Self-learning Backlash Inverse Control of Cooling or Heating Coil Valves Having Backlash Hysteresis

Transcription

1 Purdue Unversty Purdue e-pubs Interntonl Refrgerton nd Ar Condtonng Conferene Shool of Mehnl Engneerng 16 Self-lernng Bklsh Inverse Control of Coolng or Hetng Col Vlves Hvng Bklsh Hysteress Je C Ry W. Herrk Lbortores, Purdue Unversty, Unted Sttes of Amer, 4@purdue.edu Jmes E. Brun Ry W. Herrk Lbortores, Purdue Unversty, Unted Sttes of Amer, jbrun@purdue.edu Follo ths nd ddtonl orks t: C, Je nd Brun, Jmes E., "Self-lernng Bklsh Inverse Control of Coolng or Hetng Col Vlves Hvng Bklsh Hysteress" (16). Interntonl Refrgerton nd Ar Condtonng Conferene. Pper Ths doument hs been mde vlble through Purdue e-pubs, serve of the Purdue Unversty Lbrres. Plese ontt epubs@purdue.edu for ddtonl nformton. Complete proeedngs my be qured n prnt nd on CD-ROM dretly from the Ry W. Herrk Lbortores t Herrk/Events/orderlt.html

2 77, Pge 1 Self-Lernng Bklsh Inverse Control of Coolng or Hetng Col Vlves Hvng Bklsh Hysteress Je CAI 1 *, Jmes E. BRAUN 1 1 Ry W. Herrk Lbortores, Purdue Unversty, West Lfyette, IN, USA 4@purdue.edu * Correspondng Author ABSTRACT Vlves re dely used n HVAC systems to regulte lqud flo rte, suh s hot- nd hlled-ter vlves utlzed n oolng nd hetng ols. These vlves re typlly ontrolled th motorzed tutors here sgnfnt bklsh hysteress mght exst nd the bklsh mgntude mostly depends on the lerne of the mnuftured gerbox. Due to the hysteress effet, unstsftory trkng performne results hen usng onventonl PI ontroller. To understnd the ontrol effet from the bklsh hysteress, ths pper develops n emultor model for oolng ol nd vlve set derved fro m feld mesurements. Bsed on observtons of the smu lton results, selflernng bklsh nverse ontrol pproh s proposed to mtgte the bklsh effet th moderte modftons to onventonl PI ontrol. In the proposed pproh, self-lernng proedure s rred out t the begnnng of the ontrol mplementton perod to estmte the bklsh mgntude for spef vlve. Then bklsh nverse blok s dded to n exstng PI ontroller to ompenste for the hysteress effet resdng n the vlve. The vldty of the proposed method s verfed th both smulton nd expermentl tests nd sgnfnt mprovement s observed n the ontrol performne. 1. INTRODUCTION Vlves re ommonly used n ndustrl nd ommerl ppltons to regulte lqud flo rte for vrous purposes. In buldng HVAC systems, vlves re employed for regulton of hot- nd hlled-ter n oolng nd hetng ols to ontrol the het exhnge rte. For vlves th utomt ontrol pblty, motorzed tutors re typlly utlzed for drvng vlve to open or lose bsed on ontrol ommnd provded by feedbk ontroller. Bklsh type hysteress often exsts n n tutor gerbox here the stem poston dffers t gven nput ommnd hen the tuton hnges ts dreton, usng dffultes n obtnng stble ontrol. The hysteress mgntude depends on the mnufturng lerne tht n vry sgnfntly even for the sme bth of produts. Ths study s motvted by the unstsftory omfort ontrol tht hd been observed n the HVAC system servng multple offes tht re Lvng Lbortores for the Center for Hgh Performne Buldngs t Purdue Unversty. The unstsftory performne s mnly used by vlve hysteress resdng n the hlled- nd hot-ter vlves. Conventonl PID ontrollers ere not ble to provde stble ontrol due to the vlve hysteress nd the ontrol vrbles ere observed to osllte sgnfntly. As onsequene, spe tempertures flututed nd omfort requrements ould not be stsfed. A ompnon pper (C, Kurtulus nd Brun, 16) presented omprehensve set of expermentl test results omprng dfferent vlve hrtersts n vrble-r-volume (VAV) box rehet nd r hndlng unt (AHU) oolng ol vlves nd nvestgted ther mpts on ontrol performne. The results shoed severe ontrol temperture flututons for vlves hvng sgnfnt bklsh-type hysteress. In ddton, the ontrol flututons led to unneessrly hgh oolng/hetng poer so demnd osts ould be rsed for buldngs subjet to demnd hrges. Bklsh-type hysteress ommonly exsts n HVAC vlves due to the reltvely lo mnufturng tolernes employed nd emphss on lo ost solutons. All poston ontrolled vlves tht ere surveyed n C et l. (16) suffered from sgnfnt bklsh hysteress (more thn 5%). Thus, speflly devsed ontrol pproh for hndlng suh bklsh-type hysteress ould brng tremendous benefts for buldngs n energy ost reduton nd mproved omfort.

