gallo2 Lott 5. state variable Analysis avd desi on Stgnifican Ce t Tis atime do Space matel pop sesentedion - Advorages ob spate: kaa is apltcable to ONY {ype Qraeat, dime yore) main anallys'’s which Uses Sere | | | ee Sven such | os Linens, None =“ | yyesiont Ete ATE GNSS complete NHoeN state of te syste as 41 also takes ie rnttal conditions into constderod'on- a fae te ts cataly applicable 4° cing\e tnputsing L| output C5280) anol nett’ Hapuce mu Ue ocdput — |emivo) Sysrons: simple When computed to othe; * DE IS ayutte se uses makiix algebra. ccton alrout te Methods %8 States the state of ao dynamic dgsteen is defined as the enpni Tourn SEE Off Variables such dhok the know kidge a Piege Vosictlley at tot, Aogethex with Ahe benoealedge. af ypect Vedat ly gel Erte, completly duderraines The dynanetc qeme tz to polewiou’ of He syste for any wi} Stade vonfabliy the voniabla wach ane 3 oe state Ob a dy nowt sys yor ables. nvolveat on dbbersait germ *S called otecte Voniatles: oesPMU ape TMNT CARER AE HO ) Syren, E ciate yariads le (| Sp; the Abd Ve system WU) )U2p> + OM On the 5 Sp oan, the output a: i | yoput wortab\e , By 792 Fiygstabls and Ki, Xp -- Re ate Kae eae | yootcbles de / 2 a ; E By using this Sy skem Ay naire phussao coh be P| wien oS F Ra = A xtty t BOEEI-—->O | ules Saget bot —O F | ohare k= AX [ me 4$* fos ss callecl as Stoke coysctor Qud iat equocion 48 cabued ag out spat gayuottiov)- } aon au ar-7> am system mad wr) fF pe Aes Q) -+- arn] Fepuctlustt on mettre i ! i any One 2 On nx wn Brpud weet x 69 bn br ~-- bm Be 3 ; ' Condeel movi: fied E 4 bra” <--bym fv ere C\ NxM | a <> Cla mad (00 ) ce ce ou y . e aa = out attoniotti< cer Cp 7 OPN Dour 7Aan ay ~ ody doy dys App -- > tem Pie ech ver 0 Sv}. Soy * mnodtitine pay >| Hake gquction an be poten as ¥ SH ig Ry I xz |2 alxn | eplo. \ y \ ° ™ eM Jax Lom output equcdion js given by Blocks atagsas TEP rogentotton xy xl) sduors of Sterts: Baedton' Ye Homogenous solukton OSH \ ponte vI® odes of Stecbe Keb) = Keb) TBOCE) _ state equation ur ie a 7 > ef t Dior ; ) NY dee, 66 fever LD Oe free &; dynam Pe goytettion, at) equation —0 Bele VA) =0, KU) = ARCS enry Raglace Hans form conids Initial Condtt ong ? on both sioles andlg Sx)“ Klo)= Axes ) Pe “py saat made xe [sT- J= x10) “xt Keo) (sz-4] , oo eereen mats x (STH) : xh =e%* xo) toe ete sence A gs >-L{i'fsr- J ‘] ds . seQu) ; Non homo genres Ket) meee) 1? Ke) - Axck) = Bott) oe OF Ly pettest dey pe multpl oo) is : taceysen*® But) aD | ie Ob) - onside, ee asin oF e~** ety, weget | 4 a ey pot stds at gery 92 x ety —9®rhe s of OT LDA Ke) #0) = oat ts Be Mowat 4x10) x)= ee Deidre vey] ees, KW = Aya) + Boek) beply fop lace trausfex™ SxXts) — XW) = &xts) +B0G) X(O[s 5-97) = BOG) 4X10) XG)= Fst 0} Ieee) FESTA BOCS) he 4s) Reo) +S) BUCS) LAT | Tx ct) = Oth) Kw) 3" Eder: eo] icant aM ener Tans ssy) fagedles ay dale Hanssnissing Macks: dro=s Pong: guts o At ¢ to) = ot 4 fuooke Coes Ce aye e ate j =p) Tory? = bowl) | 2) {ous = gt-t) | E Pete: (gas = fem) cot | er | = ot) ) q Ca) = Us) » Ue) [tk ¥ athe) . 