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ANALOG SEEKrets
FIGURE 18.8A:
power
100%
0%
set point
proportional
band
temperature
It is initially convenient to define
the set point as the 0% end of the
proportional band. This means the
steady state temperature will
always be lower than the set
point, but it should be well within
the proportional band.
Full heater power must take
the temperature well beyond the
set point in order for the control
system to work correctly.
The proportional gain factor is set by adjusting the width of the proportional band. This
is perhaps an unfortunate term; you end up adjusting the proportional-band width. In
spoken usage this can easily be mis-heard as the ‘proportional bandwidth’ and then
confusion can occur.
FIGURE 18.8B:
I have (arbitrarily) to referenced temperatures to
0°C. 1 V represents 1°C, 1 A represents 1 W and
1 Ω represents 1°C/W: this is a simple steadystate model. In the steady state, the heater
temperature and the sensor temperature are equal
(according to the previous model, where there is
no thermal path from the sensor to ambient).
Using symbols:
TSET = set temperature
T = actual temperature
TAMB = ambient temperature
TBAND = proportional-band width
PMAX = maximum possible heater power
θH-A = thermal resistance from heater to ambient
heater power = PMAX ×
TSET − T
TBAND
Using the steady state model:
T = TAMB + (heater power ) ⋅ θ H − A
T = TAMB + PMAX ×
Simplify this by writing
K=
TSET − T
×θ H −A
TBAND
PMAX × θ H − A
giving T = T AMB + K × (TSET − T )
TBAND