Lecture 6 - SISO Loop Analysis

Transcription

1 Lctr 6 - IO Loop Aal IO gl Ipt gl Otpt Aal: tablt rformac Robt EE39m - Wtr 003 otrol Egrg 6-

2 ODE tablt Lapo tablt thor - olar tm tablt fto frt rct mtho xpotal corgc co mtho: Lapo fcto gralzato of rg pato Lapo xpot omat xpot of th corgc for a olar tm for a lar tm f b th pol x x & x δ f x, t ε x A -ax -A -ax t EE39m - Wtr 003 otrol Egrg 6-

3 x& Ax x B D tablt: pol H H haractrtc al trafr fcto pol l.h.p. for coto tm t crcl for ampl tm I/O mol. tral amc I A B D Imag Imag z Ral H N g K g0 D p p g Ral EE39m - Wtr 003 otrol Egrg 6-3

4 EE39m - Wtr 003 otrol Egrg 6-4 tablt: clo loop h trafr fcto pol ar th zro of Watch for pol-zro cacllato! ol f th clo-loop amc clg tablt Algbrac problm, ar tha tat pac m : ID cotrollr k k k D D I τ : lat - ; [ ]

5 tablt For lar tm pol crb tablt almot, xcpt th crtcal tablt For olar tm larz aro th qlbrm mght ha to look at th tablt thor - Lapo Orbtal tablt: trajctor corg to th r th tat o ot - th tmg off paccraft FM, arcraft arral EE39m - Wtr 003 otrol Egrg 6-5

6 rformac N to crb a aalz prformac o that w ca g tm a t cotrollr k k, k D Optmzr, rformac I hr ar all ma coflctg rqrmt Egr look for a raoabl tra-off k D τ D lat mol k ki m EE39m - Wtr 003 otrol Egrg 6-6

7 rformac: Exampl lctg optmal b th Watt goror - HW Agmt b Optmzr rformac lat mol, g b m ampg b rformac x a trat b EE39m - Wtr 003 otrol Egrg DAMING b

8 rformac - pol ta tat rror: t trafr fcto at 0. tp/pl rpo corgc, omat pol a m { R p } j j at A omat xpot 0 ato! Fat rpo pol far to th lft la to pakg fat rpo low rpo 0 EE39m - Wtr 003 otrol Egrg 6-8

9 rformac - tp rpo tp rpo hap charactrzato: orhoot rhoot ttlg tm r tm ta tat rror 0 EE39m - Wtr 003 otrol Egrg 6-9

10 EE39m - Wtr 003 otrol Egrg 6-0 rformac - qaratc x Qaratc prformac rpo, frqc oma 0 { π π π t t t J t E 0 ~ ~ If t a zro ma raom proc wth th pctral powr Q π Q t t t E J t 0 [ ]

11 EE39m - Wtr 003 otrol Egrg 6- rafr fcto cotrol loop otrollr lat - trbac fforwar rfrc otpt cotrol rror o

12 EE39m - Wtr 003 otrol Egrg 6- rafr fcto cotrol loop tt omplmtar tt No tt Loa tt [ ] [ ] [ ] [ ]

13 tt trbac rfrc lat otrollr otpt - rror trbac Fforwar lat F rfrc otpt - rror, L L Fback tt F FF << for L >> goo for a frqc for L << r tabl ca b ba for L - rgg, tablt EE39m - Wtr 003 otrol Egrg 6-3 Fforwar tt

14 EE39m - Wtr 003 otrol Egrg 6-4 tt rqrmt Dtrbac rjcto a rfrc trackg << for th trbac ; << for th pt o Lmt cotrol ffort << coflct wth trbac rjcto whr < No rjcto << for th o, coflct wth trbac rjcto

15 Robt Ok, w ha a cotrollr that work for a omal mol. Wh wol t r wol work for ral tm? Wll kow for r ol wh w tr - V&V - mlar to bggg proc oftwar a chck that cotrollr work for a rag of ffrt mol a hop that th ral tm cor b th rag h call robt aal, robt g Wa a mplct part of th clacal cotrol g - Nqt, Bo Mltarabl robt cotrol - Howll: G.t, G.Hartma, 8 Dol, Zam, Glor - robt cotrol thor EE39m - Wtr 003 otrol Egrg 6-5

16 otrol loop aal t lat Fback cotrollr t & g k I & gki 0 Wh cotrol mght work f th proc ffr from th mol? K factor molg rror crtat charactrzato tm cal bawth of th cotrol loop tp rpo for th g mol: tgt Molg rror 0 Actal tp rpo t lat Fback cotrollr EE39m - Wtr 003 otrol Egrg 6-6 Ucrtat t

17 Robt - mall ga thorm Nolar crtat! G.Zam Oprator ga G G G ca b a olar oprator L orm t t ~ π t G t h loop garat tabl f L ga of a lar oprator G ~ G ~ p G π 4 π EE39m - Wtr 003 otrol Egrg 6-7 G G < Op-loop tablt am Dor a Vaagar, Fback tm: Ipt-Otpt roprt, 975

18 Robt At crtat Mltplcat crtat t t t t oto of robt tablt < oto of robt tablt < EE39m - Wtr 003 otrol Egrg 6-8

19 Nqt tablt crtro - γ t G t Homotop roof G tabl, hc th loop tabl for γ0. Icra γ to. h tablt caot occr l γgw0 for om 0 γ. G 80 < a ffct coto btlt: r.h.p. pol a zro Formlato a ral proof g th agrmt prcpl, crclmt of - tabl tabl tabl a 0 γ ompar agat mall Ga horm: EE39m - Wtr 003 otrol Egrg 6-9

20 Ga a pha marg - Im L Loop ga L [ L ] Nqt plot for L at hgh frqc L ga marg - 80 ϕ m gc /g m R L pha marg EE39m - Wtr 003 otrol Egrg 6-0

21 Ga a pha marg Bo plot ga croor pha croor /g m Im L ga marg - 80 ϕ m R L gc gc pha marg 80 EE39m - Wtr 003 otrol Egrg 6-

22 Aac otrol Obrabl a cotrollabl tm a pt pol awhr a r tat awhr Wh caot w jt o th? Larg cotrol Error pakg oor robt, marg Obrablt a cotrollablt matrx rak Accrac of olto f b coto mbr Aal of th lctr al for a LI cotrol, clg aac EE39m - Wtr 003 otrol Egrg 6-