Air-Conditioning PID Control System with Adjustable Reset to Offset Thermal Loads Upsets

Transcription

1 11 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets Tknori Ymzki 1, Yuji Ymkw 2, Kzuyuki Kmimur 3 nd Shigeru Kurosu 4 1 Oym Ntionl College of Technology, 2 Univ. of Tokyo, 3 Ntionl Institute for Environmentl Studies, 4 Reserch Inst. Crotech, Jpn 1. Introduction The heting, ventilting, nd ir-conditioning (HVAC) systems hve huge different chrcteristics in control engineering from chemicl nd steel processes. One of the chrcteristics is tht the equilibrium point (or the operting point) usully vries with disturbnces such s outdoor temperture (or wether conditions) nd therml lods. The vritions of the operting point intend to vry prmeters of plnt model. Thus, the HVAC control systems re extremely difficult to obtin n exct mthemticl model (Kshr 2000). Proportionl-plus-integrl (PI) controllers hve been by fr the most common control strtegy s the complexity of the control problem incresed (Åström 1995). Tody, vrible ir volume (VAV) system hs been universlly ccepted s mens of chieving energy efficient nd comfortble building environment. While the VAV control strtegies provide high qulity environment for building occupnts, the VAV system nlysis rrely receives the ttention it deserves. As result, bsic control strtegies for the VAV system hve remined unchnged up to now (Hrtmn 2003). In ddition, pplying the model predictive control method to the HVAC systems, the control performnce hs been highly improved by pursuing the devition from the operting point (Tir 2004). According to this report, recognizing the devition from the operting point nd clculting the optiml control inputs bout the newly obtined operting point on next smpling time, the control system gives better responses thn the trditionl feedbck control system. Motivted by these considertions in these reports, we consider the room temperture nd humidity controls using the djustble resets which compenste for therml lods upsets. One of the primry objectives of the HVAC systems is to mintin the room ir temperture nd humidity t the setpoint vlues to high qulity environment for building occupnts. The room temperture nd humidity control systems my be represented in the sme blockdigrm form s single-vrible, single-loop feedbck control systems becuse this interction is wek reltive to the desired control performnce.

2 210 Advnces in PID Control In some pplictions, disturbnces cn be estimted in dvnce before they entered the plnt. Prticulrly, in the HVAC systems, it is possible tht the outdoor thermometer detects sudden wether chnges nd the occupnt roughly nticiptes therml lods upsets. Using this informtion, disturbnces cn be offset by the compenstion of the reset, which is the exctly sme function s n integrl (I) control ction. In the previous pper, the compenstion method of the reset for PID controllers ws proposed nd the control system for room ir temperture ws often effective in reducing therml lods upsets (Ymkw 2010). In this pper, of specil interest to us is how to tune PID prmeters more effective for the room temperture nd humidity control. And the control performnces for compenstion of the djustble reset re compred with the trditionl method of the fixed reset. Nmely, obtining the pproximte operting point using outdoor temperture nd therml lods profiles nd djusting the reset, the stbiliztion of the control system will be improved. The vlidtion simultions will be demonstrted in terms of three performnce indices such s the integrl vlues of the squred errors, totl control input, nd PID control input. 2. Plnt nd control system In this pper, we consider only the cooling mode of opertion in summer nd therefore refer to this system s room ir cooling system. The definition of vribles in Equtions is described in NOMENCLATURE. 2.1 Dynmics of ir-conditioning system To explore the ppliction of PID controllers to the room temperture nd humidity control system, we consider single-zone cooling system, s shown in Figure 1. It is due to the fct tht cooling nd heting modes re found to perform nerly the sme under most circumstnces. The controlled room (the controlled plnt) mesures 10 m by 10 m by 2.7 m nd is furnished with n ir-hndling unit (AHU) consisting of the cooling coil nd the humidifier to control room ir temperture nd humidity. In generl, since the responses of the AHU re fster thn those of the controlled room, the dynmics of the AHU my be neglected for ll prcticl purposes. Thus, s will be seen lter, this rough ssumption my be firly vlidted. The model, however, possesses the importnt elements (the controlled room nd the AHU) to nlyze the ir-conditioning system. With this system, the room ir temperture ( ) nd reltive humidity (φ) re mesured with thermometer nd hygrometer (sensors). The output signls from the sensors re mplified nd then fed bck to the PID controllers. Using the errors defined s the differences between the setpoint vlue ( r nd φ r ) nd the mesured vlues of the controlled vribles ( nd φ), the PID controllers generte the control inputs for the ctutors (the supply ir dmper nd the humidifier) so tht the errors re reduced. The AHU responds to the control inputs (f s nd x s (is djusted by humidifier h)) by providing the pproprite therml power nd humidity to the supply irflow. Air enters the AHU t wrm temperture, which decreses s ir psses the cooling coil, nd then the humidifier supplies stem to cooled ir if necessry. This occurs in momentry period becuse there re lot of times when the humidifier is not running. In this AHU, dehumidifier is not instlled, so n excessive demnd for humidity is difficult to chieve.

