The Absorbent's Solution Flow Process, Non-Parametric Identification into an Absorption Chiller for Air Conditioning

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1 Rcnt Rsarchs in Nral Ntwors, Fzz Sstms, Evoltionar ompting Atomation Th Absorbnt's Soltion Flow Procss, Non-Paramtric Idntification into an Absorption hillr for Air onditioning ADRIAN DANILA Dpartmnt of Atomatics Univrsit "Transilvania" of Brasov Brasov, str. M. Vitaz nr. 5 ROMANIA adrian.danila@nitbv.ro Abstract: - Th lithim bromid chillrs spplid from solar collctors ar sd to provid propr nvironmntal conditions into indstrial civil bildings. To maintain th appropriat vals for th tmpratr into th chillr's boilr, a control nit is introdcd to avoid crstallization of th absorbnt. Th liqid flow procss of th absorbnt within th pips of th chillr is a non-linar procss. Th papr focss on th xprimntal idntification tchniqs sd to dtrmin from masrmnts th nonlinar dnamic modl of th flow procss. K-ords: - flow procss, sstm idntification, absorption chillr Introdction Th absorption chillrs for air conditioning ar widl sd to provid propr nvironmntal tmpratr in indstrial civil bildings. Th chillrs ar sall drivn with wast hat from gas stam trbins. Most of th absorption chillrs s watr as rfrigrant lithim bromid as absorbnt. It is wll nown that th hot watr tmpratr in th boilr is ssntial for th cooling fficinc of th chillr to prvnt th crstallization of th absorbnt. Th rcommndd vals of th tmpratr into th boilr is from 07 to 3 0, th rcommndd val is Th prssr Figr. Th schmatic of th absorption sstm. into th boilr mst b from 3 to 87 Pa. Rcntl, th solar thrmal collctors hav bn introdcd to provid th hot watr for th chillr. Th solar nrg prodcd b solar panls with vacatd panls or b flat plat collctors is chapr has no long-trm impact on th nvironmnt. owvr, th tmpratr of watr has to b carfll controlld to maintain th fficinc to prvnt crstallization of th absorbnt. Exprimntal installations provd that solar drivn air conditioning with th cooling capacit p to 40 is rliabl in th hot rgions small siz installations p to 0 is sitabl for th tmprat rgions, [4], [5]. To avoid crstallization of th absorbnt into th boilr, casd b abnormal hat mdim inlt tmpratrs or b powr failr, th absorbnt soltion is allowd to drain ot ndr gravit, Figr. A govrnor is sd to control th flow rat of th soltion. Th dnamic modl of th flow procss is ndd to optimiz th opration of th sstm. Sstm idntification tchniqs ar to b sd to dtrmin from inpt otpt dat th actal vals of th modl. Th absorbnt soltion flow procss is basicall nonlinar. Undr crtain assmptions, th procss ma b linarizd. In this papr, a nonparamtric, rcrsiv algorithm is proposd to dtrmin th non-linar discrt-tim fnction of th solvnt flow from th boilr. In th scond chaptr of th wor, th basis of th idntification algorithm is dvlopd. Frthrmor, In haptr Thr, th non-linar modl of th flow procss is prsntd. Th practical implmntation of th idntification algorithm th rslts ar prsntd in haptr For

2 Rcnt Rsarchs in Nral Ntwors, Fzz Sstms, Evoltionar ompting Atomation Th Stochastic Approximation Algorithm In sstm idntification approach, th paramtrs of th dnamic modl rlatd to a givn sstm ar dtrmind from xprimntal masrmnts of both inpts otpts. Nowadas, thr ar svral powrfl tchniqs to idntif th paramtrs of linar stochastic sstms. If th strctr of th nnown sstm is availabl a priori, thn paramtric tchniqs ar sd. owvr, in gnral, littl a priori information abot th strctr of th sstm is availabl. Thrfor, th nonparamtric mthods ar to b sd in this cas, []. On approach to nonlinar non-paramtric sstm idntification is to assm that th nnown sstm blongs to a crtain class paramtrizd b a crtain fixd basis fnctions sch as Forir sris, polnomials orthonormal fnctions. Anothr approach is th nonparamtric idntification inclding th rnl stimators, splin smoothing, dirct wight optimization, local polnomial approach othrs. For th nonlinar stochastic sstms th idntification approach is vr stimlating. A basic rprsntation of a singl-inpt singl-otpt, (SISO) linar, stochastic, dnamic modl is th atorgrssiv with xognos inpts modl of ARX givn in notation (). a b na nb whr a na nb a b0 b () ar th sstm inpt otpt, rspctivl, is th sstm nois na, nb ar th sstm ordr. A straightforward gnralization of th linar ARX modl is th NARX modl givn in notation (). f n 0,, n,,, 0 whr 0 nnown fnction to b idntifid. () n is th nown sstm ordr f, ith X T, X f T o T is th, th NARX modl ma b rprsntd in th stat-spac form as follows. X (3) X Lt N b a sqnc of indpndnt idnticall distribtd rom variabls with zro man, E 0 varianc E with a probabilit fnction which is positiv continos on R. Th vals of th fnction f, at an fixd point, R can b stimatd basd on th inpt-otpt masrmnts ndr th following assmptions, [].. Th nois N is a sqnc of indpndnt idnticall distribtd rom variabls with zro man, E varianc E with a 0 probabilit fnction which is positiv niforml continos on R.. Both sqncs N indpndnt. 3. Th fnction f, N is continos on ar mtall R thr xist a wightd norm on R, two constants 0 c 0 sch that x x c, x R (4) ith th assmption that th NARX rprsntation of th sstm is asmptoticall stationar, th algorithm is as follows. For th givn inpt-otpt variabls, th rnl fnction, as w, sing th xprimntal data w, xp b b b with b for a fixd 0, 4., (5) ith arbitrar initial vals 0 0,, 0 calclats as follows:,,, w,, 0 thn ar rcrsivl (6)