2 eat ta) f meta. eR = 641): o Ue’gy Plla V3) qh Hy to) $a -t0) be | pears) bMs-to) 2 29 Cais) A tito) ies 2 gotta tat ty-to) a ." (ta -to) | = ¢ Ua-to) Uxpressio® p “Fanspr functor i. Given Yau state. model Sys OK LY ABO LL) OD WC) = CKCt) +P vet) =O anely Japlace Axanstorm eq) o 4 ) SKU) = ARCS) TBS) constdy Ko) = 0 Xess a- J = BUGS) Xts).(s 7-7! Bots) — © Haye T fr B® ts 2 Gets) TDUES) —0 sub Ea © 10 & © eye cfs Busse A TH = Sct = C{ss-e) 84D - XL) Prdlems + = . ' Dulin the stake model fos given Electric systems iL ; fh = AN. Jott) Us ey \ Ng - . (| We noel stele vpsiatles can be decidlea! bg | She nprege yfoot Bement Hehe giver supers “Trae the gtecle Vartagle Avguyt Ly baat stove Elements + Ye Ly Oe ee ceeaahy que dutkan te il)9% ateoss Tt CARGO fo the CRY AUD 42 (petsdt at f > % dhe yolts ay hy KNL MAYS erste vetl)= + Vie sat © BOY svi) -RiU)- Ww) 36 — i L at dvell) 2 Gtr» © da c a Rip -y il) y ‘i dvow) | > a 4 1 “| } a Ye ° 7 Q| obtain the state model pov tte given lect! dyson? A Orly Keb Tbe RA ILATC Tease VO) ah fucert 4¢ RK L mH het Svets at © ye iW bd si Eyles ith aa NS ee B TL te gue > Lu / Poteet) oe tthe om a tl © law ' ave) Ay || vas ve oe: © cpa sto Ban STARE MOAR BANG ea yee aysteore ts eer by the yelling Aer dla) ad : 7 + TAM) agit le Suet) pave sgt aay tasud) = xe Ce Lo), 3 Ue) ye) cui) pct) eRArtt)- Lge gaye yor= Ruy = X30 = x2ct) | aay 2 ¥8% jo sub r as wey ear eran’ ame vate) TENS BRR ITD : sleet LgadUste) Cyt 1 Gst2) ee. ee Ss S (sti )cse2) esti) este)Bate ates one) Ob): {3 PRL f ait gee fod dhe, ? Db Pind tne I, ep ¥esponse When xeayef) : Uw) = % xt) > dake L Eds zocs)) ; Hoe gi): b 'fUs- “Ve (eect 07 eet fa tae) etig eet bor: [sa 8g" x 33 -1 Cstry (Sta) Cs +HEF9) 2+, . s Esti) CS42) Uti enn) VES) = SB pov he 0 dink * \ Ustiyest2y Csy tsrzy (%) \ 3 ae ee gis USH USt2) Siow y 1 (Vers TR Utd | ce | a gest '9CS#2)?. SH es-l) Sr oe t Ste ei ete Albi kobe 1 pret & ae aan eS; = Qe pe Xte) = a + wot +307" eye wet 42g | ze tpt by ee xt ye |e + £ Ree 4 eee ee ety (2k wet ; aE Co asiagle Ip & le hag a makdX Bushey -frvol we TE? x =[ Stud Us i) (s Je He { oC) TF = Cf sr-ar)}-e4> e StU (ste) s aays( “3 5] | Tre c(es- -4) ys -(' °) oe a Shy saa i | oa arts (4) ve | | | ! | | | | |tthe closed Loop bros he, function is Gwen by or us), WoSE4)_—obstedn gtecte Yortable may Sey Ee BENS THO sino siqnoh flow qnary: yoy), teotste) uts) sd 48s* 41428 