Improved Gray Wolf Optimization Algorithm for Tuning Non-integer Order Proportional Integral Derivative Controller Design

Year 2025, Volume: 6 Issue: 1, 220 - 244, 30.06.2025

Kadri Doğan , Hasan Başak

https://doi.org/10.53501/rteufemud.1545913

Abstract

In this study, a noninteger-order proportional–integral–derivative (NIOPID) controller was used for controlling the speed of the direct current (DC) motor. The controller parameters have optimally been adjusted using the GWOJOS algorithm formed by combining the Grey Wolf Optimization (GWO) algorithm and the recently defined the Joint Opposite Selection (JOS) feature. The JOS brings a mutual reinforcement by a joint of the two opposition strategies Dynamic Opposite (DO) and Selective Leading Opposition (SLO). The DO and SLO improve the balance of exploration and exploitation, respectively, in a given search space. During the optimization phase, JOS helps GWO attack the target quickly by employing SLO. DO help GWO find more opportunities to find the most suitable prey. The GWO is able to improve its performance with JOS. This combination helps accelerating the convergence rate of GWO. We assessed GWOJOS's performance using the benchmark functions from the IEEE Congress on Evolutionary Computation 2017 (CEC2017). The benchmark covers composition, hybrid, multimodal, and unimodal functions. The NIOPID-based speed control system for DC-motor using the GWOJOS algorithm has been designed using a time domain objective function that takes into account the performance criteria (maximum overshoot, steady-state error, rising time, and settling time). Some analyses, including robustness, time and frequency domain simulations, have been used to evaluate the performance of the proposed novel approach. The evaluation results have shown that the performance of GWOJOS was better than the performance of GWO, Slime Mould Algorithm (SMA), Atom Search Optimization (ASO), Simulated Annealing (SA) and the hybrid optimization algorithm created by opposition-based learning (OBL) strategy of SA and SMA algorithms (OBLSMASA).

Keywords

DC Motor , GWO JOS , Metaheuristic Optimization , NIOPID

Supporting Institution

Artvin Coruh University Scientific Research Projects Coordination

Project Number

BAP2024.F15.02.01

Geliştirilmiş Gri Kurt Optimizasyon Algoritmasına Dayalı Kesirli Mertebeden Oransal İntegral Türevsel PID Denetleyici Tasarımı

Abstract

Bu çalışmada, doğru akım (DC) motorunun hızını kontrol etmek için tam sayı olmayan mertebeden oransal-integral-türevsel (NIOPID) kontrolör kullanılmıştır. Kontrolör parametreleri, GWO algoritması ve yeni tanımlanan JOS özelliğinin birleşiminden oluşan GWOJOS algoritması kullanılarak optimum şekilde ayarlanmıştır. JOS, Dinamik Karşıtlık (DO) ve Seçici Lider Karşıtlık (SLO) olmak üzere iki karşıtlık stratejisinin bir araya getirilmesiyle karşılıklı bir güçlendirme sağlar. DO ve SLO, belirli bir arama uzayında sırasıyla keşif ve sömürü dengesini iyileştirir. Optimizasyon aşamasında JOS, SLO'yu kullanarak GWO'nun hedefe hızlı bir şekilde saldırmasına yardımcı olur. DO, GWO'nun en uygun avı bulmak için daha fazla fırsat bulmasına yardımcı olur. GWO, JOS ile performansını artırabilmektedir. Bu birleşim, GWO'nun yakınsama oranını hızlandırmaya yardımcı olur. GWOJOS'un performansını CEC2017'deki kıyaslama fonksiyonlarını kullanarak değerlendirdik. Kıyaslama bileşim, hibrit, multimodal ve unimodal fonksiyonları kapsamaktadır. GWOJOS algoritmasını kullanan DC-motor için NIOPID tabanlı hız kontrol sistemi, performans kriterlerini (maksimum aşım, kararlı durum hatası, yükselme süresi ve yerleşme süresi) dikkate alan bir zaman alanı amaç fonksiyonu kullanılarak tasarlanmıştır. Önerilen yeni yaklaşımın performansını değerlendirmek için sağlamlık, zaman ve frekans alanı simülasyonları dahil olmak üzere bazı analizler kullanılmıştır. Değerlendirme sonuçları GWOJOS'un performansının GWO, SMA, ASO, SA ve OBLSMASA algoritmaların performansından daha iyi olduğunu göstermiştir.

