Chapter 4 A First Analysis of F edback edbac

Transcription

1 Chr 4 A Fr Anly of Fbck

2 4. h Bc quon of Conrol On-loo ym - Ouu - rror - On-loo rnfr funconolf Clo-loo ym U Uny fbck rucur hr xrnl nu: - : rfrnc h ouu xc o rck - W: urbnc - V : nor no Ouu: ffc by boh nu

3 Clo-Loo ym ubjc o urbnc wo nu: & W Ouu: ffc by boh nu U Y V Y W [ Y V W ] Y YV W Y V W Y W Y Y on from on from on from h rfrnc nu h urbnc W h no V W Y V V Ouu quon

4 U Smlrly nu quon U cn b obn U Y V Y V [ W V V ] [ W V V ] W rror quon cn b obn V Clo-loo rnfr funcon wll lk bou Sbly, rckng rgulon n nvy ung h quon

5 4.. rckng rckng roblm - o cu h ouu o follow h rfrnc nu oly obl 4..3 gulon gulon roblm - o k h rror mll whn h rfrnc mo conn on n urbnc r rn fbck c -o chv goo rgulon,.. o ruc rror o mll, w n -lrg mk rror u o urbnc lo -lrg howvr o no ruc rror u o no ll How o l wh h lmm? - ch rm funcon of frquncy - urbnc occur vry low frquncy nor no yclly occur hgh frquncy gn h conrollr rnfr funcon o b - lrg h low frquncy o ruc h ffc of W - mll hghr frqunc o ruc h ffc of hgh frquncy nor no - nor no yclly occur hgh frquncy hgh frquncy nor no

6 Avng of h o-loo ym Y W V Y Y W Y V L V L W V Y W Y f >> Y W Y ffc of urbnc on h ouu ur! nnn of lmn h ffc of vron of.. molng rror & rmr vron rfc conrol rformnc vn wh h ym rmr vron & molng rror Avng of h o-loo ym!

7 4. Conrol of Sy-S rror o Polynoml nu: Sym y Conrol ym nly n gn cfcon. rnn ron b. Sbly c. Sy- rror fnon of y- rror : u c whr u : nu, c: ouu Vl only for bl ym chck ym bly fr! nu for y- nu nly nu nu olynoml U o ym bly o follow Poon nucommn Conn vlocy nucommn Or lnrly ncrng nu x. Poon conrol of lvor Conn cclron commn

8 vlung Sy-S rror Sy- rror Ouu : Zro.. rror Ouu : Fn.. rror S nu m nu Ouu : Zro.. rror Ouu : Fn.. rror Ouu 3: nfn.. rror u o ffrn ouu lo Fg. 7.

9 Sy-S rror n rm of Uny fbck ym No. : on loo F Aumng WV S No. : on loo F Aumng h o-loo ym bl, n h olynoml nu gvn k k : oon nu r k k : rm nu k! : cclron nu lyng fnl vl horm No. Mu chck h ym bly! lm lm lm lm k

10 lonh bwn n h for gnl A. S nu lm lm lm lm : C gn of h forwr F frquncy vrbl rochng zro n orr o hv Zro y- rror, lm houl b f houl b of h followng form o fy lm z z L n L o n n Pol h orgn or ngror Conon for zro.. rror for un nu o uny fbck ym : A l ON ur ngron mu rn n h forwr h Fg. 7. ouu f hr r no ngronno ol orgn, hn lm z z L L Fn.. rror zz Fg. 7. ouu L L

11 B. m nu rm / lm lm lm lm n orr o hv zro y- rror for rm nu, lm houl b f mu k h form of z z L n n L Conon for zro.. rror for rm nu o uny fbck ym : A l WO ur ngron mu rn n h forwr h Fg. 7. b ouu f only on ngron, hn lm z z L L Fn.. rror z z L L Fg. 7. b ouu f hr r no ngron, hn lm nfn.. rror Fg. 7. b ouu 3

12 C. Prbolc nu 3 / rm lm lm lm n orr o hv zro y- rror for rm nu, houl b f mu k h form of lm z z L n n 3 L Conon for zro.. rror for rbolc nu o uny fbck ym : A l hr ur ngron mu rn n h forwr h Fg. 7. b ouu f only wo ngron, hn lm z z L L Fn conn.. rror Fg. 7. b ouu f hr only on or l ngron, hn lm nfn.. rror Fg. 7. b ouu 3

13 x fn h y- rror for nu of 5u, 5u, 5 u o h followng ym. whr u h un Soluon Fr chck h bly of h o loo F For h nu 5u 5 lm For h nu For h nu 5u rm 5 u rbol 5 lm lm lm lm 3 4 lm Sbl! 3

