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Technical Briefs

A Method for Recovering Linear Performance in Feedback Systems With Nonlinear Instrumentation

[+] Author and Article Information
ShiNung Ching1

Department of Brain and Cognitive Science,  Massachusetts Institute of Technology, Cambridge, MA 02139 shinung@mit.edu

Pierre T. Kabamba

Department of Aerospace Engineering,  University of Michigan, Ann Arbor, MI 48109 kabamba@umich.edu

Semyon M. Meerkov

Department of Electrical Engineering and Computer Science,  University of Michigan, Ann Arbor, MI 48109 smm@eecs.umich.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(1), 014503 (Dec 06, 2011) (6 pages) doi:10.1115/1.4004775 History: Received June 29, 2010; Revised May 03, 2011; Published December 06, 2011; Online December 06, 2011

The problem of controller design in linear systems is well understood. Often, however, when linear controllers are implemented on a physical system, the anticipated performance is not met. In some cases, this can be attributed to nonlinearities in the instrumentation, i.e., sensors and actuators. Intuition suggests that to compensate for this instrumentation, one can boost, i.e., increase, the controller gain. This paper formally pursues this strategy and develops the theory of boosting. It provides conditions under which the controller gain can be modified to offset the effects of instrumentation, thus recovering the performance of the intended linear design. Experimental verification of the technique developed is reported using a magnetic levitation device.

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Figures

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Figure 4

Boosted quasi-linear system

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Figure 5

Equivalent boosted quasi-linear system

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Figure 6

a-Boosted quasi-linear system

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Figure 7

s-Boosted quasi-linear system

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Figure 1

Basic linear feedback system

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Figure 2

Feedback system with nonlinear instrumentation

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Figure 3

Quasi-linear feedback system

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Figure 8

Histogram of eSL for a-boosting

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Figure 9

eSL as function of σyℓ/Δ

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Figure 10

Magnetically suspended ball

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