Expert Systems with Applications

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1 Exprt Systms with Applications 36 (2009) Contnts lists availabl at ScincDirct Exprt Systms with Applications journal hompag: Dsign and simulation of slf-tuning PID-typ fuzzy adaptiv control for an xprt HVAC systm Srvt Soygudr a, *, Mhmt Karakos b, Hasan Alli a a Firat Univrsity, Dpartmnt of Mchanical Enginring, Elaziğ, Turky b Firat Univrsity, Dpartmnt of Computr Enginring, Elaziğ, Turky articl info abstract Kywords: Slf-tuning PID-typ fuzzy adaptiv controllr Fuzzy PD-typ controllr Exprt HVAC systm Intllignt control Exprt systm Th modlling, numrical simulation and intllignt control of an xprt HVAC (hating, vntilating and air-conditioning) systm having two diffrnt zons with variabl flow-rat wr prformd by considring th ambint tmpratur in this study. Th sub-modls of th systm wr obtaind by driving hat transfr quations of hat loss of two zons by conduction and convction, cooling unit and fan. All modls of th variabl flow-rat HVAC systm wr gnratd by using MATLAB/SIMULINK, and proportional-intgral-drivativ (PID) paramtrs wr obtaind by using Fuzzy sts. For comfortabl of popl th tmpraturs of th two diffrnt zons wr dcrasd to 5 C from th ambint tmpratur. Th succssful rsults wr obtaind by applying slf-tuning proportional-intgral-drivativ (PID)-typ fuzzy adaptiv controllr if comparing with th fuzzy PD-typ and th classical PID controllr. Th obtaind rsults wr prsntd in a graphical form. Ó 2008 Elsvir Ltd. All rights rsrvd.. Introduction Th nvironmntal conditions of human bings always bn affct by thir work prformancs. In addition, it is wll known that th importanc of th comfort of human bings gradually incrass by th dvlopmnt of tchnology (Arbo, 995; Zhng & Zahr-Uddin, 996). That is why, humans try to dsign a mor comfortabl living nvironmnt. As a rsult, th studis rlatd to th dsign and control of ambint conditions of buildings hav bn attracting intrst in th last yars. In a multipurpos building having shopping-cntr, offics and diffrnt usag aras, thir dsird tmpraturs and air conditions may b diffrnt. For this rason, flxibl dsign of HVAC systms supplying diffrnt dmands is substantially to dcras both th first invstmnt cost and th oprational cost. Furthr, th analysis of th prformanc and oprational stratgis of HVAC systms bcoms vry important for th ffctiv usag of nrgy (Ashra handbook, 992). Th studis on th paramtrs of HVAC systms as tmpratur, volum and control stratgis in th last 50 yars wr shown that th high prformanc of HVAC systms could b obtaind by minimizing nrgy consumption (Stanfort, 998). Tchnological dvlopmnts lad to obtain systm modls of HVAC systms by simulation programms in PC mdia (Ellis, 996; Gllr, 998). * Corrsponding author. Tl.: x5330; fax: addrsss: ssoygudr@firat.du.tr (S. Soygudr), mkarakos@firat.du.tr (M. Karakos), halli@firat.du.tr (H. Alli). In this study, it was shown that th usag of modlling and simulation mthods for analyzing, tsting and dvloping of HVAC systms dcrasd th dsign cost as wll as th dsign procss. Furthrmor, obtaining bttr prformancs of th simulatd systms bcam asir. Soygudr and Alli studid th classical PID control of HVAC systm having two zons with diffrnt proprtis (Soygudr & Alli, 2006). k p, k i and k d paramtrs of PID wr obtaind to minimiz th systm rror in thir study; howvr, th stady-stat rror was not totally liminatd. In addition to PID control of HVAC systms, fuzzy logic control (FLC) of HVAC systms was studid by many authors (Huang & Nlson, 994a, 994b). Th