Distributed parameter systems
- Distributed parameter systems
A distributed parameter system (as opposed to a lumped parameter system) is a system whose state space is infinite-dimensional. A body whose state is heterogeneous has a distributed parameter. It is usually described by partial differential equations.
An example of a distributed parameter system is a bar on the real line that extends from the origin to the point 1 and whose temperature (state) is given by the function "T", where "T"("x") is the temperature at the point "x" and "x" belongs to the interval . The (infinite-dimensional) state-space could be, e.g., the space of continuous functions on , if the temperature is assumed to vary continuously along the bar.
(That space is infinite-dimensional because "T" may simultaneously have an infinite number of independent values (at different values of "x"). For an exact explanation, see Hamel dimension.)
See also
* Systems theory
* Control theory
* Systems thinking
* Causality
External links
*McCann Science: [http://www.mccannscience.com/distributed.htm "Distributed Parameter Systems, models, control..."]
* Laboratoire d’É Thermiques (France). [http://72.14.253.104/search?q=cache:ORt7-N3TinAJ:www.nd.edu/~mtns/papers/25666.pdf+Distributed+parameter+systems&hl=en&ct=clnk&cd=8&gl=us&client=safari Modeling Distributed Parameters Systems..."]
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