Effect of Phase Lead Compensator on Phase and Gain margins

[AnkleBreaker]

Homework Statement

What is the effect on the phase and gain margins of a system when a Phase Lead Controller/Compensator is added?

Homework Equations

I have designed the phase lead controller for the system so if anyone wants to see it, please ask

The Attempt at a Solution

I know, that in general, stability margins are increased, but I am unsure as to why.

 

[donpacino]

Homework Statement

What is the effect on the phase and gain margins of a system when a Phase Lead Controller/Compensator is added?

Homework Equations

I have designed the phase lead controller for the system so if anyone wants to see it, please ask

The Attempt at a Solution

I know, that in general, stability margins are increased, but I am unsure as to why.

do you know what phase and gain margin are?
in words, not mathematically

 

[donpacino]

do you know what phase and gain margin are?
in words, not mathematically

to start, why don't you put up a bode plot of your system with and without the controller.

answer this for me. what happens when the phase crosses zero before the gain crosses zero?

 

[AnkleBreaker]

Thank you for your reply.

do you know what phase and gain margin are?
in words, not mathematically

Gain Margin is the amount of gain that can be added to the system before the system becomes unstable
Phase Margin is the difference of the phase at the 0dB crossover frequency and -180

to start, why don't you put up a bode plot of your system with and without the controller.

Original:

Modified:

answer this for me. what happens when the phase crosses zero before the gain crosses zero?

I'm not really sure of the answer to that question

 

[donpacino]

those look like closed loop bode plots, can you show me the open loop plots?

when the phase crosses zero before the gain crosses zero, your system will become unstable. That is due to the fact that you will get positive feedback when you close the loop. once the gain crosses zero, your system is attenuating, and you are in the green.

so your phase margin is how much margin you have in your phase before your system goes unstable. you want a good deal of phase margin in a real system for a variety of reasons.

1. component tolerances
2. temperature variations
3. noise in your system
4. changes in load.
and more!

your phase and gain margin will also effect your systems responses to changes in input.

 

[LvW]

Homework Statement

What is the effect on the phase and gain margins of a system when a Phase Lead Controller/Compensator is added?

The answer is contained in the question: A phase-lead compensator adds a "leading" (positive) phase to the loop gain.
If you know that in case of a marginally phase margin the (negative) loop phase is too close to the critical values, it is clear that addition of a certain amount of positive phase (in the critical frequency region around the cross-over frequency) will improve the margin.