Te4o Moats gala fovea At Py ok poe gh mids s Hud degeeks +EpMrde+ Hp nolo axrtiet = 8 Go 4 fu Yo), _ see * SS ves) i URE YD gy Ss ets Lbo]s > + b 40/3 i (-£ = 125 hue SS ee RLS xa | | uct) | . KJ Ka ba YS La sa ty =e QLXy =K3 AY - akg “l4X) fa = Cue ~S4OY = 640 V~ 640K) ‘ gate votiable form xy [8 pee APR ° sp ef ee o 0 xe [4] 0 ott) fa} ( ~et0 © © [Lxs yb Lranspy function TS GRON boy A ne closed Lpop obtain state ventas Webf Yo. 2 => ens) sf tb6¢ 2 ot 2 HS+E ape | pede tae. gwen stake coodet mnto cavonical fern & atix ° of 1 4 agagaol! aN aoe sett) [i “ «lie7) Concept of Comber AI SO SION contratot tHe: controLanility # duster ts Sald to be covetro Labbe ifft is Possible fo aus vada stobentye) fang CHE dlesinad state py, an sfecifred tne Hine Yay @ contol Yectgy oO GE)- ~The comtrakoutst [My ey oo state model cant,! a cox ) Gilbert's crete destad by Wal man's metho Nycbaaeds stent Gtlbats Wetnad + al wen ane Stake matik has diffount igon values - coustdy te srecke nectel of the system KA Fe AK ted CL) yo = Cktt) pvc) the state model can be convorted tO bya Asan shor nan ton x= ME phe Mc model makin * pc wars cma ghee Vostable Veco he Awans forrmeck mort 4S qiven by 2: AzrEe comonical goon j @ = tM Sn quls cose te neccessary and Sea ffrctect Cowtiahilbt iy, os Heed We gvtton con flete joo 15 Usk we WH TOMS est Lh eros? PY CURy wows of, mnodK = 48 Yard ter dee she Systemsteke fom oy, g Csovegpeding, stoke varios i Contolableye om HU —_ pr eren Yo System Makin has seqeated pase aq / xs AKG)+BOU) 7 . Ye ext) tbo W) cL ME Zes2z 4B v ue trzeev Gages i rere y= HOSA fs \, Bers | Ese: onsen Aire system with o State equation ke exter Bud) ; ye cK) +poct) i Ge ais syste Composite Ot Oe can be formed | uch “Ho Oe = fp Ae ete -- - ante) psngge: 8S the odes ef Hoe system phe sank of the rn ck tsnyiy Me detexminug of the TK) « Covvepos tte io x Qe ss HOV ¥erO i 4 Jacl to ren Mee ayston is completely Kako, ctl | 1 Obexvatslity* fr suystesn 5 sad 40 le corn Plertelyohan vases buy slate XCt) com PE completely) scent fied preaserremenct — of yx ofp yLty © Sk obuys tedlmans titperdes 1 ethod « Giles’, roe kind : fonstdy thesy sto with ghde ayuat on)" z= A2 +Bo : {= Cz4pv whe Ach layj So. ie | the eccesscry curd SURRECREL cunclition foy completely SoSex vases 1S Thad none of column, e fy GLKO- « Th any column iS the ger Then he Orrenyl shade vantaivle qa bane ¢S not observable. a Kalwar’s method 2 ane Q=ferate” a yet. 6) ct. rai stecte combvaRouts +4 ¢ obdewvability Gor a stectewedal| Eee ‘JE Ee ‘ foal 2] Gibbent’s wnethod - Zaz +80 ¢ 2 GAP rts aed mcrerne 4 OSE le joxl= Pe eo -2 3%0 eh oO 2 -eRbOM fre a} eueo -x(a $30 48497] -heo Siyeaee aero ~ rE bat-ah -y 20 VeCM EAE So Net, -Vyr4 i e wd 7 | We