Analysis of Renewable Energy Sources, Lecture notes of Nonlinear Control Systems

Download Analysis of Renewable Energy Sources and more Lecture notes Nonlinear Control Systems in PDF only on Docsity! ‘Adaph me fuzzy contro | “op as Ateralt to precesely desortbe an ‘ caomtiallee nenlineanc kn nonlenear funckens and, Horefore, ng his weth an model. knowledge qemouns A 2 alles aD fask. As a anode free design method, fey eff defened plants. Hew over, et && « i i 5 fades bch controller pae as of ke pleat ogee change. le overtome thes problem, based’ on Ke ree ab forex imation Leorem and on- (me eos abihi fuzzy aystems, : a es ioe ed +o Ancooporel dhe expert hnowb a v Se ae ae ss Tuo approaches m the ers: a ie atecttonce ystems on lenear ayahen by aoe oft Scanned by CamScanner g The stabztety analyers <n such schemes is performed by using cf the eon abbroach , <-€., the cdualableporoner ot. ; ery ayproms are, pated ' an edaypbive law Rak AB detiqne| +o ensure dee convera anes of a Lyapunov function, Ailes Lae eevteen oe dreews Ihe derect Bee Bndimeet adlapbive fez ao bre eememes a clags as soni onuons rane { ( cance le-2s oe amudte le- out uk (MIMO) nonlinear a aLn L f P i mech a ach — Smee fuze lems ore Anted to . a ee <i $0 co Lbeallers she Pe Cele. sine 2 Meo ned ez tems ome phe te) ir —— var font boi Rab el J os 1 dies error \salpoeseneelne. nee ait rontrollers and ac contsellers , Dndirect abbavach - BN C2 [on Rucry systems one, . tocel le ab \ eae the. system’ Lenknowt nool<neave (22 » Bo at wie borsomelers of Ao apa gtome ca chet ues a aac oe of “he Heke Pee oe Wo error atncam dhe yshow's unknown nonlineanbe ana Ke used queer ems . ae ele abteroaches, Ae aie bt analyers of Ao elpeed \oelp Auyser b» perfoomed Aeon) al pense abbracd, [brackeng, errors ore elkenately unifoawl, boureled and | : seoveile do a neat of he ee im), Sada: plaid a Scanned by CamScanner bfiehion ef 5,(t) -0 ainplces Hak the teaching error €,(t) and — ts derevahves up to v.-1 conwerge to Ren? Therefore, the B hue would e- design a controller do keep § Ct) at xeve, oe ‘ s(t) can be Lerectly dranclated er £212, °°, P, Further, beunde on S(t) can i ; mde bounds on the dracking evror, and these bounds can be eley A. pedueed by Krererr (eG dhe peran | ie) be worefen aé Téme deve vakives of the fettered ao @& @ : i Seat _© g, = ¥, 75.6) age a,,¢ oe aan <n anataix fon a S 2 ant —© = V- fc - G0" where (>) (7%) v= Ne “7 By c 4. ee * fey me = i C Jl art Lclerr, P's, ral) EF <<) € J v I ¢ Ve, dp deal nonlenear cordvof law (labiods Guerra 200%) a ae ee dG gd selechiog a - a fe > Smee FB) 4 B+ KE + ie tonb (2/4) ) ) simpls eZ to Kz - K, tanh (3,) —@ yohere K 2 diag L ky, --ukp K,- diag! ka Med ect caler k.70 J kee og fer amall posshive constant, raw EY, ) = [ tach (*e.), tanh (4/6) J" an €. er ik ~ kefrok (92) Jeet ie cnplées hat G.(t) ro 28 bro , Korgre, 2(t) said all is sua to %-! converge fo Kero, However, for Ee ee dee must be completely known. Scanned by CamScanner Y ec A 1@) and G(x) are not known, we bave do tse furs / ystems fo construct adaph vely the unkpooh fenetons. } We use zero-order Takage- Sugeno furry Bystem that petro: \ a a al ear | from an emput veelor tes CR oleae do a sealar oudput varcable ie ER aD by a set of <f-ten qguleé of Fe form k lle RE If z, 4G, and....ard zm is G, Then ge oh (ket) —@) Litt atechaamae i! vn — where a é { Batak Fel, 4p Deedite ereap nuk pub of the k-fh rule, and