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1 M hnh tng quan............................................................................................ 4 2 Mt s nh ngha ............................................................................................. 4

2.1 Sai s ......................................................................................................... 4 2.2 Sai s xc lp............................................................................................. 5 2.3 Hin tng vt l ...................................................................................... 5 2.4 vt l: (Percent Of Overshoot-POT) ................................................... 5 2.5 Thi gian ln nh ..................................................................................... 6 2.6 Thi gian qu (tq) ................................................................................. 6 2.7 Thi gian ln (tr)........................................................................................ 7 2.8 Hm truyn................................................................................................ 7

3 Vn v PID(proportinal-Integral-Derivative) .............................................. 8 3.1 Ba s hng ca b iu khin.................................................................... 8 3.2 c im ca tng b iu khin P, I, D. ................................................. 9 3.3 Phng php Zeigler-Nichols (1940s) ...................................................... 9

3.3.1 Da vo p ng qu ca h thng vng h (Phng php Zeigler-Nichols 1)............................................................................................. 9 3.3.2 Da vo p ng qu ca h thng vng kn (Phng php Zeigler-Nichols 2)........................................................................................... 10


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Hnh 1 S khi PID............................................................................................. 4 Hnh 2 (Ngun c s iu hin t ng TS. Hunh thi Hong) ............................ 4 Hnh 3 (Ngun c s iu hin t ng TS. Hunh thi Hong) ............................ 5 Hnh 4 Vt l............................................................................................................ 5 Hnh 5 Thi gian ln nh ....................................................................................... 6 Hnh 6 (Ngun c s iu hin t ng TS. Hunh thi Hong) ............................ 6 Hnh 7 (Ngun c s iu hin t ng TS. Hunh thi Hong) ........................... 7 Hnh 8 http://www.engin.umich.edu........................................................................ 8 Hnh 9 http://www.engin.umich.edu........................................................................ 9 Hnh 10..................................................................................................................... 9 Hnh 11................................................................................................................... 10 Hnh 12................................................................................................................... 10 Hnh 13................................................................................................................... 11 Hnh 14................................................................................................................... 11


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TM HIU PID

Ks. on Thanh Tn [email protected] St: 01 237 237 369


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1 M hnh tng quan

Hnh 1 S khi PID

2 Mt s nh ngha 2.1 Sai s

Hnh 2 (Ngun c s iu hin t ng TS. Hunh thi Hong) Sai s l hiu s gia tn hiu vo v tn hiu hi tip

)()()()()()( sCsRsEtctrte htht == )(te : sai s )(tr : tn hiu tham chiu, t. )(tc : tn hiu iu khin.


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2.2 Sai s xc lp L sai s ca h thng khi thi gian tin n v cng

)()( limlim0

ssEetees

xlt

xl

==

Chp nhn sai s xc lp Ess nh hn 5%

2.3 Hin tng vt l L hin tng p ng ca h thng vt qu gi tr xc lp ca n.

Hnh 3 (Ngun c s iu hin t ng TS. Hunh thi Hong) 2.4 vt l: (Percent Of Overshoot-POT) L i lng nh gi mc vt l ca h thng, vt l tnh bng cng thc.

%100max =xl

xl

c

ccPOT

Chp nhn vt l nh hn 20%

Hnh 4 Vt l


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2.5 Thi gian ln nh L thi gian p ng ra t gi tr cc i ( )peakp tt =

Hnh 5 Thi gian ln nh

2.6 Thi gian qu (tq) L thi gian cn thit sai lch gia p ng ca h thng v gi tr xc lp ca n khng vt qu % , % thng chn l 2% hoc 5%.

Hnh 6 (Ngun c s iu hin t ng TS. Hunh thi Hong)


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2.7 Thi gian ln (tr) L thi gian cn thit p ng ca h thng tng t 10% n 90% gi tr xc lp ca n.

Hnh 7 (Ngun c s iu hin t ng TS. Hunh thi Hong) 2.8 Hm truyn Hm truyn ca mt h thng l t s gia bin i Laplace ca tn hiu ra v bin i Laplace ca tn hiu vo, khi iu kin u bng 0.

)()()(

sXsY

sH =

)(sH gi l hm truyn ca h thng


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3 Vn v PID(proportinal-Integral-Derivative) Ta xem xt h thng hi tip n gin sau.

Hnh 8 http://www.engin.umich.edu Plant: l h thng c iu khin. Controller: l b iu khin cn thit k.

