Observer-based Multirate Feedback Control Design for Two-time-scale System

Abstract

The use of a lower sampling rate for designing a discrete-time state feedback-based controller fails to capture information of fast states in a two-time-scale system, while the use of a higher sampling rate increases the amount of computation considerably. Thus, the use of single-rate sampling for systems with slow and fast states has evident limitations. In this paper, multirate state feedback (MRSF) control for a linear time-invariant two-time-scale system is proposed. Here, multirate sampling refers to the sampling of slow and fast states at different sampling rates. Firstly, a block-triangular form of the original continuous two-time-scale system is constructed. Then, it is discretized with a smaller sampling period and feedback control is designed for the fast subsystem. Later, the system is block-diagonalized and equivalently represented into a system with a higher sampling period. Subsequently, feedback control is designed for the slow subsystem and overall MRSF control is derived. It is proved that the derived MRSF control stabilizes the full-order system. Being the transformed states of the original system, slow and fast states need to be estimated for the MRSF control realization. Hence, a sequential two-stage observer is formulated to estimate these states. Finally, the applicability of the design method is demonstrated with a numerical example and simulation results are compared with the single-rate sampling method. It is found that the proposed MRSF control and observer designs reduce computations without compromising closed-loop performance.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 61750110524) and National Key R&D Program of China (No. 2017YFE0128500).

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Correspondence to Wei-Dong Zhang.

Additional information

Ravindra Munje received the B. Eng. degree in electrical from Mumbai University, India in 2005, the M. Eng. degree in control systems from Pune University, India in 2009, and the Ph.D. degree in electrical engineering from Swami Ramanand Teerth Marathwada University, India in 2015. He was a post-doctoral fellow with Shanghai Jiao Tong University, China from June 2017 to May 2019. Currently, he is a professor at Electrical Engineering Department, K. K. Wagh Institute of Engineering Education and Research, India. He has written a book and about 40 refereed papers. He received the Promising Engineer Award in 2016, Outstanding Researcher Award in 2018 and Best Faculty Award in 2019.

His research interests include modeling and control of large-scale systems using sliding mode and multirate output feedback.

Wei-Dong Zhang received the B.Sc. degree in instrument & measurement, the M.Sc. in instrument & measurement and the Ph.D. degree in industrial automation from Zhejiang University, China in 1990, 1993 and 1996, respectively, and then worked as a postdoctoral fellow at Shanghai Jiao Tong University, China. He joined Shanghai Jiao Tong University as an associate professor in 1998 and has been a full professor since 1999. From 2003 to 2004, he worked at University of Stuttgart, Germany, as an Alexander von Humboldt Fellow. He is a recipient of the National Science Fund for Distinguished Young Scholars of China and Cheung Kong Scholars Program. In 2011, he was appointed Chair Professor at Shanghai Jiao Tong University. He is currently the director of the Engineering Research Center of Marine Automation, Municipal Education Commission. He is the author of more than 300 refereed papers and 1 book and holds 51 patents.

His research interests include control theory and information processing theory and their applications in several fields, including power/chemical processes, USV/ROV and aerocraft.

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Munje, R., Zhang, WD. Observer-based Multirate Feedback Control Design for Two-time-scale System. Int. J. Autom. Comput. (2021). https://doi.org/10.1007/s11633-020-1268-6

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Keywords

  • Feedback control
  • multirate sampling
  • sequential observer
  • two-stage design
  • two-time-scale system