IJESR/Sept 2012/ Volume-2/Issue-9/Article No-1/ ISSN International Journal of Engineering & Science Research

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1 IJESR/Sept 202/ Volume-2/Issue-9/Artcle No-/ ISSN Internatonal Journal of Engneerng & Scence Research ADAPIVE SELF-UNING DECOUPLED CONROL OF EMPERAURE AND RELAIVE HUMIDIY FOR A HVAC SYSEM Ahmad Parvaresh*, Seyed Mohammad Al Mohammad 2 Department of electrcal engneerng of Shahd Bahonar Unversty of Kerman, Kerman. 2 Department of electrcal engneerng of Shahd Bahonar Unversty of Kerman, Kerman. ABSRAC hs paper presents an adaptve self-tunng decoupled controller for control of temperature and relatve humdty of a heatng, ventlatng, and ar condtonng (HVAC) system n order to acheve comfort condtons for occupants. It s mportant to be able to control temperature and relatve humdty ndependently. Because of nteracton of these varables n some ndustral processes, t s necessary to use decouplng technques to acheve accurate control. In ths regards, we have used recursve least square (RLS) algorthm for dentfcaton of the HVAC system to self-tunng of proportonal-ntegral-dervatve (PID) controller for temperature and relatve humdty. Smulaton results demonstrate that the adaptve selftunng decoupled controller s applcable for ths HVAC system. Keywords: Adaptve control, RLS algorthm, HVAC system, PID controller, self-tunng decoupled control.. INRODUCION Heatng, ventlatng, and ar-condtonng (HVAC) systems requre control of envronmental varables such as temperature, relatve humdty, pressure etc. the most of the controllers that have used n HVAC systems are of Proportonal-Integral-Dervatve (PID) type. HVAC systems used n lvng and ndustral buldngs should fulfll thermal comfort needs and ndoor ar qualty. he comfort of the people n ther lvng ndoor envronment s partally dependent on some factors, as qualty, humdty, pressure, and temperature of ar nsde the buldng. he purpose of the HVAC system of a buldng s to provde complete thermal comfort for ts occupants. Hence, t s necessary to understand the thermal and humdty aspects of the human body n order to desgn an effectve HVAC system. HVAC system s a non-lnear and tme varant system. It s dffcult to acheve desred trackng control performance. Over the past few years, several methods for determnng of parameters of appled controllers on these systems have been developed. As ndcated n [], more than 95% of the control loops are of PID type n process control. Over the years, there are many formulas derved to tune the PID controllers for stable processes, such as Zegler-Nchols, Cohen-Coon, nternal model control, ntegral absolute error optmum (ISE, IAE, and IAE), and recently proposed tunng methods[2,3]. Some researchers have been focused on decoupled control of temperature and relatve humdty of HVAC systems. For nstance, [4-6]. Some studes as [7,8] are about applcaton of PID controller n the HVAC systems. We know HVAC systems are non-lnear and tme *Correspondng Author 900

2 IJESR/Sept 202/ Volume-2/Issue-9/Artcle No-/ ISSN varant, so, drect controls of these systems are dffcult. Identfcaton approaches are very useful methods for acheve approxmate models. In ths regards, some of researchers use dfferent dentfcaton methods for apply on ths systems as [9]. RLS dentfcaton s one of these methods. In ths paper we developed and smulated an adaptve self-tunng algorthm for tunng PID parameters for a decoupled HVAC system n order to control of temperature and relatve humdty of a thermal zone, where thermal comfort of the system s evaluated. hs paper organzed as follow: In the frst part of ths paper the HVAC system and thermal space model s descrbed. he second part descrbed the non-nteractng control n a HVAC system. After descrbe of PID controller n a separate secton adaptve self-tunng algorthm are presented. In the last part smulaton result are presented. 2. HE HVAC SYSEM AND HERMAL SPACE MODEL We consder the sngle-zone HVAC system shown n Fgure. Components of ths system nclude thermal space, heatng/coolng col, humdfer/dehumdfer, mxng box, ar flter, supply and return fans, flters, dampers, and ductwork. In ths system, ntally, fresh ar enters and mxes wth 75% of the return ar, and remanng ar s exhausted. hen, mxed ar passes through the heat exchanger components and fnally by supply fan enter to thermal zone. Supply ar satsfes the thermal space. By changng of thermal load, the system controller smultaneously vares volumetrc flow rate of ar and water, so that the desred setponts n temperature and relatve humdty are mantaned. he dfferental equatons descrbng the dynamc behavor of the HVAC system n Fgure, can be conclude from energy-mass equatons as follow. dw3 W2 W3 M z = + () dt V ρ V z a z d2 ( ) f 0.25( ) f = + dt V V 3 2 a o 3 a he h (0.25W W W ) f ρ h f - C V ρc V w o 3 2 a w w he pa he pa he (2) 3 ( 2 ( 3 ) hfg W2 W3 ) fa ( Qz hfgm z ) a d f = + (3) dt V C V ρv C z pa z z pa Copyrght 202 Publshed by IJESR. All rghts reserved 90

