Systematic Identification of Decoupling in Dynamic System Models

[+] Author and Article Information
D. Geoff Rideout1

Dept. of Mechanical Engineering, S.J. Carew Building, Memorial University, St. John’s, NL, A1B 3X5, Canadagrideout@engr.mun.ca

Jeffrey L. Stein

Automated Modeling Laboratory, Dept. of Mechanical Engineering, University of Michigan, G029 Auto Lab, 1231 Beal Ave., Ann Arbor, MI, 48109-2121stein@umich.edu

Loucas S. Louca

Department of Mechanical and Manufacturing Engineering, University of Cyprus, 75 Kallipoleos Street, PO Box 20537, 1678 Nicosia, Cypruslslouca@ucy.ac.cy


Corresponding author.

J. Dyn. Sys., Meas., Control 129(4), 503-513 (Oct 24, 2006) (11 pages) doi:10.1115/1.2745859 History: Received November 05, 2005; Revised October 24, 2006

This paper proposes a technique to quantitatively and systematically search for decoupling among elements of a dynamic system model, and to partition models in which decoupling is found. The method can validate simplifying assumptions based on decoupling, determine when decoupling breaks down due to changes in system parameters or inputs, and indicate required model changes. A high-fidelity model is first generated using the bond graph formalism. The relative contributions of the terms of the generalized Kirchoff loop and node equations are computed by calculating and comparing a measure of their power flow. Negligible aggregate bond power at a constraint equation node indicates an unnecessary term, which is then removed from the model by replacing the associated bond by a modulated source of generalized effort or flow. If replacement of all low-power bonds creates separate bond graphs that are joined by modulating signals, then the model can be partitioned into driving and driven subsystems. The partitions are smaller than the original model, have lower-dimension design variable vectors, and can be simulated separately or in parallel. The partitioning algorithm can be employed alongside existing automated modeling techniques to facilitate efficient, accurate simulation-based design of dynamic systems.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 4

Model conditioning algorithm

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Figure 5

Model partitioning and reduction algorithm

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Figure 6

Causally strong internal junction structure bond

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Figure 7

Locally inactive energetic element bond

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Figure 8

Illustrative example system

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Figure 18

Relative activity (bond 1) versus forcing frequency

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Figure 19

Relative activity versus spring stiffness

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Figure 1

Subgraph example schematic

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Figure 2

Driving and driven partitions

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Figure 3

Inactive bond search algorithm

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Figure 14

Conditioned model, a∕b=0.89

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Figure 15

Partitioned model, a∕b=0.89

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Figure 16

Driven partition output, a∕b=0.89

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Figure 17

Computation time comparison

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Figure 9

Example system bond graph (a∕b=1)

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Figure 10

Relative activities vs. lever ratio

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Figure 11

Conditioned model, a∕b=0.16

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Figure 12

Partitioned model showing driving and driven partitions, a∕b=0.16

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Figure 13

Partitioned model outputs, a∕b=0.16



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