Table 17.3 shows that the gains resulting from the tuning procedures of Chapter 17 turned out to provide nearly equivalent transfer functions for P/PI, PI/P, and PID position control. This could also have been done analytically.

data from table 17.3

a. Using the relationships shown in Table 17.1, convert the three loop gains (KVP, KVI, and KPP) from P/PI compensation to make exact equivalence in the denominator of PI/P.

data from table 17.1

b. Repeat for PID control.

c. Convert the two feed-forward gains from P/PI compensation to make exact equivalence in two of the numerator terms of PI/P.

d. Repeat for PID control.

e. Compare the numerator terms. Which, if any, are different, and by how much?

Transcribed Image Text:

P/PI PI/P PID Numerator s Numerator s term term 0.00146 0.00146 0.00146 0.655 0.655 0.638 Numerators' term 114 122.4 100 Numerator s term 2016 2448 2000 Denominator s term 0.002 0.002 0.002 Denominator s term 0.72 0.72 0.72 Denominators' term 115 122.4 100 Denominator s term 2016 2448 2000