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Research Papers

Computationally Efficient Combined Plant Design and Controller Optimization Using a Coupling Measure

[+] Author and Article Information
Rakesh Patil, Zoran Filipi

Hosam Fathy1

Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48109hfathy@umich.edu

1

Corresponding author.

J. Mech. Des 134(7), 071008 (Jun 20, 2012) (8 pages) doi:10.1115/1.4006828 History: Received July 25, 2011; Revised April 19, 2012; Published June 20, 2012; Online June 20, 2012

This paper presents a novel approach to the optimization of a dynamic systems design and control. Traditionally, these problems have been solved either sequentially or in a combined manner. We propose a novel approach that uses a previously derived coupling measure to quantify the impact of plant design variables on optimal control cost. This proposed approach has two key advantages. First, because the coupling term quantifies the gradient of the control optimization objective with respect to plant design variables, the approach ensures combined plant/control optimality. Second, because the coupling term equals the integral of optimal control co-states multiplied by static gradient terms that can be computed a priori, the proposed approach is computationally attractive. We illustrate this approach using an example cantilever beam structural design and vibration control problem. The results show significant computational cost improvements compared to traditional combined plant/control optimization. This reduction in computational cost becomes more pronounced as the number of plant design variables increases.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Optimization framework flowchart

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Figure 2

Diagram of the beam, an example node, the initial conditions, and boundary conditions

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Figure 3

Coupling term as calculated by Eqs. 9,10

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Figure 4

Comparison of drop in objective with functions calls

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Figure 5

Optimal beam—width variation with beam length

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Figure 6

Lightest beam—width variation with beam length

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