Lecture10 - EECS 22/4 LECTWZE NOTES 10 [m 6W1 ' {mm/Mani...

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(feAH'flEMtfldT) + = AGM—h)x£ + AND-Bum) {a :: AX/f) + gulf)“ chm/L \H/La‘t fo) SMLESJCLD W im'L-a—E amabsl‘m: %(%a}=€/HO)XO —r f/ 0(1- : x0 4———» to I Wm Illa}: 7‘ l and 1,15%; IS a nmmwfl H’lfld Amplitude 252:1 I z __ :5.— Gig) (Ms) Sl—IZ (5+R)(g_;1) [Mun/Ling 72/10 LC») guy—>960 Suppose, we \waL 7L0 me cm’ZF’aM/L Ids): 323 mm E=JZ '3 ({6} m \Im'eat +0 ecu/(cu W WV)th fob. at 12 ami Vb/IMLQ if WIWL a/oou [oFm [ca/9) at W 0119mm 7L0 94w; mu deaoéj flute Prop/1W) F9” KM) ———>’C1(s) -— i6, ‘ I yaw Wang/Kn furlch IS gés+~nj Step Response 1.4 y 7 7 r > n a V0 1.2 » ‘ ‘ : 0.8- ‘ — ' ' Cloud Loo \ 3h 1’ WWW 0.4 (IEGDW W40 )9 Lam 0.2 O ............................. ......................... ._g ............ ........................ ............... ................... . .................. , ...................... .. .............. .0 Time (sec) Kai’s /001¢ af w/mfi we’ve Jon? dame ugmj a Shite Sflmot madLC: S—fl I _ . i S 1—452-th ’XL‘.— 9 'h' : 7&2 =flzx, +11 also up (fig—Q) a => it: fi—flfl— (“MUM/11:17 we 21c. an J17) gold/4m 131: 71—14 xgzflm . V’Lxe sfafL S/JGLLL Quayle/m me W1, above (Glut/L Lao/o) WAUWL 01/11.: dePdP tf('S'); 1/(5‘2—1) (s-l)/S; N O m wuw EECS221A CJT Inverted Pendulum Unstable mode "invisible" in TF but "visible" in state space model First define the transfer function and plot the closed loop step response I % unity feedback closed loop system step(K*G/(l+K*G)); % Next, define the state space model [010; [O l 11'; [l 0 0]; 0; onwzv 10-1; 0 0 0]; I235 % open loop state space model sys_ol = ss(A,B,C,D); % unity feedback closed loop system sys_cl = ss(A-B*C,B,C,D); % closed loop step responSe step(syswcl,20); % initial state response of closed loop system %initia1(sys_ cl,[l O 0]); CCQSUX Loo/7 s/L/A‘Cz’m mfmnfaklrcm M, gfadx 5/70LUL: X = Ax +Eza-cx) ' x [A—Bcjx +BK Y;Cx ~— ' IO. CQSLOC {00p flew I’M/W; INLM 57am I’qu (Wt Amplitude 1.4» 3.5' N ()1 ~?_"“””‘_7“\7—"fl- ‘ 7—" Step Response Time (sec) [ ReSponse to lnitiaI Conditions 1' 7 " is UM’mWL Time (sec) mo) me) x? (o) 7, ........................ .7. ______ ,fi... ........... .- I "_?“Mfi‘V—“'"“” H H ) Man mt)=0 and D (he/UL) an we $746M see) I could ham P/erLVC Wm thbtz mch. by Gail/({7qu? : {413Lan (A) = gf/)” , 0} JAg/cnvak/Uw) UvEC) = § I) “i— : . /ind4‘cam imlubiuj/ US/mj whaf M yww [gnaw abauf Sch/311W 710 Sfatc Sfad, mach/(D, We oat/M Jalm Wu. 0000M MASK/0L L00}? Q4/5me manaWca/gi M at A=A~'BC Wm M afoul [00/7 iQ/ffcmls 5m: Way/.0153! is: w) = 6“ x0 + feA‘JVfl B 20000" 0 E: N using .(lsi, [AMI/mm Wat A=lg (1)3] "( O o a“ = 55" ((sr—Z)">= 1* [g "8 fr) I O s 13. first Carnfufl, [(5) ‘3' 3]". “5471] Gout/t4!)— I O) jadan leVLaJ)an/VL §0VWflVmiu W\flLOO(): 3 ‘J o I 0 O O S I Q I 0 l OJ 3 O (y ; row 3 — é- - raw .1. S “I C) / OJ 0 0 $ I 0 I O O é— s—JS—o I rowB’ng‘VOWZ : 32 S “I ' O C) 83—] 55') S”! 0 I is _ I Q) 5i“) 59—! £T O O) I '5 ’1 52 59-! 85-! S3-} Xi: — 52 _ WW!) 6 "' 0% I I 31 I 83,, J S —g ’5 -l S”; PQYXZ’taL %au¢«m UL/oammm (j each Ifme M“): wrfifi“ 53” Qs—z)[(5+.§>z+.7s ~25 "I 7me in @A IS _ s?— - of'(m)‘ofi $+zggg—u}> N6 aim/Ii acWa/ Md ;@ email «MW M“ 7L€flmD [’4 6A _‘ We, W 044% I'n‘fémwfid M: I. 7cm Mm “9:0 amt xa=[of] C/ 2, y/(t) uni/um flLt)=57‘L/7 and 10 510?] 50/ alum; 1. Mt) = @Xk/é] : OZ" I S 2' S -} ‘ (s-w)((;+.§)‘+.7s) J S 7' -S 0 *5 —I s 1 0 - $2 3 0‘6 I (s-I)( ~ 3 | (5")( I: D —5 CS-I) ( n 3 Vi,— unshbk maoLL JAM. Ito Poly, @ l, 3 N» at + M €"5taos (4.75” f) Sawu, ” coreranf WW II .— a 2. HOW 760 o _ . [a] mat KHZ)’5{’€,P, 0 Wk): [1 o 0][ft€AL£-TZ—BOLT’] : [j o @j[f+€Aé+-HO(T][ f] .t S : (fix-I [(s—a)(($+.§)z+.7r) _(5_.)(I n ) NAT .6 s - (3/0 I of [1 (as/mm, 01:5?) > I “h” UWJ‘I‘IXHL moofl, 3&15 f cal/lama“. .— I O 7 shbu fe‘°‘"‘"‘> cos (WC-E'T')>a{7‘ IS. ...
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Lecture10 - EECS 22/4 LECTWZE NOTES 10 [m 6W1 ' {mm/Mani...

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