Chapter 6. PID Control

Transcription

1 Char 6 PID Conrol

2 PID Conrol Mo ommon onrollr in h CPI. Cam ino u in 930 wih h inroduion of numai onrollr. Exrmly flxibl and owrful onrol algorihm whn alid rorly.

3 Gnral Fdbak Conrol Loo D G d Y E C U + G G a G Y Y G

4 Clod Loo Tranfr Funion From h gnral fdbak onrol loo and uing h rori of ranfr funion, h following xrion an b drivd: G G G G G G G Y Y a a G G G G G D Y a d

5 Chararii Equaion Sin oin raking and diurban rjion hav h am dnominaor for hir lod loo ranfr funion, hi india ha boh oin raking and diurban rjion hav h am gnral dynami bhavior. Th roo of h dnominaor drmin h dynami hararii of h lod loo ro. Th hararii quaion i givn by: G G G G a 0

6 Chararii Equaion Examl Conidr h dynami bhavior of a P-only onrollr alid o a CST hrmal mixr =; =60 whr h mraur nor ha a =20 and a i aumd mall. No ha G =. Subiuing Afr rarranging ino h andard form, 200 ino h hararii.5 quaion

7 Examl Coninud- Analyi of h Clod Loo Pol Whn =0, ol ar and whih orrond o h invr of and. A i inrad from zro, h valu of h ol bgin o aroah on anohr. Criially damd bhavior our whn h ol ar qual. Undrdamd bhavior rul whn i inrad furhr du o h imaginary omonn in h ol.

8 Poiion Form of h PID Algorihm Rvr aing Dir aing D I d d d 0 0 D I d d d 0 0

9 Dfiniion of Trm - h rror from oin [=y -y ]. - h onrollr gain i a uning aramr and largly drmin h onrollr aggrivn. I - h r im i a uning aramr and drmin h amoun of ingral aion. D - h drivaiv im i a uning aramr and drmin h amoun of drivaiv aion.

10 Lvl Conrol Examl F in L LT LC F ou Pro gain i oiiv bau whn flow in i inrad, h lvl inra. If h final onrol lmn i dir aing, u rvr aing PID. For rvr aing final onrol lmn, u dir aing PID.

11 Lvl Conrol Examl F in L LT LC F ou Pro gain i ngaiv bau whn flow ou i inrad, h lvl dra. If h final onrol lmn i dir aing, u dir aing PID. For rvr aing final onrol lmn, u rvr aing PID.

12 Guidlin for Sling Dir and Rvr Aing PID Conidr a dir aing final onrol lmn o b oiiv and rvr o b ngaiv. If h ign of h rodu of h final onrol lmn and h ro gain i oiiv, u h rvr aing PID algorihm. If h ign of h rodu i ngaiv, u h dir aing PID algorihm.

13 Proorional Band PB 00 % Anohr way o xr h onrollr gain. in hi formula i dimnionl. Tha i, h onrollr ouu i ald 0-00% and h rror from oin i ald 0-00%. In mor frqun u 0-5 yar ago, bu i ill aar a an oion on DCS.

14 Convrion from PB o Proorional band i qual o 200%. Th rang of h rror from oin i 200 i. Th onrollr ouu rang i 0 o 00%. D 00% PB % 200i 00% 200% % / i

15 Digial Equivaln of PID Conrollr 0 d n i i Th razoidal aroximaion of h ingral. d d Bakward diffrn aroximaion of h fir drivaiv

16 Digial Vrion of PID Conrol Algorihm n i n i D I 0

17 Drivaion of h Vloiy Form of h PID Conrol Algorihm n i D I i n i D I i D I 2 2

18 Vloiy Form of PID Conrollr No h diffrn in roorional, ingral, and drivaiv rm from h oiion form. Vloiy form i h form imlmnd on DCS. Conrollr Aing Dir Conrollr Rvr Aing 2 2 D I

19 Corrion for Drivaiv ik Drivaiv kik our whn a oin hang i alid ha au a ik in h drivaiv of h rror from oin. Drivaiv kik an b liminad by rlaing h aroximaion of h drivaiv bad on h rror from oin wih h ngaiv of h aroximaion of h drivaiv bad on h maurd valu of h onrolld variabl, i.., D y 2y y 2

20 Corrion for Aggriv Soin Traking For rain ro, uning h onrollr for good diurban rjion rforman rul in xivly aggriv aion for oin hang. Thi roblm an b orrd by rmoving h oin from h roorional rm. Thn oin raking i aomlihd by ingral aion only. ubiud for by y y

21 Th Thr Vrion of h PID Algorihm Offrd on DCS Th original form in whih h roorional, ingral, and drivaiv rm ar bad on h rror from oin D I 2 2

22 Th Thr Vrion of h PID Algorihm Offrd on DCS 2 Th form in whih h roorional and ingral rm ar bad on h rror from oin whil h drivaiv-onmaurmn i ud for h drivaiv rm. y y y D I 2 2

23 Th Thr Vrion of h PID Algorihm Offrd on DCS 3 Th form in whih h roorional and drivaiv rm ar bad on h ro maurmn and h ingral i bad on h rror from oin. y y y y y D I 2 2

24 Lala Tranform for a PID Conrollr G C E I D

25 Examl for a Fir Ordr Pro wih a PI Conrollr Rarranging Equaion : i Charari I

26 Examl of a PI Conrollr Alid o a Sond Ordr Pro Chararii Rarranging 25 ; ; 2 ron wih I Equaion : 2 and a ; ond ordr and 5;

27 Filring h Pro Maurmn y f f y f y f Filring rdu h ff of nor noi by aroximaing a running avrag. Filring add lag whn h filrd maurmn i ud for onrol. Normally, u h minimum amoun of filring nary. f- filr faor 0-

28 Fdbak Loo wih Snor Filring D G d Y E C U + G G a G Y Y f G f Y G

29 Eff of Filring on Clod Loo Dynami 2 0 filring : nor ro wih ordr fir on onrollr only P for quaion i Charari f f f f

30 Analyi of Examl f i qual o /f- a f bom mall, f bom larg. Whn f i mall omard o, a f i inrad, will dra. Whn f i larg omard o, a f i inrad, will inra. Criial iu i rlaiv magniud of f omar o.