3 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets 211 Fig. 1. Overll structure of single-zone cooling system Room temperture model Simplifying this therml system to be single-zone spce enclosed by n envelope exposed to certin outdoor conditions is of significnt interest to tret the fundmentl issues in control system design (Zhng 1992, Mtsub 1998, Ymkw 2009). This simplified therml system (the room temperture model) cn be obtined by pplying the principle of energy blnce, d C wss 0 ql (1) dt where C = overll het cpcity of ir-conditioned spce [kj/k], = overll trnsmittnce-re fctor [kj/min K], q L = therml lod from internl het genertion [kj/min], w s = c p f s [kj/min K], which is het of supply ir flowrte, = density of ir [kg/m 3 ], c p = specific het of ir [kj/kg K], f s = supply ir flowrte [m 3 /min]. The physicl interprettion of Eqution 1 is tht the rte of chnge of energy in the room is equl to the difference between the energy supplied to nd removed from the room. The first term on the right-hnd side is the het loss which is controlled by the supply ir flowrte. The second term is the het gin through the room envelope, including the wrm ir infiltrtion due to the indoor-outdoor temperture differentil. The third term is the

4 212 Advnces in PID Control therml lods from the internl het genertion nd the infiltrtion. In this simplified model, ny other uncontrolled inputs (e.g., mbient wether conditions, solr rdition nd interzonl irflow, etc) re not considered. It should be noted tht ll vribles such s s q L nd w s in Eqution 1 re obviously the function of time t. For the ske of simplicity the time t is not presented. When relizing digitl controller, dedtime exists between the smpling opertion nd the outputting time of control input, thus w s, nmely f s, includes dedtime L P. These plnt prmeters hve been obtined by experimentl results (Ntionl Institute for Environment Studies in Tsukub, Ymkw 2009). The room dynmics cn be pproximted by first-order lg plus dedtime system from the experimentl dt (Åström 1995, Ozw 2003). Thus, the plnt dynmics including the AHU nd the sensor cn be represented by, KP L 0.64 Ps Ps () e e Ts1 18s1 P 2.4s. (2) Compring to Eqution 1, the plnt gin (K P ) nd the time constnt (T P ) cn be given by, K P s T w s, P C, w s = c p f s. (3) w Therefore, K P nd T P chnge with the control input (the supply ir flowrte f s ). Similrly, it is ssumed tht L P chnges with the control input. Nmely, L P s s LP0, (4) w where L P0 is determined so tht L P is equl to 2.4 [min] when f s is equl to 50 [%]. From L P = 2.4 [min], w s = c p f s = [kj/min K] nd = 9.69 [kj/min K], L P0 cn be obtined to be equl to 49.4 [kj/k]. It is esily be found tht these prmeters re strongly ffected by the operting points. Crrying out n open-loop experiment in the HVAC field to mesure K P, T P nd L P is one wy to get the informtion needed to tune control loop. To get some insight into the reltions between Eqution 1 nd Eqution 2, we will describe biliner system in detil (Ymkw 2009). Introducing smll vritions bout the operting points nd normlizing the vribles, Eqution 1 hs been trnsformed to biliner system with time delyed feedbck. A prmetric nlysis of the stbility region hs been presented. The importnt conclusion is tht the stbility nlysis demonstrted the vlidity of PID controllers nd there ws no significnt dvntge in nlyzing biliner system for VAV systems. It ws fortunte tht the liner system like first-order lg plus dedtime system derived in Eqution 2 often stisfctorily pproximted to the biliner system derived in Eqution 1. The liner system is n imginry system, but it does represent it closely enough for some prticulr purpose involved in our nlysis. Certinly the liner model derived in Eqution 2 cn be used to tune the PID controller nd the physicl model derived in Eqution 1 cn be used for numericl simultions. Over the rnge upon which this control nlysis is focused, the reltions between Eqution 1 nd Eqution 2 re determined to be sufficiently close.

