hw7-s10-430

# hw7-s10-430 - 2 10 s 10 = 4 Given a negative unity feedback...

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ECE 382 Homework 7 Due: Friday, Feb. 5, 2010 1) The open-loop transfer function of a unity feedback control system is: G ( s ) = K ( s + 1 )( s + 2 ) s ( s - 1 )( s + 3 )( s + 7 ) Determine the range of values of K within which the closed-loop system is stable. 2) Determine the number of closed-loop poles in the RHP, in the LHP, and on the j ω -axis for the following closed-loop transfer functions: a) K ( s 5 + 3 s 4 + 21 s 3 + 63 s 2 - 100 s - 300 ) b) K ( s 6 + s 5 - 9 s 4 - 9 s 3 + 14 s 2 + 14 s ) 3) Apply the Routh-Hurwitz criterion to determine (i) the number of roots in the RHP, (ii) the number of roots on j ω -axis, and (iii) the number of roots in the LHP to the following characteristic equations: a) s 4 + 5 s 3 + 2 s + 10 = 0 b) s 5 + 5 . 5 s 4 + 14 . 5 s 3 + 8 s 2 - 19 s - 10 = 0 c) 2 s 5 + s 4 + 6 s 3 + 3 s 2 + s + 1 = 0 d) s 4 + 2 s 3 + 7 s
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Unformatted text preview: 2 + 10 s + 10 = . 4) Given a negative unity feedback control system with G ( s ) = K ( s + 1 ) s 3 + ps 2 + 2 s + 1 . Find the values of K and p such that the system is an oscillator and oscillates with a frequency of ω = 2 rad/sec. Test 2 (Closed-book Test) Date: Thursday, Feb. 11, 2010 Time: 4:30 - 5:30 PM Place: EE 236 Materials: Open-loop and closed-loop poles, second-order systems, time-domain perfor-mance speciﬁcation, steady-state error, Routh-Hurwitz Stability, and Root Locus. Calculator policy will be enforced in the test....
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