eH eb : : eho -4 ies ; Aza—g -le 2 $ , 8 te 0 po ecge\een, SIR SIE -s% 6 ¢ i etfiz- ies Im wl 6 2 ‘3 } 2 oe f aD ee 5 2¥ ame) oe 6 2 | 3 oo , gob beesll b bo, fe etqen Vectors * pe Im cama 4 #1 ra Ayt3, 9 Oo 72 Ais ey 2 CHE AF Oo . an 6 [ er AB a rae qn 2C-t> mo = Mean 12 8 Alas Bair Gee (4 f2 “Aas LL Ly 4 4 Tide th Ay tba 44 dp |e =n) ~6 nT i> = aoeCase=A* Ar-\ eu) (1-649) Fy Cu |e} a 26 Jel-y Cig tp \-4 Case-ai }e-4 chy te -2 tte Ci Cta Je qk =p 2 Cle Gy = Xe+t dtr 2x24+6 aye cn 4 } 22 : ata ° “ars 3 st{-l8 Woo 7 o ~B 0 =~ 6 oe b+99 a Be ely ae eo Bl gg au & - [44 #4 We,2. en=[ioo Je a | Hl sted -y o- €=L4 yr) , iS ae 2oT2zsBu jy = Cz+dv y1 “0 0 f(z] FH By |e). Ae zrz|4) 24 a > 0 4 J\Fe Wa ppoeve Tho the glements us Ewe not all yeros - fonte cae Yo S pletaly Cowttollabls. Ts com pe pe ei de elements of te qt so, alt yenos + Hence He syste @ are not 4 colnoins 8 o ot 6 ° , eB lL, 30 |[2{2]~ a5 8 Le 4 2p = 0 2 SIC .0 & a 6 62 alr) 8 ; Jp \Wo oy 4 “14 7 € oe (8 OR ve] es af yoetiOn| Qer 32 Fe 1 _ fe joe systeen iS completely state contralany PMAr. (°°! y Co-20 cameos D e2ge 7 1 Be’ Clr (3) umtet = & . Bode plot! The plot al itor mages aginst plot & prase: angle | yao ” Logast toh Sealing against pequenty Wr Koga’ & “Adwantogess . : * Potting of Bee pit KS cefottvdy Bald aS conqaaed 140 ancthar ot ies © qaanion unter! * vadiiaioon TS equated We division & convate ®, tow & wigh Haan chase certs ak be napsest to sttgle graph « sales i study of, weloBve, *S Basy as qaxanets of analys" Coe golodive stailtty ade Gain magn, phase meal are Lie. pel) OM he ede }ETT CORO Sel an ex 1 0 pe bast ly Pu “BRI SS to, Started Ne. on lots : & bods F ; | OMapy ste (e4 toute) | w SN tve Prove OH ave Pave. [ravgi nobly ste ne) | bre pr = furstadld’) ee : | AEE by Step prete dunce PE plotting magn J Hot ek: kede plot: a | Shp ss Qowrat Ake RE into, Mme conctant frm | Cramps nbatsye oN SESH). tin dria ates Tr) (se se pgs .) pak sefuo its tO aie yn é s8C tot) f+, WE agi) SHRPRZ ~ yest dhe! Cornet Pruguenetes in He tncnasng ble as shown in ord, and Prepare a tal sO. Be pelo? zuo > t20do a 3 emae pequenty Re ; ie tw Slope 2c . Steps: Choose an orbitary fraqsenty wot eohich is tess than He Poewest comes prequentys adulate the Aecthle uquenty Magnitide of tox) ton Kw at wl ond oat Hae fowshte cornek pe ney Kyep- Nar mae eacuaayia! ‘ai! Fon bd Wognlted eset : evry ofeey Papueny Bneby One Using gain formula?jus = ‘change ™ gain prom ty tO Wy Tarn of Oy x slope or upto Wy [log [BEY] rtrare ats Nog fet slo pe Flor ure, te 9p [Jog | AO a Step g: choose a” Oras fregheeey omy “I eae, wohtch 1S. Qreakey than the wiyhest Com et prequot4y-colenbae gan ate Ph by ustag the pu! yn Skep- tt . step tb: In seont log