Problem 2: The poles (roots) of five linear systems are plotted below in the s-domain. Each system is indicated by a different marker (e.g., both triangle markers are for system iii). Imaginary axis (rad/sec) 5 4 -1 (iii) O (iv) 11 -4 -5 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 Real axis (rad/sec) (a) What is the order of each system? (i) (ii) (iii) (iv) (v) (b) Which system has the fastest settling time? (c) Which systems are stable? (i) (ii) (iii) (iv) (v) O (d) Which 2nd-order system has the largest wn? (e) which 2nd-order system has the largest ??

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Problem 2: The poles (roots) of five linear systems are plotted below in the s-domain. Each system
is indicated by a different marker (e.g., both triangle markers are for system iii).
Imaginary axis (rad/sec)
5
4
2 3 4 5
-3
-4
D
(iv)
-5
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
Real axis (rad/sec)
(a) What is the order of each system?
(i)
(ii)
(iii)
(iv)
(v)
(b) Which system has the fastest settling time?
(c) Which systems are stable?
(i)
(ii) (iii) (iv) (v) O
(d) Which 2nd-order system has the largest wn?
(e) Which 2nd-order system has the largest ??
Transcribed Image Text:Problem 2: The poles (roots) of five linear systems are plotted below in the s-domain. Each system is indicated by a different marker (e.g., both triangle markers are for system iii). Imaginary axis (rad/sec) 5 4 2 3 4 5 -3 -4 D (iv) -5 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 Real axis (rad/sec) (a) What is the order of each system? (i) (ii) (iii) (iv) (v) (b) Which system has the fastest settling time? (c) Which systems are stable? (i) (ii) (iii) (iv) (v) O (d) Which 2nd-order system has the largest wn? (e) Which 2nd-order system has the largest ??
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