temperature loop observations

[Martin Czech]

During my temperature regulation loop experiments I made some (maybe)
interesting observations:

1.) The loop has a heater, but no cooler. Thus he loop will be very
nonlinear. There is no way to compensate this nonlinearity without using
a cooler. E.g. negative output of the controlling circuit is allmost completely
ignored. The usual trick (linearising network) won't work.

2.) Therefore some losses will be needed in order to be able to lower the
temperature. This is easy when temperature is much higher then anbient,
but get's difficult when it's allmost the same.

3.) The output signal of the temperature sensor is small, some mV per K,
compared to the controller output signal (10V). This means: very high
loop gain. In order to make a overshot experiment, the gain has to be
even higher.  It gets prettey near a two point nonlinear loop. My temp
chamber needs 25*500=12500, at this point 1/f noise gets important.
I use a 10V zener as ad hoc reference, this and the sensor seems to
have excessive 1/f noise. Also the first op amp stage will contribute,
although the LF411 is not so noisy. This in combination with the high
gain makes the controller output voltage fluctuate several volts in a
few seconds. Fortunately these fluctuations get totally damped by the
inertia of the chamber air volume. Nevertheless, it could be a desaster
for on chip cheaters/sensors.

4.) I use a PID control circuit. The D really helps a lot in terms
of overshot, even if the resonant frequency of P and chamber is as
low as fr=1/42 Hz.  But it also amplifies noise. It is necessary to
cut away the frequencys higher then 10*fr via series resistor to the
differentiating cap. The natural frequency fr can be determined by a
step response experiment (very little step to linearize).  

The I part will cause a nasty problem for large signal responses,
because of the nonlinearity it may lead to instabability. The memory
functionality of the I part works well for linear applications, but can
be a desaster for nonlinear. Therefore a control logic must short the I
cap if the circuit is obviously in the nonlinear domain.  Because the I
frequency is so slow (1/10 fr), this will not really slow down the step
response. Nevertheless, an I part is really recommended, because it will
make the temperature error really to 0, this is important for higher losses
(higher temps), where the loop gain may be insufficient to hold the
error down.

5) Since the temp chamber inertia is unknown, it really pays to provide
separate control for P, I and D. First short D and I caps, and tune P
up until 80% overshot is reached. Now determine fr. Set D to this very
frequency.  A large cap will be needed (MKT). Enable D , the step response
is now much better without sacrifying P, ie. time. Finally enable I,
but be carefull to use it only in the linear region (momentarily I do
this by hand with jumpers).  The temperature error will improve very much.

6) My design is on the safe side. Ie. the heaters could take 100W, wheras
only 80W are available, I use workhorse 2N3055 power trannys, the current
is limited to 4A for full scale output of the controller (14V), it is
not possible to get higher. A transistor heat detector will be added ,
so that even a blower failure will not overheat the power stage.
All power components and heat detectors are mounted on larger heat sinks,
with heat conducting paste.

7) Even with the large inertia of the air volume in my chamber, a "linear"
controll circuit like this is far better then a nonlinear two point
switcher, because the later will never settle and cycle on to eternity.
This causes severe error, of course.

I think the observed problems may explain some of the failures of temp
servo loops that people reported on this list in the past.

I don't know if thermostat precision solutions are really dead and out.
I don't think so. They just have to be properly done.

Later more.

m.c.