Path: Thermal/ThermalAnalysis
% Creates a set of first order differential equations to model
a thermal circuit. Inputs are the nodal masses,
a conductive node map, a radiative
node map, an input node map and an output node map. The output
is a set of first order differential equations in the form
.
T = aT + bq
y = cT
where T is the nodal temperature, q is the thermal input
and y is the vector of measurements.
A node map has one row for each node and as many columns as
are necessary to specify the connections.
Each node map is accompanied by a coefficient map that gives
either the conductive or radiative heat transfer coefficents
for the node pair. Radiative heat transfer is of the form:
4 4
q = a(T - T )
ij i j
Thermnet linearizes about the nominal temperature. The result
is
3 3
q = a(T T - T T )
ij ni i nj j
where the n indicates a nominal temperature. The radiative heat
transfer coefficient causes an asymmetry between nodes.
Thermnet will automatically make the a matrix symmetric for
conduction. Thermnet will warn you if you entered a coefficient
twice and the two were different. You only have to specify the
connection in one direction.
If you want a node to conduct or radiate to infinity just
input "inf" as the node to which it is radiating or conducting.
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Form:
[a, b, c, ac, ar] = Thermnet( mn, cnm, cc, inm, onm, rnm, rc, tnom )
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Inputs
------
mn (1,n) Thermal mass of each node
cnm (n,:) Conduction node map
cc (n,:) Conduction coefficients
inm (m,:) Input node map (nodes with inputs)
onm (p,1) Output node map (nodes with outputs)
rnm (n,:) Radiation node map
rc (n,:) Radiation coefficients
tnom (1,n) Nominal temperature for linearization
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Outputs
-------
a (n,n) Plant matrix
b (n,m) Input matrix
c (p,n) Output matrix
ac (n,n) Conduction part of the plant matrix
ar (n,n) Radiative (quartic) coefficient matrix
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