Cascade Proportional Derivative Controller For A Flexible Link Robot Manipulator Using The Bees Algorithm

Abstract

In this study, a flexible robot arm model and the design of its controller are introduced. The robot arm consists of a single flexible link. It is desired to control the circular position of the robot arm and the vibration of the tip point. Cascade proportional derivative controller was used to control the position and reduce the tip vibration. Controller gains were found using the bees algorithm. The weighted function of system responses such as settling time, maximum overshoot, steady-state error is used as a performance criterion while searching for the best parameters. In addition, controller gains were obtained with the genetic algorithm to evaluate the working performance of the bees algorithm. It has been observed that the Cascade PD controller, whose gains are optimized by the bees algorithm, successfully controls the flexible robot arm system and reduces the vibration of the tip point.

Keywords

• The Bees Algorithm
• Flexible Link
• Cascade PID

References

1. [1] S. Xu, G. Sun, and Z. Li, "Finite frequency vibration suppression for space flexible structures in tip position control," International Journal of Control, Automation, and Systems, vol. 16, no. 3, pp. 1021-1029, 2018.
2. [2] B. Altıner, A. Delibaşı, and B. Erol, "Modeling and control of flexible link manipulators for unmodeled dynamics effect," Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 233, no. 3, pp. 245-263, 2019.
3. [3] X. Lang, C. J. Damaren, and X. Cao, "Hybrid frequency domain control for large flexible structures," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 233, no. 11, pp. 4272-4283, 2019.
4. [4] Bhaskarwar T, Hawari HF, Nor NBM, Chile RH, Waghmare D, Aole S, “Sliding Mode Controller with Generalized Extended State Observer for Single Link Flexible Manipulator,” Applied Sciences, vol 12, no 6, 3079, 2022.
5. [5] Zhou X, Wang H, Tian Y, “Adaptive boundary iterative learning vibration control using disturbance observers for a rigid–flexible manipulator system with distributed disturbances and input constraints,” Journal of Vibration and Control, vol 28 no.11-12, pp. 1324-1340, 2022.
6. [6] M.-T. Ho and Y.-W. Tu, "PID controller design for a flexible-link manipulator," in Proceedings of the 44th IEEE Conference on Decision and Control, 2005: IEEE, pp. 6841-6846.  
7. [7] A. Izadbakhsh and S. Khorashadizadeh, "Single-loop PID controller design for electrical flexible-joint robots," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 42, no. 2, pp. 1-12, 2020.
8. [8] S. K. Pradhan and B. Subudhi, "Position control of a flexible manipulator using a new nonlinear self-tuning PID controller," IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 1, pp. 136-149, 2018.

