Determination of LQR Controller Parameters for Flexible Link Manipulator System Using Metaheuristic Algorithms

Abstract

The presented study provides detailed analysis of the LQR controller design for motion control of a flexible link manipulator system with the optimization of control parameters. The main objective of proposed optimization ensures that the flexible link manipulator system reaches the desired angular position as soon as possible and eliminates tip deflections. The Vibrating Particle System algorithm used for the first time in the adjustment of LQR weight matrices with this study. The efficiency of the proposed approach has been showing by comparing it with well-known optimization algorithms such as Genetic Algorithm and Artificial Bee Colony. Also, multi-objective function is proposed that considers the important parameters of the control response for flexible link manipulator systems in this study. Parameters of optimization algorithms have been determined by searching a wide search space and each algorithm was examined in terms of four different population values in order to reach results for 100 iterations. Furthermore, the configurations that obtained the best control results for optimization algorithms are compared with each other according to the theoretical and experimental studies performed. The article is organized in a manner that presents the required theoretical background and the implementation-related details for each of the optimization algorithms introduced.

Keywords

• Flexible link manipulator
• Linear quadratic regulator
• Genetic algorithm
• Artificial bee colony
• Vibrating particles system algorithm

ESNEK ROBOT KOL SİSTEMİ İÇİN LQR DENETLEYİCİ PARAMETRELERİNİN METASEZGİSEL ALGORİTMALAR KULLANILARAK BELİRLENMESİ

Abstract

Sunulan çalışma, bir esnek robot kol sisteminin hareket kontrolüne yönelik LQR denetleyici tasarımı ile kontrol parametrelerinin optimizasyonu hakkında ayrıntılı analizler sunmaktadır. Optimizasyonun temel amacı esnek robot kol sisteminin istenilen açısal konuma en hızlı şekilde gelmesini sağlamak ve uç sapmalarını ortadan kaldırmaktır. Titreşimli Parçacık Sistemi algoritması ilk kez bu çalışma ile LQR ağırlık matrislerinin ayarlanmasında kullanılmıştır. Önerilen yaklaşımın etkinliği, Genetik Algoritma ve Yapay Arı Kolonisi gibi iyi bilenen optimizasyon algoritmaları ile karşılaştırılarak gösterilmiştir. Ayrıca çalışma kapsamında esnek robotik sistemler için kontrol yanıtının önemli parametrelerini dikkate alan bir çoklu amaç fonksiyonu da önerilmektedir. Optimizasyon algoritmalarına ait parametreler geniş bir arama uzayı taranarak belirlenmiş olup her algoritma dört farklı popülasyon değeri altında incelenerek 100 iterasyon için sonuçlar elde edilmiştir. Optimizasyon algoritmaları ile elde edilen en iyi kontrol sonuçları, esnek robot kol sistemine uygulanarak elde edilen sonuçlar teorik ve deneysel olarak karşılaştırılmıştır. Makale, tanıtılan optimizasyon algoritmalarının her biri için gerekli teorik arka plan ile uygulamaya yönelik ayrıntıları sunacak şekilde düzenlenmiştir.

Keywords

• Esnek robot kol
• Doğrusal kuadratik regülatör
• Genetik algoritma
• Yapay arı kolonisi
• Titreşimli parçacıklar sistemi algoritması