3 77, Pge 2 Bklsh nverse ontrol hs been studed extensvely n the ontrol ommunty s n effetve pproh to mtgte bklsh-type hysteress n ontrol system. The bklsh nverse ontroller s typlly mplemented n seres th typl feedbk ontroller, e.g., PI ontroller, to ompenste for bklsh-type non-lnerty. For systems th unknon bklsh szes, dptve nverse ontrol s often utlzed to estmte nd dpt the bklsh sze (To nd Kokotov, 1993, To nd Kokotov, 1996 nd Ahmd nd Khorrm, 1999). Hoever, most of the dptve ls n the prevous ork re only vld for lner systems nd very fe studes onsdered se studes th nonlner plnts. Hgglund (7) proposed n on-lne estmton lgorthm for bklsh mgntude bsed on losed-loop operton dt. The on-lne estmton step heved smlr gol to the self-lernng proess proposed n the urrent study. But the estmton mehnsm s dfferent: Hgglund (7) utlzed the dely tme nd mgntude n the system reton to nfer the bklsh sze tht requres nformton of the PI ontrol settngs nd estmton of the plnt stt proess gn. In ddton, the bklsh estmton qulty hghly depends on externl dsturbnes. The selflernng proess thn the present pper, hoever, s bsed on smple observtons n the ontrol behvor nd no nformton s needed n terms of plnt hrtersts or PI ontrol settngs. In ddton, t s more robust n hndlng externl dsturbnes. Some prevous reserh ork studed dynm modelng of hydron vlves th hysteress to enble ontroller desgn nd performne ssessment. For exmple, Kumr nd Mttl () developed dynm model of the lqud flo proess thn regulton vlve. A hysteress model s norported to pture the hysteress effet nd the overll model provded smulton test bed to nvestgte dfferent vlve ontrol pprohes. Tudorou nd Zheeruddn (5) onsdered smlr se study s the present pper here the vlve bklsh hysteress effet on ontrol performne of dshrge r temperture system s studed. The pper reled on dynm smulton model to nvestgte the bklsh effet nd flututons ere observed n the dshrge r te mperture hen vlve bklsh mgntude s nresed grdully. Hoever, the study mnly foused on the fult deteton problem thout ddressng the ontrol problem. Ths pper fouses on the development of dt-drven oolng ol nd vlve models tht re useful n understndng ontrol stblty ssues used by vlve hysteress nd n developng ontrollers to mtgte the bklsh hysteress effet ledng to mproved ontrol performne. Bsed on the observed ontrol htterng ptterns, self-lernng pproh s proposed to estmte the bklsh mgntude nd orrespondng bklsh nverse ontroller s mplemented to mprove the ontrol performne. The effetveness of ths pproh hs been demonstrted v both smulton nd expermentl tests lthough only smulton results ll be presented n ths pper due to spe lmttons. Note tht the proposed self-lernng bklsh nverse ontrol pproh s generlly pplble for hydron vlves lthough only HVAC pplton s demonstrted here. 2. VALVE AND COOLING COIL DATA-DRIVEN MODELS A vlve model th hysteress effets nd dynm oolng ol model ere developed bsed on feld mesurements from the Lvng Lbs t Purdue Unversty. Detls of the expermentl setup ere presented n the ompnon pper by C, Kurtulus nd Brun (16). These models re ombned n smulton tool for understndng, developng nd vldtng the bklsh nverse ontrol pproh. 2.1 Vlve Models Vlve hysteress model: the tuton of vlve openng n response to ontrol ommnd follos dynm behvor beuse of the nherent hysteress here the vlve openng does not only depend on the urrent ontrol ommnd but lso requres nformton of the prevous ontrol ton to determne the urrent tuton sttus n the bklsh regon (on the nresng or deresng urve or n beteen, s shon n Fgure 1 ()). A dsrete-tme bklsh dynm model n be formulted s

