HW 6 Solutions - OMU 324 System Dynamics & Control...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: OMU 324 System Dynamics & Control Homework # 6 Solutions J. ’21 Consider a system given by the matrix Determine all of the equilibrium points. Are they Lyapunov stable? if b 2 [1 1]T, c = [1. 0] and d m 0, is the system BIBO stable? If instead a 2 [0 0}, is the system 8180 stable? You are expected to give your homework in stapled form. Neatness will be graded. You need to make brief explanations at each step. You are expected to give your homework in stapled form. Neotness will be graded. You need to make brief expfonations at each step. You are expected to give your homework in stapled form. Neatness will be graded. You need to make brief explanations at each step. fl'fl) Consider a system given by "~02 8x+ltlu y = [W1 2]x a) Find all equilibrium sotutions x9. b) Determine which equilibria are asymptoticaiiy stable. 0) Determine if the equilibrium solutions are Lyepunov stable. d) Determine if the system is 8180 stable. You are expected to give your homework in stapled form. Neatness will be graded. You need to make brief explanations at each step. You are expected to give your homework in stapled form. Neatness will be graded. You need to make brief explanations at each step. You are expected to give your homework in stapled form. Neatness wifl be graded. You need to make brief explanations at each step. N W .. E ELMO $3) 2 14¢ F: I M f k Y g“ m% " i. 8‘ '70 X ‘ Z F K 2 M x gor hJM $9: “ “a wal—mwm AJPeQ—L‘on; M z, Emkx flax +. N __ N E: M (35der 611956?»- Kai-Sinfi) N = “mi white" M6Q+m£é sinl9’ méi+m£éms$umflé sMQ—4—N :. 0 j f9 :34- wan gu‘oslfli‘ula %W5 aquéirmfi :03“) “we” QCté-fi eciuo‘gn‘on CWQ 361% 93M”.- equoéfl‘gn 9% M-XI'OI"; M g: 3 F _~ in“ w kg 4,”. me'iam Q.§«afi$+ m'ifl $34? 9”) . 4n . I- “L d an ‘ +M‘} K 4— +kx~mflfi $ML9“+MR.@Q;A§®” an. F ® TM Q‘J’g’k‘. M W . Gain - o? MHM, “é ' "Lg 99.4" J. aguowg—fofi $33 Micflfif Sum r?0f%-$ Texfiflwdt'wlaf i0 +me —?-£in(9‘wN .;5§@’w mgsinQ— a: 9w + M @an- “1933119 — M-wgfi- - passing: mflé f-m;{_¢99(9.1 In? 8&4 “A 9-? i, am m iermgj Swim 4%. awmmlf‘é Wfiunéflflfi Cea‘rOu‘é car-Hm. mass? QM ’- +?:*i~é‘i59'+k\.fl.c,oét9— : 3.9 4?»!L—sim9m M.‘Q'ws<9'mMg-Q5M59‘ : MQ1§+M :{fiwéagg— Viz/x WK.