Keywords

NIOPID , DC Motor , GWOJOS , Metaheuristic Optimizasyon

Supporting Institution

Artvin Çoruh Üniversitesi Bilimsel Araştırmalar Projeleri Koordinatörlüğü

Project Number

BAP2024.F15.02.01

References

• Agarwal, J., Parmar, G., Gupta, R., Sikander, A. (2018). Analysis of grey wolf optimizer based fractional order PID controller in speed control of DC motor. Microsystem Technologies, 24, 4997–5006. https://doi.org/10.1007/s00542-018-3920-4
• Alavi, M., and Henderson, J.C. (1981). An evolutionary strategy for implementing a decision support system. Management science, 27(11), 1309-1323. https://doi.org/10.1287/mnsc.27.11.1309
• Ali, E.S. (2015). Speed control of DC series motor supplied by photovoltaic system via firefly algorithm. Neural Computing and Applications, 26, 1321–1332 https://doi.org/10.1007/s00521-014 1796-5
• Al-Qunaieer, F.S., Tizhoosh, H.R., and Rahnamayan, S. (2010). `Opposition based computing_A survey,' The 2010 International Joint Conference on Neural Networks (IJCNN), Barcelona, Spain, 2010, 1-7. https://doi.org/10.1109/IJCNN.2010.5596906
• Arini, F.Y., Chiewchanwattana, S., Soomlek, C., Sunat, K. (2022). Joint Opposite Selection (JOS): A premiere joint of selective leading opposition and dynamic opposite enhanced Harris’ hawks optimization for solving single-objective problems. Expert Systems with Applications, 188, 116001. https://doi.org/10.1016/j.eswa.2021.116001
• Arini, F.Y., Sunat, K. and Soomlek, C. (2022). Golden jackal optimization with joint opposite selection: An enhanced nature-inspired optimization algorithm for solving optimization problems. IEEE Access, 10, 128800–128823. https://doi.org/10.1109/ACCESS.2022.3227510
• Awad, N.H., Ali, M.Z., Suganthan, P. N., Liang, J.J. and Qu, B.Y. (2016). Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained real parameter numerical optimization, Nanyang Technological University., Singapore, Tech. Rep., 2016. [Online]. Available: https://www3.ntu.edu.sg/ home/epnsugan/index_les/CEC2017/CEC2017.htm
• Ayinla, S.L., Amosa, T.I., Ibrahim, O., Rahman, M.S., Bahashwan, A.A., Mostafa, M.G., Yusuf, A.O. (2024). Optimal control of DC motor using leader-based Harris Hawks optimization algorithm. Franklin open, 6, 100058. https://doi.org/10.1016/j.fraope.2023.100058
• Bhatt, R., Parmar, G., Gupta, R., Sikander, A. (2019). Application of stochastic fractal search in approximation and control of LTI systems. Microsystem Technologies, 25, 105–114. https://doi.org/10.1007/s00542-018-3939-6
• Cao, B., Zhao, J., Liu, X., Arabas, J., Tanveer, M., Singh, A. K., Lv, Z. (2022). Multiobjective evolution of the explainable fuzzy rough neural network with gene expression programming. IEEE Transactions on Fuzzy Systems, 30(10), 4190-4200. https://doi.org/10,1109/TFUZZ.2022.3141761
• Chen, H., Qiao, H., Xu, L., Feng, Q., Cai, K. (2019). A fuzzy optimization strategy for the implementation of RBF LSSVR model in vis–NIR analysis of pomelo maturity. IEEE Transactions on Industrial Informatics, 15(11), 5971-5979. https://doi.org/10.1109/TII.2019.2933582
• Črepinšek, M., Liu, S.H., Mernik, M. (2013). Exploration and exploitation in evolutionary algorithms: A survey. ACM computing surveys, 45(3), 1-33. https://doi.org/10.1145/2480741.24807
• Çelik, E., Öztürk, N. (2018). First application of symbiotic organisms search algorithm to off-line optimization of PI parameters for DSP based DC motor drives. Neural Computing and Applications. 30, 1689–1699. https://doi.org/10.1007/s00521-017-3256-5