graph mork the veoquirad Tange of freasuenly eae “< cox C ) and xarge Of Prager on yarts Corolinaty Sébe) } te Vv ger = og chensit pores skepa: Mark ob Hoe fonts oltamed iM stepssy 5 fone gray Sk and jotn de pols by & | skyatand LiKe with Ye Whe of the Scale. Hak the slope of evey poi in sia geafhske 7 rossi. jos asd Wed Mp bacegied? sp phase plot iS an exactylot and no opproxtto ation ode mode utile clown, He phos. plot: | Meng, the Seack Those camofo— of Gitlin) oe ompbitad gps Hofous velasgag, ub avel tabulate’ VX Moker the chofce ek greauensies ate preppesanle ys ho fReqencter Chon sen 40% mragnaude plot/ L cketch Ane dock plot and dokexmine opin CrOSS ovey f panyainy Jose” caossour ffeaqvendy, TH GH (5): to. slitor S$ CFOS) 2 10 (5). = ——___—__ - §CUFOSS Yato-1s) : gC tt Tis) C42 Ge ps Ik Ame const” foot pur segue iw Gls) [oOo ie OO fot rao $e) Lito 34) Te And COMME fueguency ur = = awdlsec 9 12 GU) = og change i” store dbpoc a |e geal = pa ved [se< fl ak fe i} = a= alag| 297) oy (ga) > say hodb © a) at way = g vadlsec | o \ ~ (2-aadbs | a= seteghton| > otog [1o) = aadh ene | ven at t=Weg = torad/cec wo ‘i * Estepe yrom Be, to Mca x beg] PY) esate =F woxleg (%) Jr -B42 8 -Mdb WW) a4 wsuthe Sovadlve a: (slo yum waco Uhh [a deena e (-60 log ft2y) tO) > ~ 5593 A56db > PHAM aye [6 He) . 7 ce Deedes | [Gy Chey = ae? kan eon ey tae” (On * papytaucle = (ote : ce prose = tan (2) | {tor jd i is taw Cord jr) 1 olde So | tales : ou HW a8 ae to ~ain® ea a — =| De i oaeney fo bt Wg c= Sradhe< Lu @lsd= Ks CLtoxS) Cte 02S) a gt ta TST OUTS? 8) Ge ts Whe | Fyn CS) | @es) = K (Sey ia Crt orays) Crt 0 02508) ; gorendk corner gua ven 5 vod (se - Goro lsec ‘ Lk Bou > 7 OA ! } sede’ 2A | Te 00% yl geet. We Pood plod fpr bus on 1 | > : Crt0°9 Ct 4 0-028) | pring the System gain spy ee gales Soles, | ye cowstan® pm put sey | \- Corner slope Bee ¢ Chage iv Slope ab hee | cae be Jem Preyer +ho | kyu" a avon ON \ oe =2Lo0 wr? | Urorage 7 1 we, ~S0 \ F009) -20 wheot ee wWCrES a Weg = So WS, = 100 At B= uh o- Az Qnlog(-wr) 4 oy xad(sec ~WOL20 = QB NRQo-20~0seintoa aren sercitssy, 2sony ane tog(-o-™”) = -Lodb at Ba bwdlcec Musee = Qofog] us cot Bolog] ul gon = Bolog ( ot v QHT 228 at Bege Borad(se ¢ Urea Pe stor Werte Beg x LO (423) +Geana ea: : = Rol0og |S) tag= ued Aton: wovadfrec. les {store rem weg to wh x t04 (=) reo aL 3 ; "> dog (22] cus = usdb SyStON gain frequency ~E valuy : Fo lo4k = a3 Pogigk =u katoG)=a2( ReronsYtasies) oe ae a 7 cngitorally stable and also fund te ange | aly systen to be Stable. Gis) s (it O-00lS) (14 00055) pek se jw tw Ges) eorgja)LHt oor sje Ge) = a aS Ged LU 0-001 Je? C(t o-00SS4) Ford corners frequen y i i = woo raalsec . = 1 . Beye Ty rer pete 7 i wes = 75 asog 780" vad (sec nee 5 5 yadlsec ]% oar: \ - 4 eres pbs | ‘0 xadSec whe od , wh = 200° Terms comerfreyuenty] slope db), ade. k (yey i uo - (\to-af0) 5 £20 | t40-90=95 (14 o-casjuy 3 é , \to-ophja 200 | J \to-ch Bie) {O00way Adi ws nop sored \ iP yp 1 | ero keg (“52 )ioteor 1 = pol04 (erm) . ttodb/se wat = Mer = golog ( ss date fs = geloq (2p) = R415 S -aa pd wt vtggeizg 2 arteg (= At Oe wWeg = owed Ke C 68 fe ~aolog| 1 + c-as) z “HO 06 HE w= uhca * ROP vad /eec Hors #8 ep Looe Log es.) &Galvat Pebceg > { str £ Seq | a 8 bog [222 |. Awe i | = hog (22S) 4 CNbe6) 2-H bob | AL We Gey zlaoovarl /s ec ryot Pucu® [stots from ley fowey x log (fox Sy > ranteg Lees ]4oweg > ~ 2ipbo9, [see \+ te tGr06) = —~hO03=-tro 104 l ao0e yRee qk webs g000 TO" pSec em wey town Flog (FB ae \ — bey 2 7u oteg (2222 )~ 60 03 = ~AQ 07 aod _ Joo jai. 5 -\8 0" + ton! cae +64! cree taal — ye potas. Je the) “19° Gia sent mae late | -20 ve? we JeSerrat oy OsaSKRK | | |wl > pelor plod! KT iso plod angle ok Gy (for) Ke Thts gpolav glee con ststS and radial mes: x Covite we € circles are used bo magnitude ypbue and vadio Ahe qhase ange «zt. our” between magi tucle andl ph oye of Conceive Circles wdt cote te dines indicate > 1a? U0" | o° - Wo 5 not OY | 290" pee Sg phd aso" i 5 chottd be Hive ang le ae Tn polal plot Ake yor poise dinectfon, Ve avglss measure Wn ant’ clock ured th clock totse divectton * Foxe Meas J Type} | alr Type t E | taxiing point of Ending point of al | Por plox golod pot | | Bkezovordt=4' ao guest 2s > | ea wero Gtr (Be Gt{w) = wee » Gta) elke \t jer end ™ F \ ie). ——— ghee OS Ne——_—— CSOT) Utje ae) ‘y yi? a TWyperd, onder “e: aot Gls )* “a s(t sv) W9= OG EJe iE oo 240" aa) fleerchy : joys obeet G64) jot) orm me) ET she “a0 corel aie Detar Lae sate: ag ae a0 “ao! Tyfaso , ovdax "2 “0 ee) 2 weo road! (OT : Caan testa yor “OUmNeee, Geyer) = t Vata THR — 0, oder’ Gls) = Gehwo) = wa0 , 60% wee 7 Gl fa ' \ eae es Cs Ty) Gees UTS) 0 Catlett Cr bot aajeny EMIT) _ ays “fawn fae’ joa Sotelo. 20 B30 i tonyType 2, OWer-S* Gts)= = ___—_——— SCMST) LUSH) STS Gj) . 32? Cuajenh) Uefep assets) cs OS RE e/euntyatont (at 3 , Be) Wp ,& jaydhe magn tude of ercfeo) 1 WPe is defined as { | Groin Maagin cer): er med as hase Engl. el, Gilfeo) Gain marg" is Asgi at phase Crossover Hey ueney the peqeney which te Pp tg 480°: Joative) =190" Phase Margn(prot dy¢ ot ps the gain cross ov Tes dyin as Fes pac : bye faa tney 5 bge i dogined an gain & Ge) ts untty [fotier} = 2 Jain margin. Problem: Datermine wpe ‘ond ge , coresponding i and pase margin + HE qomye ts wth S CUESICITAS) Gts) = = SCritsdC1tas) GG) = \ Fa Crgey case) z= .5 VIF wy Tt Vr R ah a —ao-tan-bs- targus 2 ! “hs FY ROLE a Si Gti? |= 03 fd we 2 rOrl je Je op a 