PID-Type Iterative Learning Control for Output Tracking Gearing Transmission Systems

(1) * Luong Thuy Anh Mail (Vietnam - Korea Vocational College of Technology, Viet Nam)
(2) Tran Thi Thanh Nga Mail (Thai Nguyen University of Technology, Viet Nam)
(3) Vu Van Hoc Mail (Thai Nguyen University of Technology, Viet Nam)
*corresponding author

Abstract


In this paper, we propose a modified version of the Proportional Integral Derivative (PID)-type iterative learning algorithm. It is very simple to implement on a digital control device for tracking control a continuous-time system. Matlab software is used to model and simulate control algorithms. The simulative application of it to control a gearing transmission system, such that its output response follows the desired trajectory, is then carried out computationally. Obtained studying results proves that this proposed iterative learning algorithm has provided a good output tracking behavior as expected and which is robust in the sense of reducing external disturbance effects.

Keywords


Machine Learning Control; Controller; Iterative Learning Algorithm; PID

   

DOI

https://doi.org/10.31763/ijrcs.v1i3.395
      

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References


[1] J. Wang, R. Li, and X. Peng, “Survey of nonlinear vibration of gear transmission systems,” Appl. Mech. Rev, vol. 56, no. 3, pp. 309-329, 2003. https://doi.org/10.1115/1.1555660

[2] N. T. Dzung, D. P. Nam, and N. Q. Dich, "Modelling and Control Design of a V-Shaped Thermal Actuator System via Partial Derivative Equation Approach," Proceedings of the 5th International Conference on Mechatronics and Robotics Engineering 2019, pp. 78-82. https://doi.org/10.1145/3314493.3314516

[3] K. (Stevanović) Hedrihand V. Nikolić-Stanojević, “A Model of Gear Transmission: Fractional Order System Dynamics,” Mathematical Problems in Engineering, vol. 2010, p. 972873, 2010. https://doi.org/10.1155/2010/972873

[4] Z. Xiao, J. Cao, and Y. Yu, “Mathematical Modeling and Dynamic Analysis of Planetary Gears System with Time-Varying Parameters,” Mathematical Problems in Engineering, vol. 2020, p. 3185624, 2020. https://doi.org/10.1155/2020/3185624

[5] E. Brassitos and N. Jalili, “Dynamic Model Development and Characterization of Gear Bearing Transmission Systems: Theory and Experiments,” IEEE/ASME Transactions on Mechatronics, vol. 24, no. 4, pp. 1651 – 1661, Aug. 2019. https://doi.org/10.1109/TMECH.2019.2916333

[6] A. Zhang, J. Wei, L. Shi, D. Qin , and T. C. Lim, “Modeling and dynamic response of parallel shaft gear transmission in non-inertial system,” Nonlinear Dynamics, vol. 98, pp. 997–1017, 2019. https://doi.org/10.1007/s11071-019-05241-w

[7] A. Zilouchian and M. Jamshidi (Eds.), Intelligent control systems using soft computing methodologies, CRC Press, 2001. https://doi.org/10.1201/9781420058147

[8] P. J. Antsaklis, “Intelligent control,” in Wiley Encyclopedia of Electrical and Electronics Engineering, vol. 10, pp. 493-503, 1999. https://doi.org/10.1002/047134608X.W1019

[9] M. Uchiyama, “Formation of high speed motion pattern of mechanical arm by trial,” Trans. of Society of Instrumentation and Control Engineer, vol. 19, no. 5, pp. 706-712, 1978. https://doi.org/10.9746/sicetr1965.14.706

[10] S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering operation dynamic systems by learning: A new control theory for servomechanism or mechatronic systems,” Proceedings of 23th Conference on Decision and Control, Nevada 1984, pp. 1064-1069. https://doi.org/10.1109/CDC.1984.272176

[11] S. Arimoto, “Mathematical theory of learning control with application to robot control,” Proceedings of 4th Workshop on applications of adaptive systems, Connecticut, 1985, pp. 379-388. https://doi.org/10.1007/978-1-4757-1895-9_27

[12] K. L. Moore, M. Dahleh, and S. P. Bhattacharyya, “Iterative learning for trajectory control,” Proceedings of Conference on Decision and Control, Florida, 1989, pp. 860-865. https://doi.org/10.1109/CDC.1989.70243

[13] K. L. Moore, Iterative learning control for deterministic systems, London Springer Verlag, 1993. https://doi.org/10.1007/978-1-4471-1912-8

