Identify Condition of lag and lead compensator

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Discussion Overview

The discussion revolves around the conditions for lag and lead compensators in control systems, focusing on the relationships between poles and zeros. Participants explore the implications of these relationships on the answers to a homework problem, examining the criteria for determining the dominance of poles and zeros.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • Some participants assert that 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.
  • Others argue that for a lead compensator, the zero (Z2) is closer to the origin than the pole (P2), suggesting that the magnitude of Z2 is less than that of P2.
  • A participant questions the correctness of their answer compared to the book's answer, indicating confusion about the conditions for determining dominance in compensators.
  • One participant attempts to clarify the misunderstanding by posing a related mathematical question, which leads to a further exploration of the conditions for poles and zeros.
  • Another participant provides specific examples of poles and zeros to illustrate the relationships, reinforcing the earlier claims about their positions relative to the origin.
  • There is a suggestion that for lead compensators, the zero must be of smaller magnitude to ensure it is near the origin, and a similar reasoning is proposed for lag compensators.

Areas of Agreement / Disagreement

Participants express differing views on the correct interpretation of the conditions for lag and lead compensators, with no consensus reached on the correct answer to the homework problem. Some participants appear to agree on the general principles, but there is uncertainty regarding their application to the specific problem.

Contextual Notes

Participants' claims depend on the definitions of poles and zeros and their respective positions in the complex plane. There are unresolved details regarding the specific values and conditions that lead to the conclusions drawn in the discussion.

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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