Frequency Domain based Conditions for Determining Convergence Learning Parameters in Linear Iterative Learning Control
Main Article Content
Abstract
This article proposes four sufficient conditions to determine the convergent learning parameters in iterative learning control of linear batch processes. These conditions are established in frequency domain with transfer functions of elementary linear learning functions of P-, D-, PD- and PID-Type, instead of their state space models as usual. Hence, they can overcome all conservative difficulties occurred by using conditions created in time domain. To obtain these conditions in frequency domain, first an overall sufficient condition belonging to time domain is created, and then realized it particularity in frequency domain for four different linear learning functions by using their transfer function. The obtained conditions in frequency domain are expressed in algebraic inequality of matrix norm, so they are very convenient in use. To illustrate the applicable ability of proposed conditions in various practical applications some numerical simulations had been carried out in the paper. Obtained simulation results authenticated the advantage of these conditions.
Keywords
ILC, learning function, update law, intelligent control
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
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[4] D.A. Bristow, M. Tharayil, 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, June 2006. https://doi.org/10.1109/MCS.2006.1636313
[5] Y. Wang, F. Gao and F. J. Doyle, Survey on iterative learning control, repetitive control and run to run control, Journal of Process Control, vol 19, no 10 pp.1589-1600, Dec. 2009. https://doi.org/10.1016/j.jprocont.2009.09.006
[6] R. Lee, L. Sun, Z. Wang, M. Tomizuka, Adaptive iterative learning control of robot manipulators for friction compensation, IFAC PapersOnLine, Vol 52 , no 15, pp.175–180, 2019. https://doi.org/10.1016/j.ifacol.2019.11.670
[7] F. Bouakrif, D. Boukhetala and F. Boudjema, Velocity observer-based iterative learning control for robot manipulators, International Journal of Systems Science, vol. 44, no 2, pp. 214-222, 2013.
[8] R. N. Jayawardhana and B.K.Ghosh, Observer based iterative learning controller design for MIMO systems in discrete time, in Annual American Control Conference, Wisconsin Center, Milwaukee, USA, 2018, pp. 6402-6408. https://doi.org/10.23919/ACC.2018.8431853
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[11] T.H. Nguyen, H.N. Nguyen, D.P. Nguyen, Iterative Learning Control, Textbook, Hanoi, Vietnam: Bach Khoa Publishing House, 2021 (in Vietnamese).
[12] D.P. Nguyen, H.N. Nguyen, An intelligent parameter determination approach in iterative learning control, European Journal of Control, Vol. 61, pp. 91-100, Sept. 2021. https://doi.org/10.1016/j.ejcon.2021.06.001