[14] J. X. Xu and Y. Tan, Linear and nonlinear iterative learning control, Springer Verlag, 2003. https://doi.org/10.1007/3-540-44845-4

[15] M. Norrloef, Iterative learning control: Analysis, Design and Experiment, Diss., No.653, Linkoepings University, Sweden 2000. https://www.researchgate.net/publication/2866895

[16] V. Vita, A. Vitas, and G. E. Chatzarakis, “Design, implementation and evaluation of an optimal iterative learning control algorithm,” WSEAS Trans. on Circuits and Systems, vol. 2, no. 10, pp. 39-48, 2011. http://www.wseas.us/e-library/transactions/circuits/2011/52-094.pdf

[17] S. Tian and X. Zhou, “State tracking algorithm for a class of singular ILC systems,” J. Syst. Sci. Math. Sci., vol. 32, no. 6, pp. 731-738, 2012. http://sysmath.com/jweb_xtkxysx/EN/abstract/abstract11902.shtml

[18] Cha’o-Kuang Chen and Kai-Sheng Li, “Iterative learning control for robotic contouring,” 2009 IEEE International Conference on Control and Automation, IEEE, 2009, pp. 1092-1097. https://doi.org/10.1109/ICCA.2009.5410311

[19] S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering operation of robots by learning,” J. Robot. Syst., vol. 1, no. 2, pp. 123–140, 1984. https://doi.org/10.1002/rob.4620010203

[20] D. Kim and S. Kim, “An iterative learning control method with application for CNC machine tools,” IEEE Trans. Ind. Appl., vol. 32, pp. 66–72, 1996. https://doi.org/10.1109/28.485814

[21] D. D. Roover and O. H. Bosgra,Synthesis of robust multivariable iterative learning controllers with application to a wafer stage motion system,” Int. J. Control, vol. 73, pp. 968–979, 2000. https://doi.org/10.1080/002071700405923

[22] H. Havlicsek and A. Alleyne, “Nonlinear control of an electrohydraulic injection molding machine via iterative adaptive learning,” IEEE/ASME Trans. Mechatron., vol. 4, pp. 312–323, 1999. https://doi.org/10.1109/3516.789689

[23] A. D. Barton, P. L. Lewin, and D. J. Brown,Practical implementation of a real-time iterative learning position controller,” Int. J. Control, vol. 73, pp. 992–999, 2000. https://doi.org/10.1080/002071700405941

[24] D. R. Yang, K. S. Lee, H. J. Ahn, and J. H. Lee, "Experimental application of a quadratic optimal iterative learning control method for control of wafer temperature uniformity in rapid thermal processing,” IEEE Trans. Semicond. Manuf. 2003, 16, 36–44. https://doi.org/10.1109/TSM.2002.807740

[25] S. Kawamura and N. Sakagami, “Analysis on dynamics of underwater robot manipulators basing on iterative learning control and time-scale transformation,” in Proc. IEEE Int. Conf. Robot. Automat., 2002, pp. 1088–1094. https://doi.org/10.1109/ROBOT.2002.1014688

[26] C. V. Giessen, Q. Zou, and S. Devasia, “Inversion-based precision positioning of inertial reaction devices” in Proc. Amer. Contr. Conf., 2004, pp. 3788–3793. https://doi.org/10.23919/ACC.2004.1384502

[27] Y. Chen, C. Wen, J.-X. Xu, and M. Sun, “High-order iterative learning identification of projectile’s aerodynamic drag coefficient curve from radar measured velocity data,” IEEE Tran. Contr. Syst. Technol., vol. 6, no. 4, pp. 563–570, 1998. https://doi.org/10.1109/87.701354

[28] C.T. Abdallah, V.S. Soulian, and E. Schamiloglu, “Toward “smart tubes” using iterative learning control,” IEEE Trans. Plasma Sci., vol. 26, no. 3, pp. 905–911, 1998. https://doi.org/10.1109/27.700869

[29] S. Tian, Q. Liu, X. Dai, and J. Zhang, “A PD type iterative learning control algorithm for singular discrete systems,” Advances in Difference Equations, 2016, vol. 321 Springer. https://doi.org/10.1186/s13662-016-1047-4

[30] D. H. Owen, N. Amann, and E. Roger, “Iterative learning control, an overview of recent algorithm,” Applied Mathematics and Computer Science, vol. 5, no. 3, pp. 425-438, 1995. https://www.sciencedirect.com/topics/engineering/iterative-learning-control

