Identify Condition of lag and lead compensator

In summary, for a lag compensator, the pole is closer to the origin than the zero, so the modulus of the pole is less than the modulus of the zero. This means that the pole is greater than the zero. For a lead compensator, the zero is closer to the origin than the pole, so the modulus of the zero is less than the modulus of the pole. This means that the zero is greater than the pole.
  • #1
jaus tail
615
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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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  • #2
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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Likes ishfaq731 and jaus tail
  • #3
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.
 
  • #4
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:

What is a lag compensator and when is it used?

A lag compensator is a control system component that introduces a phase lag into the system's output. It is typically used when the system has a fast response and needs to be slowed down to meet stability and performance requirements.

How can I identify the condition of a lag compensator?

The condition of a lag compensator can be identified by analyzing the frequency response of the system. A lag compensator will have a low-frequency gain that is less than one and a high-frequency gain that is close to one. Additionally, the phase shift will increase as the frequency increases.

What are the benefits of using a lead compensator?

A lead compensator is used to improve the transient response of a control system. It increases the system's stability and reduces the settling time. It also improves the steady-state error and reduces the overshoot of the system.

How do I design a lag compensator?

The design of a lag compensator involves selecting the appropriate gain and time constant values to achieve the desired frequency response. This can be done using techniques such as root locus or Bode plot analysis. The design should also consider the stability and performance requirements of the system.

Can a lag compensator be used in all control systems?

No, a lag compensator is not suitable for all control systems. It is most effective in systems with fast response that need to be slowed down. In some systems, a lead compensator or other control components may be more suitable for achieving stability and performance requirements.

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