obtaind rsults wr compard with thos of PID control and ths studis indicatd that FLC had bttr rsults. FLC is xtnsivly usd in procsss whr systms dynamics is ithr vry complx or xhibit a highly nonlinar charactrs and FLC is on of th usful control schms for plants having difficultis in driving mathmatical modls or having prformanc limitations with convntional linar control mthods. FLC is dsignd on th basis of human xprinc, which mans that a mathmatical modl is not rquird for controlling a systm. Bcaus of this advantag, fuzzy logic-basd control schms wr implmntd for many industrial applications (Hung, Lin, & Chung, 2007). FLCs wr succssfully applid to many complx industrial procsss and domstic appliancs in th rcnt yars (Tsang, 200). Th first FLC algorithm implmntd by Mamdani was dsignd to synthsiz th linguistic control protocol of an xprincd oprator (Mamdani, 974). Although this typ of FLC application has bn succssful compard to th classical controllrs, th dsign /$ - s front mattr Ó 2008 Elsvir Ltd. All rights rsrvd. doi:0.06/j.swa

2 S. Soygudr t al. / Exprt Systms with Applications 36 (2009) procdur dpnds on th xprinc and knowldg of th oprator and it is limitd by th lucidation of th huristic ruls of control. To avoid this major disadvantag of dpnding on th control xprinc of th oprator, MacVicar-Whlan first proposd som gnral ruls for th structur of fuzzy controllrs (Macvicar-Whlan, 976). Ths fuzzy ruls dvisd by MacVicar-Whlan approach to a dtrministic (PI) or (PD) controllr in th limit as quantization lvls of control and masurmnt variabls bcom infinitly fin. It was shown that bttr rsults for th sam systm wr obtaind by using FLC with rspct to PID control (Tang & Mulholland, 987). Howvr, control rul sts for FLC ar quit difficult to rdsign. To liminat this ngativ condition, slf-tuning FLC can b dsignd and applid to HVAC systms. Th obtaind rsults showd that th slf-tuning advancd FLC rachd th optimal solution according to th dscribd prformanc critria (Huang & Nlson, 999). In addition to PID control and FLC of HVAC systms, th studis on combining PID and FLC for HVAC systms wr prformd (Haissig & Wossnr, 2000; Huang & Nlson, 99). Various typs of fuzzy PID (including PI and PD) controllrs hav bn proposd. In th litratur, th application of FL to PID controllr dsign can b gnrally classifid into two major catgoris according to dsign typ (Xu, Hung, & Liu, 2000): (i) Th gains of th classical PID controllr ar tund on-lin in trms of th knowldg bas and fuzzy infrnc, and thn th classical PID controllr gnrats th control signal (Zhao & Tomizuka, 993). (ii) FLC is dsignd as a st of huristic control ruls, and th control signal is dirctly dducd from th knowldg bas and th fuzzy infrnc as it is don in MacVicar-Whlan or diagonal rul-bas gnration approachs (Xu, Hung, & Liu, 998). Th scond typ controllrs ar rfrrd to as PID-typ FLC s bcaus, from th input output rlationship point of viw, thir structurs ar analogous to that of th classical PID controllr. Th quivalnc of PD-typ FLC s and classical PD controllrs has bn stablishd undr th spcial conditions (Qiao & Mizumoto, 996). Diffrnt control tuning mthodologis hav bn proposd in th litratur such as auto-tuning, slf-tuning, pattrn rcognition, artificial intllignc, and optimization mthods (Santos Colho, 2007). A nw approach has bn proposd for tuning th cofficints of PID-typ fuzzy logic controllrs (FLCs) (Güzlkaya, Eksin, & Ysßil, 2003). In addition, Wi proposd a slf-tuning mthod for a class of nonlinar PID control systms basd on Lyapunov approach (Changa, Hwangb, & Hsiha, 2002). Th slf-organizing fuzzy controllr has an xtnsion of th rul basd fuzzy controllr with an additional larning capability (Kazmian, 200). By rlating to th convntional PID control thory, Zhi-Wi proposd a nw fuzzy controllr structur, calld PID typ fuzzy controllr (Woo, Chung, & Lin, 2000). A fuzzy auto-tuning proportional-intgral-drivativ (PID) controllr for th robot has bn xprimntd, in which a simpl mthod to tun paramtrs of th PID typ fuzzy controllr on-lin has bn dvlopd(sun, Xing, Zhao, & Huang, in prss). Basd on ths studis, th modlling of an xprt HVAC systms with variabl flow-rat has bn stablishd by using MAT- LAB/SIMULINK, and k p, k i and k d paramtrs of PID hav bn dtrmind by using slf-tuning PID typ fuzzy adaptiv controllr. Th prformanc of th proposd control algorithm has bn compard with thos of th classical PID and fuzzy-pd typ controllrs. As a rsult of th simulations, it has bn shown that th prformanc of th proposd controllr is bttr among th othrs. Th instantanous tim-dpndnt solution of th systm has bn obtaind for ach zon and modl by considring th input and output valus of ach dvic and th dsird comfortabl conditions. Th tmpraturs of two diffrnt zons for ach tim-stp and th rquird dampr gap rats for supplying th dsird comfortabl conditions hav bn found in th rsult of th numrical simulations. Th obtaind rsults hav bn prsntd in a graphical form. Th outlin of this papr can b summarizd as follows: Sction 2 dscribs th lmnts and structur of an xprt HVAC systms. Th hat transfr quations usd for th numrical modl of th HVAC systm ar obtaind in Sction 3. Thn, Sction 4 includs th dsign of th classical PID, fuzzy PD-typ and slf-tuning PID-Fuzzy Adaptiv control of th considrd systm. MATLAB/ SIMULINK numrical simulations of th HVAC systm ar prsntd in Sction 5. Finally, conclusions ar givn in Sction Dsign of an xprt HVAC systm having two diffrnt zons Th cooling procss has bn prformd for two zons having diffrnt proprtis as shown in Fig.. Th volum of ach zon is 0.5 m 3. All surfacs of Zon- wr covrd by th isolation matrials (strafor); howvr, thos of Zon-2 wr not covrd. Th purpos of this typ of dsign is to s and dtrmin clarly th stady-stat diffrncs to obtain th rfrnc tmpraturs for two zons having diffrnt proprtis. Th coold air transfr has bn ralizd from th main channl having th supply fun to th rgions of Zon- and Zon-2. Th tmpratur controls of th two zons wr ralizd by th proposd controllrs by rgulating th dampr gap rats. Th air supply fan first absorbs 5 C air from th vaporator, thn snds to th zons as shown in Fig.. Th mass flow-rat ð _m ca Þ absorbd from th cooling unit dos not chang bcaus th supply fun has th constant numbr of rvolution. Howvr, th mass flow-rat of th air ntring to th zons changs dpnding on th tmpraturs of th zons. Th continuous variations of th input mass flow-rat ð _m za;in Þ Zon- and ð _m z2a;in Þ Zon-2 ar ralizd by rgulating th gap rats of damprs into th ntrancs of zon-channls, dpnding on th control output signals. Th continuity quation of th controlld systm can b formd as _m ca ¼ _m za;in þ _m z2a;in þ _m sva;out : Th mass flow-rat _m sva;out in Eq. () blongs to th safty valv discharging th xcssiv air coming from th zons. Th variabl-input mass flow-rats of th zons ar providd by th dampr motors. Th dampr gap rats ar changd btwn 0 and 90, dpnding on th zon tmpraturs. In th bginning of th control procss, th dampr gap rat for ach zon is 90 as a maximum valu. Th dampr gap rats dcrasingly bcom 0 dpnding on th control paramtrs whn th zon tmpraturs rach th dsird tmpraturs. Th dsignrs should tak account that th flow-spd of th air in th zons dos not xcd 0.5 m/s bcaus of th comfortabl conditions. This condition has bn ralizd by using th xhaust valv mountd to th xit of th zons. Th xhaust mass-flow-rat ð _m xha;out Þ has bn manually controlld in this study. 