Chapter 7 Stead St y- ate Errors

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1 Char 7 Say-Sa rror

2 Inroucon Conrol ym analy an gn cfcaon a. rann ron b. Sably c. Say-a rror fnon of ay-a rror : u c a whr u : nu, c: ouu Val only for abl ym chck ym ably fr! nu for ay-a a nu analy U o a ym ably o follow Poon comman Conan vlocy comman Or lnarly ncrang nu Conan acclraon comman

3 valuang Say-Sa rror Say-a rror Ouu : Zro.. rror Ouu : Fn.. rror S nu am nu Ouu : Zro.. rror Ouu : Fn.. rror Ouu 3: nfn.. rror u o ffrn ouu lo Fg. 7.

4 Say-Sa rror n rm of Uny fback ym Uny fback ym No. : on loo F : clo loo F Clo-loo F C Clo-loo conrol ym Clo loo conrol ym C C ] [ A w r nr n, l aly Fnal val horm No. Mu chck h ym ably! ] [ lm lm lm x fn h.. rror of h clo-loo ym of for a un nu ] [ lm

5 Say-Sa rror n rm of Uny fback ym No. : on loo F C C alyng fnal val horm No. Mu chck h ym ably! lm lm Aumng h clo-loo ym abl, hn

6 laonh bwn an h for gnal A. S nu / lm lm lm lm : C gan of h forwar F a frquncy varabl aroachng zro lm In orr o hav Zro ay-a rror, houl b af houl b of h followng form o afy lm z z L n n L ngraor Conon for zro.. rror for a un nu o a uny fback ym : A la ON ur ngraon mu rn n h forwar ah Fg. 7. a ouu If hr ar no ngraon, hn lm z z L L Fn.. rror zz Fg. 7. a ouu L L

7 B. am nu ram / lm lm lm lm In orr o hav zro ay-a rror for a ram nu, houl b af mu ak h form of z z L n n L Conon for zro.. rror for a ram nu o a uny fback ym : A la WO ur ngraon mu rn n h forwar ah Fg. 7. b ouu If only on ngraon, hn L lm L z z Fn.. rror z z L L Fg. 7. b ouu If hr ar no ngraon, hn lm nfn.. rror Fg. 7. b ouu 3

8 C. Parabolc nu 3 / ram lm lm lm In orr o hav zro ay-a rror for a ram nu, houl b af mu ak h form of lm z z L n n 3 L Conon for zro.. rror for a ram nu o a uny fback ym : A la hr ur ngraon mu rn n h forwar ah Fg. 7. b ouu If only wo ngraon, hn L lm L z z Fn conan.. rror Fg. 7. b ouu If hr only on or l ngraon, hn lm nfn.. rror Fg. 7. b ouu 3

9 x fn h ay-a rror for nu of 5u, 5u, 5 u o h followng ym. whr u h un Soluon Fr chck h ably of h clo loo F For h nu 5u 5 5 lm lm 5u 3 4 For h nu For h nu ram 5 u arabola bl 5 5 lm lm 3 4 lm lm Sabl! 3

10 Sac rror conan Summarzng h ay-aa rror lm whr lm : oon conan ram lm v v lm : vlocy conan Sac rror conan lm arabola Sym y a a lm : acclraon conan rmn h.. rror Say a rror n on h numbr of ngraon n h forwar ah.. on loo F fnon of ym y Numbr of ngraon n h forwar ah Valu of n n h nomnaor of h on-loo F y,, for n,,

11 laonh bwn nu, ym y, ac rror conan, an ay-a rror

12 x valua h ac rror conan an fn h xc.. rror for h, ram, an arabolc nu y ym y ym y ym v a lm 5 5 lm lm v lm v lm lm lm a 8 lm a lm ram arabola.6 v a ram.3 v 3.5 arabola a ram arabola v 875 a

13 Say-Sa rror Scfcaon Sac rror conan can b u a cfcaon for a conrol ym ay-a rror x f a conrol ym ha h v, man. h ym abl. Sym y nc conan v x only for y ym 3. A ram nu h gnal nc v cf 4. h ay-aa rror / v x fn h valu o ha hr % rror n h ay a for h gvn conrol ym Sym y fn.. rror x only for ram nu v ram lm v

14 Say-Sa rror for urbanc Avanag of fback comna for urbanc or unwan nu ha nr a ym F b k l h b Fback conrol ym wh urbanc :urbanc Fg. 7. [ ] C Plug n C C [ ] F rlang o F rlang o