• Dhargupta, S., Ghosh, M., Mirjalili, S., Sarkar, R. (2020). Selective opposition based grey wolf optimization. Expert Systems with Applications, 151, 113389. https://doi. org/10.1016/j.eswa.2020.113389
• Dorigo, M., Stützle, T. (2003). The Ant Colony Optimization Metaheuristic: Algorithms, Applications, and Advances. In: Handbook of Metaheuristics, Glover, F., Kochenberger, G.A. (eds). International Series in Operations Research and Management Science, Springer, Boston, MA. https://doi.org/10.1007/0-306-48056-5_9
• Ekinci, S., D. Izci and B. Hekimoğlu, "PID Speed Control of DC Motor Using Harris Hawks Optimization Algorithm," 2020 International Conference on Electrical, Communication, and Computer Engineering (ICECCE), Istanbul, Turkey, 2020, pp. 1-6, doi: 10.1109/ICECCE49384.2020.9179308.
• Ekinci, S., Izci, D., Hekimoğlu, B. (2021). Optimal FOPID speed control of DC motor via opposition-based hybrid manta ray foraging optimization and simulated annealing algorithm. Arabian Journal for Science and Engineering, 46(2), 1395-1409. https://doi.org/10.1007/s13369-020-05050-z
• Ergezer, M., Simon, D., Du, D. (2009, October). Oppositional biogeography-based optimization. 2009 IEEE International Conference on Systems, Man and Cybernetics, San Antonio, TX, USA, 2009, pp. 1009-1014. https://doi.org/10.1109/ICSMC.2009.5346043
• Gonzalez, T.F. (2007). Handbook of Approximation Algorithms and Metaheuristics, CRC Press, Boca Raton, FL, USA. https://doi.org/10.1201/9781420010749
• Griffin, I. (2003). On-line PID Controller Tuning using Genetic Algorithms, Master’s Thesis, Dublin City University, August 22, 2003.
• Gursoy, F., Gunnec, D. (2018) Influence maximization in social networks under Deterministic Linear Threshold Model. Knowledge-Based Systems, 161(2018), 111–123. https://doi.org/10.1016/j.knosys.2018.07.040.
• Hekimoğlu, B. (2019). Optimal tuning of fractional order PID controller for DC motor speed control via chaotic atom search optimization algorithm. IEEE Access, 7, 38100-38114. https://doi.org/10.1109/ACCESS.2019.2905961
• Holland, J.H. (1992) Genetic Algorithms. Scientific American, 267, 66-72.
• http://dx.doi.org/10.1038/scientificamerican0792-66
• Izci, D., Ekinci, S., Zeynelgil, H. L., Hedley, J. (2021). Fractional order PID design based on novel improved slime mould algorithm. Electric Power Components and Systems, 49(9-10), 901-918. https://doi.org/10.1080/15325008.2022.2049650
• Izci, D., Ekinci, S. (2023). Fractional order controller design via gazelle optimizer for efficient speed regulation of micromotors. e-Prime-Advances in Electrical Engineering, Electronics and Energy, 6, 100295. https://doi.org/10.1016/j.prime.2023.100295
• J. Kennedy and R. Eberhart, "Particle swarm optimization," Proceedings of ICNN'95- International Conference on Neural Networks, Perth, WA, Australia, 4, 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
• Lampinen, J., Storn, R. (2004). Differential Evolution. In: New Optimization Techniques in Engineering. Studies in Fuzziness and Soft Computing, Springer, Berlin, Heidelberg. 141, 123-166. https://doi.org/10.1007/978-3-540-39930-8_6
• Li, N., Wang, L., Jiang, Q., Li, X., Wang, B., He, W. (2021). An improved genetic transmission and dynamic-opposite learning strategy for multitasking optimization. IEEE Access, 9, 131789-131805. https://doi.org/10.1109/ACCESS.2021.3114435
• Lin, Y., Song, H., Ke, F., Yan, W., Liu, Z., Cai, F. (2022). Optimal caching scheme in D2D networks with multiple robot helpers. Computer Communications, 181, 132-142. https://doi.org/10.1016/j.comcom.2021.09.027