3. Th modl of th HVAC systm Th transint and stady-stat bhaviors, controllability, control prformancs, dsign of nrgy-ffctiv systms and analysis of HVAC systms can b prformd by obtaining systm modls and using simulation tools. Furthrmor, th ffcts of controllrs on th controlld systm can b xamind. In addition to this, systm modlling lads to minimiz th dsign procss of mchanical systms (Mathws, Arndt, & Gysr, 2002). Fig. shows th ðþ

3 4568 S. Soygudr t al. / Exprt Systms with Applications 36 (2009) Cooling Unit Laboratory pump Dampr-2/Air flow snsor Air-duct Cold-air Dampr- Air flow snsor Zon-2 Evaporator Fan Cold-air Cold-air Thrmocoupl Zon- Rsistanc Strafor Thrmocoupl 2 Exhaust Manual dampr Fig.. Th schmatic viw of th HVAC systm having two zons. schmatic diagram of th modlld systm in this study. Th main lmnts of th systm ar th cooling zon-aras, vaporator, cooling unit, fan, damprs motors, channls, and thrmocoupls. W dfin th symbol list indicatd in Tabl. Obtaining th mathmatical modl of th coold zon by considring all paramtrs is quit difficult. For this rason, w considr th following assumptions: () Th ffct of th instantanous variations of air spd in th zons on th prssur is nglctd. (2) Thr is no air lakag xcpt th xhaust valvs of th zons. (3) Th air flow in th zons is homognous. Tabl Symbol list A Ara (m 2 ) _m ca Th mass flow-rat in fan channl (kg/s) _m za;in Th mass flow-rat ntrd to Zon- (kg/s) _m z2a;in Th mass flow-rat ntrd to Zon-2 (kg/s) _m sva;out Th mass flow-rat xist from safty valv (kg/s) _m xha;out Th mass flow-rat xist from xhaust (kg/s) Q Convction and transmission hat (J) W Work (J) _m za;in ¼ _m za Th mass flow-rat ntrd to Zon- (kg/s) h in Spcific nthalpy(j/kg) h out Spcific nthalpy (J/kg) U Th intrnal nrgy (J) C v Constant hat (kj/kgk) C p Constant prssur (kj/kgk) T Innr _ tmpratur ( C) T n Instant _ tmpratur ( C) T n Vicious circl tmpratur ( C) T sh,gir Cool air tmpratur ( C) T out Outsid tmpratur ( C) h out Convction cofficint for outsid-surfac (J/m 2 K) h in Convction cofficint for innr-surfac (J/m 2 K) k Transmission cofficint (J/mK) L Thicknss for Zon- (m) Thicknss for Zon-2 (m) L 2 Thr is no chang in th flow-rats of th zons sinc th input flow-rat quals th output flow-rat. That is why w can writ th continuity quation as _m za;in ¼ _m xha;out ¼ _m z : According to thrmodynamic first law, th intrnal nrgy quation can b statd as follows: Q W þ X _m za;in h in X _m xha;out h out ¼ du dt ; whr u rprsnts tim-dpndnt variation of hat. Furthrmor, Eq. (3) can b r-writtn as th following form, assuming that thr is no work in th systm: Q þ _m za ðh in h out Þ¼ du dt ¼ m za C v ðt n T n Þ ; dt ð4þ h in h out ¼ C p ðt ca;in T n Þ: ð5þ If Eq. (4) is rarrangd, w gt Q þ _m za C p ðt ca;in T n Þ¼ m za C v ðt n T n Þ ; dt ð6þ Q þ _m za C p ðt ca;in T n Þ¼m za C v dt dt ; ð7þ whr T rprsnts th instantanous tmpratur variation. Th hat transfr from th outsid to th systm can b statd as Q ¼ T out T n R or T out T n Q ¼ þ L þ L 2 þ : ð9þ h outa k A k 2 A h in A If Eq. (9) is substitutd in Eq. (8), w gt: dt dt ¼ Q þ _m za C p ðt ca;in T n Þ : ð0þ m za C v ð2þ ð3þ ð8þ