9. [9] P. Sarkhel, N. Banerjee, and N. B. Hui, "Fuzzy logic-based tuning of PID controller to control flexible manipulators," SN Applied Sciences, vol. 2, pp. 1-11, 2020.
10. [10] A. Urbaś, J. Kłosiński, and K. Augustynek, "The influence of the PID controller settings on the motion of a truck-mounted crane with a flexible boom and friction in joints," Control Engineering Practice, vol. 103, p. 104610, 2020.
11. [11] H. Açikgöz, Ö. F. Keçecioğlu, M. Güneş, And M. Şekkeli, "Öz Ayarlamalı Bulanık-Pid Denetleyici İle Hidrolik Türbinin Benzetim Çalışması," Academic Platform Journal Of Engineering And Science, Vol. 3, No. 1, Pp. 7-15, 2015.
12. [12] R. Aisuwarya and Y. Hidayati, "Implementation of ziegler-nichols PID tuning method on stabilizing temperature of hot-water dispenser," in 2019 16th International Conference on Quality in Research (QIR): International Symposium on Electrical and Computer Engineering, 2019: IEEE, pp. 1-5.
13. [13] K. S. Chia, "Ziegler-nichols based proportional-integral-derivative controller for a line tracking robot," Indonesian journal of electrical engineering and computer science, vol. 9, no. 1, pp. 221-226, 2018.
14. [14] J. Fišer and P. Zítek, "PID controller tuning via dominant pole placement in comparison with ziegler-nichols tuning," IFAC-PapersOnLine, vol. 52, no. 18, pp. 43-48, 2019.
15. [15] N. I. M. Azmi, N. M. Yahya, H. J. Fu, and W. A. W. Yusoff, "Optimization of the PID-PD parameters of the overhead crane control system by using PSO algorithm," in MATEC Web of Conferences, 2019, vol. 255: EDP Sciences, p. 04001.
16. [16] M. A. Ibrahim, A. K. Mahmood, and N. S. Sultan, "Optimal PID controller of a brushless DC motor using genetic algorithm," Int J Pow Elec & Dri Syst ISSN, vol. 2088, no. 8694, p. 8694, 2019.
17. [17] H. Suwoyo, Y. Tian, C. Deng, and A. Adriansyah, "Improving a wall-following robot performance with a PID-genetic algorithm controller," in 2018 5th International Conference on Electrical Engineering, Computer Science and Informatics (EECSI), 2018: IEEE, pp. 314-318.
18. [18] Z. Xiang, D. Ji, H. Zhang, H. Wu, and Y. Li, "A simple PID-based strategy for particle swarm optimization algorithm," Information Sciences, vol. 502, pp. 558-574, 2019.
19. [19] M. Arif Şen, M. Tinkir, and M. Kalyoncu, "Optimisation of a PID controller for a two-floor structure under earthquake excitation based on the bees algorithm," Journal of Low Frequency Noise, Vibration and Active Control, vol. 37, no. 1, pp. 107-127, 2018.
20. [20] E. A. Esleman, G. Önal, and M. Kalyoncu, "Optimal PID and fuzzy logic based position controller design of an overhead crane using the Bees Algorithm," SN Applied Sciences, vol. 3, no. 10, pp. 1-13, 2021.
21. [21] C. Conker, H. Yavuz, and H. H. Bilgic, "A review of command shaping techniques for elimination of residual vibrations in flexible-joint manipulators," Journal of Vibroengineering, vol. 18, no. 5, pp. 2947-2958, 2016.
22. [22] D. K. Thomsen, R. Søe-Knudsen, O. Balling, and X. Zhang, "Vibration control of industrial robot arms by multi-mode time-varying input shaping," Mechanism and Machine Theory, vol. 155, p. 104072, 2021.
23. [23] T. Mansour, A. Konno, and M. Uchiyama, "Modified PID control of a single-link flexible robot," Advanced Robotics, vol. 22, no. 4, pp. 433-449, 2008.
24. [24] D. Pham, E. Koç, M. Kalyoncu, and M. Tınkır, "Hierarchical PID controller design for a flexible link robot manipulator using The Bees Algorithm," Methods (eg. genetic algorithm), vol. 25, p. 32, 2008.
25. [25] H. H. Bilgic, M. A. Sen, A. Yapici, H. Yavuz, and M. Kalyoncu, "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, pp. 1-14, 2021.
26. [26] Ü. Önen, A. Çakan, and I. Ilhan, "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, 2019.
27. [27] C. Sun, H. Gao, W. He, and Y. Yu, "Fuzzy neural network control of a flexible robotic manipulator using assumed mode method," IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 11, pp. 5214-5227, 2018.
28. [28] İ. H. Akyüz, Z. Bingül, And S. Kizir, "Cascade fuzzy logic control of a single-link flexible-joint manipulator," Turkish Journal of Electrical Engineering & Computer Sciences, vol. 20, no. 5, pp. 713-726, 2012.
