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hw10-s10-430

hw10-s10-430 - G s = K s 2 s s-4(a Sketch the complete...

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ECE 382 Homework 10 Due: Friday, Feb. 19, 2010 1) For each of the following open-loop transfer functions (for K > 0), (a) Sketch the Nyquist plot, (b) Determine whether the system is stable from part (a), (c) Check your answer to part (b) by applying the Routh-Hurwitz criterion. (i) G ( s ) H ( s ) = K ( s + 1 ) 2 (ii) G ( s ) H ( s ) = K ( s + 1 ) s 2 ( s + 4 )( s + 5 ) (iii) G ( s ) H ( s ) = K ( s + 2 ) ( s + 1 )( s - 3 ) (iv) G ( s ) H ( s ) = K ( τ s + 1 ) 3 , τ > 0 (v) G ( s ) H ( s ) = K s ( s + 2 ) 2 2) Given the open-loop transfer function as G ( s ) = K ( s + 1 )( s + 2 )( s + 3 ) , find the value of K such that the Nyquist plot of G ( s ) H ( s ) will pass through the ( - 1 , j 0 ) point. Find the phase margin and gain margin of this system when K = 30. 3) Given a negative unity feedback control system with
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Unformatted text preview: G ( s ) = K ( s + 2 ) s ( s-4 ) . (a) Sketch the complete Nyquist plot. (b) Determine the values of K for which the closed-loop system is stable without using the Routh-Hurwitz stability test. (c) Determine the phase crossover frequency, the gain crossover frequency, the gain mar-gin, and the phase margin when K = √ 6. Test 3: Date: Wednesday, February 24, 2010 Place: in class Material: Bode plot and Nyquist Plot. Only simple calculators are allowed in the test. 1...
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