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Research Papers

A Frequency-Based Interpretation of Energy-Based Model Reduction of Linear Systems

[+] Author and Article Information
Loucas S. Louca

Mem. ASME
Department of Mechanical and
Manufacturing Engineering,
University of Cyprus,
75 Kallipoleos Avenue,
P.O. Box 20537,
Nicosia 1678, Cyprus
e-mail: lslouca@ucy.ac.cy

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 25, 2015; final manuscript received July 8, 2016; published online August 17, 2016. Assoc. Editor: Ardalan Vahidi.

J. Dyn. Sys., Meas., Control 138(12), 121005 (Aug 17, 2016) (11 pages) Paper No: DS-15-1587; doi: 10.1115/1.4034242 History: Received November 25, 2015; Revised July 08, 2016

Various modeling techniques have been proposed in order to make modeling a more systematic procedure and to facilitate the development of modeling software that provide users, even experienced users, more ease when developing good models for control and design. The author has previously developed an energy-based modeling metric called “element activity” that was implemented in the model order reduction algorithm (MORA). While MORA was originally developed for the reduction of nonlinear models, the purpose of this paper is to gain insight into this methodology when applied to the reduction of linear models. Toward this end, the steady-state response to sinusoidal inputs is considered. Element activity is calculated analytically for any given excitation frequency, and a series of reduced models, which depend on the excitation frequency content, are generated. The results show through a quarter-car vehicle model that MORA generates a series of models whose spectral radius increases, as successively lower activity elements are included. It is demonstrated that low activity elements are related with high-frequency dynamics.

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Figures

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Fig. 1

Activity index sorting and element elimination

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Fig. 2

Frequency content of input power flow

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Fig. 3

Full quarter-car model—ideal physical model and bond graph

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Fig. 4

Activity and activity indices as a function of road frequency

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Fig. 5

Included elements in the reduced model as a function of frequency, β= 98% (element notation in y-axis refers to Fig. 3)

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Fig. 6

Model complexity as a function of frequency, β= 98%

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Fig. 7

Model comparison (contact force)—full versus reduced

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Fig. 8

Excitation amplitude for broadband input

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Fig. 9

Activity (33) and activity indices (8) as a function of input bandwidth

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Fig. 10

Included elements in the reduced model as a function of bandwidth, β= 98%

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Fig. 11

Model complexity as a function of road bandwidth, β= 98%

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