ECE171A_Quiz2_2007

ECE171A_Quiz2_2007 - I---<~ Y (s + 6 + 2j)(s + 6...

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Jea0 ran AO{~~701S ECE 171A, QUIZ 2, Spring 2007 Consider the system shown below. AIJVV"I"ClWi pol~ A:(40): Find K from the root locus to achieve a settling time of 8s. If there are two - solutions, give the one with the highest COn. B:(20): With the gain found in A, find the closed loop transfer function in factored form from the root locus. If some ofthe poles are too hard to locate, make a guess compatible with the root locus rules you have learned. C:(20): What is the peak time for a unit step input with the above gain? Use the dominant pole pair approximation. D:(20): What is the steady state error for a step disturbance W 2 ? What is the steady state error for a step disturbance WI? Y(s) 2.0 / ,~,.O // ~I III :'\ l\ / {·0.3 /1/ , -OJ ~ I II V / ~.o)· ,. ... ~ 1// II/ // ~.()~ ~ 1\ ..••. .... r If//~ ~. 1\ "- /I J V~ \ ~ / I /JII'. \ II 1/ \ / 1.8 1.6 , 1.4 100
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Unformatted text preview: I---<~ Y (s + 6 + 2j)(s + 6 -2j) R ::; 1.2 t~. 1:0 ;: 0,8 0,6 OA 0.2 o o 2 J Root Locus-----I 3 -2 '" ~ ~ m c '0, m E-1-2-3-4-5-12-10-8 I I-6-4-2 4 s ,/ 6 7 8 / f-C f: 11( It 1\;\ Cctt(vw! 2-JeQVJ FaVl 5/25/07 A-ob?)?01 S otOJYLfYlonr (,ore~ ; fj:;: =Q.4 t 1.~ t' p,--c--C). 4 -'5,1 L l<. ~ 7i (>tPi) :::(&.1,[t!.~) 5.'i) s.lil 7f (t;t ~r) s:~ [K--::::-[-7 1-.9:1.-l~ 13 4 cle5ed (oor PQle{ 2:2. rJp0/11 [(}-Op POre) p \ t P2 r P5 t P u ~ t 0 ~ bf L q{ -b + r -(H'- 0 }i -o. ~ T p" 1-P If ;::-12 f 1-t P if-=--\ 2 T 0 -< r-~tP~ :::-11.7 p ~ ~-s .t. (/Vr'1J p~ ~-r;'0 1{S)_~ 171,9 C~tl) ($t6P.j;(S+b-2 j) CstS.b 2..-3"-= (J9t; J$ 4 G-r; co S ~ .J Y. If ~ , 0,102. Wn-;0 J o.LFH.C(. . . W Y1 '=1. 't 2 , ! , "...
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ECE171A_Quiz2_2007 - I---<~ Y (s + 6 + 2j)(s + 6...

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