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Observer-based Iterative Learning Control for the Discrete-time Systems with Time Delay and Finite Frequency Domain Specifications

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  • Control Theory and Applications
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Abstract

This paper investigates the problem of the observer-based iterative learning control law for a class of discrete-time linear systems with a single delay. Particularly, the design is composed of a stabilizing feedback controller in the time domain and a PD-type of feedforward controller in the iteration domain that guarantees the monotonic convergence of the resulting control scheme. Furthermore, sufficient conditions for the stability analysis and the design method of the iterative learning control law are given based on the repetitive process stability theory and a version of generalized Kalman-Yakubovich-Popov (KYP) lemma. As the result, the control law design problem is cast into the convex optimization problem over linear matrix inequalities (LMIs) and therefore it is amenable to effective algorithmic solution. Also, it allows designers to impose control performance requirements over specific frequency ranges and obtain the conditions which are dependent on the delay size. Finally, an example is given to verify the effectiveness of the proposed method.

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Authors and Affiliations

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

    Yingjie Gong & Rongni Yang

  2. Institute of Automation, Electronic and Electrical Engineering, University of Zielona Góra, ul. Szafrana 2, 65-516, Zielona Góra, Poland

    Wojciech Paszke

  3. Key Laboratory of Advanced Process Control for Light Industry of Ministry of Education, Jiangnan University, Wuxi, 214122, China

    Hongfeng Tao

Authors
  1. Yingjie Gong
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  2. Rongni Yang
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  3. Wojciech Paszke
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  4. Hongfeng Tao
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Corresponding author

Correspondence to Rongni Yang.

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This work was supported in part by the National Natural Science Foundation of China (61873147), the National Science Centre of Poland (2017/27/B/ST7/01874), the Foundation for Innovative Research Groups of National Natural Science Foundation of China (61821004), the Key Project of National Natural Science Foundation of China (61733010), the Qilu Youth Scholar Programme from Shandong University, and Youth Innovation Group Project of Shandong University (2020QNQT016).

Yingjie Gong received her B.S. degree in mathematics from Shandong Normal University, China in 2019. She is currently pursuing an M.E. degree in the School of Control Science and Engineering at Shandong University, China. Her research interests include iterative learning control and networked control systems.

Rongni Yang received her B.S. degree in mathematics from Shandong University, China in 2006, an M.E. degree and a Ph.D. degree in control theory and control engineering both from Harbin Institute of Technology, China, in 2008 and 2012, respectively. From 2009 to 2011, she was a Research Associate in the Faculty of Advanced Technology, University of South Wales, Pontypridd, U.K. From February 2013 to April 2013, she was a Research Associate in the Department of Mechanical Engineering, The University of Hong Kong. From February 2017 to February 2019, she was a Research Fellow in the School of Computing, Engineering and Mathematics, Western Sydney University, Sydney, Australia. She is currently a Professor in the School of Control Science and Engineering at Shandong University, Jinan, China. Her research interests include networked control systems and multidimensional systems.

Wojciech Paszke received his M.Sc. and Ph.D. degrees in electrical engineering from the Technical University of Zielona Góra, in 2000 and 2005, respectively. Between 2008 and 2010 he was affiliated to Eindhoven University of Technology, the Netherlands, where he has been a control systems expert on high precision positioning of electron microscope. Currently, he is affiliated to the Institute of Automation, Electronic and Electrical Engineering at the University of Zielona Góra, Poland. His research interests include multidimensional (nD) systems, repetitive processes, iterative learning control schemes, and convex optimization in robust control problems.

Hongfeng Tao received his Ph.D. degree in control theory and control engineering from the Nanjing University of Aeronautics and Astronautics, China, in 2009. He is currently a Professor with the Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, Jiangnan University, China. His research interests include iterative learning control, fault diagnosis, and fault tolerant control for repetitive dynamical process.

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Gong, Y., Yang, R., Paszke, W. et al. Observer-based Iterative Learning Control for the Discrete-time Systems with Time Delay and Finite Frequency Domain Specifications. Int. J. Control Autom. Syst. 20, 48–57 (2022). https://doi.org/10.1007/s12555-020-0875-x

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  • DOI: https://doi.org/10.1007/s12555-020-0875-x

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