4 S. Soygudr t al. / Exprt Systms with Applications 36 (2009) Slf-tuning PID-typ fuzzy adaptiv control Th slf-tuning PID-typ fuzzy controllr is an auto-adaptiv controllr that is dsignd by using an incrmntal fuzzy logic controllr to tun th paramtrs of PID controllr on-lin by fuzzy control ruls. Th controllr uss th rror and th rat of chang of rror as its inputs and can mt th dsir of slf-tuning paramtrs basd on tim-varying and _ uðkþ ¼k p ðkþþk i X k ðiþþk d ½ðkÞ ðk ÞŠ; ðþ NB NS Z PS PB u Fig. 4. Th mmbrship functions for th output u. whr k p is th controllr gain; k d = k p T/ T i ; k d = k p T D /T; T is th sampl tim; T i is th intgral tim paramtr; T D is th drivativ tim paramtr (Tao, Yin, & G, 200). Bcaus th proposd fuzzy slf-tuning PID controllr aims to improv th control prformanc yildd by a PID controllr, it kps th simpl structur of th PID controllr and it is not ncssary to modify any hardwar parts of th original control systm for implmntation. Fuzzy slf-tuning of PID paramtrs is to find out th fuzzy rlation btwn thr paramtrs of PID and, _. It Tabl 2 Th rul bas for fuzzy PD-typ control Fig. 5. Th mmbrship functions for th inputs and _ Fig. 6. Th mmbrship functions for th outputs k p k d k i. NB NS Z PS PB incssantly xamins and _ in work, thn tuns thr paramtrs by fuzzy control ruls on-lin so that controlld objcts achiv bttr dynamic stady prformanc. Th slf-tuning adaptiv control mthod has bn applid to HVAC systms as th othr systms. Thr ar many studis on dtrmining th paramtrs of controllrs and finding nw valus of controllr paramtrs according to changing situations. Th optimum control mthod has bn usd to find th rquird-control paramtr valus that th hatr provids th dsignd tmpraturs and humiditis in HVAC systms (Kasahara t al., 200) Tabl 3 Th rul bas for k p Fig. 2. Th mmbrship functions for th input. NB NS Z PS PB ė Fig. 3. Th mmbrship functions for th input _.

5 4570 S. Soygudr t al. / Exprt Systms with Applications 36 (2009) Tabl 4 Th rul bas for k d Tabl 5 Th rul bas for k i of mmbrship) btwn 0 and. In this cas, th triangular mmbrship functions ar usd for all variabls and { 2,.5,, 0.5, 0, 0.5,,.5, 2} physical domain is slctd for all variabls basd on trial and rror mthod. Th fuzzy variabls ar dfind for th rul bas as:, (_), u = {th rror, th variation of rror, th control variabl {NB (Ngativ Big), NS (Ngativ Small), Z (Zro), PS (Positiv Small), PB (Positiv Big)}, [ 2, 2], l}. Th fuzzy rul bas is constructd by using svral if-thn statmnts and prmis and consqunt of ach statmnt which ar fuzzy propositions. Tabl 2 indicats that 25 ruls dfin th rul bas for th fuzzy-pd typ controllr. For th aim of th comparison of th control prformanc, th control of th sam HVAC systm has bn ralizd by applying th slf-tuning PID-typ fuzzy adaptiv controllr. W combin th classical PID and FLC thoris in this study. Th k p, k i, k d valus of PID paramtrs hav adaptivly bn dtrmind by using th dynamic FLC for ach tim-stp. In this cas, FLC has two inputs (, _) and thr outputs (k p, k i, k d ). Th gauss mmbrship function is usd for all variabls shown in Figs. 5 and 6. Th physical domain of th inputs (, _) is{, 0.8, 0.6, 0.4, 0.2, 0, 0.2, 0.4, 0.6, 0.8, } and that of th outputs (k p, k i, k d ) is {0, 0., 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, }, slctd again basd on trial and rror. Th fuzzy variabls ar dfind for th rul bas as:, (_) = {th rror, th variation of rror, {NB (Ngativ Big), NS (Ngativ Small), Z (Zro), PS (Positiv Small), PB (Positiv Big)}, [, ], l}. k p, k d, k i = {th control paramtrs, {Z (Zro), PS (Positiv Small), PM (Positiv Mdium), PB (Positiv Big), PVB (Positiv Vry Big), [0, ], l}. Tabls 3 5 indicat th rul bass for k p, k d and k i, rspctivly. 