Controller in the feedback path?

What happens if the controller of a closed-loop system is placed in the feedback path before the summation point instead of bewtween the summation point and the plant to control?

Is it allowed to do so? If so, what are the main differences???

Thanks!

Answer 1

[Mathieu NOE]

hello Matteo

both schemes are OK, they only differ for tracking performance

assuming :

• plant transfer is P
• controller transfer is C
• your input is t (before the summing point) and the output is y

for controller in the main path : tracking performance = y/t = C*P / (1 + C*P) , so you see the controller transfer is also in the numerator of the closed loop

for controller in the feedback path : tracking performance = y/t = P / (1 + C*P) , so you see the controller transfer is only in the denominator of the closed loop

for output perturbation rejection (that is assume y is corrupted by perturbation p ) , both schemes give exactly the same performance :

y/p = 1 / (1 + C*P)

one typical example of feedback is PID; usually we put the P and I action in the main path , but it is not recommended to put the D term here because we want to avoid to derive the input data, so the D term is located only in the feedback path - so damping applies only on the measured output and not on the input.

hope it helps !