Root Locus - 3 - Answers
Example 1 - Answers
1) Make a pole/zero plot.
2) How many closed-loop poles are there?
3 (= number of open-loop poles)
3) What are the closed-loop poles for K = 0?
When K = 0, CL poles = OL poles, so CL poles are s = -1, -9, -20
4) What are the closed-loop poles when K = ¥?
There are as many finite zeros as there are poles. Therefore, there are no
infinite zeros.
At K = ¥,
CL poles = OL zeros. So CL poles are s = 0,
-4, -12.
5) Are there any infinite closed-loop poles for any K, 0 <= K <= ¥?
No. You only get infinite CL poles if there
are infinite zeros, i.e. if the number of poles
is greater than the number of
(finite) zeros. Here there are 3 of each, so there are no infinite zeros.
6) Make a guess at the system's root locus and draw it in on your pole/zero plot.
The arrows show how the roots travel as K increases from 0 to ¥.
7) Is the system oscillatory and, if so, for what values of K?
For an oscillatory system, you need complex closed-loop poles. The
closed-loop poles
in this example stay on the real axis
as K changes. So there is no value of K for which
the poles are complex.
Therefore, the system is never oscillatory.