4 open flo 77, Pge 3 If md[ t] md[ t 1] x x[ t 1] x[] t Elsef BL [ ] [ ] BL md[ t] md[ t 1] x x[ t 1] ndmd[ t] md[ t 1] x[ t 1] x[ t] x[ t 1] md[ t] md[ t 1] open[ t] md[ t 1] x[ t 1] BL Else xt [ ] open[ t] md[ t] x open t md t x BL (1) here t s the tme step ndex, md s the model nput nd lso the vlve ontrol ommnd, x s stte of the dynm system tht represents the poston thn the bklsh urves (nresng or deresng urve or n beteen), open s the model output hh s the vlve openng n perentge. The model hs one ndependent prmeter x BL, hh s the bklsh mgntude hle the prmeter α s dependent prmeter representng the slope of the nresng/deresng urve tht n be determned by the vlue of x BL. x BL md open () (b) Fgure 1. (): bklsh hysteress urves. (b): vlve stt hrterst urve Vlve stt hrterst urve: there s stt hrterst urve for the vlve tself tht orreltes the delvered flo gong through the vlve to the vlve openng, s shon n Fgure 1 (b). For equl perentge ontrol vlves, the urve typlly exhbts n exponentl form n the loer rnge nd the urve beomes flt n the hgher rnge due to loss of uthorty (Chpter 47 of ASHRAE Hndbook-HVAC Systems nd Equpment, 12). The ext shpe of the urve s dependent on the vlve type, the shpe of vlve openng, nd pressure hrtersts of the hydron system. It s dffult to fnd generl model form nd thus, n emprl model utlzng the generlzed logst model (Rhrds, 1959) s used here to pture ths stt orrelton: m m mx b( open ) 1 e 1/ (2) here m s the delvered flo, m mx s the vlve nomnl flo t % openng nd open s the vlve openng perentge s desrbed n the prevous sub-seton. Prmeters, b nd together determne the shpe of the urve nd ther vlues ere estmted bsed on trnng dt. Prmeter b determnes the groth rte, orresponds to the openng here the mxmum groth rte ours nd hrterzes the symmetrl pttern Vlve model estmton: the prmeters x BL,, b nd n Equtons (1) nd (2) ere estmted smultneously from trnng dt set olleted from the Lvng Lbs oolng ol vlve. W thn the trnng dt, the ontrol ommnd (md) s rndomly perturbed thn the rnge of % to 5% (the mxmum oolng ommnd s thn 45% durng the yer of ) nd eh perturbton s held for 5 mnutes to llo the flo to reh stedy stte. The ntl ontrol ommnd s strted from % so tht the experment strted on the nresng urve. Fgure 2 shos the model vldton results here the stter plot on the left hnd sde shos the predted nd mesured hlled ter flo rtes nd the plot on the rght hnd sde shos the dt ponts long th the estmted urves. Very good greement s heved beteen the model predtons nd tul mesurements nd thus, the