N 4s ie -lefol number of ules. dhe amglefen fuerifier and the product ~nferenes engine, By Len, ; bo fhe ZRY ¢ form aé ven as the fool oudpub of He fares fs wll 4 4, (z) = kel — here ped <TTT fee 2), gh Na Fate | Scanned by CamScanner  5 4 Cy here Pei (x, : as the membershep . henetean of the fuzzy seb Fe! | i : Bete Using - feezzy bans fenetrons , output an @® can be ee A wn fhe compact ae y(z)= W "(z) 6 —@& ¢ jes where Oz a fon gl] 9 gore Zz - @ tpaersieet pee ha w= fw@), ---,y ah 4B Aa set © of fuzzy basrs func ckons defened as [%©) | keto ® : J 2 wel! defened 8o Hat ms @) an the of @ HA has been proved Wat furzy ale @ # fowm f Le clrons can ae conk’nuong wit, GausHie anembers p fic onbitrary Es of OREM oO a com josh Pie ruber of woe ave cone Vee control Dieect as ah — Se ‘ht ote e < che trod objec VE. The problem | | Ce i dhe aaa contsaller de, pene on ace fenchions: Te ong ge oduct ee 2 error be stems for oP oo og hae ae updat @ te i Redary or word of Ae fuz zy conteller. Scanned by CamScanner Raion sf) 6 - cyetp EE tll) a OO a?) law 64) 4s not - | “The arama ter daking ease the derevahre of @ cs met available . “The drserefe <n lemerdable version of @4) fe a Lyapunev ste nality achems as pct = o(t- “aye f ‘pottedes [44 bt t-At @ st) ue _ 6(t-At) + + | pies a pede. s(4-4t) ee , phere d= wee) , gp = 01le)( KS r KAO foarh (fre -ne?, alert pa: as add Lia spore wrobwetneds de cen. ee | 6 choosing At suppeciery smal) ond ascuming Hat é) eS Za) are enbinucht dime fanctrms, © $0) $ eserete ob frontmeston and iw vernon af As ae eee eben © 64) pct-Abt at ay (4er-e0) Scanned by CamScanner © Jndérect a daptive fuzzy control HE Resall the say fae Decherd law {Ca)+ 0 +KE+k, faok ()) 1G 4 %) can be ardirecly afforeximated d, compost get Da 28 follows. ee) “The funcleens a and Using fuzzy ayetem over : : hays f,@)+ lA) Es Ee ‘ (2) (x) = (B+ & ae 4; ) ye 4 a b ete a bite hdl ve MX prox IX oS, whe Et 4) ana a are fucy ze a 1m ee evro Mat ore 0 femal p arameber veelors 6 and 6" fp ¢ 4; : 7 eneme xe Jeane teens [ 0} ae {€. ( ‘) veeperbvcly, m Ww @) are Ch lll wy (4) ond G4, Swnca he <i. parameters ee Gy. ‘ans rnd 5 ave, unknow, Scanned by CamScanner ISIE S. he odophwe conto) low) a Heo adaphve fezry approximaliens f() and G(@ enna oe porehen 08 we g'(@ _f(R) +E HKE rent) (adh Bome oly bane dnanepulokions we can ware Kg -k tonh HA) - ($0-{) _ Ger) ba aye / “The vebot eystem can be expressed Bn onatnix form / : * y £ca+ G(R u “The zondro | abjechve 4S do fore Be aystem ouputs Ye and ae otis fellewo the desired frajee On kE EO xin (t) and 3) = cost) | respect vey, ze lems of tke. ney ae ee = w @) o ae axqoale a“, and %, f 7 famihas = fater, € 4, 241, et) ] ay ae) oie each enpot vartable sy pfebryd QS ea ee mborcbep <fune bon as follows chosen - dyree Gouen an Ge Zit [o2S t J ie yee (-4 es be Ee ise do generate J ues 4 0-06 1-0/2 Ea0s2c,, Farameler vol a0); Gee te 2 ee Aa a g-80° efi & Robt Gribat condition 7 er poe «oe ole Scanned by CamScanner Design paramefers of “he SR ee Sa nD 7 Dil AP k= diag [1,11] Kye ing 5,5 J EO, ee 6~ = 0.00 Feq i Feg2, Fég 3 | shows how aeduall drag ectortes al ad + Lhe desired hoped. Gnelutrm :O Temjecteries converse ty letined Aoajeebricn i (A Conkeol enynalt are alanest errvolh QO Bhows the rocking capabelhies of the Aicret odopbve tontroller : Q) Meo show te fPecbvenese f contr timcbing of (peoctone mA variehe. nonlinenn syctons : Ex Scanned by CamScanner