Evaluating Tuning Parameters (2) - Answers

Part A

When the loop is open the following values are obtained from the Bode Diagrams:

Critical Frequency = 1.20
Gain Margin = 7.57 dB (2.39)
Crossover Frequency = 0.45
Phase Margin = 87.13

Part B

The gain of a PI controller is equal to GM/2.2.

GM = 2.39
Gain = 2.39/2.2 = 1.09

To obtain the reset time of a PI controller we have to convert the frequency to the correct units, take the reciprocal and then divide by 1.2.

CF = 1.20 / = 0.191
Pu = 5.24
Reset Time = 4.36

Part C

When the controller is added to the loop, using the above values for the controller parameters the following values are obtained from the Bode Diagrams:

Critical Frequency = 1.07
Gain Margin = 5.24 dB (1.83)
Crossover Frequency = 0.55
Phase Margin = 48.5

In this case when you look at the actual response of the process and controller you see that the gain is a little low and the reset is a little high - the response is smooth but takes a long time to reach steady state.

Now try a gain of 1.25 and a reset of 3.1. Notice how the response is improved. When the above figures are evaluated again the following is obtained:

Critical Frequency = 1.02
Gain Margin = 3.61 dB (1.52)
Crossover Frequency = 0.65
Phase Margin = 33.5

Note that the values are still a bit on the low side.

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