Evaluating Tuning Parameters (3) - Answers

Part A

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

Critical Frequency = 1.84
Gain Margin = 1.87 dB (1.24)
Crossover Frequency = 1.36
Phase Margin = 32.46

Part B

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

GM = 1.24
Gain = 1.24/2.2 = 0.564

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 = 1.84 / = 0.293
Pu = 3.41
Reset Time = 2.85

Part C

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

Critical Frequency = 1.71
Gain Margin = 6.11 dB (2.02)
Crossover Frequency = 0.57
Phase Margin = 81.12

As you can see, in this case the new phase margin with control is still rather high. Looking at the process response you see that there is rather a lot of oscillation before it reaches steady state. Try changing the controller parameters to a gain of 0.4 and 1.5 and re-evaluate the above figures.

Critical Frequency = 1.58
Gain Margin = 7.8 dB (2.45)
Crossover Frequency = 0.55
Phase Margin = 64

Now the phase margin is nearer to the limits in the guidelines.

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