5. Th numrical simulation of th HVAC systm First of all, th rror and th variation of rror dpnding on th masurd T and T2 tmpraturs, which blong to two zons having diffrnt proprtis, ar takn as th inputs of fuzzy-pd typ controllrs. Mamdani s fuzzy infrnc mthod is usd in th systm with two inputs and on output. Th output (th control variabl), which is th mass flow-rat of th coold air ntring th zons, is dtrmind dpnding on th dfind rul bas of and (_), with th aim of minimizing th rror. Onc w dfin th rul bas indicatd in Tabl 2, w now nd to dtrmin th mmbrship functions for, (_) and u shown in Figs. 2 4, rspctivly. A mmbrship function is a curv that dfins how ach point in th input spac is mappd to a mmbrship valu (on dgr Th modl, control and numrical simulation of th HVAC systm having two zons with diffrnt proprtis hav bn ralizd by using MATLAB/SIMULINK packag programm. Th instantanous tim-dpndnt solution of th systm has bn obtaind for ach zon and modl by considring th input and output valus of ach dvic and th dsird comfortabl conditions. Th tmpraturs of two considrd zons for ach tim-stp and th rquird dampr gap rats for supplying th dsird comfortabl conditions hav bn found in th rsult of th numrical simulations. Th obtaind rsults hav bn prsntd in a graphical form. Figs. 7 and 8 show th block diagrams of th considrd xprt HVAC systm controlld by th fuzzy-pd typ and th slf-tuning PID-typ fuzzy adaptiv controllr, rspctivly. In ths figurs, T rf and T2 rf ar th dsird rfrnc tmpraturs of Zon- and Zon-2, rspctivly. FLC provids th control signals (u, u2) to minimiz rror dpnding on and (_). Th obtaind control sig- Trf d/dt Fuzzy PD Controllr U Dampr Zon T T2rf d/dt Fuzzy PD Controllr U2 Dampr 2 Zon 2 T2 Fig. 7. Th block diagram of th considrd HVAC systm controlld by th fuzzy-pd typ controllr.

6 S. Soygudr t al. / Exprt Systms with Applications 36 (2009) Trf - d/dt Fuzzy Algorithm Fuzzy Slf-Tuning PID Controllr Kp Kd Ki PID Controllr U Dampr Zon T U2 PID Controllr Dampr 2 Kp Kd Ki Zon 2 T2 T2rf - d/dt Fuzzy Algorithm Fuzzy Slf-Tuning PID Controllr Fig. 8. Th block diagram of th slf-tuning PID-typ fuzzy adaptiv controllr. Start Trf and T2rf Calculat and d =Trf-T d=d/dt 2=T2rf-T2 d2=d2/dt Fuzzy rul bas Fuzzification and d Infrnc Mchanism Dfuzzification with cntr of gravity Evaluat,d and calculat Kp,Kd,Ki with Fuzzy Algorithm Fig. 0. Th tmpratur variation of Zon- whn th classical PID, fuzzy-pd typ and th slf-tuning PID-typ fuzzy adaptiv controllr ar applid. Calculat U PID=(Kp+Kd.s+Ki/s) Damprs and Zons Fig. 9. Th flow-chart of th slf-tuning PID-typ fuzzy adaptiv controllr. nals chang th dampr gap rats and th air mass flow-rats ntrd that th zons to rach th dsird rfrnc tmpraturs. Fig. 9 shows th flow-chart of th considrd xprt HVAC systm controlld by th slf-tuning PID-typ fuzzy adaptiv controllr. For numrical simulation, th ambinc tmpratur has bn takn as 3.3 C. Th dsird rfrnc tmpratur has bn slctd as 26.5 C for Zon-. Fig. 0 shows th tmpratur control of Zon- whn th classical PID, fuzzy-pd typ and th slf-tuning PID-typ fuzzy adaptiv controllr ar applid. Th prformanc of th slf-tuning PID-typ fuzzy adaptiv controllr is th bst among th othrs in trms of both th stady-stat rror and th sttling tim. Thr is no stady-stat rror and th systm rachs th dsird rfrnc tmpratur with th minimizing sttling tim. Although th fuzzy-pd typ controllr has no stady-stat rror, it has longr sttling tim. Th worst prformanc blongs to th classical PID controllr. Fig. shows th variation of th dampr gap rats for Zon- for th considrd thr controllrs. Th on and off positions of dampr ar also shown in this figur. Th channl ara is 0.02 m 2. Th 90 position of th dampr is th full opn position and th systm has th maximum mass flow-rat. Th 0 position of th dampr is th closd position of th dampr and th coold air cannot pass through th Zon-. Th dsird rfrnc tmpratur for Zon-2 is 27.5 C. Fig. 2 shows th tmpratur variations of Zon-2 whn th considrd

