Hints For Problems

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1. 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.
2. 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 set-point 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 1.0e-20, which is negligible except it does eliminate the offset, for reasons explained in the technical notes.