEEE Int. Conference on Evolutionary Computation (ICEC), Anchorage, pp. 69–72, May 1998.

    Google Scholar 

  18. X. Hu, Y. Shi, and R. C. Eberhart, “Recent advances in particle swarm,” Proc. of the Congress on Evolutionary Computation, Portland, pp. 90–97, June 2004.

    Google Scholar 

  19. J. Kennedy and R. Eberhart, “Particle swarm optimization,” Proc. of ICNN’95 - Int. Conference on Neural Networks, Perth, pp. 1942–1948, November-December 1995.

    Chapter  Google Scholar 

  20. N. Nedic, D. Prsic, L. Dubonjic, V. Stojanovic, and V. Djordjevic, “Optimal cascade hydraulic control for a parallel robot platform by PSO,” Int. J. Adv. Manuf. Technol., vol. 72, no. 5–8, pp. 1085–1098, May 2014.

    Article  Google Scholar 

  21. D. T. Pham, A. Ghanbarzadeh, E. Koc, S. Otri, S. Rahim, and M. Zaidi, Bee Algorithm: A Novel Approach to Function Optimisation (Technical Note: MEC 0501), Manufacturing Engineering Centre, Cardiff University, 2005.

    Google Scholar 

  22. L. A. Zadeh, “Fuzzy sets”, Inform. Control, vol. 8, no. 3, pp. 338–353, June 1965.

    Article  Google Scholar 

  23. Y. W. Chang, C. J. Hsieh, K. W. Chang, M. Ringgaard, and C. J. Lin, “Training and testing low-degree polynomial data mappings via linear SVM,” J. Mach. Learn. Res., vol. 11, pp. 1471–1490, April 2010.

    MathSciNet  MATH  Google Scholar 

  24. Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature, vol. 521, pp. 436–444, May 2015.

    Article  Google Scholar 

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Correspondence to Yi-Chang Kuo.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Editor Kyoung Kwan Ahn. The authors appreciate Director Yao-Tsung Chang and Deputy Director Hsi-Hsiang Chang of the contributions provided from Taiwan Power Company Southern Region Construction Office. Funding: This study was funded by a grant from Ministry of Science and Technology, Taiwan, under Grant no. MOST 108-2218-E-110-005.

Jau-Woei Perng was born in Hsinchu of Taiwan in 1973. He received his B.S. and M.S. degrees in electrical engineering from Yuan Ze University located in Chungli of Taiwan in 1995 and 1997, respectively, and a Ph.D.degree in electrical and control engineering from National Chiao Tung University (NCTU) located in Hsinchu of Taiwan in 2003. From 2004 to 2008, he was a Research Assistant Professor at the Department of Electrical and Control Engineering, NCTU. Since 2008, he has worked for the Department of Mechanical and Electromechanical Engineering at National Sun Yat-Sen University in Kaohsiung of Taiwan, where he is currently a Professor. His research mainly concerns robust control, nonlinear control, fuzzy logic control, neural networks, mobile robots, systems engineering and intelligent vehicle control.

Yi-Chang Kuo was born in Kaohsiung of Taiwan in 1976. He received his B.S. and M.S. degrees in biomedical engineering respectively in 2001 and 2003 from Chung Yuan Christian University located in Zhongli of Taiwan. From 2004 to 2008, he was a computer information maintenance engineer. Since 2008, he has worked for the TaiPower Company in Taiwan, where he is currently an Electrical and Mechanical Design Specialist. In 2014, he also became a Ph.D. student, and he was selected as a doctoral candidate in 2016. His research mainly concerns fuzzy logic control, neural networks, optimal ground system, optimal electric grid, signal processing, optimal substation, optimization algorithms, power system.

Kuan-Chung Lu was born in Kaohsiung of Taiwan in 1991. He received his B.S. degrees in Systems and Naval Mechatronic Engineering in 2014 from National Cheng Kung University, and an M.S. degrees in Mechanical and Electro-mechanical Engineering in 2016 from National Sun Yat-Sen University. His research focus on MOPSO, fuzzy logic control and motor control.

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Perng, JW., Kuo, YC. & Lu, KC. Design of the PID Controller for Hydro-turbines Based on Optimization Algorithms. Int. J. Control Autom. Syst. 18, 1758–1770 (2020). https://doi.org/10.1007/s12555-019-0254-7

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