Answer b) for the first question, d) for second question. how to count poles and
ID: 2988172 • Letter: A
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Answer b) for the first question, d) for second question.
how to count poles and zeros on Nyquist plot in general?
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For the given Nyquist plot, find the following for the open-loop system: the DC gain n- m (number of poles-number of zeros) Find the following for the closed-loop system, assuming it is stable: Gain margin. Show your work on the drawing. Be sure to indicate ALL the regions that would be stable. Phase margin. Show your work on the drawing. Refer to the Nyquist curve at right {only the portion for to omega > 0 is plotted), The closed-loop system is stable. How many unstable poles can the open-loop system have? Show why. Does the open-loop system have any poles at the origin? How do you know? If yes, how many? What is (are) the gain margin(s)? Does the open-loop system have more poles than zeros? If yes, how many?Explanation / Answer
For the Nyquist diagran, N = P-Z. where N = number of antic-clokwise encirclements of zero in the Nyquist plot. P = number of poles of 1 + G(s)H(s), which is the same as the number of poles of open-loop transfer function G(s)H(s), and is known.
Z = number of zeroes of 1 + G(s)H(s), and is the same as the poles of the closed loop transfer function. Thus, Z = P - N can be used to find number of closed loop poles in the right half plane and hence the stability. This link would be helpful : http://lpsa.swarthmore.edu/Nyquist/NyquistStability.html#Counting
(b) for 1st question.
Since you have not shown the anti-clockwise or clockwise direction in Nyquist plot, I assume anti-clockwise (going by the dark line first). So, N = 1 = n- m (1 encirclements of 0).
(d) for 2nd question, Here, N = -1. So, Z = P +1. So, Number of zeroes of 1+G(s)H(s) is more than number of poles of G(s)H(s). But Z is not number of zeroes of open loop system function, G(s)H(s).
If that is what you need, then answer is zeroes exceed poles by 1.
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