29. [29] I. Tijani, R. Akmeliawati, A. A. Muthalif, and A. Legowo, "Optimization of PID controller for Flexible link system using a Pareto-based Multi-Objective differential (PMODE) evolution," in 2011 4th International Conference on Mechatronics (ICOM), 2011: IEEE, pp. 1-6.
30. [30] W. Bolton, Instrumentation and control systems. Newnes, 2021.   [31] Y. Hu, C. Chen, H. Wu, and C. Song, "Study on structural optimization design and cascade PID control of maglev actuator for active vibration isolation system," Journal of Vibration and Control, vol. 24, no. 10, pp. 1829-1847, 2018.
31. [32] J. Liu, Y. Li, Y. Zhang, Q. Gao, and B. Zuo, "Dynamics and control of a parallel mechanism for active vibration isolation in space station," Nonlinear Dynamics, vol. 76, no. 3, pp. 1737-1751, 2014.
32. [33] B.-J. Yang, A. Calise, J. Craig, and M. Whorton, "Adaptive control for a microgravity vibration isolation system," in AIAA guidance, navigation, and control conference and exhibit, 2005, p. 6071.
33. [34] H. John, "Holland. genetic algorithms," Scientific american, vol. 267, no. 1, pp. 44-50, 1992.
34. [35] P. J. Angeline, "Evolution revolution: An introduction to the special track on genetic and evolutionary programming," IEEE Intelligent Systems, vol. 10, no. 03, pp. 6-10, 1995.
35. [36] A. Sadık, A. Kahraman, And R. Şahin, "Determination Of Optimum Pinch Point Temperature Difference Depending on Heat Source Temperature and Organic Fluid with Genetic Algorithm," Academic Platform Journal of Engineering and Smart Systems, vol. 10, no. 1, pp. 19-29..
36. [37] J. Zhang, J. Zhuang, and H. Du, "Self-organizing genetic algorithm based tuning of PID controllers," Information Sciences, vol. 179, no. 7, pp. 1007-1018, 2009.
37. [38] A. Mirzal, S. Yoshii, and M. Furukawa, "PID parameters optimization by using genetic algorithm," arXiv preprint arXiv:1204.0885, 2012.
38. [39] D. Karaboga, "An idea based on honey bee swarm for numerical optimization," Technical report-tr06, Erciyes university, engineering faculty, computer …, 2005.
39. [40] D. Karaboga and B. Akay, "A comparative study of artificial bee colony algorithm," Applied mathematics and computation, vol. 214, no. 1, pp. 108-132, 2009.
40. [41] D. Pham, A. Ghanbarzadeh, E. Koc, and S. Otri, "Application of the bees algorithm to the training of radial basis function networks for control chart pattern recognition," in Proceedings of 5th CIRP international seminar on intelligent computation in manufacturing engineering (CIRP ICME’06), Ischia, Italy, 2006, pp. 711-716.
41. [42] D. Pham, A. J. Soroka, A. Ghanbarzadeh, E. Koc, S. Otri, and M. Packianather, "Optimising neural networks for identification of wood defects using the bees algorithm," in 2006 4th IEEE International Conference on Industrial Informatics, 2006: IEEE, pp. 1346-1351.
42. [43] D. T. Pham, A. Ghanbarzadeh, E. Koç, S. Otri, S. Rahim, and M. Zaidi, "The bees algorithm—a novel tool for complex optimisation problems," in Intelligent production machines and systems: Elsevier, 2006, pp. 454-459.
43. [44] V. Bakırcıoğlu, M. Şen, and M. Kalyoncu, "Dört Ayaklı Robotun Bir Bacağı İçin PID Kontrolcü Tasarımı ve Arı Algoritması Kullanarak Optimizasyonu," Uluslararası katılımlı 17. Makina Teorisi Sempozyumu (UMTS 2015), pp. 661-665.
44. [45] D. Pham and M. Kalyoncu, "Optimisation of a fuzzy logic controller for a flexible single-link robot arm using the Bees Algorithm," in 2009 7th IEEE International Conference on Industrial Informatics, 2009: IEEE, pp. 475-480.
45. [46] M. A. Şen, V. Bakırcıoğlu, and M. Kalyoncu, "Performances comparison of the bees algorithm and genetic algorithm for PID controller tuning," in Proceedings of the 5th International Conference on Mechatronics and Control Engineering, 2016, pp. 126-130.
46. [47] M. A. Sen and M. Kalyoncu, "Optimisation of a PID controller for an inverted pendulum using The Bees Algorithm," in Applied Mechanics and Materials, 2015, vol. 789: Trans Tech Publ, pp. 1039-1044.
47. [48] Baronti, L., Castellani, M., & Pham, D. T. “An analysis of the search mechanisms of the bees algorithm,” in Swarm and Evolutionary Computation, 2020, vol. 59, 100746.
48. [49] K. Ogata, “Modern Control Engineering,” in Prentice Hall, Vol. 5, 2010.