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A#20_Solutions - Assignment#20 — Solutions p.1...

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Unformatted text preview: Assignment #20 —- Solutions - p.1 ECSE—2410 Signals & Systems - Spring 2009 Due Fri 04/10/09 . . Y (S) . , 1(30). End the closed loop transfer functlon, X ( ) , 1n terms of the H 5 shown. 3 (b) Assignment #20 - Solutions - p.2 ECSE~2410 Signals & Systems — Spring 2009 Due Fri 04/10/09 . . . . Y(s) 2(20). (a) Leavmg K unspeelfled, find X( ) . s K _ . .. . Hag: $3 3 M a, K z W1 319 K ” {wymzfiK 32+. 3%(2HO K 1+ sax—8+2) l Zflhxa wag/z: f WE Zi-K 41:7 7:4.me fltéz‘W: i ( j" ‘l 3(10). For the system shown, find the value of K and (00 so that two of the c losed—loop poles Y(s) (P0168 0f X(s)) are at S = ija)O (i.e., they lie on the jw—axis). K K Hfilawa. 1: 2, 3 Z is“ H. “L...“ S(§+t)1—l<~ 5 +23; +S+K siSl-ll?’ 00w 41w "felts W St: $516? :7- $522+th 0 Mtha~é1da% g +2. SWOZW w 34% mafia W 2s1+C:-aa’le—tKL / twwgzao =’> w: L leg: 33% M < 2%: 0 1/50"- (:»w§E+ ((620%) W 1....) Assignment #20 — Solutions - pa ECSE—2410 Signals & Systems - Spring 2009 Due Fri 04/10/09 4(25). Given +4 M ’ X (ST A): SM K1 11% (+ £3th 113+(i’i‘K) (b). For unspecified K, find y(t)= ym (I) i..,e when x(t)= u(t) K p 3:— L .13. "T LS: K diff}; 23”” 4:11.... 1+1< “‘9“? 311341111191 6» s+0+f9 S sHHK) .. K {S --a+K>t‘ WWW” Ma 1.4111 WK e W 1 (c). Find K so that ympfi I) of the closed- -loop system has a time constant 2' —- — .4: gezé‘f’cga “0*“: 24:1 1+1: $114233 ((1). For K: 2 find the transfer function, 12(5) (Note, you need to eliminate Y(s )+ from the equation) X(s) “<51 51$):xwzxcgw) x(c~‘< r/z/f’d 515} 9+! Em W gm MM) Sfl+K S$~H+K (e). For K = 2, find e(t) when x(t)= 11(1). y; -3 £5): 3+1 "‘- Ki: 3/ Assignment #20 —- Solutions - p.4 ECSE~2410 Signals & Systems — Spring 2009 Due Fri 04/10/09 5(15). Consider the RLC circuit shown. + W + R L (a). Find H (s) in terms of R, L and C . 96(1) C W) (b). Evaluate the exact [H(a))] at - Owl—O — l . a) = a)" = —————. Express answer 1n «[1? terms of some or all of R, L, C. (0). Suppose that R210000hms and a)" = 10 rad/sec . For the Bode magnitude plot shown, find the values of L and C. Note that the value of ]H(a))] is exactly 3 dB at (0:10 rad/sec. lit) __1__ SC. .. 1 W5): 2+3“; “Ext-s10?! SC; 22.2 ...
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