EEL5173_sam_exam4 - UCF ECE Dept EEL 5173 LINEAR SYSTEM...

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Unformatted text preview: UCF ECE Dept EEL 5173 LINEAR SYSTEM THEORY EXAM TWO Spring 2004 h PLEASE READ AND FOLLOW THE INSTRUCTIONS. PRINT NAME: 50 L 0 [la/J E 11) NO. The exam is closed book and closed notes. Note sheets (two sides) with no solved problems is permitted. Do your work '5 t t a I. Use the back if necessary. The problems have equal weight. Answers given without sufficient justification will result in diminished credit. Good luck! (1) (a) (i) Does asymptotic stability imply BIBO stability? Justify your answer. 0 l 1 I] , use the Lyapunov equation to determine if the equilibrium state of this system is asymptotically stable. Given the system ti: ilxiflu y=[-2 11* (ii) Given the systemic = Ax , where A = [ C 4 a e / rC/éJ A5! ('19 :63 ¥Lg Q?) The equilibrium state of this system ( With u = 0) will not b asymptotically stable. Does this ..L \E * therefore imply that this system will not be BIBO stable? Just‘ y your g g ‘1 answer. ' ’ bl Y SI 5 is “5‘ 5: (an Us biz/WE“ 3 => 193: cor-74) 15 9"!“ ( " 3 [133; go K 7:;cx ch3 deg, (SI-fl) , . ' . ‘i l I i ' _ r41 5 4 \ WU LET O’lACjJ(SI_A)B.—(§+O;\l’5402) ( tm m olet(SI~A)=-(§%7\,){§+flz> ‘ ~- wean) . ‘ __\ -Ifl»: (11+ij t" (g4m.l($+a0” (“a”) /‘ - . i at.sz {32) : (5+7.,)(5'+92) -' (“7%) 5A As wish-Cid 1‘ 71 ,1. Re art-H4“ o? wl‘el‘l‘QV‘ 45, [fit half {tube A ‘szLiDVS b“ {LEWGMMO‘J Vi ‘ ‘ ‘ . Cancel Willa teleth TFULi‘DIi‘S 5 lb l’lUmetm3m5 Hue V€SU H4 7:3 3:} 001K be, in lie-£4. Nil-F plane. .km‘ ‘0 {he eageanvcdues care ‘ivs Lippi v J") fig“ . ‘ i (1" iokoniaitlki’ rm MS (33: S j ThUL) 5 M, . ‘ l 098 Sine-amine, S'yS‘iem m net 1 (We ot‘Wwf‘fi ~‘L- entraiue; mu (not til)? L! P W W We wt? 9&7 flu." *” We? 9 Cwflsfwdirg ifuélflr) [Sl’fiAI may e ahaewv’el‘) 7H1? 19 mm [of eaten if} 2’ Wyn/h “ /r flee—255m \ \t [bl‘dchéfiflL C0 Adults”; 0/4 50 ‘55; a, 0L hUin'CdraW \‘CKCHVU Say away)‘ {Lego Hung fwxdxdm) if?) 1— Um " (3%) (9%) WE“ hen/’6 L—QF‘F hCLLermve J70 1—6/5) X: glgb/daLD-E, ’ e‘i‘. 5cm“ -. ‘4 v vi "‘ .r >77 (’70 ’ V‘s“ Mgr/ME :[~2 (3&3. NJ [‘11 ’1‘, “079) 3 r; V. . 9-? f 0 [L I) [2 SJL Sky-2, ‘2 [‘2 GP] ,4; t 35 $954- LHPI%Ie,.". :. é??- ‘1 ._. 3 TL 4.. 3180 @(‘91‘0 5‘" 57/4315 {Er (#115 '59] mgiwe'pefinle) [? til] 33:; gm ix; 2:][3 4]; [34 3 I EZLnf/e— Uffer : “film/)1), t”, :5 P12 : l/Z h H (carer Tl1_’>]L‘PLLT—O :> 52/21 : ‘lv2(_2,L):'Z >3 . : '>}’u 3 3931+le _ f2; I >— 7: 1L I ; 3/; . P: [it (1/2] Check “QCKJI‘Ng yrcmrlfi WNW} £131wa Fouczzb/d 1 ad? 3/17 0 . _ 6/' _ f/‘sz/Le> 0 W56): WPX‘ :ZL {3901‘*Z/\’)XL‘*£X§) [M ‘3 3]; " W " W ' I my): ~(xfi+xf) >3 77 V3 yogfiue a75ka => 71% A h WK) i} 705. Dem/m; / 4! I ,9 ,_ ‘ t . ‘ \’ J17}an 0;! 