Research Papers

Design of Robust Modified Repetitive-Control System for Linear Periodic Plants

[+] Author and Article Information
Lan Zhou

School of Information Science and Engineering, Central South University, Changsha 410083, China; Department of Mathematics and Applied Mathematics,  Hunan Institute of Humanities, Science and Technology, Loudi 417000,, Chinazlly98@yahoo.cn

Jinhua She

 School of Computer Science, Tokyo University of Technology, Hachioji, Tokyo 192-0982, Japanshe@cs.teu.ac.jp

Min Wu1

 School of Information Science and Engineering, Central South University, Changsha 410083, Chinamin@csu.edu.cn

Jie Zhang

 School of Information Science and Engineering, Central South University, Changsha 410083, Chinazhangjie@toki.waseda.jp


Corresponding author.

J. Dyn. Sys., Meas., Control 134(1), 011023 (Dec 06, 2011) (7 pages) doi:10.1115/1.4004770 History: Revised June 08, 2010; Received October 30, 2010; Accepted June 08, 2011; Published December 06, 2011; Online December 06, 2011

This paper concerns a linear-matrix-inequality (LMI)-based method of designing a robust modified repetitive-control system (MRCS) for a class of strictly proper plants with periodic uncertainties. It exploits the nature of control and learning and the periodicity and continuity of repetitive control to convert the design problem into a robust stabilization problem for a continuous-discrete 2D system. The LMI technique and Lyapunov stability theory are used to derive an LMI-based asymptotic stability condition that can be used directly in the design of the gains of the repetitive controller. Two tuning parameters in the condition enable preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the effectiveness of the method.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Configuration of basic repetitive-control system

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Figure 2

Configuration of MRCS

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Figure 4

Chuck-workpiece system: (a) vibration model and (b) stiffness variation [11]

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Figure 5

Relationship among J1 , α, and β

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Figure 6

Relationship among σ, α, and β

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Figure 7

Tracking error for parameter sets (a) and (b) in Eq. 42

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Figure 8

Relationship among J10 , α, and β

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Figure 9

Simulation results for periodically time-varying plant (34) with (48)

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Figure 10

Tracking error for MRCS with white Gaussian noise (SNR: 45 dB) in the output



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