• Liu, H., Wu, Z., Li, H., Wang, H., Rahnamayan, S., Deng, C. (2014). Rotation-Based Learning: A Novel Extension of Opposition-Based Learning. In: Pham, D.N., Park, S.B. (eds) Trends in Artificial Intelligence. PRICAI 2014. Lecture Notes in Computer Science (), 8862. Springer, Cham. https://doi.org/10.1007/978-3-319-13560-1_41
• Liu, C., Wu, D., Li, Y., Du, Y. (2021). Large-scale pavement roughness measurements with vehicle crowdsourced data using semi-supervised learning. Transportation Research Part C: Emerging Technologies, 125, 103048. https://doi.org/10.1016/j.comcom.2021.09.027
• Mahdavi, S., Rahnamayan, S., Deb, K. (2018). Opposition based learning: A literature review. Swarm and evolutionary computation, 39, 1-23. https://doi.org/10.1016/j.swevo.2017.09.010
• Meng, F., Pang, A., Dong, X., Han, C. Sha, X. (2018). H∞ optimal performance design of an unstable plant under bode integral constraint. Complexity, 2018 (2018) 1–10. https://doi.org/10.1155/2018/4942906
• Meng, F., Wang, D., Yang, P., Xie, G. (2019). Application of sum of squares method in nonlinear H∞ control for satellite attitude maneuvers. Complexity, 2019(1), 5124108. https://doi.org/10.1155/2019/5124108
• Mirjalili, S., Mirjalili, S.M., Lewis, A. (2014). Grey wolf optimizer. Advances in Engineering Software, 69, 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007
• Morales-Castañeda, B., Zaldivar, D., Cuevas, E., Fausto, F. and Rodríguez, A. (2020). A better balance in metaheuristic algorithms: Does it exist? Swarm and Evolutionary Computation, 54, 100671. https://doi.org/10.1016/j.swevo.2020.100671
• Nasrabadi, M. S., Sharafi, Y., Tayari, M. (2016). A parallel grey wolf optimizer combined with opposition-based learning. 2016 1st Conference on Swarm Intelligence and Evolutionary Computation (CSIEC), Bam, Iran,18-23p. https://doi.org/10.1109/CSIEC.2016.7482116
• Petras, I. (1999). The fractional order controllers: Methods for their synthesis and application, Journal of Electrical Engineering, 50, (9-10), 284-288. https://arxiv.org/pdf/math.OC/0004064
• Podlubny, I. (1999). Fractional-order systems and PIλDδ controllers. IEEE Transaction on Automatic Control, 44(1) 208-213. https://doi.org/10.1109/9.739144
• Potnuru, D., Mary, K.A., Babu, C.S. (2019). Experimental implementation of Flower Pollination Algorithm for speed controller of a BLDC motor. Ain Shams Engineering Journal, 10(2), 287-295. https://doi.org/10.1016/j.asej.2018.07.005
• Pradhan, M., Roy, P.K., Pal, T. (2018). Oppositional based grey wolf optimization algorithm for economic dispatch problem of power system. Ain Shams Engineering Journal, 9(4), 2015-2025. https://doi.org/10.1016/j.asej.2016.08.023
• Qu, S., Han, Y., Wu, Z., Raza, H. (2021). Consensus modeling with asymmetric cost based on data-driven robust optimization. Group Decision and Negotiation, 30(6), 1395-1432. https://doi.org/10.1007/s10726-020-09707-w
• Rahnamayan, S., Tizhoosh, H. R., Salama, M. M. (2008). Opposition versus randomness in soft computing techniques. Applied Soft Computing, 8(2), 906-918. https://doi.org/10.1016/j.asoc.2007.07.010
• Rahnamayan, S., Jesuthasan, J., Bourennani, F., Salehinejad, H. Naterer, G.F. (2014). Computing opposition by involving entire population. IEEE Congress on Evolutionary Computation (CEC), 22 September 2014, Beijing, China, 1800–1807. https://doi.org/10.1109/CEC.2014.6900329
