Identify Condition of lag and lead compensator

[jaus tail]

Homework Statement

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?

 

[donpacino]

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

 

[jaus tail]

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.

 

[ishfaq731]

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 .