Midterm_F09_2

Midterm_F09_2 - Midterm 2 for EE3530 Fall 2009 Figure 1:...

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Unformatted text preview: Midterm 2 for EE3530 Fall 2009 Figure 1: Feedback System I. (7pts) In Figure 1 above, let e(t) :2 r(t) — y(t) K(s+5) 10 T’ We 0(3) 2 (a) (4pts) Find the range of K > 0 so that the system is stable; (b) (1pt) Let K : 2. Find the steady state error e(t) when -r(t) = t and d(t) = D; (c) {1pt) Let K = 2. Find the steady state error e(t) when 7'05) 2 0 and d(t) = 1(t); (d) (lpt) Let K : 2. Find the steady state error e(t) when r(t) : O and d(t) : sin 2t. 2. (4pts) In Figure 1, let 10 :s(s~1)' 13(5) Find a first order stabilizing controller 0(5) = GUS +111 P03 + P: such that the closed-loop poles are at —1,—2,—3. 3. (4pts) In the following feedback system, (a) Find the values of K1 and K2 so that KI, : 2 and C = 0.5; (b) With the above values, estimate the percentage overshoot and settling time (2% tolerance). gCaWovx M‘cl/WM; EEBrgo 11- demélm “T- 7:- T: ;:I<cs+r) : man-s) s cg+4s+9> +tuK 3+5“) 5 3r4si¢9+1olgs+g~o1< L a c ‘ @ (L own/{LU shcd'DOl‘Ir 53+4f-52i—(84—(ot)s+fo}< $5 _1_ 8+!0K 52 4 $‘oK S «gioK)-fo|< _________9 32*[DK . ‘1— 5 50K 37 Rmmhmfi mm...) me “Ecol, fly, am; “I: >0 H’wnt fww‘wéifiy/ Mama! 4. (5) K52- 77;? 51/57L'7'" "J 575:5]? . 7Keq§¢nlvm {k} fife- /(/:,§~:54m = chflme fig 7%w75641 571.71 —9 q '5 Jfiw‘f"? *7 @595; _.: “f” “3"” .— n KV 53K to»? 2 0' of C9 mare. Jlfl=1fl/' 71-»: (any): 0. _ P (0 ya) _ 320 EN) = -—)’c.o WM Frw. IT‘PC ‘ 3 (,5 H, 3 I702 \ 5 j //rsz)a;:) danmfiéfp) 77693?) '# loS _/ 2"; H My“) my) séwfi-aym» 5sz H @175? w 20 N -. :___,____. 1 0.2857 43 2cm L ’35‘77 2.; SCS—I) (p05+/.)r/0( (20%” -_~. 0+1) (5+2) (1+5) 2. [2053+ («/pffl/QO)S+(IVfI7’-fogo‘)$ f/O fl 2151'- K3 allf'fg fil’w 7"“7’°=5' “772+”?w/L Mir/=6. $74074, ¢z=7j fa=/-cP- 27:06 M ' a [.4957‘6'44 g0“ Jf7 TA; WA? 7;- '2 Lou: ,' S1: L=ifi pm A; S 5(5r/1‘2sz MW -: 2K1 : 2 e Ky hazel. 2* . / Cu”: 2(/ [-2gwaz/71ZK2 : /+2~K2. Q I g .2/1; ._ eJ :> [(1 :/+2Kz ! /+ 25sz Home K f— l: 2K: :> £32 _ i I K “ 2. 6O Ounfllzkl :‘2 -ZLL 19.020537 "5’2: “'32' 4/ 1‘5 :- i '1 2 4% ...
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This note was uploaded on 02/03/2012 for the course EE 3530 taught by Professor Chen during the Fall '07 term at LSU.

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Midterm_F09_2 - Midterm 2 for EE3530 Fall 2009 Figure 1:...

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