Everything about Distributed Parameter Systems totally explained
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, for example, 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.)
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