5 Est. flo GPM Flo rte GPM 77, Pge 4 estmted vlve model ptures the vlve hrtersts nludng bklsh hysteress. The estmted bklsh mgntude (x BL ) s lose to 7% In. pts De. pts Dedbnd pts In. urve De. urve 5 Mes. flo GPM Control md % Fgure 2. Left: omprson of model predtons nd tul mesurements. Rght: dt ponts on top of the estmted model urves. 2.2 Dynm Coolng Col Model A dynm model s estblshed for the oolng ol here multple key prmeters ere estmted from operton dt olleted from the Lvng Lbs. The model s dpted from Zhou (5) hh utlzes fnte volume method th the hole oolng ol beng dsretzed nto mult ple ontrol volu mes. The mu lt-ro ross/ounterflo ol s ssumed to be pure ounter-flo rrngement nd n effetveness-ntu nd enthlpy potentl method s used to lulte het trnsfer rtes for eh of the ontrol volumes. Control Volume 1 1 m 1 T 1 T T T 1 T 1 T 2 T m Fgure 3. Control volumes n the oolng ol model Fgure 3 llustrtes the fnte volume method for the oolng ol under the ounter-flo ssumpton. For eh ontrol volume, ter nd ol mterl energy blnes re rtten n dsrete-tme formulton. If no mosture s ondensng on the ol surfes thn the ontrol volume, then the resultng equtons re: 1 T[ t 1] T[ t] 1 T [ t] T [ t] m p, [ ] [ ] t R C T t T t 1 1 T [ t 1] T [ t] T [ t] T [ t] T [ t] T [ t] C t R R (3) The vrble t nsde the brkets s the tme step ndex nd the supersrpt ndtes ssoton to the th ontrol volume. Equton (3) s formulted under n explt form to vod solvng systems of equtons for eh tme step. Hoever, the explt soluton sheme requres the tme step to be smll enough to obtn stble soluton th ny gven sptl dsretzton. The number of ontrol volumes determnes the model ury but s onstrned by the hosen tme step. The present study used 1 seond s the tme step nd dsretzed the ol nto 8 ontrol volumes, hh s the lrgest number of ontrol volumes to reh stble soluton (for gven tme step, there s mnmum sptl dsretzton step to heve stble numerl soluton, hh orresponds to the dsretzton th 8 ontrol volumes for ths spef se). Ths dsretzton grnulrty ell leverged model ury nd omputtonl requrements. Unform temperture s ssumed for the ol mterl n eh ontrol volume nd the

6 77, Pge 5 r nd ter tempertures n eh ontrol volume re ssumed to follo some stedy-stte profles nsted of beng unform nd the effetveness-ntu method s used for ter nd r sde het trnsfer rte lultons. T nd T n these equtons represent the ontrol volume ext tempertures, hh equl the nlet tempertures of the donstrem ontrol volumes. T s the bulk temperture of the ol mterl. C nd C re therml ptnes of the ter body nd ol mterl, respetvely, nsde eh ontrol volume nd they re estmted prmeters n the trnng proess. m nd m re ter nd r mss flo rtes. p, nd p, re spef hets for ter nd r, respetvely. The r-sde nd ter-sde het trnsfer resstnes, R nd R, re nverses of the effetveness ptne rte produts tht re hrterzed through emprl reltons trned usng dt. When the onerned ol seton s et (r depont temperture s hgher thn the ol temperture), the drvng potentl for het nd mss trnsfer s enthlpy dfferentl nsted of temperture dfferentl nd thus, the follong formulton s used for the ol energy blne: T t T t] h, [ t] h [ t] T t] T [ t] C. 1 1 [ 1] [ s [ * t R R here h s, s the r sturted enthlpy t the ol temperture nd mss trnsfer. T nd * R s n r-sde resstne for ombned het Dynms n the r strem re negleted due to the lo therml nert nd the outlet r ondtons for eh ontrol volume re lulted bsed on r sde het trnsfer for both dry- nd et-ol ses: T t T t T t T t. 1 1 [ 1] [ ] [ ] [ ] here s n overll r-sde effetveness for het trnsfer tht ounts for both fored-r onveton nd onduton though the fn mterl. For dry-ol ondtons, the outlet r humdty rto stys the sme s the nlet hle for et-ol ondtons, the outlet r humdty s lulted th psyhrometr routnes bsed on the outlet r dry-bulb temperture nd enthlpy tht s lulted s follos: h [ t 1] h [ t] h [ t] h [ t]. 1 * 1 s, * Here s n overll r-sde effetveness for both het nd mss trnsfer tht ounts for fored-r onveton, ondenston, nd onduton though the fn mterl. The r- nd ter-sde resstnes re lulted bsed on effetveness orreltons n terms of mss flo rtes usng the follong forms : here R, R, R * * m p, m p, m 4 1 exp 3m 2, 1 exp 1m * 6, 1 exp 5m (4) The key prmeters n the model ere estmted from feld mesurements nd the estmto n prmeters re C, C n Equton (3) nd β 1 to β 6 n Equton (4). A trnng dt set th severl rndom step hnges n the r nd ter flo rtes s olleted for the oolng ol servng the Lvng Lbs nd the trnng results re plotted n Fgure 4. Sne the present study mnly onerns the supply r temperture behvor, regresson s rred out to mnmze the root men squre error beteen the predted nd mesured supply r tempertures. All ntl temperture sttes ere ssumed to be ºC nd 3-mnute rm-up perod s onsdered so tht the regresson proess only mnmzed the root men squre of the errors from the 181 seond onrds. Note tht both the vlve nd ol estmton problems nvolved nonlner regressons nd the Levenberg-Mrqurdt method (Mdsen et l., 4) s used to fnd the optml prmeter vlues. As n be seen from Fgure 4, very good greement s heved