References

1. Abdel-razak, M. H., Ata, A. A., Mohamed, K. T., Haraz, E. H., 2020, “Proportional–integral-derivative controller with inlet derivative filter fine-tuning of a double-pendulum gantry crane system by a multi-objective genetic algorithm.”, Engineering Optimization, Vol. 52, No. 3, pp. 527-548.
2. Basturk, B., 2006, “An artificial bee colony (ABC) algorithm for numeric function optimization”, In IEEE Swarm Intelligence Symposium, Vol. 39, No. 3, pp. 459-471.
3. Bilgic, H. H., Sen, M. A., Kalyoncu, M., 2016, “Tuning of LQR controller for an experimental inverted pendulum system based on The Bees Algorithm”, Journal of Vibroengineering, Vol. 18, No. 6, pp. 3684-3694.
4. Bilgic, H. H., Sen, M. A., Yapici, A., Yavuz, H., Kalyoncu, M., 2021, “Meta-Heuristic Tuning of the LQR Weighting Matrices Using Various Objective Functions on an Experimental Flexible Arm Under the Effects of Disturbance.” Arabian Journal for Science and Engineering, 1-14.
5. Bilgic, H. H., Conker C, Yavuz H., 2021, “Fuzzy logic–based decision support system for selection of optimum input shaping techniques in point-to-point motion systems”, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 235(6), 795- 808.
6. Bilgiç, H. H., Tutumlu, M. S., Conker, Ç., 2021, “Top ve çubuk sistemi için kaskad denetleyici parametrelerinin meta-sezgisel algoritmalarla optimizasyonu.” Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, Vol. 23, No. 67, pp. 157-167.
7. Bingul, Z., Karahan, O., 2018, “Comparison of PID and FOPID controllers tuned by PSO and ABC algorithms for unstable and integrating systems with time delay”, Optimal Control Applications and Methods, Vol. 39, No. 4, pp. 1431-1450.
8. Cao, Q. S., Zhou, J. H., Li, L., Ye, L., 2010, “Vibration control of piezoelectric flexible manipulator based on fuzzy self-tuning PID algorithm”, Journal of Vibration and Shock, Vol. 29, No. 12, pp. 181-186.

