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Research Papers: Design Automation

On Decentralized Optimization for a Class of Multisubsystem Codesign Problems

[+] Author and Article Information
Tianchen Liu

Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: tianchen@umd.edu

Shapour Azarm

Professor
ASME Fellow
Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: azarm@umd.edu

Nikhil Chopra

Associate Professor
Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: nchopra@umd.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 1, 2016; final manuscript received September 1, 2017; published online October 26, 2017. Assoc. Editor: Gary Wang.

J. Mech. Des 139(12), 121404 (Oct 26, 2017) (11 pages) Paper No: MD-16-1405; doi: 10.1115/1.4037893 History: Received June 01, 2016; Revised September 01, 2017

Codesign refers to the process of integrating the optimization of the physical plant design and control of a system. In this paper, a new class of codesign problems with a multisubsystem architecture in both design and control is formulated and solved. Our work here extends earlier research on models and solution approaches from single system to multisubsystem codesign. In this class, the optimization model for the physical design part in each subsystem is assumed to have a convex objective function with convex inequality and linear equality constraints. The optimization model for the control part of each subsystem belongs to a class of finite time-horizon linear quadratic regulator (LQR) feedback control. A new multilevel decentralized method is proposed that can obtain optimal or near-optimal solutions for this class of codesign problems. Details of the model and approach are presented and demonstrated by a numerical as well as a more complex spring–mass–damper system example. The proposed decentralized approach has been compared with a centralized approach. Using a scalable test problem, it is shown that as the size of the problem is increased, the computation effort for the decentralized approach increases linearly while that of the centralized approach increases nonlinearly.

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Figures

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Fig. 1

Problem structure—three coupled subsystems

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Fig. 2

Scheme of multilevel decentralized approach

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Fig. 3

Flowchart of the approach

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Fig. 4

Illustrative numerical example: SS2 optimal controller

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Fig. 5

Engineering example: series of three spring–mass–damper subsystems

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Fig. 6

Engineering example: optimal control variables (ui(t), i = 1, 2, 3): (a) decentralized and (b) centralized

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Fig. 7

Engineering example: optimal state variables—velocity (xi2(t), i = 1, 2, 3): (a) decentralized and (b) centralized

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Fig. 8

Example: series of multiple spring–mass–damper subsystems

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Fig. 9

Comparison of computational time between centralized and proposed decentralized approaches

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