31 Filrd Tmraur Eff of h Amoun of Filring on h On Loo Ron f=0.3 f=0.2 f= Tim ond

32 Tim Eff of a Noiy Snor on Conrolld Variabl wihou Filring Produ Tmraur Maniulad Variabl

33 Tim Eff of a Noiy Snor on Conrolld Variabl wih Filring Produ Tmraur Maniulad Variabl

34 Tmraur ºC An Examl of Too Muh and Too Lil Filring f=0.2 f= f= Tim ond

35 Prori of Proorional Aion 0 Y Y Clod loo ranfr funion ba on a P-only onrollr alid o a fir ordr ro. Prori of P onrol Do no hang ordr of ro Clod loo im onan i mallr han on loo Do no limina off.

36 Off Ruling from P-only Conrol.0 Soin Off Tim

37 Proorional Aion for h Ron of a PI Conrollr y y ro Tim

38 Prori of Ingral Aion Bad on alying an I- only onrollr o a fir ordr ro Prori of I onrol Off i liminad Inra h ordr by A ingral aion i inrad, h ro bom far, bu a h xn of mor uaind oillaion I I I I I I Y Y d

39 Ingral Aion for h Ron of a PI Conrollr y y in Tim

40 Prori of Drivaiv Aion Y Y D d d 2 D D Clod loo ranfr funion for drivaiv-only onrol alid o a ond ordr ro. Prori of drivaiv onrol: Do no hang h ordr of h ro Do no limina off Rdu h oillaory naur of h fdbak ron

41 Drivaiv Aion for h Ron of a PID Conrollr y y dr Tim

42 PID Conrollr Dign Iu Ovr 90% of onrol loo u PI onrollr. P-only: ud for fa ronding ro ha do no rquir off fr oraion.g., rain lvl and rur onrollr PI: ud for fa ronding ro ha rquir off fr oraion.g., rain flow, lvl, rur, mraur, and omoiion onrollr

43 PID Conrollr Dign Iu PID: u for luggih ro i.., a ro wih larg dadim o im onan raio or ro ha xhibi vr ringing for PI onrollr. PID onrollr ar alid o rain mraur and omoiion onrol loo. U drivaiv aion whn:

44 Comarion bwn PI and PID for a Low / Raio PI PID Tim

45 Comarion bwn PI and PID for a High / Raio PI PID Tim

46 Analyi of Svral Commonly Enounrd Conrol Loo Flow onrol loo Lvl onrol loo Prur onrol loo Tmraur onrol loo Comoiion onrol loo

47 Flow Conrol Loo FC Flow Soin FT Sin h flow nor and h ro ar o fa, h dynami of h flow onrol loo i onrolld by h dynami of h onrol valv. Almo alway u PI onrollr.

48 Dadband of a Conrol Valv Sm Poiion Air Prur Tim Dadband of indurial valv i bwn ±0%- ±25%. A a rul, mall hang in h air rur alid o h valv do no hang h flow ra.

49 Flow Ra Dadband of Flow Conrol Loo Tim ond A onrol valv dadband of ±0-25% in a flow onrol loo or wih a oiionr yially ha a dadband for h avrag flow ra of l han ±0.5% du o h high frquny oning and loing of h valv around h ifid flow ra.

50 Lvl Conrol Loo L F in Dynami of h nor and auaor ar fa omard o h ro. LC LT RSP FT FC F ou If oraor wan onrol o oin, u PI onrollr wih mall amoun of ingral aion, ohrwi u P- only onrollr.

51 Prur Conrol Pro P PC PT C.W. Vn Th ro and h nor ar gnrally far han h auaor. U P-only onrollr unl off liminaion i imoran hn u a PI onrollr.

52 Tmraur Conrol Loo TT TC T Th dynami of h ro and nor ar uually lowr han h auaor. Pro Sram FC RSP FT Ga U a PI onrollr unl h ro i uffiinly luggih o warran a PID onrollr.

53 Analyi of PI Conrollr Alid o Tyial Tmraur Loo I 30; 60; v τ ζ

54 Furhr Analyi of Dynami of a Tyial Tmraur Conrol Loo No ha a h onrollr gain i inrad, i.., inra, h lod loo im onan bom mallr. Alo, no ha a h onrollr gain i inrad, h valu of dra.

55 Comoiion Conrol Loo C.W. Th ro i uually h low lmn followd by h nor wih h auaor bing h fa. FC FT RSP AT AC U a PI onrollr unl h ro i uffiinly luggih o warran a PID onrollr.

56 Ovrviw Th hararii quaion drmin h dynami bhavior of a lod loo ym Thr ar a numbr of diffrn way o aly a PID onrollr. Proorional, ingral, and drivaiv aion ah hav uniqu hararii. U a PI onrollr unl off i no imoran or if h ro i luggih. Whn analyzing h dynami of a loo, onidr h dynami of h auaor, h ro, and h nor araly.