A second order control system has the settling time of 5 seconds (for ±2) tolerance ) and the peak time of 2 seconds. The locations of poles in the s-plane are
A
(−0.8±j3.14)rad/sec
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B
(−2±j0.628)rad/sec
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C
(−0.8±j1.57)rad/sec
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D
(−2±j5)rad/sec
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Solution
The correct option is C (−0.8±j1.57)rad/sec Settling time ts=4ζωπ5=4ζwnζwn=45=0.8rad/sec
Peak timetp=πωd2=πwdwd=π2=1.57rad/sec
For second order system, the location of poles =ζwn±jwd=(−0.8±j1.57)rad/sec