EEL5173_sam_exam3

# EEL5173_sam_exam3 - UCF SEECS EEL 5173 LINEAR SYSTEM THEORY...

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Unformatted text preview: UCF SEECS EEL 5173 LINEAR SYSTEM THEORY EXAM TWO Spring 2003 PLEASE READ AND FOLLOW ALL INSTRUCTIONS. PRINT NAME: . v i ID NO. Viewing Location: The exam is closed book and closed notes. Note sheets (four sides) with no solved problems is permitted. Do your work on this test paper. Use the back if necessary. The problems have equal weight. Answers given without sufﬁcient justiﬁcation may result in diminished credit. Good luck! -— 1 l (1) 5c=Ax,where A: . 2 — 2 (a) Determine and plot the equilibrium state(s). 1 (b) Assuming x(0) = [2] , solve the state equation, i.e.ﬁnd 161 (t) and x2 (t) , t Z 0. V .. v-X «ll-X :3 (a) Let 73AX\$O / W ’ L x X):>(‘2_ 7A2 ezzmigLn‘m states We flu; News am a Law “ex. ~ zxz :0 (2) l” E?" i av «— } (1:5: .LQ, \/ )‘A' i H \ (a) Consider the circuit above. (i) Use the expression for stored energy to determine whether the equilibrium state is asymptotically stable, stable ISL, or unstable. (ii) Use any other method to answer (i). (b) (i) Determine whether the circuit shown is BIBO stable. (ii) Is the state controllable? Observable? (a) ‘ I :in W 7‘). ‘l‘ VL. "-1 M n V X L. "-’~IH , 0:; F L. . t __ ‘ . __3_._ "if “r X' ‘ L“ + UL {xl+>3.= 2) 7":“’7‘1 x. -+ y} - >11+>¢L s; 71 :X. +X.-—XL z u +>(I.2xz m: [0 *mm )6. ﬂ ’L 'XL 7 l 7" X1 13 t: m E "33) EVE—m: 370+; L - W“ O Z 795).“ TX‘z XL :X‘ C’y).> "+ x1( xi ’1X1) '2 -ZXZ‘ E (x) is néjocf-‘ve say/wwtef‘ufe, \$9 the sgswm (>3 ij me’v _ = 1 A , - “'5 0’7, Y1. ED X4: *XL 50 /‘ Xzzxu’ZX‘LE-O 2”) -Xlgo ’W E Clam flea/w [9 e :‘th'mle? (9 EXCPTM‘ Ové 1L“ at”; [mm f9 iw+ £0, 0). Tiara-ﬁre 4w, 6175 tam U .fffiiéfl M 5a. Ma _ L L) ‘5 ‘ ------------- —- MM 1 C 8‘ sub/mg the, eiM’hm I [LI -A[;‘O whoa-:2 A :[0 .We +141 ﬂz‘ath/LuZ/S: [Li a; A; z __ k . 3 . 4; bot/'11 Awe he afv‘ve ra L . t e 5 HM ‘ ﬁ'r".m,vm L101? 3 at Paris, f7 “I ('2’ 109% same 1&1“ Mel asgmr-toﬂmﬁL/j ﬁnite, do) Q?) - é-‘nca GLSWFToMOWL «ab; Jmfta‘a 37-30 Stwl-vi'le‘tj_ ’ 451%.] 5,-7st also if can be 1/5 8‘54 M +9 t . La 3-} Ls-Hﬁ LSEMI r i ' 3;. <4 L J 1 (\$44)" 6“)! I —-— 9H TMefa’re ﬂue, gqjsw/M b; W m mmtéeiég (3) Given the differential equation + — 2)) = 12 + u , ﬁnd an ineducible state space representation. 51' \{L5) +s‘fés) "2 Yés) :: 5 Uts)=-=+ucs)y v— ._ 3-H , * 5+! Hg) U19) .— §L+ svz, : 14/0 CW --{»mc'be'r‘ Shanei ﬂu», Mme/mew Moi 1W»: Aenm;nqm, mt» iAA/B wwwst 1LW0+3WL ‘55 “Mamba . (LIN/4’ Ed? mswu) W 151+“ Wj-‘i r“— *1 X2: 5+3?“ )(‘L'fUL'LJ : >21 ‘(J=X. "7% We 3&9 {761: nth/L17 : ‘X"+y1'r“ XL 2 13+ :4, : LX, + [A 3 z: X, WLWOA W’VeSPWS To the wbwe nannies _ (4) Given the state space description of the plant ﬁt: Mt y = [50 O]x Design a state feedback system such that the desired characteristic equation has damping ratio C = 0.707 and undamped natural frequency con = 10 What requirements must be met in order that state feedback and state estimation may be used? L Recbcu‘re mw‘f .‘ ales K: «[6 *3 P”'€I>,< (A) ‘1 {19:95 CA) 2 A14? zswaﬂ + OWE]: 1 ’4 a.— A2~+ 1414/4 +100 1 . .4 f 1 _, 0 I ”’ ’ «ml -[0 I] [I -2‘] < [1-21’1'1 7. * Z 3 a - 44H rm ‘1 j -— to If) [ l <[,,é é ] 1 Lazy; 49.13 i [00 “ ~2_ 0 [00 V 90 - + ’ 1 0700 K t M A, [I 0:) [93% HALF/l “ml ’2 7 22:3“ij a; — [agree HA4] Rea/octane»! if” L. L “- __ cb‘ESC/Lt) (2—,?) 'jT' W [0:] :0] .awat,’ “:1 4753556) ’= A‘er LS’Wn/A + will I 9” g’wu’ :35 wt least. 1mg tun“ \$3001: 7‘07 in WK)” +0 Ina/AA. €5‘t‘3ma‘tar The)” f& Sbis‘tw ‘ SCL’i‘l‘sfyaj ‘ 1‘ .1, 1._ ___L___ ~ __, _‘ ...
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EEL5173_sam_exam3 - UCF SEECS EEL 5173 LINEAR SYSTEM THEORY...

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