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MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.151 Advanced System Dynamics and Control Linear Graph Modeling: One-Port Elements 1 1 Introduction In the previous handout Energy and Power Flow in State Determined Systems we examined elemen- tary physical phenomena in fve separate energy domains and used concepts oF energy flow, storage and dissipation to defne a set oF lumped elements . These primitive elements Form a set oF building blocks For system modeling and analysis, and are known generically as lumped one-port elements , because they represent the spatial locations (ports) in a system at which energy is transFerred. ±or each oF the domains with the exception oF thermal systems, we defned three passive elements, two oF which store energy and a third dissipative element. In addition in each domain we defned two active source elements which are time varying sources oF energy. System dynamics provides a unifed Framework For characterizing the dynamic behavior oF sys- tems oF interconnected one-port elements in the di²erent energy domains, as well as in non-energetic systems. In this handout the one-port element descriptions are integrated into a common descrip- tion by recognizing similarities between the elemental behavior in the energy domains, and by defning analogies between elements and variables in the various domains. The Formulation oF a unifed Framework For the description oF elements in the energy domains provides a basis For development oF unifed methods oF modeling systems which span several energy domains. The development oF a unifed modeling methodology requires us to draw analogies between the variables and elements in di²erent energy domains. Several di²erent types oF analogs may be defned. In this text we have chosen to relate elements using the concepts oF generalized “through” and “across” variables associated with a linear graph system representation introduced by ±.A. ±irestone [1] and H.M. Trent [2], and described in detail in several texts [3-5]. This set oF analogs allows us to develop modeling methods that are similar to well known techniques For electrical circuit analysis. The set oF analogies we have selected is not unique, For example another widely used analogy is based on the concepts oF “e²ort” and “flow” variables in bond graph modeling methods, developed by H.M. Paynter [6] and described in D.C. Karnopp, et al. [7]. These two methods lead to di²erent analogies both oF which are valid. ±or example, in this text we consider Forces and electrical currents to be analogous, while in the bond graph method Forces and electrical voltages are considered to be similar. 2 Generalized Through and Across Variables ±igure 1 shows a schematic representation oF a single one-port element, in this case a mechanical spring, as a generic element with two “terminals” through which power flows, either to be stored, supplied, or dissipated by the element. This two-terminal representation may be thought oF as a mechanical analog oF an electrical element, in this case an inductor, with two connecting “wires”. IF
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This note was uploaded on 02/08/2010 for the course MECHANICAL 6537 taught by Professor Stiharu during the Winter '10 term at Concordia Canada.

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