14 Sc rror conn Summrzng h y- rror lm whr lm : oon conn rm lm v v lm : vlocy conn Sc rror conn rbol lm Sym y lm : cclron conn rmn h.. rror h gr of h nu olynoml h h ym cn ronbly rck Sy rror n on h numbr of ngron n h forwr h.. on loo F f h roc rmr chng w/o rmovng h ol h orgn, ym y rmn n h y rror wll b h m rgrl of h rmr chng ym y robu rory fnon of ym y Numbr of ngron n h forwr h Vlu of n n h nomnor of h on-loo F y,, for n,,

15 lonh bwn nu, ym y, c rror conn, n y- rror y y y S m Prbol v

16

17 x vlu h c rror conn n fn h xc.. rror for h, rm, n rbolc nu y ym y ym y ym v lm lm lm lm lm lm v v lm lm lm l rm rbol.6 v rm rbol v rm rbol v 875

18 x 4. Sym y for S Conrol rmn h ym y n h rlvn rror conn for h ym Soluon y, rror conn x 4. Sym y for S Conrol rmn h ym y n h rlvn rror conn for h ym Soluon y, rror conn

19 Sy-S rror n rm of CLF Uny fbck ym N l F Uny fbck ym No. : on loo F : o loo F Clo-loo F H Y Clo-loo conrol ym Clo loo conrol ym Y Y ] [ A w r nr n, l ly Fnl vl horm No. Mu chck h ym bly! k k ] [ lm ] [ lm ] [ lm lm lm x fn h.. rror of h o-loo ym of for un nu 7 5 Sym y k f h nonzro conn ] [ lm

20 x 4.3 Sym y for Srvo wh chomr Fbck rmn h ym y n h rlvn rror conn for n lcrc moor oon conrol roblm h nu non-uny fbck ym cu by chomr fx o h moor hf n volg whch rooronl o hf f bck r of h conrol Soluon For olynoml rfrnc nu y- rror k Sym y wh f k > v mllr hn wh mly h uny fbck vlu of k y- rror uully ncr f chomr fbck u o mrov h ynmc ron!!!

21 Sy-S rror Scfcon Sc rror conn cn b u cfcon for conrol ym y- rror x f conrol ym h h v, mn. h ym bl. Sym y nc conn v x only for y ym 3. A rm nu h gnl nc v cf 4. h y- rror / v x fn h vlu o h hr % rror n h y for h gvn conrol ym Sym y fn.. rror x only for rm nu v rm lm v

22 Sy-S rror for urbnc Avng of fbck Avng of fbck comn for urbnc or unwn nu h nr ym rnfr funcon from h urbnc W o h rror :urbnc [ ] C Plug n C C [ ] F rlng o F rlng o

23 o ly fnl vlu horm o fn h.. rror l l l lm lm lm.. rror u o.. rror u o Aumng urbnc / lm lm lm lm Sy rror rouc by urbnc cn b ruc by lm l ncrng h C gn of h C f lm crng h C gn of rrngng Fg. 7. wh

24 Sy-S rror for Nonuny Fbck Sym Acung gnl No n rror C nrl nonuny fbck ym Conrollr & ln Convr no uny fbck form nu rnucr fbck H H / rror C Unyfbck ym A & ubrc uny fbck h

25 x Fn h ym y, rror conn,.. rror for un nu Sym y? X Sym y : rmn from h onloo F of uny fbck ym nonuny fbck ym S convr no uny fbck ym l H 5 quvln forwr F of uny fbck ym Sym y H lm /

26 4.3 hr-rm Conrollr: P Conrol Prouc conrol gnl h wll ruc h rror o zro or o mll vlu b on h rror gnl Low owr gnl ln frnc nu rror conrollr conrol nu U ln Clfcon of nurl conrollr. wo-oon or on-off conrollr. Prooronl P conrollr 3. ngrl conrollr 4. Prooronl-ngrl l P conrollr 5. Prooronl-ngrl P conrollr 6. Prooronl-ngrl-rvv P conrollr

27 . wo-oon or on-off conrollr u U for > Uully U hr zro or U U for < x olno vlv

28 . Prooronl P conrollr fbck u: conrollr ouu Conrol con u : cung rror gnl : rooronl gn Conrol con lnrly rooronl o h ym rror rnfr funcon of P-conrollr U f P-conrollr u for n orr ym P conrollr kn of mlfr wh n jubl gn Chrcrc quon By jung k, obl o chng h nurl frquncy ω bu no obl o conrol lh mng Ak n y.. rror cn b m mll by ung lrg P gn k Ak Ak lm lm Bu mng cnno b conroll wh P-conrol lon!! Cn chng h ym ron

29 . Prooronl lu ngrl Conrol P U u τ τ U L.. U F P conrol r h ym y o y comlly rjc conn b urbnc P conrol for orr ym, U A U Y τ P conrol for orr ym A A A τ τ Chrcrc quon n n A A τω ς τ ω, Nurl frquncy & mng ro Cn b conroll by conrollr gn P conrol for n orr ym A 3 A A A Chrcrc quon wo of h hr coffcn cn b un by conrollr gn n on mor rm of conrollr!

