closed loopcontrolcontrol systemcontrol-looproot locus
Which transfer function ,open loop or close loop do we use/need as a pre req to perform root locus analysis?
I have also attached a snapshot of the relevant webpage of university of Michigan.
I have also highlighted in my snapshot both contradictory terms used in the webpage article.
It's not a paradox. Adding that zero makes it a completely different system. I checked in MATLAB and both plots look right (for an arbitrary a and b, |b|>|a|). That new zero annihilates with a pole which is why you are getting a different root locus plot. Adding LHP zeroes, among other things, improves the stability of your system, though at the cost of transient performance.
Start by putting some equations on it: -
simulate this circuit – Schematic created using CircuitLab
The output of A is called Vout, but clearly ....
\$V_{out} = A(V_{in} - B\cdot V_{out})\$
This boils down to \$\dfrac{V_{out}}{V_{in}} = \dfrac{A}{1+AB} \$
Best Answer
The answer is relatively simple:
From stability considerations we know that the poles of the closed-loop function H(s)=N(s)/D(s) must not enter the right side of the complex s-plane.
The poles of the closed-loop function are identical to the roots (zeros) of the denominator D(s) (which is identical to the characteristic polynominal of the system). Therefore, the root locus analysis is performed for the closed-loop system.
Comment (EDIT): I think, the wording of the quoted text is a bit confusing (..."root locus of an open-loop transfer function"...). For my opinion it should read: ...the root locus for a transfer function H(s) under full negative feedback for different proportional gain values K"...