7 Flo rte kg/s Temperture Flo rte kg/s C Temperture C Temperture C Flo rte kg/s Temperture C Temperture C 77, Pge 6 beteen the mesured nd predted supply r tempertures (denoted by 'TA lvg' n the plot). Although the le vng ter temperture (denoted by 'TW lvg') behvor s not ounted for expltly n the regresson proess, the predted nd mesured levng ter tempertures lso sho good greement nd the smll dsrepny s beleved to be ttrbuted to sensor bses for the ter nd r flo rtes (energy mblne beteen the ter nd r sdes). The only sgnfnt dfferenes n ter temperture our for zero ter flo rte, hh ould hve no mpt on smulton results TA lvg Mes TA lvg Est TW lvg Mes TW lvg Est mwt mar Tme se. Fgure 4. Model trnng results th rtflly perturbed r nd ter flo rtes. To vldte the model performne, TA lvg Est vldton dt set s olleted under norml operton th resettng supply r temperture strtegy to redue VAV box rehet. Fgure 5 shos the vldton results nd good ury s heved n the supply r temperture predton even though the opertng ondtons dffered sgnfntly from those n the trnng dt set. 3 TW TA lvg lvg Mes TW TA lvg lvg Est Est TA lvg Mes mwt TW mar lvg Mes TW lvg Est x 4 x mwt Tme se. x 4 1 mar Fgure 5. Coolng ol vldton results th rel operton dt SIMULATION TESTS Tme se. x Smulton Test Setup An emultor model s onstruted by ombnng the vlve nd oolng ol models developed n the preedng seton. Fgure 6 shos the omponent lyout of the emultor models long th the feedbk ontrol loop. For typl oolng ol operton, feedbk ontroller, e.g., PI ontroller, s used to generte ontrol ommnds for the vlve tutor to djust vlve openng so tht the supply r temperture fo llos the setpont. The emultor

8 77, Pge 7 onssts of three omponent models developed n the preedng seton: n tutor bklsh model tht tkes the PI ontrol ommnd nd outputs the tul vlve openng; vlve stt urve model trnsltng the vlve open ng to ter flo rte; nd dynm oolng ol model tht provdes outlet r nd ter ondtons bsed on the hlled ter flo rte nd other boundry ondtons. The oolng ol outlet r temperture s used s the ontrol vrble. In the smulton tests, boundry ondtons, suh s rflo rte nd nlet ter nd r tempertures, ere extrted from tul mesurements n the Lvng Lbs. Fgure 6. Smulton nd ontrol dgrm. 3.2 PI Control Results Fgure 7 shos smulton results th onventonl PI ontroller th proportonl nd ntegrl gns fne tuned by feld engneers. The supply r temperture setpont s rtflly perturbed to test the setpont trkng performne. Note tht n tul system opertons, resettng supply r temperture setpont strteges re usully employed s n energy effent opton to redue rehet n termnl VAV boxes. Wth the onventonl PI ontroller, the ontrol vrble,.e., the supply r temperture, flututed sgnfntly due to the vlve hysteress. 3.3 Bklsh Inverse Control Results Fgure 8 shos the bklsh nverse ontrol dgrm. It smply dds bklsh nverse (BI) ontrol blok beteen the onventonl PI ontroller nd the ontrol plnt. The bklsh nverse blok s dynm system tht s n nverse of the bklsh model formulted n Equton (1) so tht the net effet s unty. The bklsh mgntude n the bklsh nverse blok should mth tht of the tul ontrol plnt to fully ompenste for the bklsh effet. Hoever, the tul bklsh mgntude s unknon so self -lernng proess s proposed to dpt the bklsh nverse blok for spef vlve, hh ll be desrbed t the end of ths seton. Fgure 9 nd Fgure sho the test results of bklsh nverse ontrollers th 6% nd 95% bklsh mgntude estmtes reltve to the true vlve (7%), respetvely. The bklsh nverse ontrol th 6% bklsh estmte hs led to redued flututon n the supply r temperture ompred to the bselne PI ontroller. Hoever, the ontrol ton s stll delyed due to the underestmted bklsh sze nd ontrol flututon stll exsted. The 95% bklsh nverse ontrol provded lmost perfet temperture trkng s the bklsh hysteress effet s ell ompensted for.