064Ljenya 11795,}. )4 d- .~ [716“; V001} NEG DEF/M/Tb [‘5] 0'7 fog, U6 e75” / s—l (2) (a) Given the transfer function 2 2 3 , find a two-state variable realization for this second order , S + S — transfer function. (b) Can it be Mr observable and controllable? Justify your answer. ‘ o v . . _ 3 \{m :C;~—1)E’($) =5 y‘“ : Elf) d e 6%) Y5)- 94’ NEE? z» _ i. 1:. , _ 59 I175) ° {Li—25% E65) (MST-{St {*zsv3)t5‘$)- g L“) +ZS‘;(‘) 3 fl ' i/ttl’tfl—Zélfl +3666) {at} rt 1 :> (if; :iasevvaué~ \flg _ W -_ Wafigi ddfire CUPQ Common. ,— ~ . “’ $T UCS) (“3) ’(rvr i deflomEMilvr— (1.9. at Zeroé Q’rO-le) IV % lows LU; ‘iio Conch/4E: “that emf {lag/e 0H" ‘ re, Qflku‘ UACOI’leO Qrmc \ S”. S) Sly 4L9V(§)"§Y(S)= SUG)’ . , ‘,_ f L. " ucg) s L+29~3 A“ ) n . ' s- __ I“ a - ‘ 50' [email protected]&mf\ Fof‘W‘x *1 1:97 _ S”‘ t S“. t A"; g: 1 UCS’) _ $7125”; (3"?)(91’33 S"? 3+3 “‘> ‘fm—z i . . i 3: W991 ()0) Jr EJE‘L/(Sg Wkere kilkz:o New gr); meant VHS") : U15) :3- M -7‘I txdt)’ ~> >7; 4:,“ + y, :5‘+ + 9’43 3L" {1 : XVLH “Z; 22 '3 ,w—zzz V V: ACLZH’EEz [K A61: [ 1:: f Earl: Va?" 1.} Q‘CtkL12 (T19 4425-?! 5) QLS‘QJ‘VCLLEQ. :I n: K112 >> UMLSQWALQ‘ Tim’s: Aime lukzro 5% kl 4‘1 C5 0 U RCO “Ra {[ak‘eé L,me Eeir Va O ( UACO raffle R bof 0L Servqme . l a Co klfi‘o “disk: but stobgermm £95 [Iv/15% jé’izgréédi 2, /5 UnamfiadzZ/e Unfsézé/fi [fag/Me ~25 enuduej fir!) ,— flérgflre) flh-e SfS‘lem L} (See 72.33%). m (Nib JEF'EIKZZU/ «3-,- fler—e/QN, “#16 xfskm xi “ Ii unalierifagff ,5 U/LJ-Lléfifr (3) Given the state space description of the plant _ O l O x: x+ u 20.6 0 l y = [ l 0 ]x (a) Design a state feedback system. Specifically, find feedback gain vector K such that the desired characteristic equation has eigenvalues 7%,}? = -l .8 i‘ 2.4 . (b) Design an observer to estimate the state. Specifically, find observer gain vector L so that observer eigenvalues are 1.01 = koz = -8 . (at n<~.-[ o. (3 [a ,M] 4304) A _ 47(9) '1: (3+ “5/ +j2ifldf/J U24? : Q 0 91 0 9] m: 2“ 3‘4 ¢ 17%“; 294 m mm (Pet‘s): (3+5): 57"? “97L” ._ wb O 0 @315 /M n '0 ( ’[0 [é] ,er O 3167!: O ...
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This note was uploaded on 01/14/2012 for the course EEL 5173 taught by Professor Staff during the Fall '11 term at University of Central Florida.

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EEL5173_sam_exam4 - UCF ECE Dept EEL 5173 LINEAR SYSTEM...

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