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Research Papers

A Unified Design Approach to Repetitive Learning Control for Systems Subject to Fractional Uncertainties

[+] Author and Article Information
Mingxuan Sun

Professor
College of Information Engineering,
Zhejiang University of Technology,
Hangzhou 310023, China
e-mail: mxsun@zjut.edu.cn

He Li

College of Information Engineering,
Zhejiang University of Technology,
Hangzhou 310023, China
e-mail: hlihz@hotmail.com

Yanwei Li

College of Information Engineering,
Zhejiang University of Technology,
Hangzhou 310023, China
e-mail: lyw199202@163.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 25, 2017; final manuscript received November 6, 2017; published online December 19, 2017. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 140(6), 061003 (Dec 19, 2017) (11 pages) Paper No: DS-17-1125; doi: 10.1115/1.4038488 History: Received February 25, 2017; Revised November 06, 2017

Fractional uncertainties are involved in many practical systems. Currently, there is a lack of research results about such general class of nonlinear systems in the context of learning control. This paper presents a Lyapunov-synthesis approach to repetitive learning control (RLC) being unified due to the use of the direct parametrization and adaptive bounding techniques. To effectively handle fractional uncertainties, the estimation method for such uncertainties is elaborated to facilitate the controller design and convergence analysis. Its novelty lies in the less requirement for the knowledge about the system undertaken. Unsaturated- and saturated-learning algorithms are, respectively, characterized by which both the boundedness of the variables in the closed-loop system undertaken and the asymptotical convergence of the tracking error are established. Experimental results are provided to verify the effectiveness of the presented learning control.

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Figures

Grahic Jump Location
Fig. 2

Index Jk by the unsaturated learning control

Grahic Jump Location
Fig. 3

Error e1,k by the unsaturated learning control

Grahic Jump Location
Fig. 5

Estimate l̂g,k in the case of increasing γ1 and γ2

Grahic Jump Location
Fig. 6

Estimate ûd,k in the case of increasing γ1 and γ2

Grahic Jump Location
Fig. 7

Control input uk in the case of increasing γ1 and γ2

Grahic Jump Location
Fig. 8

Index Jk in the case of increasing γ1 and γ2

Grahic Jump Location
Fig. 9

Estimate l̂f,k by the saturated learning control

Grahic Jump Location
Fig. 10

Estimate l̂g,k by the saturated learning control

Grahic Jump Location
Fig. 11

Estimate ûd,k by the saturated learning control

Grahic Jump Location
Fig. 1

Experimental setup

Grahic Jump Location
Fig. 4

Estimate l̂f,k in the case of increasing γ1 and γ2

Grahic Jump Location
Fig. 12

Control input uk by the saturated learning control

Grahic Jump Location
Fig. 13

Index Jk by the saturated learning control

Grahic Jump Location
Fig. 14

Error e1,k by the saturated learning control

Grahic Jump Location
Fig. 15

The tracking error e by the VSRC

Grahic Jump Location
Fig. 16

Index Jk by the VSRC

Grahic Jump Location
Fig. 17

Control input u by the VSRC

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