§~MQL%€n9 -; mfil.§ +MKR-wae" ® M w w Wife .4 ' a" I. UUQ con mmflkb Mum“, £5.49... 6351mm {9% ugehg; (6-20") sane-w; owe—xi, .920 Eeluain‘ovflfi cg Mal-3m" ; LM+M331 + M; 4» kxmmR-S'Lsme- +mfi§nm$k9 m. g \D ,= “mai'S'ufiQ’ @ (M%m)3{+£g§g+‘c.x - O +mié :1 ‘F b-PMK’LIST' +m3€k : ~M399” (M+M)${ +kk+lqg+mi§ as: ® "E W99. aw’ flag.” - E%M£LE.§+M3{£: “mgQ-Kg‘ ® The. giggle, Spam... WrewW-“MMM mama x3»: 52 , x3=9‘, M: «3 .ié: {D W%M)RA+EKL+\<XL+M~JQ‘;L{:E ® LL £3: XL? [fi+m£11,£¢_, +m£19~ 9» --m3.€2..2<3 @ [mowmghg 463-3”! E) ; .%_L, .= “mfigxg— MA (mar—L Hm wow W WW”) I+mfiflv E+MAL a , Q mvk. ‘ 4— 3 +E L mi- flw—‘K -- ~"~L 2:. LL W‘M x1 x14— m-i- [i4 {a 3 mm; ‘ m» MUM 1 Ci Lmi.) m (Tm-L X+M£ZW iim‘iq’ WWW WW MMMMMM WWWme .Lkumb KL"! I‘- xi+ czwgugwxg CL €144. fiflwfiz. QWC.L ‘ I m fl we» 5w cum £2“ $9M m (D 7:. x l: a» k“ m. M. i m r- “2.. m»- - WK W‘ x w. I O M+m M+M "A Méwm W M+MI 9 (AM -!~ n—L Wn© ) .- :‘f 1+ 1f" i.~5m'-J3mx_gé~ Xpmi " ‘_u i; will] Ref +M mm 2.}: \‘ii germ XL? h MEQ-xg 9 1w (a Q Xgifilbé‘va—km ]4; mi Lb» M2 Kl”, aim-Qch _‘ 5M8 K3 r M+M M+M Abhm _. . MM” 52' I+MQ1J~MWA)1- =vm31x3» M’Q’ M’rwwa-‘r m‘él‘xui r' ‘ J. M+M .Mr-Fm M+m I a W M m CH ' Ch .‘ C's ‘ .L I A . C3=[(;;+ML1)-»(vmf3) 3 , M at: 3 m3 M+m kg. 42-3 a; “mgfixgm-QM.M+CQEK7_+CL4)<—Ki. M , , mmmmvmlm «kmwm “ h m, n W»!!! “ & “MS’U3 w Sim-t»— gmkflalr'fikgixf 7W a <13 (9% 6% C3 WWW Immnm “mmng m ,, K1: K1 £33“ ( q” 10 *3. k Ki“? C2” “SXZS (“fl—CL CVCL fifi"(~L art); £17) :. >2 1 ---»m% M Sim flaw“ a,ng an L! a 5’5 Cr? Qgg CE a.) a -- LL: “E Kl “ Ck»sz C‘"(Zr aawaa 6:) XL . 4. O O 0 .1. X; 2.8.1:. mm._.€; O ; (:3 Cg LL: 42w ,, @YMA UV, gw&% Sinker UsfiM-e, 0Q a“) when 00‘): O MchU); LuSU), Wank Hag, WNme om *Hme. vehe$ oi) 01 and K SOHOJ Hm Whoa Us w&, _ L303) w l 9-05) > E14) 3 KU'r '3.) , 3%) (SL— 0 its) _ em (21(5); was.) I a ‘ Kcs+mks+~°a> LTSWL gag-em) ELs) 5L5?“ d.) “:0 QWEP Error“ Cbn‘bi-onk ( Ky” ‘Kv: ism Sffififl) a: km t 4-3Kog gave em) (aqua 1) L4) 84 fig GAG. Ewe!“ ass a .5“. WW 3mg.) rahgumsu) V. . wim- ®56= £i—w 3Ko< «3) ‘ ’ Cm Ee- 300‘“; yvom ywwcL-COM.<T- F =— “9) Me) {CRLefiaLgfl §+0L 30% “54%) E : 23m) .s ski fl / (t (‘1):0 an) :0” $2.. {mg}. L iii)". w.§).