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Unformatted text preview: 5. (20 paints) The deneminater of a elesed—leep transfer flmctien is given belew. 0 am = e“
1+____.._{f_  0 as a .4 I
s(s+4Xs+lO) F0 ‘ S? a." '1' b
Sketch the system’s reet leeus far If a 0. Be sure te calculate all vital
data such as breakaway pair1ts,j—axis eressings, angle ef arrival er
departure, etc. 4/
g ._ t ' ' r _____ an, astral1m
0 Q1 i... Pi R1 3 (a)+.' ('4) 4' flu) 1* 1.14 aé 4Ibfﬂrﬂq In" C'ﬁ “L
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(MC 33435 ”I“? H EGR 4332 _ Name (meeﬂ ME, IZE tauf
Seeend Exam
Oeteber 25, 2007
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3 (O
4 4' ,
5 f”
6 EL. _
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Tetal 7 i
Clesed hunk, elesed elsss netesr
Twe 3 5’2" x 11" sheets ef netes permitted.
Calculaters permitted.
1. (10 paints) A system has the ﬂﬂrderder transfer funetien G(s) given belew.
Determine en apprexirnste seeendderder system Ga (3) by using the
deminsnt—pele sppreximatien.
15 '3?”
G(s)=——°9—. .2 5 _
s(s+3Xs+50) 595*?)(‘E2 4 l > 51:
_______ ”WH'” “" i
05* {151“ (@541) s .5; 1590 {’53 { at.)
5—) er 7 W 1? (7r; [5) 2 I ECEVB) ) 5(5+‘3) E 5.3+?‘Swh Siiwni j‘ﬁ *jwﬂ i ”h jg“! 2. (20 pnints) A seeenderder system has its peles leested at s = —5'i j 6 . s. Determine the damping ratin C and the natural frequency n1” . b. Fer the timedemsin respense, determine the peak time TP. e. Per the timedemain respense, determine the settling time T3 . d. For the timedomain response, determine the rise time Tr] . e. Fer the timedemsin respense, determine the pereent evershent P.0. .r  _
 if L 1H
I ”(“511 1/ _ 3. (15 points) A unity lIJeetzlbaek system shewn below has the plant transfer funetien
shewn belew. Assume that the elnsed leap system is stable fer all eases
considered m this problem __ _H_'—_—I—__ .ﬂ'JlLLHr Tia")? E212 (axis)! {I {11 . an) , as} [21 i + s
S I + (21's) {Acts3"} ' "  GU :
M
( ) 3 +1 7 1496 0
G s = 1'3
Si32+65+2i "Tlfﬁt {7‘
W571 61(5) Q5051 " REX a if r(f) (f) and G (s) l fmd the steadystate errer
ls 6(5) was) 65310 / K.
‘I‘I IIIE'“I
Ema51 5(;;Hsﬁ) it 3 L}. b. If r(t) = £140), what farm ef GAS) will give a zero steadystate errer'? 616‘ if?) 1 6 Egg: :4 a 5.}: 3+ Gc(s)=Ks" / . 4. Gc(s)=Ks"
5. Gc(s)=Ks'4 ener'? 4. (15 points) A clcsedlccp system’s characteristic equaticn is given by
Q(s)=st +15?3 +11%1 +4s+K=0 Find the range cf values fer the gain K tc ensure that the system remains imam Millie...
3+ 1W; If}
'55» 3 ’3 4 c
:51 ?3_ b
i '5' ‘5
é” a; 
in H“ H _'I'\.—r.nrn— ‘1' \J 6. (20 points) The deneminater ef a elesedleep transfer ﬁmctien is given belew. K5(a+3) _
m4 F F"”"Lri‘i‘ﬁﬂ 32 +5++" Sketch the system’s rent lneus fer K 32 O . Be sure tn ealeulate all vital data such as breakaway points, jaxia ereasings, angle nf arrival er
departure, etc. 4a 4% "3 Mwm wes m @1115“? 3} 6H“: i‘Pj‘ {1;
”I?  'Y ...
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 Spring '08
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