3 IJESR/Sept 202/ Volume-2/Issue-9/Artcle No-/ ISSN Fgure. HVAC system model 3. NON-INERACIVE CONROL In order to control of mult-nput mult-output (MIMO) systems, we can use many dfferent methods. One of these methods s non-nteractve control method. In ths method the feedback s used transform the MIMO system, from the nput-output pont of vew, to an aggregate of ndependent sngle nput SISO channels. Assume a system n state-spacee form wth m nput u and n output y j that = =,2,,m and j=,2,,n. for ths system we can wrte x& = f ( x) + g ( x) u = y= h ( x) n m (4) he problem s to fnd a feedbackk control law as follow m u ψ ( x) δ v = + j j j= (5) Such that for the closed-loop system x& = f ( x ) + g ( x) ψ ( x) + ( g ( x) δ ( x) v ) y = h ( x) m m m j j = j= = (6) he resultng closed-loop systemm s a decoupled system n whch the th outputt s controlled only by th nput. he non-nteractng control law s gven by u A = ( x) b( x) + A ( x) v (7) Copyrght 202 Publshed by IJESR. All rghts reserved 902

4 IJESR/Sept 202/ Volume-2/Issue-9/Artcle No-/ ISSN Where A(x) s decouplng matrx, for defnton and calculaton see [4], v s the new nput for control of control varables ndependently, and b(x) s defned as m h ( f ( x )) = x f ( x) x m h 2 ( f ( x )) = x b( x) = f ( x) x M m h n ( f ( x )) = x f ( x) x For presented HVAC system we want to control temperature and relatve humdty of the zone. In ths regards, we need two control loops and two control sgnals. After calculaton of A(x) and b(x) we can obtan the non-nteractng control sgnals as followng expresson (8) u u = 2 ( αx4β4g( x) αx4β4g3 ( x)) α x g ( x).388α x β v B ( x) g3( x) g( x) v2 B2 ( x) (9) x = W, x =, x =, x = fa And Where g = (5000α W + 07α α x.388 α x +.388α W α x α x α ) g = (.5 0 β x β x + ( β β 2. 0 β ) x β 0.25β W + β W β ) 2 o 3 o g ( x) = ( α ( W 0.024)) α x + α x + ( α ) x 2 3 α = 60 / V α = 60 h / C V α = / ρ C V α = / ρ V z 2 fg pa z 3 a pa z 4 a z β = 60 / V β = 5 / V β =60 h / C V β = 6000 / ρ C V he 2 he 3 w pa he 4 a pa he B ( x) = ( α x α x )( f ( x) + g ( x) x ) (.388 α x ) g ( x) x + ( α x ) ( f ( x) + g ( x) x ) + ( x g ( x)) B ( x) = (2 0 α x )( f ( x) + g ( x) x ) + ( α x )( g ( x) x ) ( α2 α)( f3( x) g3( x) x4 ) x4 ( g3( x) x4) (0) () (2) (3) (4) (5) Copyrght 202 Publshed by IJESR. All rghts reserved 903

5 IJESR/Sept 202/ Volume-2/Issue-9/Artcle No-/ ISSN In Eq. 4 and Eq. 5 f ( x) and f ( x ) are 3 f ( x) = 5000α M.388 α ( Q h M ) 4 z 3 z fg z f ( x) = α ( Q h M ) 3 3 z fg z (6) 4. PID CONROLLER A PID controller s a knd of lnear controller, as t composes the control error accordng to the settng value and process output and then makes the controller output value based on the lnear resultant of error s proporton, ntegral and dervatve. For a PID controller, the control sgnal at tme t s determned from Where u( t) s the controller output, parameter, t ( ) ( ) ( ) de( t) (7) u t = K pe t + K e t dt+ K 0 d dt K p s the proporton parameter, K s the ntegral K d s dervatve parameter, e( t ) s the error sgnal at tme t defned as e( t) = ysp ( t) y( t), where y SP s the set pont for process output at tme t and y( t ) s process output at tme t. 5. ADAPIVE SELF-UNING CONROL ALGORIHM hs s a tradtonal adaptve flter algorthm that s useful for dentfcaton of control systems. It estmates the current parameter vector ˆ( θ k) based on the prevous estmated vector ˆ( θ k ), as follows [5,6]: ˆ θ ( k) = f ( ˆ θ ( k ), D( k), k) (8) Where, D(k) denotes data avalable at tme (k), and f(.,.,.) denotes an algebrac functon, the form of whch determnes the specfc algorthm. In the case of dynamc system, data D(k) normally consder the form of present and past observaton of the system outputs and nputs. For mult-parameter system, ths form can be represented as follows: Where, y( k) = ψ ( k) θ (9) ψ ( k) = [ y( k ),..., y( k m), u( k),..., u( k m)] (20) = [ a,..., a, b,..., b ] (2) θ m m+ he estmaton of the parameters vectorθ s performed n a way such that the estmated ˆr θ mnmzes the cost ndex J (r) where r denotes the number of sets of measurement, r ψ ˆ θ 2 (22) k= J ( r) = ( y( k) ( k) ( k)) Equaton (5) can be wrtten n a recursve form as: Copyrght 202 Publshed by IJESR. All rghts reserved 904