( M :— Ms) S :3 51.....L amgmwm :akg) new) .sw M {iv-.5. S 31-..L 5 W, W M M M a; KUH "axew; SL453.) |<(s+ 37kg“: 5 13;: w) = M. : emu—if WM tag-t Ewamg + i $leui) fits) ILA-H. *3: F a r. .(s-t'éd" ) Ab—mN—m-mh r um !\ figfiiflzEKX-E- figk ~f)+3w w“: Chm—oust QA‘S‘E‘X'CH .,-_“_‘..,,_ S i EK—WLK-§_ 3"" K 3cm. 3 A KCSK+¢£K4}-3 wok K 5° Boflé W? 1K+0LK~4~3>OK7Q m. K> I whan rL4):Q(nL4)aQ5L-E)/ m3): #5 ngef Qumaéian a __ K (s nmg tam) ° Mg) q t s A; 5A. “Mafia-«3) 93 ‘ +K§L+EI€LS+¢O4 gtéki) lSfigk (3% = um ELM : kmgflits) = Q / 13 4%. liert'g Uo‘b‘civ/ Amman s—DO ® Eauuflg when It“: Luau) mc‘z T4 U3 2 Q - Ddeamna Law How ughag of: K mg K4 €499,ch Hm. 516—0443 flake“- wflue. 9.? mu). FMA {kt-2.. res—\fi‘é-iang on K anal K4 so ~Hmé- gastm €53 fiimgfia. FHW. 4m93e1 gnu-mine” be,ka FALS) M ELS) ; 61m... 3L5) @ U1; _ 3.0K. I EM) 91:35 umfiua; Ice} 5(0-00L57“+o.o{$+\0\<.£) When 9(4): \<Vg MM ‘3 r. / ass 3‘— 1 == Jagan 5.7:.) Kg: Kw K. (Q When fb‘) g; Q o "Dz-germane“, Low vague-a 9% K. mnt§ K4; mggaaL-U-Q, S4m$43 Sim-la. urging, 8:? 5U) huh-‘3“ cia'fiimvkmca inyuaé "Egg MLMSU) 303) z L+ TS ‘L+0.LS TENS) S[TSs(i+Ts) 4-hqu K K; s (o-ooL§+o.oAs—Holctwm\c Fer z“— , _: gfijfls) z 4 “L... i “g {Lagkésiem (s game. 5 “Lyon 5470 L93; Q m Chaim-Qua. mom“ :3; MM. QKMLLQQ? swam a; 0004 51+ ©-om%%"“'+ o-&g+io\< = O (Tl/LE. QjSLw {‘3 un'SL-‘ofia. £43! SO wQ Cam 93* éo jug—\— ng 4rka 0’3— .‘chm ,‘Hruz. Mm‘wm veal-4.6.... 9?. HM. S'LG—OAJS- $1.346” vogue. 0.2 3H) is; 4 a L 40K + K;O"L_ Howeuor! wi’ik—kh‘s Velma 0,9 , {:Lm figs-kw ragganSe. miki Ba Has-3 Malaya, (“at maximum Quwshpfi—L mum be. will; “[0100 ., For K:O-Ll ckmkwsk; miuaiw‘on (g! O-OOisg+©-0ksl Moms—+1. a O or, S 4- 4065 +f0 {(+3 +1000 1: Ver ’6‘“; 4wo wmflex r9045 Jae Laue. Peal Fw-PS mg “IL/5‘. We. [alt ‘Ekew CLmaevLQn‘fiL'c— equa-iw'ooq \oe, wri'Heaa one, Kg+g)(‘<5,1+qg+ :0 «ar- $3+C€a+ 9)31+ L§0+L)s+ eta: O "Ham; Qv’eqcka agar»? ( oLv=lOOO=?\.‘J=1©Q gq+b am}; K453 Q’OZiEIfi. TM moo-L5» oar-Q. / Stuck:- wi)‘, 9-: -Q..‘§:§: H.913; WWW ...
View Full Document

This note was uploaded on 04/01/2012 for the course MECHANICAL MMU-324 taught by Professor Çağlarbaşlamışlı during the Spring '12 term at Hacettepe Üniversitesi.

Page1 / 15

HW 6 Solutions - OMU 324 System Dynamics &amp;amp; Control...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online