7 4572 S. Soygudr t al. / Exprt Systms with Applications 36 (2009) Fig.. Th dampr gap rat variation for Zon- whn th classical PID, fuzzy-pd typ and th slf-tuning PID-typ fuzzy adaptiv controllr ar applid. Fig. 4. Th variations of k p k i k d for Zon- whn th slf-tuning PID-typ fuzzy adaptiv controllr is applid. Fig. 2. Th tmpratur variation of Zon-2 whn th classical PID, fuzzy-pd typ and th slf-tuning PID-typ fuzzy adaptiv controllr ar applid. Fig. 5. Th variations of k p k i k d for Zon2 whn th slf-tuning PID-typ fuzzy adaptiv controllr is applid. thr controllrs ar applid. Th systm has bn coold from 3.3 C to th dsird tmpratur 27.5 C. Again, th slf-tuning PID-typ fuzzy adaptiv controllr prforms th bst without th stady-stat rror and having th minimum sttling tim if w compar with th othrs. Fig. 3 indicats th dampr gap rat variations for Zon-2. Th tim historis of th dampr positions ar clarly sn in this figur. Fig. 4 shows k p k i k d variation of Zon- whn th slf-tuning PID-typ fuzzy adaptiv controllr is applid. Furthr, Fig. 5 shows k p k i k d variation of Zon-2 whn th slf-tuning PID-typ fuzzy adaptiv controllr is applid. As a rsult, th slf-tuning PID-typ fuzzy adaptiv controllr is mor applicabl for HVAC systms among th othrs. 6. Conclusions Fig. 3. Th dampr gap rat variation for Zon-2 whn th classical PID, fuzzy-pd typ and th slf-tuning PID-typ fuzzy adaptiv controllr ar applid. Th numrical simulation of th cooling procss from th ambint tmpratur to th dsird rfrnc tmpraturs of th HVAC systm having two zons with diffrnt proprtis has bn ralizd. Th instantanous tim-dpndnt solution of th considrd HVAC systm has bn found for ach zon and modl by considring th input and output valus of ach dvic and th dsird

8 S. Soygudr t al. / Exprt Systms with Applications 36 (2009) comfortabl conditions. Th tmpraturs of two zons and th rquird dampr gap rats for providing th dsird conditions for ach tim-stp hav bn obtaind by using th numrical simulations. Th numrical simulation of th systm applying th classical PID [7], fuzzy-pd typ and th slf-tuning PID-typ fuzzy adaptiv controllr has bn ralizd by using MATLAB/SIMULINK packag programm. Th obtaind figurs indicat that th prformanc of th slf-tuning PID-typ fuzzy adaptiv controllr is th bst among th othrs, in trms of both th stady-stat rror and th sttling tim. Th proposd controllr lads to th considrd xprt HVAC systm having th minimum sttlings tim and without th stady-stat rrors. Th obtaind rsults mak th proposd controllr mor ffctiv among th othrs. Rfrncs Arbo, M. B. (995). Enrgy managmnt stratgis for facility managrs. SA Rfrigration and Air Conditioning,, Ashra handbook (992). HVAC systms and quipmnt. ASHRAE Publications. Changa, W. D., Hwangb, R. C., & Hsiha, J. G. (2002). A slf-tuning PID control for a class of nonlinar systms basd on th Lyapunov approach. Journal of Procss Control, 2, Ellis, M. W. (996). Practical valuation and intgratd simulation of building HVAC systm prformanc. Mastr thsis, Mchanical Enginring, Univrsity of Prtoria. Gllr, H. S. (998). Commrcial