3.1 Ba s hng ca b iu khin Hm truyn ca b iu khin PID c dng nh sau

++=

++=++= sT

sTK

s

KsKsKsK

s

KKsG DI

PIPD

DI

Pc11)(

2

PK : h s t l IK : h s tch phn DK : h s vi phn

I

PI K

KT = : thi hng tch phn

P

DD K

KT = : thi hng vi phn

Trc tin chng ta hy quan st cch m b iu khin PID lm vic trong h thng vng kn c m t hnh 6. Bin s (e) i din cho vic gim st li. N l sai khc gia gi tr ng vo mong mun v ng ra thc t (Y). Tn hiu li (e) s c a vo b iu khin PID, b iu khin s tnh ton hai gi tr tch phn v vi phn ca tn hiu li (e). Tn hiu (u) khi qua b iu khin s bng KP ln ln ca li cng vi KI ln tch phn ca li, cng vi KD ln vi phn ca li.

dttdeKdtteKteKtu DIP)()()()( ++=

Khu t l Khu tch phn l tng cc sai s trong qu kh. Khau vi phn l tc thay i ca sai s.


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Tn hiu (u) s c a vo h thng c iu khin, khi ta c tn hiu ng ra (Y) mi. Tn hiu ng ra (Y) mi ny s c hi tip, so snh tm ra tn hiu li mi (e). Tn hiu li mi ny tip tc c x l nh trn cho n khi t yu cu.

3.2 c im ca tng b iu khin P, I, D. B iu khin t l (KP) c tc dng lm gim thi gian tng (tr) nn p ng nhanh, tuy nhin gy ra sai s xc lp. B iu khin tch phn (KI) c tc dng loi b sai s xc lp, tuy nhin lm tng vt l. B iu khin vi phn (KD) lm gim vt l, tuy nhin gy ra p ng chm. nh hng ca cc thng s KP, KI, KD c tm tt theo bng di y.

Hnh 9 http://www.engin.umich.edu Ch rng nhng s tng quan ny c th khng chnh xc, bi v cc thng s KP, KI, KD cn ph thuc vo thit b. Trong thc t s thay i ca mt trong nhng thng s ny c th thay i nh hng ca hai thng s cn li. Chnh v th bng hnh 7 ch nn c s dng tham kho khi bn xc nh cc thng s KP, KI, KD.

3.3 Phng php Zeigler-Nichols (1940s) 3.3.1 Da vo p ng qu ca h thng vng h (Phng php

Zeigler-Nichols 1) Phng php Zeigler-Nichols vng h da trn p ng ca hm nc n v (step function), khi h thng khng c hi tip.

Hnh 10


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Nu h thng iu khin l vng kn th ta phi tho g tn hiu hi tip v. iu ny c th thc hin bng cch thit lp b iu khin ch iu khin bng tay. Thay i gi tr ca tn hiu hm nc ng vo, quan st p ng ng ra. Gi tr tng ca hm nc va phi (khong 10% gi tr t) p ng ng ra khng vt qu gi tr mong mun. Sau khi iu chnh xong, ta tin hnh c cc gi tr ca p ng ng ra .

Hnh 11 L: thi gian tr ca p ng so vi tn hiu kch (s) T: thi gian tnh t khi tn hiu p ng tng t 10% n 90% (s). Sau tnh ton cc thng s PID da vo bng sau

Hnh 12 Sau khi tm c cc thng s ca b PID, ta tin hnh np cc gi tr ny cho b iu khin, v thit lp li ch hot ng t ng kim tra.

3.3.2 Da vo p ng qu ca h thng vng kn (Phng php Zeigler-Nichols 2)

u tin ta iu chnh khu t l trc. Tng dn h s khuch i KP ca h kn cho n khi p ng ng ra trng thi xc lp iu ha, ta k hiu gi tr ca KP lc ny l KC. ng thi xc nh chu k ca dao ng k hiu l TC.


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Hnh 13 Sau ta tnh ton cc h s ca b iu khin PID da vo bng sau.

Hnh 14 (http://webber.physik.uni-freiburg.de/~hon/vorlss02/Literatur/

Ingenieurswiss/pid/pid+matlab/PID%20systems%20tutorial.htm)

Nhng gi tr theo bng trn cha phi l nhng gi tr ti u. Mc d i lc, iu chnh ti u c th c yu cu h thng t c hiu sut tt nht. S la chn b iu khin PID, PI, PD, cng ty thuc vo ng dng ca h thng, v d iu khin bnh p sut ln th b iu khin PID khng vt l c s dng.

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