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Iterative Learning Control for Fractional Order Linear Systems with Time Delay Based on Frequency Analysis

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Abstract

To overcome the deficiencies of time delay in the repetitive control of fractional-order linear systems, PDα-type iterative learning control (ILC) law and P & convolution-type ILC law are designed for input and state time delay, respectively. Convergence conditions are derived in frequency domain via contraction mapping principle. Besides, the convergence frequency domain of proposed feedback controllers is obtained over a finite frequency range to design the controllers effectively. Then, the effectiveness of the proposed theoretical schemes is demonstrated using two numerical examples. The influence of time delay is eliminated, and output trajectory convergence to the desired one is guaranteed. Moreover, the Nyquist diagram of transfer function G(s) and time delay variation are analyzed in frequency domain to reveal the influence of convergence on the system.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Yugang Wang, Fengyu Zhou, Lei Yin & Fang Wan

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  1. Yugang Wang
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  2. Fengyu Zhou
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Corresponding author

Correspondence to Fengyu Zhou.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommanded by Editor PooGyeon Park. This work was supported by the National Key R & D Program of China (Grant no. 2017YFB1302400), National Natural Science Foundation of China (Grant no. 61773242, No.61803227 and No.61375084), Major Agricultural Applied Technological Innovation Projects of Shandong Province (SD2019NJ014). Shandong Natural Science Foundation (ZR2019MF064), Intelligent Robot and System Innovation Center Foundation (2019IRS19). In addition, the authors would like to thank the Associate Editor and the anonymous reviewers who contributed their valuable comments to this paper.

Yugang Wang is currently a Ph.D. candidate at the School of Control Science and Engineering at Shandong University, Jinan, China. He received a B.E. degree in mathematics from China University of Mine and Technology, XuZhou, China, in 2014. His research interests include control theory, fractional order calculus, iterative learning control and robotics.

Fengyu Zhou received a Ph.D. degree in electrical engineering from Tianjin University, Tianjin, China, in 2008. He is currently a professor of the School of Control Science and Engineering at Shandong University, Jinan, China. His research interests include service robotics and automation, control theory and control engineering.

Lei Yin is currently a Ph.D. candidate in the school of control science and engineering at Shandong University, Jinan, China. He received his M.S. degree in Control Engineering from the School of Control Science and Engineering at Shandong University, Jinan, China, in 2010. His research interests include cloud robot, cloud computing and control theory.

Fang Wan is currently a Ph.D. candidate in the School of Control Science and Engineering at Shandong University, Jinan, China. He received his B.E. degree in control engineering from the School of Control Science and Engineering at Shandong University, Jinan, China, in 2016. His research interests include mobile robot indoor navigation and control theory.

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Wang, Y., Zhou, F., Yin, L. et al. Iterative Learning Control for Fractional Order Linear Systems with Time Delay Based on Frequency Analysis. Int. J. Control Autom. Syst. 19, 1588–1596 (2021). https://doi.org/10.1007/s12555-019-0295-y

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