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me375_fa10_hwk12_soln

me375_fa10_hwk12_soln - ME 375 HOMEWORK#12 Fall 2010 Out...

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Unformatted text preview: ME 375 HOMEWORK #12 Fall 2010 Out: Deeember 3", 2010 Due: December 10", 2010 PROBLEM 1: (40%) Sketch the root locus for K 20 in the equation l+KL(s)=Oand the listed choices for L(s). Clearly show your steps in order to receive credits. Also, analytically determine the value of K when the root locus cross the imaginary axis (if applicable) for each case. 1 s(s +6) _‘_ s(s + 4)(s + 7) + s(s2 + 33 + 7) (3 +3) s(s + 2)(s + 6) (a) L(S) = (b) L(S) = (c) L(s)= (d) L(S) = PROBLEM 2: (30%) Problem 11.] in Palm textbook, page 696. Also, what values of K results in a percentage overshoot of 5% or less? PROBLEM 3: (30%) Problem 11.21 in Palm textbook, page 700. In addition to the requirements on the dominant closed- loop roots, the third closed-loop root is -5. Imndnuy Axb 1.5 0.5 43.5 Roam- ~15 -10 Rum O C L..— " ‘A | D ' L __° 3- z - t’ -1 La — —n —m. n in —_ _ = r. r I- fl! {A A, L to 3:0 1‘ 1‘! 1‘ - l 'O V'x’ 7. .0:-- -0° = " M‘s -—l “by : _ 9'00- 0; 44 ~12 40 -8 -6 4 .2 0 2 4 6 a . I o T - , . .— A q , ' . + O O I o .. o _T 0 bl . A a . a. . . . v . A n o O _ . m *1 no. a. o _ . 1 a 0 ~ \7 = . . .4, t = g a . a I o . Q 3 . . . '\_A I.. + a» A n. ., I» s .. .4 . 5 IM I n a 1 0| .P. n . 1. s . - . .d O . O a x 3 . .u, s 1 ,. AM : . m 3 .0 l- .2 >\r‘ RootLoal 15 10 0'. 40 MM c.4535 (Oi-uh) : 1- 3/“ U-‘J-J O-qa‘k H (5/0 K K41. B." m k Jo - u (an? in. am th‘sahth AA“ “pad ...
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