• Rodríguez-Molina, A., Villarreal-Cervantes, M.G., Aldape-Pérez, M. (2017). An adaptive control study for a DC motor using meta-heuristic algorithms. IFAC-PapersOnLine, 50 (1), 13114–13120. https://doi.org/10.1016/j.ifacol.2017.08.2164
• Sarma, H., Bardalai, A. (2024). Improvisation of artificial hummingbird algorithm through incorporation of chaos theory in intelligent optimization of fractional order PID controller tuning. International Journal of Information Technology, 2024. https://doi.org/10.1007/s41870-024-01791-4
• Sebald, A.V. and Fogel, L. J. (1994). Evolutionary Programming. Proceedings of the Third Annual Conference. 24-26 February 1994, San Diego, CA, USA. 384p. https://doi.org/10.1142/2401
• Tepljakov, A. (2017). FOMCON: fractional-order modeling and control toolbox. In: Fractional-order Modeling and Control of Dynamic Systems. Springer Theses, Springer International Publishing AG, Cham, ISBN: 978-3-319-52949-3. https://doi.org/10.1007/978-3-319-52950-9_6
• Tizhoosh, H.R. (2005, November). Opposition-based learning: A new scheme for machine intelligence. In International conference on computational intelligence for modelling, control and automation and international conference on intelligent agents, web technologies and internet commerce (CIMCA-IAWTIC'06), 28-30 November 2005, Vienna, Austria. https://doi.org/10.1109/CIMCA.2005.1631345
• GitHub, (2024) https://github.com/FlorentinaJOS/JOS_in_Optimization/releases/tag/v1.1.1, Accession date: 5 September 2024.
• Wang, N., Xu, Q., Fei, R., Wang, L., Shi, C. (2019). Are two opposite points better than one. IEEE Access, 7, 146108-146122. https://doi.org/10.1109/ACCESS.2019.2946089
• Wang, Y., Wang, H., Zhou, B., Fu, H. (2021). Multi-dimensional prediction method based on Bi-LSTMC for ship roll. Ocean Engineering, 242, 110106. https://doi.org/10.1016/j.oceaneng.2021.110106
• Wolpert, D.H., Macready, W.G. (1997). No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1(1), 67-82. https://doi.org/10.1109/4235.585893
• Xu, X., Wang, C., Zhou, P. (2021). GVRP considered oil-gas recovery in refined oil distribution: from an environmental perspective. International Journal of Production Economics, 235, 108078. https://doi.org/10.1016/j.ijpe.2021.108078
• Xu, Q., Wang, L., Wang, N., Hei, X., Zhao, L. (2014). A review of opposition-based learning from 2005 to 2012. Engineering Applications of Artificial Intelligence, 29, 1-12. https://doi.org/10.1016/j.engappai.2013.12.004
• Xu, Y., Yang, Z., Li, X., Kang, H., Yang, X. (2020). Dynamic opposite learning enhanced teaching_learning-based optimization. Knowl.-Based Systems., 188, 104966. https://doi.org/10.1016/j.knosys.2019.104966.
• Xue, D., Zhao, C., Chen, Y.Q. (2006). Fractional Order PID Control of a DCMotor with Elastic Shaft: A Case Study, 2006 American Control Conference, 14-16 June 200, Minneapolis, Minnesota, USA, 3182–3187p. https://doi.org/10.1109/ACC.2006.1657207
• Yang, X.-S., Deb, S., Fong, S. (2014). Metaheuristic algorithms: Optimal balance of intensi_cation and diversi_cation. Applied Mathematics & Information Sciences. 8(3), 977. https://doi.org/10.12785/amis/080306.
• Zhang, S., Luo, Q., Zhou, Y. (2017). Hybrid grey wolf optimizer using elite opposition-based learning strategy and simplex method. International Journal of Computational Intelligence and Applications, 16(02), 1750012. https://doi.org/10.1142/S1469026817500122
• Zhang, Z., Wang, L., Zheng, W., Yin, L., Hu, R., Yang, B. (2022). Endoscope image mosaic based on pyramid ORB. Biomedical Signal Processing and Control, 71, 103261. https://doi.org/10.1016/j.bspc.2021.103261.