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controls test2 - 5(20 paints The deneminater of a...

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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, astral-1m 0 Q1 i... Pi R1 3| (a)+.' ('4) 4' flu) 1* 1.1-4 aé 4Ibfflrflq In" C'fi “L -"v- 1‘2 3 3' -- ~~~~~ M! a? L ”.5 W 3 Li: m M? (Pk a '50 3:35 «we! 3 F E10 ,/// Q. —- '54 (‘5 7 Rs: 5( H “1:649ch ( "1612‘???- (MC 33435 ”I“? H EGR 4332 _ Name (meefl ME, IZE tau-f Seeend Exam Oeteber 25, 2007 1 1Q 2 _J_S: _ 3 (O 4 4' , 5 f” 6 EL.- _ “f" 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 flflrd-erder transfer funetien G(s) given belew. Determine en apprexirnste seeendd-erder 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 seeend-erder 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 time-demsin respense, determine the peak time TP. e. Per the time-demain respense, determine the settling time T3 . d. For the time-domain response, determine the rise time Tr] . e. Fer the time-demsin respense, determine the pereent evershent P.0. .r- -- _ - if L 1-H 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'J-l-LLH-r Tia")? E212 (axis)! {I {11 . an) , as} [21 i + s S I + (21's) {Acts-3"} ' " | 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 steady-state errer ls 6(5) was) 65310 / K. -‘I‘I II-IE'“I Ema-51 5(;;H-sfi) it 3 L}. b. If r(t) = £140), what farm ef GAS) will give a zero steady-state 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 clcsed-lccp 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 elesed-leep transfer fimctien is given belew. K5(a+3) _ m4 F F"”"Lri‘i‘fifl 3-2 +5++" Sketch the system’s rent lneus fer K 32 O . Be sure tn ealeulate all vital data such as breakaway points, j-axia 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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