[31] D. H. Owens and J. Hatonen, “Iterative learning control: The state of the art,” IFACT Workshop on Periodic Control Systems, 2004, pp. 51-62. https://doi.org/10.1016/S1474-6670(17)31443-X

[32] L. Zhou, H. Tao, W. Paszke, V. Stojanovic, and H. Yang, “PD-Type Iterative Learning Control for Uncertain Spatially Interconnected Systems,” Mathematics, vol. 8, no. 9, p. 1528, 2020. https://doi.org/10.3390/math8091528

[33] H. F. Tao, W. Paszke, E. Rogers, H. Z. Yang, K. Galkowski, “Iterative learning fault-tolerant control for differential time-delay batch processes in finite frequency domains,” J. Process Control, vol. 56, pp.112–128, 2017. https://doi.org/10.1016/j.jprocont.2016.12.007

[34] B. Sulikowski, K. Gałkowski, A. Kummert, and E. Rogers, “Two-dimensional (2D) systems approach to feedforward/feedback control of a class of spatially interconnected systems,” Int. J. Control, vol. 91, no. 12, pp. 2780–2791, 2018. https://doi.org/10.1080/00207179.2018.1522451

[35] H. F. Tao, W. Paszke, H. Z. Yang, and K. Gałkowski, “Finite frequency range robust iterative learning control of linear discrete system with multiple time-delays,” J. Franklin Inst. vol. 356, no. 5, pp. 2690-2708, 2019. https://doi.org/10.1016/j.jfranklin.2019.01.040

[36] H. L. Xu, Z. P. Lin, X. K. Zhai, H. Y. Feng, and X. F. Chen, “Quadratic stability analysis and robust distributed controllers design for uncertain spatially interconnected systems,” J. Franklin Inst., vol. 355, no. 16, pp. 7924–7961, 2018. https://doi.org/10.1016/j.jfranklin.2018.07.013

[37] W. Paszke, E. Rogers, and M. Boski, “Repetitive process based design of PD-type iterative learning control laws,” In Proceedings of the Mediterranean Conference on Control and Automation, Zadar, Croatia, 19–22 June 2018. 10.1109/MED.2018.8442499

[38] Y. Wu, M. Yang, and J. Zhang, “Open-Closed-Loop Iterative Learning Control with the System Correction Term for the Human Soft Tissue Welding Robot in Medicine,” Mathematical Problems in Engineering, vol. 2020, p. 2458318, 2020. https://doi.org/10.1155/2020/2458318

[39] D. Luo, J. Wang, D. Shen, and M. Fečkan, “Iterative learning control for fractional-order multi-agent systems,” Journal of the Franklin Institute, vol. 356, no. 12, pp. 6328–6351, 2019. https://doi.org/10.1016/j.jfranklin.2019.06.001

[40] Y. Zhang, J. Liu, and X. Ruan, “Iterative learning control for uncertain nonlinear networked control systems with random packet dropout,” International Journal of Robust and Nonlinear Control, vol. 29, no. 11, pp. 6328–6351, 2019. https://doi.org/10.1002/rnc.4568

[41] A. C. Antoulas, B. Zhu, Q. Zhang, B. York, B. W. O’Malley, and C. C. Dacso, “A novel mathematical method for disclosing oscillations in gene transcription: A comparative study,” In: PloS one, vol. 13, no. 9, 2018. https://doi.org/10.1371/journal.pone.0198503

[42] L. Blanken and T. Oomen, “Multivariable iterative learning control design
procedures: From Decentralized to Centralized, Illustrated on an Industrial printer,”
IEEE Transactions on Control Systems Technology, vol. 28, no. 4, pp. 1534-1541, 2019. https://doi.org/10.1109/TCST.2019.2903021

[43] D. Shen and X. Li, Iterative Learning Control for Systems with Iteration-Varying Trial Lengths, Springer, 2019. https://www.springer.com/gp/book/9789811361357

[44] D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A Survey of Iterative Learning Control: A learning-based method for high-performance tracking control,” IEEE control systems magazine, vol. 26, no. 3, pp. 96-114, 2006. https://doi.org/10.1109/MCS.2006.1636313

[45] L. Tao, D. Tian, S. Tang, X. Wu, and B. Li, “Dynamical Modelling and Simulation of Spur Gears with Flank Pitch Error,” Chinese Journal of Mechanical Engineering, In Review, 2021. https://doi.org/10.21203/rs.3.rs-534359/v1


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