6 IJESR/Sept 202/ Volume-2/Issue-9/Artcle No-/ ISSN ˆ θ ( k) = ˆ θ ( k ) + P( k) ψ ( k)( y( k) ψ ( k) ˆ θ ( k )) P( k ) u( k) ψ ( k) P( k ) P( k ) = [ P( k ) ] + ψ ( k) P( k ) ψ ( k) (23) (24) We use from ths algorthm for dentfcaton of HVAC system ntroducedd n prevous secton. Fgure 2 shows the dagram sketch of RLS-PID control of decoupled HVAC system. Fg. 2. Dagram sketch of RLS-PID control of decoupled HVAC system 6. SIMULAION RESULS For nstance, we consder a system by nonlnear equaton as follow 2 y ( t ) y( t) = + u( t) 2 + y ( t ) (25) Where u( t) = 0.4sn(2 πt / 50) for t=0,,2,, 00 and u( t) = 0.3sn(2 πt / 50) + 0.sn(2 πt / 5) for t= 0, 02,, 200. Fgure (3) shows the proposed dentfcaton result of the system that ntroduced n Eq. 25. he normalzed error of the dentfcaton s 0.29 that s a performance measure defned as E ( t) = ( e e ) / ( y y ), where s a transpose of the vector. n After dentfcaton model s completed, the trackng operaton takes command of the RLS process control to track the desred set-ponts r ( t) = 25 u( t) + 50 u( t 200), that t= 0,,, 200 for emperature and r. ( t ) = 0 u( t) + 20 u( t 00), that t=0,,, 2000 for Relatve R H Humdty. he results of trackng performance are llustrated n fgure (4) and fgure (5) wth the mean square error (MSE) for the plant and for RLS self tunng algorthm response of Copyrght 202 Publshed by IJESR. All rghts reserved 905

7 IJESR/Sept 202/ Volume-2/Issue-9/Artcle No-/ ISSN Output Plant Identfcaton 0.6 Ampltude me(s) Fg. 3. RLS algorthm dentfcaton of a nonlnear system Set pont emperature RLS algorthm 250 emperature(c) me(s) Fg. 4. Output results of trackng operaton for emperature Copyrght 202 Publshed by IJESR. All rghts reserved 906

8 IJESR/Sept 202/ Volume-2/Issue-9/Artcle No-/ ISSN Set Pont Relatve Humdty RLS algorthm 00 Relatve Humdty me(s) Fg. 5. Output results of trackng operaton for Relatve Humdty 7. CONCLUSION AND RECOMMENDAIONS In ths paper, the performance of a HVAC system that uses a nonlnear decouplng algorthm for control of temperature and relatve humdty s studed. We show that decouplng control law works satsfactorly. We used RLS algorthm for dentfcaton of the system and results of the dentfcaton are used for tunng of PID controller parameters. Smulaton results were used to demonstrate of the proposed adaptve self-tunng decoupled control. REFERENCES [] Astrom KJ, Hagglund. PID Controllers: heory, Desgn, and unng, Instrument Socety of Amerca. Research rangle Park, NC, 995. [2] Wang YG, Shao HH. PID autotuner based on gan and phase margn specfcatons. Ind.Eng.Chem.Res. 999; 38: [3] Wang YG, Shao HH. Optmal tunng for PI controller. Automatca 2000; 36: [4] Rentel-Gomez C, Velez-Reyes M. Decoupled control of temperature and relatve humdty usng a varable ar volume HVAC system and non-nteractng control. In: Proceedng of the IEEE nternatonal conference on control applcatons, Mexco Cty, Mexco; 200.p [5] Rentel CH. Nonlnear decouplng of temperature and relatve humdty for an ar condtonng system. MS. hess, Unversty of Puerto Rco, Mayaguez Campus; December 996. [6] Cu J, Watanabe, Ryu Y, Akash Y, Nshyama N. Numercal smulaton on smultaneous control process of ndoor ar temperature and humdty. In: Sxth nternatonal IBPSA conference, proceedngs, 999; 2; Copyrght 202 Publshed by IJESR. All rghts reserved 907

9 IJESR/Sept 202/ Volume-2/Issue-9/Artcle No-/ ISSN [7] B Q, Wen-Jan C. Advanced controller auto-tunng and ts applcaton n HVAC systems. Control Engneerng Practce 2000; 8: [8] Guang Q, Zaheeruddn M. Real-tme tunng of PI controllers n HVAC systems. Int J Energy Res 2004; 28: [9] B Q, Ca WJ, Lee EL, Wang QG, Hang CC, Zhang Y. Robust dentfcaton of frstorder plus dead-tme model from step response. Control Engneerng Practce, 999; 7: Copyrght 202 Publshed by IJESR. All rghts reserved 908