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Research Papers

Control Proxy Functions for Sequential Design and Control Optimization

[+] Author and Article Information
Diane L. Peters1

P. Y. Papalambros

A. G. Ulsoy

 University of Michigan, 2250 G. G. Brown Building, 2350 Hayward Street, Ann Arbor, MI 48109ulsoy@umich.edu

1

Corresponding author.

J. Mech. Des 133(9), 091007 (Sep 15, 2011) (11 pages) doi:10.1115/1.4004792 History: Received May 25, 2010; Revised June 17, 2011; Published September 15, 2011; Online September 15, 2011

Optimal system design of “smart” products requires optimization of both the artifact and its controller. When the artifact and the controller designs are independent, the system solution is straightforward through sequential optimization. When the designs are coupled, combined simultaneous optimization can produce system-optimal results, but presents significant computational and organizational complexity. This paper presents a method that produces results comparable with those found with a simultaneous solution strategy, but with the simplicity of the sequential strategy. The artifact objective function is augmented by a control proxy function (CPF), representing the artifact’s ease of control. The key to successful use of this method is the selection of an appropriate CPF. Four theorems that govern the choice and evaluation of a CPF are given. Each theorem is illustrated using a simple mathematical example. Specific CPFs are then presented for particular problem formulations, and the method is applied to the optimal design and control of a micro-electrical mechanical system actuator.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Control proxy function problem formulation

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Figure 2

Gradients at Points A and B

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Figure 3

Comparison of angle ξ and distance ɛ

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Figure 4

Pareto-optimal Point B and CPF Points A and C

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Figure 5

Comparison of simultaneous and CPF solutions for appropriate and inappropriate monotonicity

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Figure 6

Unconstrained minima of fc and χ

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Figure 7

Comparison of simultaneous and CPF solutions for two choices of CPF

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Figure 8

MEMS actuator configuration

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Figure 9

Microhinge structure

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Figure 10

Control architecture and system dynamics

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Figure 11

CPF points for optimization of MEMS actuator

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Figure 12

Displacement and voltage profile for sample MEMS actuator design

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