Nyquist Stability

I've got a question on the Nyquist Stability criterion.

Consider a unity negative feedback system with plant L(s) and gain K in the forward loop.

A nyquist plot is to be generated for this system to meet the following criteria:

1) L(s) has one unstable right half plane pole

2) The closed loop system is stable for (1/3 < K < 2) and unstable for K=1/3 and K=2.

3) Phase margin of 30 degrees

4) Zero steady state error to a step reference input.

Help !

Reply to
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I don't generally do homework here and i won't do yours. I will point pit, though, that somebody probably left something out. The phase margin is clearly a function of gain. (The zero steady-state error implies that the system contains an integrator.)


Reply to
Jerry Avins

Just as a hint. Sketch a prototype/known Nyquist plot and evaluate each of your criteria for this known plot. Then work backwards to find a answer. Ray

Reply to

Dnia 09-07-2010 o 06:02:28 Mohit napisa=B3(a):

You are asking for help because.... you are tired of thinking? You don't like it and you think that thinking is bad and dirty?

Make your muscles grow. Become a person.

You are asking for help because....?

Reply to

Assuming that this is a class, go over your notes or the recent reading assignments in the book -- it may have been done as an example already; that will tell you your instructor's expectations.

If you're doing self-study then review the chapter of the book out of which this problem comes.

There _are_ ways to do this by construction, but we'd have to know how much you know before we could tell you how to do it that way.

Reply to
Tim Wescott

1: What feature does L(s) need to have to stabilize that unstable pole? 4: What feature does L(s) need to have to have zero steady state error to a step input? 2: What does the Nyquist plot have to have to make the system stable for the given gain range? 3: What feature does the Nyquist plot have to have for 30 degrees phase margin?

Answer these, then see if the answer to your overall problem doesn't start taking shape.

Reply to
Tim Wescott

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