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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 ZiK 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
siSlll?’
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“; “Exts10?! SC;
22.2 ...
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