3 Rcnt Rsarchs in Nral Ntwors, Fzz Sstms, Evoltionar ompting Atomation w,,,, Th stimat of th fnction xprssion (7) f, is givn b th,, (8), Th convrgnc of th algoritm strong consistnc of th stimat ar provn in []. 3 Th nonlinar dnamic modl of th liqid flow Th schmatic diagram of th sstm is prsntd in Figr. At stad-stat th inflow rat Q I th otflow Q O rat ar qal. Th liqid flow rat is rlatd to th had as follows, [3]. Figr. Th schmatic of th flow procss. T QI K T () Q K (9) Assm that at t 0 th inflow rat is changd from Q i Q to Qi Q Qi this cas th had to chang from to. Th otflow rat will chang fromqo Q QO. For this sstm, th following diffrntial qation is obtaind. d QI QO QI K (0) dt whr is th capacitanc of th tan. Th qation (0) ma b writtn as follows. d QI K () dt Assm that th sampling priod ist th xprssion () ma b writtn as a diffrnc qation as follows. Th inpt to th sstm is th inflow rat, Q I th otpt is th had. From th notation (), a NARX of ordr zro is obtaind b th addition of th nois sqnc as follows. T QI K T (3) Th nonlinar fnction to b stimatd from masrmnts is th following. f, Q T Q I I K T (4)

4 Rcnt Rsarchs in Nral Ntwors, Fzz Sstms, Evoltionar ompting Atomation Figr 3. Th inpt-otpt signals. 4 Th Implmntation of th Stochastic Algorithm Th inpt signal is a whit nois with normal distribtion. Th masrmnts' nois is a normal distribtd whit nois. Th sampls of th inpt signal otpt rspons of th sstm ar prsntd in Figr 3. Th magnitd of th masrmnts whit nois is 0% of th magnitd of th inpt signal. Th paramtrs of th nonlinar sstm wr as follows: th capacitanc of th tan m th flow rsistanc K 0.06, th sampling priod T s th paramtr / Th thortical vals of th nonlinar fnction f, Q I ar prsntd in Figr 4. For th implmntation of th stochastic algorithm a Figr 5. Th stimat of th nonlinar f, Q I. MatLab application was dsignd. Th comptation rslts ar prsntd in Figrs 5 6. Th analsis of th rslts provs that th rcrsiv stochastic algorithm provids a consistnt stimat of th nonlinar fnction f, Q I. Th choic of th paramtr in notation (5) has bn provd vr important for th total amont of th stimation rrors. Th nmbr of data points sd to compt th stimat is also important for th total amont of th stimation rrors. Th largr th nmbr of data points th smallr th stimation rrors. As w aspct, th magnitd of th masrmnts nois in comparison with th inpt signal is also prohibitiv to th stimat total rrors amont. An important improvmnt of th algorithm is prsntd in []. In this approach a trncation bond is introdcd whn th stimat is gnratd. In comparison with th local linar stimator, th NARX stimator provids an stimat valid on th ntir scop of th inpt-otpt variabls. fnction Figr 4. Th thortical vals of th nonlinar fnction f, Q I. 4 onclsions In this papr an implmntation of th rcrsiv stochastic algorithm to th nonlinar flow procss of th absorbnt soltion into th lithim bromid chillrs was prsntd. In this approach th nonlinar fnction that charactrizs th non-paramtric dnamic modl of th procss is dtrmind dirctl from data masrmnts. Th implmntation rslts prov that th stimat is consistnt asmptotical stabl

5 Rcnt Rsarchs in Nral Ntwors, Fzz Sstms, Evoltionar ompting Atomation Figr 6. Th stimat's rrors btwn th nonlinar fnction f Q, I its thortical vals. Th aim of this implmntation is to dsign th appropriat control nit for th chillr. A comparison btwn th local linar stimator th rcrsiv stochastic algorithm prsntd abov cold b an intrsting frthr rsarch to this sbjct. Rfrncs: [] n-xiao Zhao, an-f hn i Xing Zhng, Rcrsiv Idntification for Nonlinar ARX Sstms Basd on Stochastic Approximation Algorithm, IEEE Transactions on Atomatic ontrol, Vol.55, No.6, Jn 00, pp [] Er-i Bai, Non-Paramtric Nonlinar Idntification: An Asmptotic Minimm Man Sqard Error Estimator, IEEE Transactions on Atomatic ontrol, Vol.55, No.7, Jl 00, pp [3] Katshio Ogata, Modrn ontrol Enginring Third Edition, Prntic all, Uppr Saddl Rivr, Nw Jrs, Pblishing os, 997 [4] Argino A. A., Balaras. A., Intgration of Small Siz Solar Assistd Air-onditioning in Bildings, Procdings of th Intrnational onfrnc on th Intgration of th Rnwabl Enrg into th Bildings Strctrs, Patra, Grc, pp5. [5] ang K.S. Air-onditioning Rfrigration- Mchanical Enginring boo, R Prss,