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-0.0005606 S - 4.574e-05
P ( s )  2
S  0.06858S  0.004006
Equation5.5
TheIMCcontroller(C)wasobtainedthenastheequation5.6(Seesection2.9.2.2).
Avalueof   24.5 wasusedforthetimeconstantoftheclosed‐loopsystem.Thisvalue
wasmanipulatedbytrialanderroruntilasatisfyinggain,phaseanddelaymarginwas
obtainedforthecontroller.
C
340.7491( S  0.005194S  0.000356)
S ( S  0.0816)
2
Equation5.6
TheIMCcontrollerasasecondordertransferfunctionwasthenwritteninform
ofaPIDcontrollerwithalow‐passfilterappliedonitsderivativeaction(Wemaysaya
PIDFcontroller).
APIcontrollerwasalsoobtainedbyreducingtheorderofIMCcontrollerto1.
Therelatedtuningrulesareshownintable5.5.
Table5.5:IMC‐basedPIDandPItuningparameters
Kc0 Kc I D F PIDF 250
3.4736
2.3368
1189.9378
12.2552
PI 250
340.7491
229.2276
_
_
Thefunction“PIDAdvancedVI”fromLabVIEWwasusedtoimplementthelow‐
passfilterintheexperiments(seeappendixA).
ThePIDtuningparameterswereimplementedinLabVIEW.Firstthesystemwas
runinopen‐loopmannerwithamanualvalveopeningofZ=0.2anddatawerelogged.
Then the loop was closed with a set‐point P=170 kPa that results in an average valve
openingofZ=0.16.Aftercoupleofminutesitwastriedtodecreasetheset‐pointvaluein
a stepwisemanner. At each step it was waited until the steady state was reached and
then a new step of reduction was applied. The same was done with PI tuning
parameters.Figures5.11and5.12describetheresultsofcontrolusingthe IMC‐based
PID and PI controllers respectively. The experimental slugging system could be
stabilizeduptoZ=0.30withIMC‐basedPIDcontrolleranduptoZ=0.29withIMC‐based
PIcontroller.
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