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Research Papers

Power Conserving Bond Graph Based Modal Representations and Model Reduction of Lumped Parameter Systems

[+] Author and Article Information
Loucas S. Louca

Department of Mechanical and
Manufacturing Engineering,
University of Cyprus,
75 Kallipoleos Street,
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 February 6, 2013; final manuscript received June 12, 2014; published online August 8, 2014. Assoc. Editor: Yang Shi.

J. Dyn. Sys., Meas., Control 136(6), 061007 (Aug 08, 2014) (13 pages) Paper No: DS-13-1061; doi: 10.1115/1.4027900 History: Received February 06, 2013; Revised June 12, 2014

Dynamic analysis is extensively used to study the behavior of continuous and lumped parameter linear systems. In addition to the physical space, analyses can also be performed in the modal space where very useful frequency information of the system can be extracted. More specifically, modal analysis can be used for the analysis and controller design of dynamic systems, where reduction of model complexity without degrading its accuracy is often required. The reduction of modal models has been extensively studied and many reduction techniques are available. The majority of these techniques use frequency as the metric to determine the reduced model. This paper describes a new method for calculating modal decompositions of lumped parameter systems with the use of the bond graph formulation. The modal decomposition is developed through a power conserving coordinate transformation. The generated modal decomposition model is then used as the basis for reducing its size and complexity. The model reduction approach is based on the previously developed model order reduction algorithm (MORA), which uses the energy-based activity metric in order to generate a series of reduced models. The activity metric was originally developed for the generic case of nonlinear systems; however, in this work, the activity metric is adapted for the case of linear systems with single harmonic excitation. In this case closed form expressions are derived for the calculation of activity. An example is provided to demonstrate the power conserving transformation, calculation of the modal power and the elimination of unimportant modes or modal elements.

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Figures

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Fig. 1

Activity index sorting and element elimination [6]

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Fig. 2

Complex modal bond graph

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Fig. 3

Complex and real bond graph for a single mode

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Fig. 4

Real modal bond graph

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Fig. 5

Complex modal bond graph—zero causal path

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Fig. 6

Real modal bond graph—zero causal path

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Fig. 7

Physical quarter car mode

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Fig. 8

Modal decomposition bond graph

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Fig. 9

Activity and activity indices of modes

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Fig. 10

Reduced model comparison

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Fig. 11

Modal elements activity analysis

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Fig. 12

Included elements, threshold = 99%

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Fig. 13

Real modal decomposition bond graph—no causal path

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Fig. 14

Activity indices of modes—no causal path

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Fig. 15

Reduced model comparison—no causal path

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Fig. 16

Modal elements activity analysis—no causal path

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Fig. 17

Included elements, threshold = 99.9%—no causal path

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