Evaluating Tuning Parameters (1) - Answers

Part A

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

Critical Frequency = 2.19
Gain Margin = 21.67 dB (12.12)
Crossover Frequency = 0.11
Phase Margin = 143.53

Part B

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

GM = 12.12
Gain = 12.12/2.2 = 5.51

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 = 2.19 / = 0.349
Pu = 2.87
Reset Time = 2.39

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 = 1.94
Gain Margin = 5.41 dB (1.86)
Crossover Frequency =1.05
Phase Margin = 32.5

These values are more or less within the limits. As you can see they are both a little on the small side which indicates instability. If you look at the process response then you will see that, yes - the process does return to the setpoint but with a little oscillation.

Now try fine tuning the controller parameters using the process response. A smoother response is obtained when you use a gain of 4.4 and a reset time of 2.7. Working backwards and using these in the Bode Diagram Applets results in the following values:

Critical Frequency = 1.96
Gain Margin = 7.95 dB (2.5)
Crossover Frequency = 0.831
Phase Margin = 40.5

As you can see these are closer to the limits specified at the start of the exercise.

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