Advance control systems notes, Lecture notes of Advanced Control Systems

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ee SE Untes ds iy > Yoo eattol Condtibvy meang We Nob tohirg ¢ + Ate oe Conditoo 4Hhak meon mot gare comely x(8) #0 ‘ x00), * In borin func ihe onreqflact satfoh | Condor Ate | Akot pace analysts vo nek * use BOS Oo, > Any Ayskrn papresenk fo x Me stole space ayilom ond * bronufot arystern - QD? Aralyre | on Wikig ‘Sytem wnodallirg ok thot +e ste one oro ib aS 8 he i 2 Stoke apoce anodo . furckion reco ah 8 DEpffowrees _ leo Transfer ecttin’ “medal @ “Stofe ere enodedds— | /-ceardentprntion soot Slate re rel: f Th% a priicoble Lo 1\ Tbe apdfcalle te aa! , 9 3150 nA cag ) als, ; ? Bingls ofp) * Yirte Tron foo moddl| 2 alathepace medal fs 2), —_ ve . ciel Vee bot? ‘tie it Eo ond non th ; ( 3) ~tiel Afton of 8) =Total — Condiidor 0x2 augers axe. mot t Cone? dena oe fol the, given Oak ectia. Cond tons | sypleen u) Tk trappicalle | to a) She ppltable to Aes @ both " plea and time Savaxiant spree! ¢ovaxfant “apilerns + states. (ate a at of mintnol vartables auch that the © Knowledge of tHe Vasa bles ot e t= t, and Knowledge off Pnput at tseto whith Analy ais the dynarnfc bochavfour of the ghen aytarn Complétdy. ) Dynamic behaviour = cont to time, behavfour of sytem: Vaxiables- Thin vasutables by wshtchy Stoke 1.9 fama au Known as state Vooa.bles ( sepewrented woth Hy Ar Bt eed: xn) y Bote space. he space region & % formed. oepuunting atote vautables af 4 Co-ordit ants. Stofe_vects\ * - Shout ralew } Clement ae , Considerxud , Tes a veckd whose os Stote vadabla » T&, supextted wrth %). KX = CooumN matzfr (4 coloumn ) X=] ay un Arse enyvattons- iy: ) iain aycie spe) eee fadionds Aterential | elernernts - hy sole votables , 5 x+e where A, Seohors +o Syftien ronda « Bytem matree = SQuasw makste | ee 6 oufou to Ton put matey X = flout order diffemtiol vectdl f— Olote variables. ; from the Output eqwatioo Y= ¢x +00 Y= 4 -57/x\+i [2] 0 ya been x3 Wdentty he — rput & Output of o gen (2) Tdentity te —- tov elements Pn +e A CInductor ¢ “Copactbs ) ® Cons?der the cunt —forou gh ard Tn d and aroltage acvofs Copach® ha& stote vosuto hed ' (4) wintte fe difential equatins WP pout on vetng Kye sikKet fol the gen beyblarn- 4 (Fae step-y corte the > eke equtation and Outpt equotbn — Sh matstx faim, ; (0) For the efscufl vehown fo, Fieger: Obtain the . crate space xeprerentation — Ue 4 prystcal . Vestal % 3 Ri uy “ ; lg’ 7 .— vel Ruce 5 = ) Output Voto ge ac 104k Ro - athe tdage clerrens fy Ae creat 4, Ly nC. ‘ avoent Ahrou Bodiuct® CL, sly Consider eusount riRrough lg 4s Tly ry Volto ge acKed Capac td is Ve By ong A fect Qoops - E d It Ve Qyfly #4 4TH yy, tee PSE ge a) KA | * [dtto ex second Qeop s - x3 fi ¥ “ y ——— eS Lgd TLy te Ve. 4 Iu, Tl ondve ee x3 -- --%n S bles eee shat: vob! oma toy : Arde] Tlg, a3 2Ve Vo & supreronted as TR (Vo 2 BiterR). en \- a = Ne 2 AZl2 4 las | iO) dk , from ey © - 4 E Ly ATL) ae VR, Tey sage My i at Ax, Sete Ve eee a 4 ui mia hn Fenieg @) - dale ' rf Me 2 TRSR “ues ac Pee et? ©) la Lg i trem ea : a cee “The aharte Yanciables ave AR Mies... tn LL ~The State eqwuattor, 4. % = AK +80 ‘ ( a ‘e] ‘ ve ’ Bat : a ‘ \ ; neh BCI + zl (vJ 4 |\Necr Wes ¢C ray J Rea Rea mv NC : the “| oh Salt & Ta send the cute ent Applying kel In trerctvetett ¢ ~ T= Jqt+ TQ Tey =v at- tage Wey = Tt ae Tg r ; dt i rng avec) Snag Soe BY ' Sco the otras at. eae. - ie Vepy= | at a if T= a cy Ch (Vv. Ri i VeVGy vey VCR & Xie, -VCR “ke ¥ ( ORB ; = Ro Ve = (va as) re Rc = NCL Pa NC 4 VOR “i Re, Bal : ' Me, = setae ae Veg as ae) Race ue fiopat Aas = Cope’ Krottage): eds Po Ictreuit ; at Ry i) B ‘ . é Vex e Vv ; ; F - oh NE a) . EWG Ra yee e ae ‘Output vectsl - y =@X+tDv- NAN x y Vee ¢ i) rw) [MJ = Co mas} [tl + Co] el)” © Represent the atake «pace fay, 0 ee efreutt an Stepi:- Tetentify' Grpat ahd Output: fret . as Vv and utp as Ue Cacrow C apac? tot) ® —-Ahe Slovage element fm the cfruuf ee and! 6 5 1 @ — Contaer tHE ween, rough Raductu and Vo Hage. * acoA Copodty) Ve. e,: ; he Aote voice an DLandve. TIRe Stotevecd Pe | xe HS Axt+bU Py , 5X, a OM x 0 . ae wey + Y [v +? Bote Ui. o5c O . Ve au (a rely faplace tranufeten te +the. equatforr-(1) C Converting Hime clornafn ento S.dorafin coho Y(t) and WCE) we functors, @ s"y(s) +9, o* Dycs) +a, 5" y + - + Of- 1) & VCs) +7 On YGs) a ™m 4 : > bes™ucs) + b,s™ ls) + b,s-2 ren FE ts ~ be S u(S) + a bmULs ) from these equettons ys). _. bes b, gr ba 2, OCS) | = Sha a, MD yg gO), he above eaquattn reproents Lranifn chtiog worth —Zeroslrumedand poles (denerrfratd) a /Stote_space pope Bit Br the tromger function cotthout Ley e Y(s) bo WS) S148 +a,$° a psc) Aan -)S + WH Xt, ko = if aay me . yasco Bes Peas = 4 el = x6 (N-2) LAY = 9 Ss3/aRaveluconus bay dotg Aranefer feratfor Stake — ertoins of | | Y(s) bo : i | : bots ee E = UGS) e+ as7! + O25" Roe any een | 4 ¥Cg) (204 0h Caer aT On) = gt) Oy-1eo) a . Us) ~ et S*4 as"4 as! ‘ fot Ys) 2 PYCs) pms) ) Wy * [ 0 | es —- 1) fy har (| wen ey iD) (u| vac veda Her, © fordh ond preveriled rea) Demay® th One tan LN bs Ps © \ Aq a ¥ OH ta + 6 PUES oe «GAs Way = 64; UW=0 ©) aa ® Conv ob'ng ®,@,@ *% eat? fern rq be ON ay o 5 0 14/%| +? (v} a6 eae ee ee ap eidotn Ane Out put Vecto + fron eq @ a pk >. © i 1 . Risto} ol¥) Xa Btote space sepexentotion unto phase vasa bleg The tvons{or functor uA Zook Ord oy ae ae - Ss pow ¢- Conside te given cys ° stepse Sey troupe functfon pode | ay bedao - Y(s) LoS albeit 1 RS bem) thm 5) feta 5 30RD g == On 18 FAN Comidey N=aM= oye Ys) _ be "+ yo thes ------ Bo tba 0 OCs) a fe, ; ea kar) + 0)\S + O59 - - oe ot Oe dak Yes) “oa i) ° XG v(s) x(5)} / OCS) oe CD) 5 ¥Cs) i J WS) _ beste bys bo8'r bs —@) %\(S) f ¢: vs) S34a\5'¢a35) +03 FELIS Fra Gry) Ee SON - b, a YCb) = boO - bog)x3, 5 bo Xo > boas x, + bx3 4 boxg + b3x; | YE = {bo}V +) bg - boas x; +f ba - boas xg CaF { by - boa, & x3. il (yr By Obtafining moa trex Posery from eq, @+&¢@- x| @) A ~© x ce) rahe | © Aileayl-t | © (vJ x, = G3 S49 “Ailes 1 by obteining output equation 7 ee eq (): YS b3-bod, bo “boas, b-bea] x f xa | bo} [v] x3 Compania woth — ewltheut — Zosios, & — voth Zoot C&D rrabtx ave dPfferent, but A&B mats Ps Came. © Asyitm % seproented wth -Pllowhe transfer fenctin mode Obtain “+4he State m tO) phase Voalle fale. y(3) 10S +4) | ris Inca Oe) & SCs+t\(S+3) ‘ e103 ane -Y : ieon 6 af iil Ph ea 1o(544) ) é WS) ~ sis )G+3) YS), = .0(s+) —_® x CS) ‘ x) 4 cs) ‘ OS) ~ seri)(stD 4 Yoe vo) x6) OS). xls) 005) @ q Prom eq @ Vis) = 0S) 10(5 $4) eC usr= xs) 8 +4) (843) —®© ws) = vcs) (S48) tO 9 V® |= ks) CaS aS + 35: uS) = \\¢s) (st+248"+ 32) wok pny dace tovone fe) ND YePos Ys) = toS%(S) be ets : Vc) = flo XC + 4 HE) OW = XU) + uxjty +3%W x 2x xX a. \ ® Xs = Ky gubsitute @) eq tn above y(t) and ulk)- SON Hh US % +4x%3+4 3%. —® SY = xs ux pr ey © Ks = O -4x3 3X2 —) Ps » Leedback + SL onal ama RE)? TH. RIS) {aco 5 ¢(s) pa Mesalve Loedkacks. —Gi— = Cs) Ye fjative Leo ck ¢ LOH Ris) YG) > bo ne 4 cr a uls) ra, G -Xe) 7 Plo thts Ph & porttive feedback SSA Apply to . AFfPerentéal, Yg-terns apely Lo the rvtegapd « o(S) free] a Ls [>the | as eo ©) TO Mepruarnt the Vel ar o M dhe. toublten coeraqubey anise onveduedPory Seat, te) ty Wh One fuk onder Aefovers equation * ts) ty Pie {4 xr xn’ &)* +e block tfaguan aepresertalton for the above tooruhet gunetfon % a bellouo hee RX 2U.. Xo = Art u ® { : Kn = Ankit aye = Cit Caxy + |) <-seee Cnxn + bo