15 o aly fnal valu horm o fn h.. rror l l l lm lm lm.. rror u o.. rror u o Aumng urbanc / lm lm lm lm Say a rror rouc by urbanc can b ruc by lm l ncrang h C gan of h C f lm crang h C gan of arrangng Fg. 7. wh

16 Say-Sa rror for Nonuny Fback Sym Acuang gnal No an rror a C nral nonuny fback ym Conrollr & lan Convr no uny fback form Inu ranucr fback H H / rror C Unyfback ym A & ubrac uny fback ah

17 x Fn h ym y, rror conan,.. rror for a un nu Sym y? X Sym y : rmn from h onloo F of uny fback ym I a nonuny fback ym S I convr no uny fback ym l H 5 quvaln forwar F of uny fback ym Sym y H lm /

18 Say-Sa rror for Nonuny Fback Sym wh a urbanc

19 Snvy

20 Auomac Conrollr Prouc a conrol gnal ha wll ruc h rror o zro or o a mall valu ba on h rror gnal Low owr gnal lan frnc nu rror conrollr conrol nu U lan Clafcaon of nural conrollr. wo-oon or on-off conrollr. Prooronal P conrollr 3. Ingral I conrollr 4. Prooronal-Ingral l PI conrollr 5. Prooronal-Ingral P conrollr 6. Prooronal-Ingral-rvav PI conrollr

21 . wo-oon or on-off conrollr u U for > Uually U hr zro or U U for < x olno valv. Prooronal P conrollr Conrol acon u ranfr funcon of P-conrollr U 3. Ingral I conrollr u u: conrollr ouu : acuang rror gnal : rooronal gan P conrollr a kn of amlfr wh an ajuabl gan : ngral gan akng L la o a F of I-conrollr U U

22 4. Prooronal-Ingral PI conrollr L whr : ngral m u U L whr : ngral m L.. -Comaron bwn P & PI a a u vn for h conan rror gnal, conrol gnal connuouly ncra g, g y ffcv o ruc ay-a rror

23 -Comaron bwn P & PI A. S nu ron P-conrol U I-conrol C lm lm lm A, Bu unl, rman fn C lm lm lm lmna h ay-a rror n ron o h nu!

24 B. urbanc rjcon Aumng an un- urbanc P conrol PI conrol P-conrol PI-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 lmna h ay-a rror comlly n ron o h urbanc! A,

25 I-conrol O l f PI l h b J C Or rcly from PI conrol wh b J b J b J b J 3 3 b J 3 b J 3 Characrc quaon 3 b J Unabl ym! Characrc quaon Pur I-conrol mak h ym unabl nvr u alon

26 5. Prooronal-rvav P conrollr L whr : rvav m u U L L.. U or a u a P a P a u a a a rror gnal의변화율을초기에감지하여 즉, rror gnal의추이를사전에예상하여 rror gnal 커지기전에 corrcv acon 취함. amng 효과 Nvr u alon Bu n combnaon wh P or PI conrol bcau ba on h ra of chang of h rror an no on h rror lf

27 -P v. P U C J CLF C.L..F. C J J Imagnary ym ol Ocllaory ron o nu characrc quaon J wo LHP ol for ov J,, am ron o nu hank o a amng! ζ J J ω n J

28 6. Prooronal-Ingral-rvav PI conrollr u U U a a a u a

29 Summary P-conrol Sablz h ym Far ron uc ωn J I-conrol lmna or ruc ay-a rror o varou nu Mak h ym ocllaory or unabl whn u alon br u n PI or PI -conrol A amng ncra ym ably Allow larg whch ruc Nvr u alon Amlf no

30 PI conrol xaml Hyuna lanra.6 OHC ngn orqu Conrol τ θ.99.7 P, I, P, I, P, I,

31 PI conrol xaml Ma-Srng-amr ym >> roo[ ] an Unr-am ym P, I, P3, I, Ovrhoo & rror P3, I, 5 L ovrhoo u o a amng bu rror y P3, I, 5 L ovrhoo u o a amng an zro rror u o ngral conrol

32 PI conrol xaml 3 C moor oon conrol V mωm L J && θ b & θ τ τ n m m m r : gar rao f loa l : loa rf l θ V [ J b L ] m n m Aumng mall nucanc L, Moor can b aroxma a n orr ym θ m V n [ J b ] m m m P, I, P 5, I, P 5, I, 5

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