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Research Papers

A Green's Function-Based Design for Deformation Control of a Microbeam With In-Domain Actuation

[+] Author and Article Information
Amir Badkoubeh

e-mail: amir.badkoubeh@polymtl.ca

Guchuan Zhu

e-mail: guchuan.zhu@polymtl.ca
Department of Electrical Engineering,
École Polytechnique of Montreal,
2900, Boulevard Edouard-Montpetit
Montreal, Quebec, Canada H3T 1J4

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 24, 2012; final manuscript received September 21, 2013; published online October 23, 2013. Assoc. Editor: Srinivasa M. Salapaka.

J. Dyn. Sys., Meas., Control 136(1), 011018 (Oct 23, 2013) (8 pages) Paper No: DS-12-1353; doi: 10.1115/1.4025552 History: Received October 24, 2012; Revised September 21, 2013

This paper presents a Green's function-based design for deformation control of a microbeam described by an Euler-Bernoulli equation with in-domain pointwise actuation. The Green's function is first used in control design to construct the test function that enables the solvability of a map between the original nonhomogeneous partial differential equation and a target system in standard boundary control form. Then a regularized Green's function is employed in motion planning, leading to a computationally tractable implementation of the control scheme combined by a single feedback stabilizing loop and feedforward controls. The viability and the applicability of the proposed approach are demonstrated through numerical simulations of a representative microbeam.

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Figures

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Fig. 1

Schematic of the deformable microbeam

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Fig. 2

Stabilizing feedback control

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Fig. 3

Green's function of the beam for ξ={0.1,0.2,…,0.9}

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Fig. 4

Deformation control: (a) desired shape; (b) beam deflection; and (c) tracking error

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Fig. 5

Control signals: (a) α1α5 and (b) α6α10

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