230° Qo* -gQano tite7 | BAIN "4 1S LO te) =1y0° ~ Gor - fan! yp ban” gus 2180" oT 2 wh fan aig = Qd0° ~ tar tan [> tales -tan™'gco)= Fanta) 4 tan (tan ee) Uetan tan) tan (tales) ' (RR lacjor! = ! Ud (ae | et EUR | | Mean sees / Mere rela ue c orbs [EU hacpe Fee a O66 Gr tw de = 0 log hm -———_— | = Belo C51) 2/57 4B i] pret crag — ! | q sito +bgc l@qudls: ——— weet teu et aw) | i wre ¥ Cue) a be eyed Plaxd +5x74x-1 20 KX 0326 ws 0326 c eagten, . $4 = -qo- tan (wage) =tan’'(g.8g¢) = Go’ tant ( 0:5707) —tar"! (@x0-5307) = lbs ea PM dz 1804 O90 PH 150"] consiies open Ioop trawsyt fusion bts) Teen sketch te qolan plot and drtamme tae ale eh So Wek gata rang in Pod B , Phase Margine 20° (4 ) K 622 ——S : $ (MoS CYS) Guy) = Ke Sus UiFo5j0) LY fu) fact tare 5 — tow! yet K eV Sur Vink a4 Ks [Rottan bur = tanh yo ve BF oaset Sate fo - gad Bro GW Isp Ete" W050) 20 Lag?Get Lacie epyo” | = Got~ haw» BW - jaw 1 wo = io" fe Xaw Torn tan’ yd = 7230" gan [daw'o5od = baw yes) = © tan (EAN! esos )Y tan ave i!) ag ) ban Ceaw lobo ) tay [ava AERP 0: 0% Gr ao bog : [athe Nurceope 1 &o = 8 bog, kK | PCT og sug jae = bo9 15 7 —= = = 0-903 [yo R35 Fae Wee sak 1 fogs |zasl r Q.Rb K | K 285 =08a5, ‘ rats tbgc Ww < okt bgedye - 150" -qo° -taw' (0'5 on ytd sits wyta (8) 150 Ply tan gor tan 10'S w) tant enw) ) = ant (so) +460 ( uo “) erhav Go tan(- [aes [tattoo mene ne > stawlGo' ) 1 ban ltaw |or539) — tan Caw feew oso ty er ideale oleate }2O5 volt) k-Bws = V5> 8Go™ afer ty-Se ~VB=O Wace * prs, ——— FI 9g ¢ jy o-a 50 ge Vi tog : o'2ah : : RB o-21y tt lor 22) bor rAB) af LEO 205 16 PM=z Oh 44 “61 ,0°3)8 agouti plodt gs used igo gina the closed toop Amb lity Ty 4 * T 5 es tee Complete fuqueney of Ofer log used Transfer function. : ie 94 iS Used to gd ae pr and eR ip Used “to pod nore qoles eke whenever Aaext ts poles at OxIg NK AEE” Gektsts cates eikave dora ex) must be nayquutsé cw Tmage and end Ake wave at The slaving wat: qiatst eoppus 75 Nyquist contour = WT FUL) 2088 whe WTS Ayes of Ae dysterm Stability Painctple: pyquist plot ode doveloped based ont parc ple ofearguments Ne PZ whe NE Boek encircles Pz Noro pols on Ryls me Ne ro Bos oh RUS The tondrton fev State [tty actoxding fo myaud glob ks Nzpez 1S HST Telosed Loop system As staple feo Sabtsi kt Ge) ¥s ee Aystems co) EGE HOS Stable Ges) t Lying OF FE Reahy i oAginal tos) ach Og eat Sect ive! t +Problencs: oo sty Deteemime je Stabe Wey of Ake System hace Pe ” bop woe eee Ose ae wel aes aussi jst plot: ane rl 8 (rts, SCs Ct as) 1 | GUGOS) eg pee jus (je) Ags) oo Gh) ea uszeo » bli) 0 L830" A188 = BHD 3507 9, us #In order fo draw PYY [ ko fake — rartor jrsage oe du ye Often ping the‘ etrror mage sts uist lob We have polar plot - have tke Inqusse comtouy