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Research Papers: Design Automation

Nested and Simultaneous Solution Strategies for General Combined Plant and Control Design Problems

[+] Author and Article Information
Daniel R. Herber

Industrial & Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: herber1@illinois.edu

James T. Allison

Industrial & Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: jtalliso@illinois.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 23, 2018; final manuscript received June 24, 2018; published online October 10, 2018. Assoc. Editor: Harrison M. Kim.

J. Mech. Des 141(1), 011402 (Oct 10, 2018) (11 pages) Paper No: MD-18-1066; doi: 10.1115/1.4040705 History: Received January 23, 2018; Revised June 24, 2018

In this paper, general combined plant and control design or co-design problems are examined. The previous work in co-design theory imposed restrictions on the type of problems that could be posed. This paper lifts many of those restrictions. The problem formulations and optimality conditions for both the simultaneous and nested solution strategies are given. Due to a number of challenges associated with the optimality conditions, practical solution considerations are discussed with a focus on the motivating reasons for using direct transcription (DT) in co-design. This paper highlights some of the key concepts in general co-design including general coupling, the differences between the feasible regions for each strategy, general boundary conditions, inequality path constraints, system-level objectives, and the complexity of the closed-form solutions. Three co-design test problems are provided. A number of research directions are proposed to further co-design theory including tailored solution methods for reducing total computational expense, better comparisons between the two solution strategies, and more realistic test problems.

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Copyright © 2019 by ASME
Topics: Design
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Figures

Grahic Jump Location
Fig. 1

Two co-design solution strategies where indicates an optimization problem: (a) simultaneous strategy and (b) nested strategy

Grahic Jump Location
Fig. 2

Scalar plant, scalar control problem (TP1) results with q = 10, r = 1, wc = 1, and wp=0.3: (a) Ψ(b,K) and (b) ψ(b)

Grahic Jump Location
Fig. 3

Co-design transfer problem (TP2) results for various values of the problem parameters and different values of k marked: (a) results demonstrating a large number of local solutions with tf = 2, x0=0, and v0=−1; (b) results demonstrating single global minimum with tf = 1, x0=1, and v0=2; and (c) results demonstrating degenerate plant solution with tf = 2, x0=5, and v0=−5

Grahic Jump Location
Fig. 4

Simple SASA test problem (TP3) results with J = 1, tf = 2, and umax=1: (a) k = 0, (b) k*=0.8543, and (c) k = 50

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