9 Control md % mwt kg/s Temperture C 77, Pge 8 TA lvg SP TA lvg x x Tme s x 4 Fgure 7. Conventonl PI ontrol results. Fgure 8. Bklsh nverse ontrol dgrm. Although bklsh nverse ontrol s effetve n mtgtng bklsh hysteress effets, n overestmted bklsh ould ompromse the ontrol performne th sgnfnt htterng n the ontrol ton. Wth n overestmted bklsh, the bklsh nverse ontroller over-ompenstes for the bklsh effet t eh sth tme ledng to exessve ontrol ton n the reverse dreton. Ths leds to hgh frequeny mode sthes nd ontrol htterng. Fgure 11 shos the vrtons of mode sth frequeny nd trkng error (RMSE beteen the setpont nd ontrol vrble) th respet to dfferent reltve bklsh estmtes (normlzed th the tul bklsh mgntude). The mode sth frequeny s lulted by vergng the numbers of mode sthes thn eh - mnute tme blok. It n be seen tht s the bklsh estmte pprohes the tul vlue from zero, trkng performne mproves onsstently th deresng trkng RMSE. Hoever, hen the bklsh estmte rses beyond the tul vlue, the trkng error nreses s onsequene of ontrol htterng. The mode sth frequenes shon on the left hnd sde of Fgure 11 re reltvely onstnt hen the bklsh estmte s belo the tul vlue. One the estmte psses the tul bklsh mgntude, the mode sth frequeny nreses drmtlly. Ths pttern forms the bss of the proposed self-lernng proess: nrese the bklsh estmte untl sgnfnt ontrol htterng ours. Fgure 12 shos the self-lernng proess for estmtng the bklsh sze th.7% (equl to % of the tul bklsh mgntude) step djustment. When the mode sth frequeny stys thn % of the frequeny orrespondng to the mnmum bklsh estmte (.7% for the onsdered se), the bklsh estmte s stepped up nd f mode sth frequeny goes beyond % of the frequeny th the mnmum bklsh estmte, the bklsh estmte s stepped don. In the demonstrted se shon n Fgure 12, bklsh estmte updtng s performed every 3 mnutes nd the lernng proess took less thn 3 hours to dentfy the orret bklsh sze. Note tht the ntl guess nd step djustment of the bklsh estmte ould tke ny rbtrrly s mll but nonzero vlue lthough the number of tertons to reh onvergene ll vry.

10 Num. of mode sthes / mns Trkng RMSE C Control md % mwt kg/s Temperture C Control md % mwt kg/s Temperture C 77, Pge 9 TA lvg SP TA lvg x x Tme s x 4 Fgure 9. Bklsh nverse ontrol th 6% of the estmte. TA lvg SP TA lvg x x Tme s x 4 Fgure. Bklsh nverse ontrol th 95% of the estmte Reltve bklsh estmte Reltve bklsh estmte Fgure 11. Control behvors th dfferent bklsh estmtes normlzed th the tul bklsh mgntude (7%).

