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Research Papers

Output Regulation in Bimodal Systems With Application to Surface Tracking in the Presence of Contact Vibrations

[+] Author and Article Information
Zhizheng Wu

Department of Precision Mechanical Engineering,
Shanghai University,
Shanghai, 200072, China
e-mail: zhizhengwu@shu.edu.cn

Foued Ben Amara

Department of Mechanical
and Industrial Engineering,
University of Toronto,
Toronto, ON, M5S 3G8, Canada
e-mail: benamara@mie.utoronto.ca

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received November 3, 2010; final manuscript received July 10, 2012; published online November 7, 2012. Assoc. Editor: Nariman Sepehri.

J. Dyn. Sys., Meas., Control 135(2), 021003 (Nov 07, 2012) (10 pages) Paper No: DS-10-1322; doi: 10.1115/1.4007550 History: Received November 03, 2010; Revised July 10, 2012

Motivated by a class of surface tracking problems in mechanical systems subject to contact vibrations, this paper considers a regulation problem for discrete-time switched bimodal linear systems where it is desired to achieve output regulation against exogenous input signals featuring known deterministic and unknown random components. A first step in the regulator design involves constructing a set of observer-based parameterized stabilizing controllers that satisfy a sufficient regulation condition for the switched system against the known deterministic disturbance or reference signals. In the second step, an additional performance constraint is added to identify, from among the already constructed regulators, those that provide the best regulation performance against the unknown random disturbances. A corresponding regulator synthesis algorithm is developed based on iteratively solving properly formulated bilinear matrix inequalities. The proposed regulator is successfully evaluated on an experimental setup involving a switched bimodal mechanical system subject to contact vibrations, hence demonstrating the effectiveness of the proposed regulation approach.

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Figures

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Fig. 1

Closed loop system with a Q parameterized controller

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Fig. 2

Diagram of the experimental setup

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Fig. 3

Results for the case of dw = 0 and obtained using the controller designed without accounting for the H2 performance constraint: (a) performance variable e and tip position yt and (b) random disturbance dw and coil current i

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Fig. 4

Results for the case of dw≠0 and obtained using the controller designed without accounting for the H2 performance constraint: (a) performance variable e and tip position yt and (b) random disturbance dw and coil current i

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Fig. 5

Results for the case of dw≠0 and obtained using the controller designed by accounting for the H2 performance constraint: (a) performance variable e and tip position yt and (b) random disturbance dw and coil current i

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