Identify Condition of lag and lead compensator

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SUMMARY

The discussion focuses on the identification of conditions for lag and lead compensators in control systems. For a lag compensator, the pole (P1) is closer to the origin than the zero (Z1), leading to the conclusion that the magnitude of P1 is less than that of Z1. Conversely, for a lead compensator, the zero (Z2) is closer to the origin than the pole (P2), resulting in Z2 having a greater magnitude than P2. The confusion arises from misinterpreting the relationships between poles and zeros, which is clarified through examples involving specific values.

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jaus tail
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Homework Statement


upload_2018-2-5_14-9-11.png


Homework Equations


For lag compensator pole is dominating
For lead compensator zero is dominating

The Attempt at a Solution


So for lag compensator:
P1 is closer to origin than Z1,
so
mod of P1 < mod of Z1
So P1 > Z1 (since the poles and zeroes are negative)

And for lead
zero is closer to origin
so mod of Z2 < mod of P2
So Z2 > P2

So I get answer as C
Book answer is B
How am I wrong?
 

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jaus tail said:

Homework Statement


View attachment 219728

Homework Equations


For lag compensator pole is dominating
For lead compensator zero is dominating

The Attempt at a Solution


So for lag compensator:
P1 is closer to origin than Z1,
so
mod of P1 < mod of Z1
So P1 > Z1 (since the poles and zeroes are negative)

And for lead
zero is closer to origin
so mod of Z2 < mod of P2
So Z2 > P2

So I get answer as C
Book answer is B
How am I wrong?
You are looking at the concept correctly, but you have one detail wrong. I am going to pose a question, hopefully this helps you get the right answer.x+3 = 0

which of the following is correct.
x=3
x=-3
 
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x + 3 = 0,
so x = -3

So for lag compensator:
P1 is closer to origin than Z1,
so
mod of P1 < mod of Z1
Let there be pole at 0
So P1 = 0
And let there be zero at -1
So Z1 = 1
Oh yeah P1 < Z1.

Likewise
For lead
zero is closer to origin
Let there be zero at origin
Z2 = 0.
There can be a pole at -1
So P2 = 1
So Z2 < P2

Got it. Thanks.
 
jaus tail said:

Homework Statement


View attachment 219728

Homework Equations


For lag compensator pole is dominating
For lead compensator zero is dominating

The Attempt at a Solution


So for lag compensator:
P1 is closer to origin than Z1,
so
mod of P1 < mod of Z1
So P1 > Z1 (since the poles and zeroes are negative)

And for lead
zero is closer to origin
so mod of Z2 < mod of P2
So Z2 > P2

So I get answer as C
Book answer is B
How am I wrong?
Actually for lead compensator the value of S in numerator has to be such that it is near to origin . Now s= -z ,so for value of s to be near to origin, z has to be of smaller magnitude as it has negative sign...similarly you can understand for lag compensator .
 
Last edited:

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