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DCLRSequential Loop Closing

, , , *

, *

Sequential Loop Closing Method for Multiloop Control Systems with Desired Closed-

loop Responses

Changgeun Kim, Daewoong Chun, Jietae Lee, Soon Young Kwon*

Department of Chemical Engineering

Kyungpook National Unier!ity, Seohan "e#tile*

Introduction

$ultiloop control !y!tem! which u!e multiple !ingle%input !ingle%output &S'S()

controller! are !till ominantly u!e in the chemical proce!!e! +ecau!e of their !implicity an

ro+u!tne!! -or multiaria+le proce!!e! with n input! an n output!, n S'S( controller! are

u!e to control n paire input! an output! in multiloop control !y!tem!, an hence re!pon!e!

of n paire loop! can +e e!igne to +e what we want .lthough re!pon!e! other than the

paire loop! are not guarantee, the oerall re!pon!e! are u!ually !ati!factory compare with

tho!e of well%known e!ign metho! !uch a! the +igge!t log%moulu! tuning &/L") metho

&Luy+en, 0123) an the !e4uential autotuning &S.") metho &Loh et al, 01156 Shen an Yu,

0117) "o e!ign !uch multiloop control !y!tem!, Jung et al &0111) propo!e an iteratie

metho +a!e on the Newton%8aph!on metho "heir metho work! well for ariou!

proce!!e! when pairing! are e!ira+le 9oweer, it! eriation i! rather comple# an it wa!

ierge for !ome proce!!e! 9ere, a !imple iteratie metho +a!e on the concept of

!e4uential loop clo!ing metho i! propo!e

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Multiloop Control System with Desired Closed-loop Responses

Con!ier the multiloop control !y!tem where an n#n proce!!, :&!);, i! controlle

+y a iagonal controller, C&!);iag "he clo!e%loop tran!fer function! +etween !et

point! an output! +ecome

9&!)8&!)Y&!) = , ( ) :&!)C&!):&!)C&!)'9&!) 0+=

&0)

Since C&!) ha! n element!, we may !et n iagonal element! in 9&!) a!

0!?

&!)g&!)h

@&!)h

i

iiiii

+=

+

, i;0,A,B,n &A)

where &!)gii+

i! the nonminimum%pha!e part of g ii&!) with the !teay%!tate gain of one

$ultiloop controller !ati!fying E4 A can +e foun +y the Newton%8aph!on iteration &Jung et

al, 0111) "he iteratie !cheme i! rather comple# an conergence i! !u!cepti+le 9ere the

!e4uential loop clo!ing metho i! applie to fin C&!) !ati!fying E4 A e e!ign c i&!)

!e4uentially to !ati!fy E4 A hen loop! e#cept the i%th loop are clo!e, the tran!fer function

for the i%th pair +ecome! &-igure 0)

( )

{ }

{ }"

in0i

i

n0i0i0i

n0i0i0i

ii

0

i

"

iii

D,EE,,0,,EE,Fe

&!)c,&!),c&!),0,c,&!),c*iag&!)G

&!)c,&!),c&!),E,c,&!),c*iag&!)H

&!)e:&!)G&!)):&!)H'e&!)gI

+

+

=

=

=

+=

e e!ign ci&!), for the a+oe tran!fer function of &!)gI ii , !uch that the clo!e%loop tran!fer

function !ati!fie! E4 A appro#imately Since &!)gI ii i! epenent on other controller!, we

!houl apply the e!ign proceure iteratiely until conergence De!ign proceure i! a!

follow!

Step 0) -or i;0,A,B,n, !et E)J&=ci = , J for a gien fre4uency !et , an

choo!e the e!ign parameter, i?

Step A) -or i;0,A,B,n, calculate )&=JgI ii an

)J&=g0)J=&?

)J&=g

)J&=gI

0

)J&=h@

0

)J&=h@

)J&=gI

0)J&=c

iii

ii

iii

i

ii

i +

+

+=

=

Step 5) 'terate the !tep A until conergence

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Step 7) .ppro#imate the conerge )J&=ci , i;0,A,B,n, +y the G'D controller -or thi!,

the lea!t !4uare! metho &the routine of infre4! in Signal Groce!!ing "ool+o#

for $."L./ &011M)) can +e u!e

Example

Conergence of the propo!e metho i! te!te +y applying it to pro+lem! in Luy+en

&0123) "a+le 0 !how! the re!ult! -or Douka! an Luy+en column, we cant control with

po!itie controller! like propo!e controller! +ecau!e 8:. i! negatie "hi! mean! a +a

fairing "hu!, we can !imulate +y e#changing the thir row for the forth row e can !ee that

the propo!e metho ha! +etter conergence than the metho in Jung et al &0111)

"he control performance! e!igne +y the propo!e metho an the metho of Jung et al

&0111) are ery !imilar .! an illu!tratie e#ample, the (gunnaike an 8ay column &Luy+en,

0123) i! con!iere .ll e!ign parameter! are tho!e in Jung et al &0111) -igure A !how!

re!pon!e! of multiloop G' control !y!tem! Slight ifference! are mainly ue to the

appro#imation metho! for G' controller!

Conclusion

. new iteration metho +a!e on the !e4uential loop clo!ing metho i! propo!e to e!ign

multiloop control !y!tem with e!ire clo!e%loop re!pon!e! "hi! metho i! ery !imple an

gie! goo re!pon!e! a! well

c!nowledgment

-inantial !upport from K(SE- uner grant A%0%5M%3%0 i! gratefully acknowlege

Literature Cited

Jung, J, Choi, J Y an Lee, J, O(ne%Garameter De!ign $etho for a $ultiloop Control

Sy!tem De!ignP,Ind. Eng. Chem. Res., 52, 0Q2%0Q22 &0111)

Ly+en, L, OSimple $etho for "uning S'S( Controller! in $ultiaria+le Sy!tem!P, Ind.

Eng. Chem. Process Des. Dev, AQ, 3Q7%33 &0123)

Loh, . G, 9ang, C C, Huek, C K an Ra!nani, R U, O.utotuning of $ultiaria+le

Groportional%'ntegral Controller! U!ing 8elay -ee+ackP,Ind. Eng. Chem. Res.,5A, 0A%

0M &0115)

Shen, S 9 an Yu, C C, OU!e of 8elay%-ee+ack "e!t for .utotuning of $utiaria+le

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Sy!tem!P,AIChE J, 7, 3AM%373 &0117)

Student Edition of MATLAB, ersion !, "ser#s $uide , Grentice%9all, N J, &011M)

"a+le 0 Conergence of the propo!e metho an the metho in Jung et al &0111)

'"* the num+er of iteration!

&a) &+)

-igure 0 $ultiloop control !y!tem where the i%th loop i! open

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-igure A Control re!pon!e! for the (gunnaike an 8ay column proce!!