9. Conker, Ç., Kilic, A., Mistikoglu, S., Kapucu, S., Yavuz, H., 2014, “An enhanced control technique for the elimination of residual vibrations in flexible-joint manipulators”, Strojniški vestnik-Journal of Mechanical Engineering, 60(9), 592-599.
10. Çınaroğlu, S., Bulut, H., 2018, “K-ortalamalar ve parçacık sürü optimizasyonu tabanlı kümeleme algoritmaları için yeni ilklendirme yaklaşımları”, Journal of the Faculty of Engineering & Architecture of Gazi University, Vol. 33, No. 2, pp. 413 - 424.
11. Dağdeviren, U., Kaymak, B., 2018, “Yapay arı koloni algoritması kullanılarak betonarme istinat duvarlarının optimum maliyet tasarımını etkileyen parametrelerin incelenmesi”, Journal of the Faculty of Engineering & Architecture of Gazi University, Vol. 33, No. 1, pp. 239-253.
12. Fahmy, A. A., Kalyoncu, M., Castellani, M., 2012, “Automatic design of control systems for robot manipulators using the bees algorithm”, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, Vol. 226, No. 4, pp. 497-508.
13. Fathi, H., Vaez, S. H., Zhang, Q., Alavi, A. H., 2021, “A new approach for crack detection in plate structures using an integrated extended finite element and enhanced vibrating particles system optimization methods”, In Structures, Elsevier, Vol. 29, pp. 638-651.
14. He, W., Zhang, S., Ge, S. S., 2012, “Boundary output-feedback stabilization of a Timoshenko beam using disturbance observer”, IEEE Transactions on Industrial Electronics, Vol. 60, No. 11, pp. 5186-5194.
15. Huang, J. W., Lin, J. S., 2008, “Backstepping control design of a single-link flexible robotic manipulator”, IFAC Proceedings Volumes, Vol. 41, No. 2, pp.11775-11780.
16. Jacknoon, A., Abido, M. A., 2017, “Ant Colony based LQR and PID tuned parameters for controlling Inverted Pendulum”, 2017 International Conference on Communication, Control, Computing and Electronics Engineering, IEEE, 1-8.
17. Jans, R., Degraeve, Z., 2007, “Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches”, European journal of operational research, 177(3), 1855-1875.
18. Jnifene, A., 2007, “Active vibration control of flexible structures using delayed position feedback”, Systems & control letters, Vol. 56 No. 3, pp. 215-222.
19. Karaboğa, D., 2017, “Yapay Zeka Optimizasyon Algoritmalari”, Nobel Akademi Yayıncılık. Kaveh, A., Ghazaan, M. I., 2017, “A new meta-heuristic algorithm: vibrating particles system, Scientia Iranica”, Transaction A: Civil Engineering, Vol. 24 No. 2, pp. 551.
20. Kaveh, A., Rahmani, P., Eslamlou, A. D., 2021, “A Multistage Damage Detection Approach Using Graph Theory and Water Strider Algorithm”, Iranian Journal of Science and Technology, Transactions of Civil Engineering, 1-22.
21. Lahdhiri, T., Elmaraghy, H. A., 1999, “Design of an optimal feedback linearizing‐based controller for an experimental flexible‐joint robot manipulator”, Optimal Control Applications and Methods, Vol. 20 No. 4, pp. 165-182.
22. Mansour, T., Konno, A., Uchiyama, M., 2008, “Modified PID control of a single-link flexible robot.”, Advanced Robotics, Vol. 22 No. 4, pp. 433-449.
23. Mirshekaran, M., Piltan, F., Esmaeili, Z., Khajeaian, T., Kazeminasab, M., 2013, “Design sliding mode modified fuzzy linear controller with application to flexible robot manipulator”, International Journal of Modern Education and Computer Science, 5(10), 53.
24. Oliveira, M., 2005, “Modern heuristics review for PID control optimization: a teaching experiment”, In 2005 international conference on control and automation. IEEE, Vol. 2, pp. 828-833 ÖNEN, Ü., Cakan, A., Ilhan, I., 2019, “Performance comparison of optimization algorithms in LQR controller design for a nonlinear system”, Turkish Journal of Electrical Engineering & Computer Sciences, Vol. 27 No. 3, pp. 1938-1953.
25. Pieper, J. K., 1998, “Optimal control of a flexible manipulator and controller order reduction”, Optimal Control Applications and Methods, Vol. 19 No. 5, pp. 331-343.
26. Quanser Inc., 2011, Rotary Flexible Link Module Datasheets, www.quanser.com Sen, M. A., Kalyoncu, M., 2016, “Optimal tuning of a LQR controller for an inverted pendulum using the bees algorithm”, Journal of Automation and Control Engineering, Vol. 4 No.5, pp. 384-387.
27. Sen, M. A., Kalyoncu, M., 2020, “Grey Wolf Optimizer Based Tuning of a Hybrid LQR-PID Controller for Foot Trajectory Control of a Quadruped Robot”, Journal of the Faculty of Engineering & Architecture of Gazi University, Vol. 32 No. 2, pp. 674-684.
28. Siddique, M. N. H., Tokhi, M. O., 2002, “GA-based neuro-fuzzy controller for flexible-link manipülatör”, In Proceedings of the International Conference on Control Applications, IEEE, 1, 471-476.
29. Sooraksa, P., Chen, G., 1998, “Mathematical modeling and fuzzy control of a flexible-link robot arm”, Mathematical and Computer Modelling, Vol. 27 No. 6, pp. 73-93.
30. Talebi, H. A., Khorasani, K., Patel, R. V., 1998, “Neural network based control schemes for flexible-link manipulators: simulations and experiments”, Neural networks, Vol. 11 No. 7-8, pp. 1357-1377.
31. Tinkir, M., Önen, Ü., Kalyoncu, M., 2010, “Modelling of neurofuzzy control of a flexible link”, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, Vol. 224 No. 5, pp. 529-543.
32. Wilson, D. G., Robinett, R. D., Parker, G. G., Starr, G. P., 2002, “Augmented sliding mode control for flexible link manipulators”, Journal of Intelligent and Robotic Systems, Vol. 34, No.4, pp. 415-430.
33. Wongsathan, C., Sirima, C., 2009, “Application of GA to design LQR controller for an inverted pendulum system”, In 2008 IEEE International Conference on Robotics and Biomimetics, IEEE, 951-954.