30 3. P Conrol rvv conrol gv hr ron o unly chngng gnl rror gnl 의변화율을초기에감지하여 즉, rror gnl 의추이를사전에예상하여 rror gnl 커지기전에 corrcv con 취함 gnl 커지기전에 corrcv con 취함. mng 효과 Nvr u lon Bu n combnon wh P or P conrol bcu b on h r of chng of h rror n no on h rror lf u τ τ U L L.. U F

31 wo obl wy o mlmn P conrol P wh rm n h forwr h P wh -rm n h fbck h x. chomr on h hf of moor P wh -rm n h forwr h A A A A A ffrnon of h rfrnc nu! A A A A A 3 A A A A A A 3 A A A A A A B hh h h B h f ff Boh hv h m chrcrc quon - oo of chrcrc quon cn b unquly rmn by conrollr gn Bu h rfrnc nu no ffrn n Unrbl ron o un chng vo! - oo of chrcrc quon cn b unquly rmn by conrollr gn,, - bl o conrol h ynmc ron of h o loo ym comlly by locng h CL ol whrvr r

32 x 4.6 P conrol of Moor S C moor mol - ng ncr ocllory ron bu lmn h y- rror - ng ruc h ocllon whl mnnng h zro y- rror

33 x 4.6 P conrol of Moor S C moor mol wh uny fbck rmn h ym y n y- rror wh rc o urbnc nu for boh P conrol n P conrol W -h B Ah B h A τ A hb W h Ah τ Ah τ lm lm W lm lm k k P conrol h nonzro conn whn k y n.. rror o un orqu nu b P conrol h nonzro conn whn k hb τ Ah hb k k τ Ah k k B Ak y n.. rror o un rm urbnc B Ak h

34 4. Prooronl-ngrl P conrollr L whr : ngrl m u U L whr : ngrl m L.. -Comron bwn P & P u vn for h conn rror gnl, conrol gnl connuouly ncr g, g y ffcv o ruc y- rror

35 -Comron bwn P & P A. S nu ron P-conrol U -conrol C lm lm lm A, Bu unl, rmn fn C lm lm lm lmn h y- rror n ron o h nu!

36 B. urbnc rjcon Aumng n un- urbnc P conrol P conrol P-conrol P-conrol C b J C b J C b J b J b J b J b J lm b J 3 lm b J lm lm 3 b J lmn h y- rror comlly n ron o h urbnc! A,

37 -conrol O l f P l h b J C Or rcly from P conrol wh b J b J b J b J 3 3 b J 3 b J 3 Chrcrc quon 3 b J Unbl ym! Chrcrc quon Pur -conrol mk h ym unbl nvr u lon

38 5. Prooronl-rvv P conrollr L whr : rvv m u U L L.. U or u P P u rror gnl의변화율을초기에감지하여 즉, rror gnl의추이를사전에예상하여 rror gnl 커지기전에 corrcv con 취함. mng 효과 Nvr u lon Bu n combnon wh P or P conrol bcu b on h r of chng of h rror n no on h rror lf

39 -P v. P U C J CLF C.L..F. C J J mgnry ym ol Ocllory ron o nu chrcrc quon J wo LHP ol for ov J,, m ron o nu hnk o mng! ζ J J ω n J

40 6. Prooronl-ngrl-rvv P conrollr u U U u

41 Summry P-conrol Sblz h ym Fr ron uc ωn J -conrol lmn or ruc y- rror o vrou nu Mk h ym ocllory or unbl whn u lon br u n P or P -conrol A mng ncr ym bly Allow lrg whch ruc Nvr u lon Amlf no

42 P conrol xml Hyun lnr.6 OHC ngn orqu Conrol τ θ.99.7 P,, P,, P,,

43 P conrol xml M-Srng-mr ym >> roo[ ] n Unr-m ym P,, P3,, Ovrhoo & rror P3,, 5 L ovrhoo u o mng bu rror y P3, 4, 5 L ovrhoo u o mng n zro rror u o ngrl conrol

44 P conrol xml 3 C moor oon conrol V mωm L J && θ b & θ τ τ n m m m r : gr ro f lo l : lo rf l θ V [ J b L ] m n m Aumng mll nucnc L, Moor cn b roxm n orr ym θ m V n [ J b ] m m m P,, P 5,, P 5,, 5