11 BklshEst Control md % mwt kg/s Temperture C 77, Pge TA lvg SP TA lvg x x x Tme s x 4 Fgure 12. Self-lernng proess to estmte the bklsh sze. 6. CONCLUSIONS Ths pper proposed self-lernng bklsh nverse ontrol pproh to mtgte the bklsh hysteress effets ssoted th typl hydron vlves nd to mprove ontrol performne. A spef HVAC pplton s onsdered s se study tht ppled the proposed bklsh nverse ontrol pproh to oolng ol vlve. To ssess the ontrol performne mprovement, n emultor s onstruted ombnng dynm models of n tutor (bklsh effet) nd oolng ol lbrted th feld mesurements obtned from Lvng Lbs t Purdue. Smulton test results shoed tht for vlves th noteble bklsh hys teress, onventonl PI ontroller led to lo frequeny flututons n the supply r temperture (ontrol vrble). The proposed bkl sh nverse ontrol dded to onventonl PI ontroller demonstrted sgnfntly mproved ontrol performne n mtgtng the bklsh effets nd the best performne s heved hen the bklsh sze estmte s equl to or slghtly less thn the tul vlve bklsh. Intensve ontrol htterng ours hen the bklsh sze s overestmted so self-lernng proess s proposed tht nrements the bklsh estmte from zero untl sgnfnt htterng ours. Ths self-lernng proess s tested thn the emultor model nd the tul bklsh sze s dentfed thn three hours of operton. The proposed bklsh nverse ontrol pproh s lso tested n the tul oolng ol operton servng the Lvng Lbs. The expermentl testng results shoed lose mth th the smulton results under both bselne nd bklsh nverse ontrols. Hoever, the mesurement nose n the expermentl test ndued severe mode sthes. Ths ssue s prevously reported by Den et l. (1995) here bklsh nverse ontroller s ppled nd tested thn servomotor. To overome ths ssue, buffered bklsh nverse ontroller s proposed nd the testng results shoed sgnfntly mproved ontrol performne th moderte mode sthes. Due to spe lmttons, the buffered bklsh nverse ontroller nd the expermentl testng results ll be reported n future publtons. NOMENCLATURE md ontrol ommnd (%) x BL bklsh mgntude (-) α bklsh urve slope (-)

12 x bklsh stte (-) m mss/volumetr flo rte (kg/s or l/s) open vlve openng (%) t tme ndex (-) T temperture (K) p spef het t onstnt pressure (kj/kg-k) h enthlpy (kj/kg) R therml resstne (K/W) C therml ptne (kj/k) є effetveness (-) Tsup/Tlvg AHU supply r temperture (K) 77, Pge 11 Subsrpt sp mx r ter ol mterl setpont mxmum Supersrpt the -th ontrol volume * het nd mss trnsfer REFERENCES Ahmd, N. J., nd Khorrm, F., "Adptve ontrol of systems th bklsh hysteress t the nput." Amern Control Conferene, ASHRAE. ASHRAE Hndbook- HVAC Systems nd Equpment, 12. C, J., Kurtulus O. nd Brun, J.E., " Expermentl performne nvestgton of oolng or hetng ol vlves nd ther mpt on temperture ontrols", 16th Interntonl Refrgerton nd Ar Condtonng Conferene t Purdue, 16. Den, S.R., Surgenor, B.W. nd Iordnou, H.N., "Expermentl evluton of bklsh nverter s ppled to servomotor th ger trn." IEEE Conferene on Control Appltons, Hägglund, Tore. "Automt on-lne estmton of bklsh n ontrol loops." Journl of Proess Control, 7. Kumr, V. nd Mttl, A.P., "Dynm modelng of lqud-flo proess due to hysteress of pneumt ontrol vlve", Interntonl Journl of Intellgent Control nd Systems, Mdsen, K., Nelsen, H.B. nd Tngleff, O., Methods for Nonlner Lest Squres Problems, Informts nd Mthemtl Modelng, Tehnl Unversty of Denmrk, 4. To G. nd P. Kokotov. "Adptve ontrol of systems th bklsh". Automt, 1993 To G. nd P. Kokotov, Adptve Control of Systems th Atutor nd Sensor Nonlnertes, John Wley & sons, 1996 Tudorou, N., nd M. Zheeruddn, "Fult deteton nd dgnoss of vlve tutors n HVAC systems." IEEE Conferene on Control Appltons, 5. Zhou, X., Dynm modelng of hlled ter oolng ols, Ph.D. dssertton, Purdue Unversty, 5.