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Hints For Problems
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 Problem 1.
The proportional gain is independent of frequency and gives a horizontal line.
The integral level causes a decrease in gain of 10 dB per frequency decade which
is only significant at low frequencies. The derivative gain causes
an increase in gain, also at a rate of 10 dB per decade,
which becomes apparent at high frequencies.
 Problem 2.
The problem here is to pick values of parameters that show the overshoot clearly, but
which don't distort the results by causing the heater to hit its maximum,
or zero, power. Leave the oven parameters at their default values and set the
sensor lag to zero. To give the setpoint a nice scale on the graph
use the centigrade units and set T_{e} to −273°C.
Then use a ramp that starts at
0°C at 100 s, and finishes at 0.01°C, also at 100 s.
Set D and I to zero, and with a proportional gain of 20000
there is lots of overshoot but the difference between
T_{s} and T_{o} impedes the accuracy with
which it can be measured. This can be eliminated
by using a very small value for the integral gain, say 1.0e20, which is
negligible except it does eliminate
the offset, for reasons explained in the technical notes.