building quipmnt fficincy: A stat-of-th-art rvi. Washington, DC: Amrican Council for an Enrgy-Efficint Economy. Güzlkaya, M., Eksin, _ I., & Ysßil, E. (2003). Slf-tuning of PID-typ fuzzy logic controllr cofficints via rlativ rat obsrvr. Enginring Applications of Artificial Intllignc, 6, Haissig, C. M., & Wossnr, M. (2000). An adaptiv fuzzy algorithm for domstic hot watr. Tmpratur control of a combi-boilr. ASHRAE Transaction, 06(2). Huang, S., & Nlson, R. M. (99). A PID-law-combining fuzzy controllr for HVAC applications. ASHRAE Transaction, 97(2), Huang, S., & Nlson, R. M. (994a). Rul dvlopmnt and adjustmnt stratgis of a fuzzy logic controllr for an HVAC systm: Part on-analysis. ASHRAE Transaction, 00(), Huang, S., & Nlson, R. M. (994b). Rul dvlopmnt and adjustmnt stratgis of a fuzzy logic controllr for an HVAC systm: Part two-xprimnt. ASHRAE Transaction, 00(), Huang, S., & Nlson, R. M. (999). Dvlopmnt of a slf-tuning fuzzy logic controllr. ASHRAE Transaction, 05(), Hung, L. C., Lin, H. P., & Chung, H. Y. (2007). Dsign of slf-tuning fuzzy sliding mod control for TORA systm. Exprt Systms with Applications, 32, Kasahara, M., Yamazaki, T., Kuzu, Y., Hashımoto, Y., Kamimura, K., Matsuba, T., t al. (200). Stability analysis and tuning of PID controllr in VAV systms. ASHRAE Transaction, 07(). Kazmian, H. B. (200). Comprativ study of a larning fuzzy PID controllr and a slf-tuning controllr. ISA Transactions, 40, Macvicar-Whlan, P. J. (976). Fuzzysts for man machin intraction. Intrnational Journal of Man Machin Studis, 8, Mamdani, EH. (974). Aplication of fuzzylogic algorithms for control of simpl dynamic plant. Procdings of th Institut of Elctrical Enginring, 2, Mathws, E. H., Arndt, D. C., & Gysr, M. F. (2002). Rducing th nrgy consumption of a confrnc cntr A cas study using softwar. Building and Environmnt, 37, Qiao, W. Z., & Mizumoto, M. (996). PID typ fuzzy paramtrs adaptiv mthod. Fuzzysts and Systms, 78, Santos Colho, L. D. (2007). Tuning of PID controllr for an automatic rgulator voltag systm using chaotic optimization approach. Chaos, Solitons and Fractals, doi:0.06/j.chaos Soygudr, S., & Alli, H. (2006). Simulation and modlling of HVAC systm having two zons with diffrnt proprtis. In TOK2006 confrnc (Vol., pp ). Stanfort, H. W. (998). Analysis and dsign of HVAC Systms. Prntic Hall. Sun, Z., Xing, R., Zhao, C., & Huang, W. (in prss). Fuzzy auto-tuning PID control of multipl joint robot drivn by ultrasonic motors. Ultrasonics. Tang, K. L., & Mulholland, R. J. (987). Comparing fuzzylogic with classical controllr dsigns. IEEE Transactions on Systms Man and Cybrntics, 7(6), Tao, Y. H., Yin, Y. X., & G, L. S. (200). Nw-styl PID control and applization (Vol. 5). Bijing: Engin Industry Publishing Company. Tsang, K. M. (200). Auto-tuning of fuzzy logic controllrs for slf-rgulating procsss. Fuzzy Sts and Systms, 20, Woo, Z. W., Chung, H. Y., & Lin, J. J. (2000). A PID typ fuzzy controllr with slftuning scaling factors. Fuzzy Sts and Systms, 5, Xu, J. X., Hung, C. C., & Liu, C. (998). Tuning and analysis of a fuzzy PI controllr basd on gain and phas margins. IEEE Transaction on Systms Man and Cybrntics, 28(5), Xu, J. X., Hung, C. C., & Liu, C. (2000). Paralll structur and tuning of a fuzzy PID controllr. Automatica, 36, Zhao, Z. Y., & Tomizuka, M. (993). Fuzzygain schduling of PID Controllrs. IEEE Transaction on Systms Man and Cybrntics, 23(5), Zhng, G. R., & Zahr-Uddin, M. (996). Optimization of thrmal procsss in a variabl air volum HVAC systm. Enrgy, 2(5),