CNT) - esthe plot Starts een pros TROQE ana EROS Se original mage ending. Pore of the starting polossuster Canbe adetums, | * J ate stars lhty tf Hoa 4 ty ol cat ‘ ~ Hee her el encircles Ae by Hau Sep do ite jem = 4+40)- | | 3 Ths ton be or ted oy Knott tue distante of: # ILC {4 jo) lees rte 16 oh don We get Ena, Iw addle” by Be glee te He Gat CG UAGO D oben.) daken as'o' | ue gincivclemence should be Le of = [65) | pape - gc 8° -4o_taw'es — 1a" ns usp c= O*20% =the" of = [6 C) pp to209 ee | \ Mol = 4 0766 ‘ Nga stply Hente tee pot -1tjo ts udtside He. RgTH Sty =O pe. O70 eo NBs y gacydcles ‘N= AS Me P=P-2 Condi tron isis sak si freak tho Syst ee ts stable he ps bree neo closed oop system a uae PEO Open hoop ayer! Gin dp + Rokeg Gr Ro Log (FS) ) lon 3st ae aby Fone wage” 1-_— check We claw IY AMeNe GCs yo \o oe Ga order for dvaw Ph pate wiFeey Image pa?” SEU tora spe rt 0°58) stably ch Be costo by My eye ae oe 8? CORKS CHCOES) erie ss) bs etaw lange len!a yo ~ 8* Faatewriat 2. PY dt LORI to Buoy” ier tho : @g@eyt @ é peo HG a are oat © L Fe See) ao s ( yaa tse plot we have te oh pols plot: js Reo (closed Loop 3 unstable D | AS Pao q ope ndy op Stetble ). Gn «ketch Mgquist plat PI Ane ange’ E' tora ging 2 Syste Grisd bi ‘oh SCSA 2 )U+16) Gls). k SC Sta rCstto) Kk es 80} = = Jet -? 4089(0°55-41) foasin Gifs py i EAE 30} (o-B ju 41 LOr1Gr4 1) {ee : \ EActtaiy.eu tanw ae —— | vw CoH po) cone ye ee Ce a —=—-— v9, VF ORsy2 U4, 0.0102 qo° Weo OGD) > 00-40" 0 cj): OLRI0Gam? LGrtGw) = 180" -Go' ~tan'g- 5 ~ 9: Bud 7 tanto tus = 230° tana lw 21 40° ~tan™ tan (- tan7!o5 uo - Law gh us) = dan tan" 5 us)+ ban (tanto: Ite) 2 po tan(tar"! 554) Yan Lew! ole), ot bw t orld ; | Te ERO!) | OT a gee taco ciate eee 18 ) 1 tors rrorwer= © tore (ote) = O ;- 005 =z 0 wy? = 1 0°05 we Hu 9a| bore = Hs UFRof= |G (ite ag. espe 2 OD ookk Nio Pezeo WP 2 (ictosed Loop system 1s Stal) r=+ Coyen Joop syste 's ste] oo ert Pyyuist plot crosses the veal oats at SOOUIFK fy Sra lity the range of k con be colcudoted oooulF k=)/{Peequeney domain specigicadlons | Tn a deaeney domain auclysis the chravactertstts Yo followley of asystem ade measur in Fes of | guauen ty dertain spect 4) Res nant peak (Mx)i- e marimar GY) Peak veto af ficah’ons* | Tt 's defined 45 the wrogiide of ctosede oop Ost fandkon My = Speen e _ 26i-t* a) Resonant: wun oy WO) FE 1S dapnet as the youve de vohich TH meget a closed boop system ts mare wy = 1-47-80 | 1d as Aus. range of Gioqquercig 2)| Banduidtn lob): st 3 caffe polth fos wth the Syskem ep ts moyetnan rad B @s) ! fe : aw ames My) — Sit x | o> wn in + aang ng" | UW) qutcoft Rote: Fe iS dogined 03 Ue slope of ney Uxve abtot Oat magnitude inalB& Vosus fiw freayen?) ts known 4S cortreftr rate: