Suy todutio to Po otol Rf iut Fdbk otol hoy Fowd oto Fdbk oto tuto o ditub Plt Zhyu Yg otol yt obl: Albog Uivity Ebjg A lt: hyil yt dd to b otolld Sifitio: did yt fo DE5 Fll 4 A thodology: to dig otoll uh tht th lodloo (fdbk otol yt tifi th ifitio htt://uudk/~yg/ou/4fll/ fdbk otol thoy o4htl /6/4 todutio to Po otol /6/4 todutio to Po otol lil otol thoy (fquy doi Fdbk otol Sifi toi (itodutio to dvd otol od otol thoy (tt doi obut i dly oli O /6/4 todutio to Po otol 3 Wht you ld though 5 5 : 5: hitoy of fdbk otol 4: blok dig fo yt odlig tt 678: Bi oti of fdbk ll : 63: tidoi ifitio 7985: PD otoll b : tdytt tkig d yt ty & 3: 337349: fquy o (Bod lo S 375379: Gi d h gi ii 388397: Dyi otio u 4: 44: dyi otio ll 3: Stbility ii 5: 36375: yquit tbility itio k /6/4 todutio to Po otol 4 Sod t: 6: odllig u d otol Sifitio 7: PD otol d Exl 8: Fquy Ro thod d Exl 9:Root lou thod od otol thoy (Stt( thod : todutio to tt thod : otol Dig fo Full Stt Fdbk : otol dig uig tito 3: todutio of Rf ut 4: tgl otol, Robut kig d LQR otol 5: uy /6/4 todutio to Po otol 5 ott: lil otol thoy thtil odl of L yt: F, ZP, ODE L yt ly: fquy oti, iul, t, bod, yquit, tbility, otol yt dig Root lou dig Fquy o dig Digitl otol t Dit quivl Slig tho ASD tlb/siulik /6/4 todutio to Po otol 6
otio Blok Dig Rf iut Fowd oto Fdbk oto tuto o ditub Plt D( A(S P( F( S( /6/4 todutio to Po otol 7 w otiuou L Syt odl Difftil qutio y ω y ω y f futio ud fo Y ( b b G ( U ( Zool fo Y ( G ( U ( i u Ptil ftio xio i ( z ( L b L b i i g, X FX Y HX g, GU JU G ( /6/4 todutio to Po otol 8, G ( ( (, ω ± ω ω ω i doi lyi ul/t o Dyi Syt Alyi good tit o: Ri ti t, Sttlig ti t, Ovhoot, Pk ti t good tdytt o: Poitioo ott (ty ; Vloity ott (ty ; Altio ott (ty Stbility: h(/h[] i bolutly ubl Fquy doi lyi Bdwidth d ot k: bod lot Pol d zo lotio lyi yquit lot: G, P Routh tbility itio tlb: L Viw /6/4 todutio to Po otol 9 lodloo loo tbility BBO tbility otiuou yt h( Dit yt h[] Pol lotio Stbility Alyi otiuou yt LHP l dit yt uit il zl Routh thod gtiv oot of olyoil: Routh y yquit itio ZP Gi d h gi otiuou yt gi(y Dit yt gi(yd /6/4 todutio to Po otol otol Syt Dig otol gt: Good od o lodloo tbility Ditub ttutio Robut otol Dig thodology: lil thiqu (fquy thod Root lou (Ev 95 fquy o dig (Bod lot PD otol od thiqu (tt thod Pol igt Etto bd dig LQR otil dig /6/4 todutio to Po otol Syt Sifitio: Good Ro Good od o Good tit o Ri ti t Sttlig ti t Ovhoot Pk ti t Good tdytt o Poitioo ott Vloity ott Altio ott ω H ( ω ω : dig tio ω : tul 8 t ω fquy Good l fquy fo dit yt yilly, th l fquy hould b ho to b to 35 ti th lod loo tul fquy t t otiu /6/4 todutio to Po otol 4 ω π ω d uity v 6 5 6 35, %, fdbk li li %, li %, 4 ω G G σ o d ( o G 6 ( o ( ω y 7 5 3 v
Bdwidth (fo lodloo yt h xiu fquy ω B oodig to 3dB i th lodloo gitud Bod lot ω B ω fo P9; ω B ω fo P45 (ω : oloo oov fquy Ro k G(jω /(ξ t ω ω Gi gi d Ph gi (fo oloo yt G: u of how lo th yquit lot i to il th P: u of how uh dditiol h lg (ti dly b toltd Dg foul: ξ P/, d ω ω B ω D( G( otiu /6/4 todutio to Po otol 3 /6/4 todutio to Po otol 4 PD Fdbk otoll PD : P: Pootiol (otol : tgl (otol D: Divtiv (otol PD otol Syt Stutu: d otol ( ( PD otoll htiti Stdy tt offt/o obl Ditub jtio obl Good tit o ( t ( d τ τ t & ( Plt G( /6/4 todutio to Po otol 5 D y( Piil: uig th PD otoll t ( ( ( d D( τ τ & t U( D( ( D E( ig d / td to du yt o ig D td to iov tbility Ziglihol uig thod(94943 Qut dy tio thod: Slo t R/τ, Lg L Ultit Sitivity thod ul o Ultit gi: u Ultit iod: P u /6/4 todutio to Po otol 6 tgto Atiwidu otivtio: tuto tutio ho itgtio itgto widu Atiwidu thiqu: u off th itgl tio oo th tuto tut lt with dd zo lt with oliity FquyRo Dig thod Fquyo dig thod ot oul i iduty hy ovid good dig i f of utity i th lt odl hy y to oot with xitl ifotio hy oft th ot otfftiv thod Fquyo dig tool f futio Bod lot: Gi, h lot, G, P, tbility yquit lot: tbility /6/4 todutio to Po otol 7 /6/4 todutio to Po otol 8 3
Dyi oto Dig Objtiv: f tiftoy o dyi ot b obtid by gi djutt lo, o odifitio o otio of th o dyi i dd D(G( ool: bod lot P, G, oov fquy, Ld d lg otio Ld otio: t ily to low i ti d d th tit ovhoot: D((/(α, α < Lg otio: t ily to iov th tdytt uy: D((α/(, α < otioi tyilly ld i i with th lt i th fdfowd th otoll D( Plt G( /6/4 todutio to Po otol 9 Ld oto Dig F396 F396397397 Ld otio: D((/(α, α < Ld oto i high filt (PD otol t i ud whv ubttil iovt i dig i quid Dig odu: St : Dig th low fquy gi with t to th tdytt o ifitio St : Dti th dd h ld St 3: Dti i β x i 45 α 76 i β x i 45 St 4: Dti 548 ω α ( ω / α 9 α x St 6: tt o th dig util ll ifitio t /6/4 todutio to Po otol Root Lou Dig thod Root lou i th t of vu of fo whih G( hold fo o oitiv l vu of G( htiti: Show how hg i th yt fdbk htiti d oth t iflu th ol lotio By tudyig th fft of dditiol ol d zo, th dig of dyi otio lo b odd h fft of zo i to ov th lou to th lft h fft of th ol i to th lou towd th ight Dig of ld d lg oto D((z/( with z <, D((z/( with z > /6/4 todutio to Po otol Pkowldg: Li lgb tix outtio Ltu: : todutio to Stt S Dig : otol Dig fo Full Stt Fdbk 3: Etito Dig 4: todutio of th Rf ut 5: tgl otol d Robut kig od otol thoy (tt doi ott: thtil odl of L yt: SS, SSF Pol igt though full tt fdbk: otollbility, otol oil fo, Stt Etito dig: obvbility, otol dig bd o tito: tio iil todutio of f iut: Zo igt tito, utooou tito, tkig o tito tgl otol ASD tlb/siulik /6/4 todutio to Po otol f Futio fo Stt Equtio fo futio X AX BU Y X DU Y ( G ( ( A U ( Stt ditio X AX BU Y X DU Eigvlu of A ig(a iio zo tzo(a,b,,d [A,B,,D] tf(u,de [U,DE] tf(a,b,,d A B dt D G ( dt( A B D fquy o ditio Pol of G( oot(doito Zo of G( oot(uto /6/4 todutio to Po otol 3 otollbility A L yt i otollbl if d oly if [B AB A B A B ] i full ow k Ftu of otollbility f th yt i otollbl, th th yt b tfod ito otol oil fo; oigul li tfotio do ot hg th yt otollbility; otollbility ot b didd fo th tf futio; f th yt i otollbl, th th lodloo yt ol b ut i y bity lotio though tt fdbk; ol igt /6/4 todutio to Po otol 4 4
Pol Plt though Stt Fdbk Poditio: h oidd yt i otollbl Au th did htiti qutio of th lodloo G ( ( d ( L( St : otut olyoil of tix vibl σ ( A A α A α A L α St : lult th otollbility tix [B AB A B A B ] α α L St 3: lult th gi vto [ k k k ] though XAXBu [ L ] σ ( A X ( A B X BU ux Y X dt( ( A B /6/4 todutio to Po otol 5 α k k(a,b, l(a,b,; Objtiv Etit th yt tt though th outut d iut igl Etito Stutu l A Bu L( y wh L, d X AX BU Y X l (A,B (A,B Eo Equtio Etito Dig X( L Y( ~ ~ X ( A L X, dt( ( A L /6/4 todutio to Po otol 6 Obvbility Obvbility h oidd yt i lld obvbl if d oly if th obvbility tix i full olu k: obvbil ity tix A : O A Etito Gi Dig (Ak tito foul St : otut olyoil of tix vibl σ ( A A α A α A L α St : lult th obvbility tix St 3: lult th gi vto L [ l l l ] though σ ( A O /6/4 todutio to Po otol 7 A O A Dulity of Etitio d otol otol obl to lt ow tix fo tifoty lt of th ol of th yt tix AB otollbility tix [B AB A B A B ] Ak otol foul [ L ] σ ( A Etitio obl to lt olu tix L fo tifoty lt of th ol of th yt tix AL A Obvbility tix O O A Ak tito foul L σ ( A O Dulity: otol obl: A, A, B, B, Etitio ol: A,,,, B Lk(A,, /6/4 todutio to Po otol 8 obid otol Lw d Etito todutio of th Rf ut Plt X AX Bu So YX XAXBu y otoll Etito A Bu L( y A B x x A B D u u D u u ( X x X ( u x X lod loo yt d ol X A B B X ~ ~ Stio iil X A L X ( A B B dt( dt( ( dt( ( ( A B A L A L /6/4 todutio to Po otol 9 Plt X & AX Bu otoll So YX Etito X ( A B L Ly /6/4 todutio to Po otol 3 ˆ 5
How to dti th t,? Zo igt tito: Objtiv: ll zo of th lod loo b igd Poditio: (ABL, i obvbl Y ( γ ( b( f futio: ( R( α( α( α( : olyoil ult i tito gi L, i, dt (AL α( : olyoil ult i otol gi, i, dt (AB b( : ogil lt zo olyoil γ ( : did zo olyoil γ ( dt( ( A B L : totl yt gi Autooou tito: Etito o i iddt of Y ( b( ( R( α ( B Plt X AX Bu otoll So YX Etito X ( A L Bu Ly /6/4 todutio to Po otol 3 ˆ How to dti th t,? kigeo Etito : otol dig wh th o u oly th outut o Stutu: Ld oto i th fowd th f futio: zo dd o th ltio of d L, L Plt X AX Bu otoll Y ( γ ( b( ( R( α ( α ( ( A B L L dt( γ ( So YX Etito ( A B L L( y /6/4 todutio to Po otol 3 / ugtl tt qutio with itgl fdbk lw with itgl otol : u tgl otol XAXBu f X& otol : X& X [ f ] X X u A X B htiti: obut h lod loo yt tk odyig iut with zo tttt o d jt odyig ditub with zo tdytt o y LQR Otil otol Li Qudti Rgultig (LQR otil otol Otil idx: ij( U ( X QX U RU dt U Otil otol: U( X( R BPX( Algbi Riti q: PA A P PBR B P Q [,S,] lq(a,b,q,r lult th otil gi tix uh tht th ttfdbk ux, iiiz th qudti ot futio XAXBu ux /6/4 todutio to Po otol 33 /6/4 todutio to Po otol 34 otol utoil fo tlb htt://wwwgiuihdu/gou/ t/hotxthtl /6/4 todutio to Po otol 35 6