5 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets Room humidity model The room humidity model cn be derived by pplying the principle of mss blnce, dx n V fsxs x p (5) dt where V = room volume ( [m 3 ]) x = bsolute humidity of the room [kg/kg (DA)] x s = bsolute humidity of the supply ir [kg/kg (DA)] p = evportion rte of occupnt ( [kg/min]) n = number of occupnts in the room [-]. Eqution 5 sttes tht the rte of chnge of moisture in the room is equl to the difference between the moisture removed from nd dded to the room. The first term expresses dehumidifying effect by the supply ir flowrte. The second term is the moisture due to the occupnts in the room. The bsolute humidity x cn be converted to the reltive humidity φ s described in the next section. In the sme wy s the room temperture model, the humidity model cn be pproximted by first-order lg plus dedtime system s shown in Eqution 2. Thus, the plnt dynmics concerned with the room humidity model cn be represented by, KPh 1.0 P() s e e T s1 13.5s1 Ph LPhs 2.4s The gin constnt K Ph nd the time constnt T Ph re given by, K Ph. (6) fs V 1, TPh. (7) f f s Thus, K Ph nd T Ph chnge with the supply ir flowrte s sme s those represented in the room temperture model. Similrly, the dedtime L Ph is ssumed to be chnged with the supply ir flowrte. Thus, L Ph s s LPh0, (8) f where L Ph0 is the constnt. The dedtime L Ph of the humidity model is ssumed in the sme wy s one of the temperture model. Thus, the dedtime L Ph0 cn be clculted by L Ph f s = = Fig. 2. Block digrm for AHU.

6 214 Advnces in PID Control The room humidity cn be determined by regulting the moisture of the supply ir to the room. This implies tht the room humidity cn be indirectly controlled. Similrly the firstorder lg plus dedtime model by Eqution 6 cn be used to tune the PID controller nd the physicl model by Eqution 5 cn be used in numericl simultions. It does not men tht Eqution 5 nd 6 re mthemticlly equivlent Air-hndling unit (AHU) model Figure 2 shows the simple block digrm for the AHU tht conditions supply ir for the room. Air brought bck to the AHU from the room is clled return ir. The portion of the return ir dischrged to the outdoor ir is exhust ir, nd lrge prt of the return ir reused is recirculted ir. Air brought in intentionlly from the outdoor ir is outdoor ir. The outdoor ir nd the recirculted ir re mixed to form mixed ir, which is then conditioned nd delivered to the room s supply ir. The AHU consists of cooling coil, humidifier, nd fn to control supply ir temperture ( s ) nd humidity (x s ). The mixed ir enters the cooling coil t given temperture, which decreses s the ir psses through the cooling coil. The temperture of the ir leving the cooling coil is c. Since the responses of the cooling coil nd the humidifier re significntly fster thn those of the room ( principl controlled plnt), it cn be generlly ssumed tht the cooling coil nd the humidifier re sttic systems. Nmely, it is common for the cooling coil to be controlled to mintin the supply ir temperture t setpoint vlue ( sr ). Thus, the temperture ( c ) nd the bsolute humidity (x c ) of the cooling coil cn be given by; c sr xsi ( pw pws ) xc 0.622pws ( pw pws) P pws where θ sr is the setpoint of the supply ir temperture, p w is the prtil pressure of wter vpor, p ws is the prtil pressure of sturted vpor t temperture, P (=101.3 [kp]) is the totl pressure of mixed ir, nd x si is the bsolute humidity of the ir entering the cooling coil. The humidity is divided into two clcultions depending on the difference between p ws nd p w. This constrint mens tht the reltive humidity does not exceed 100 %. The humidifier is the most importnt ctutor to control the room reltive humidity (φ) for heting mode in winter. Nevertheless, we re interested here in exmining control chrcteristics in the opertion mode of cooling. Note tht the control input h(t) does not hve strong effect on the room reltive humidity (φ) in cooling mode. From the energy nd mss blnces, the dynmics of the humidifier cn be described by, (9) where d C w q q dt dxs h Vd fs( xc xs) dt s d s c s d 0 s B d C d = overll het cpcity of humidifier spce [kj/k], (10)

7 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets 215 V d = room volume of humidifier [m 3 ], d = overll trnsmittnce-re fctor [kj/min K], q B = fn lod (59.43 [kj/min]), q d = lod by humidifier (( θ h )h) [kj/min]), nd h = rte of moist ir produced in the humidifier. Considering the stedy-stte of the dynmics of the humidifier, the supply ir temperture θ s nd the supply ir bsolute humidity x s cn be obtined by, c f q q s c f x s p s c d 0 B d h xc f s p s d (11) As cn be seen in Eqution 11, the supply ir temperture ( s ) cn be influenced by the humidifier (h), so tht the errors in the reset (f s0 ) cn be produced. Thus, the control performnce my be deteriorted. The ir flowrte from the outdoor ir is considered 25% of the totl supply ir flowrte. This rtio will be held constnt in this study. Note tht the pressure losses nd het gins occurring in the duct hve negligible effects on the physicl properties of ir for simplifiction. The bsolute humidity of mixed ir entering the cooling coil cn be described by, f x 0.25 f x 0.75 f x. (12) s si s 0 s where x 0 nd x re the bsolute humidity of outdoor ir nd of indoor ir, respectively. All the ctul vlues of the plnt prmeters used in the numericl simultions re listed in Tble 1. Since we ssume tht the supply ir temperture for the cooling coil cn be controlled so s to mintin the setpoint vlue ( sr ) of the supply ir temperture, the energy-blnce of mixed ir is not needed to consider. C [kj/k] V 270 [m 3 ] c p 1.3 [kj/kg K] [kg/m 3 ] 9.69 [kj/min K] d [kj/min K] q L f smx f smin h mx h min sr [kj/min] [m 3 /min] 0.00 [m 3 /min] 0.33 [m 3 /min] 0.00 [m 3 /min] 13.1 [ C] Tble 1. Summry of significnt prmeters in the development of the room nd the AHU

8 216 Advnces in PID Control Clcultion of reltive humidity In this section, the conversion from the bsolute humidity to the reltive humidity is briefly explined. The reltive humidity is derived from the ir temperture nd the bsolute humidity of the ir (ASHRAE 1989; Wexler nd Hylnd 1983). First, the ir temperture must be converted to the bsolute temperture s, , (13) where θ is the ir temperture, nd is the bsolute temperture of the ir. Second, to evlute the supply ir temperture θ c reches its dew-point temperture, the two prtil pressures p w nd p ws cn be conveniently defined. The prtil pressure of wter vpor p w cn be obtined by, p w Pxi, (14) x where x i is the bsolute humidity of wter vpor nd P is the totl pressure of mixed ir (101.3 [kp]). And, the prtil pressure p ws of sturted vpor t temperture cn be given by, i Fig. 3. Overll of the temperture-humidity control system.

9 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets ws ln(10 p ) / Finlly, the reltive humidity φ for the room cn be given by, ln (15) pw 100. (16) p ws 2.2 Control system Figure 3 shows block digrm of the room temperture nd humidity control systems using djustble resets which compenste for therml lods upsets. In this figure, signls pper s lines nd functionl reltions s blocks. The primry controlled plnt is the room. The cooling coil, the humidifier nd the dmper re defined s the secondry controlled plnts (to produce pproprite ctuting signls). The following control loops re existed in our room temperture nd humidity control system: Room ir temperture control system Room ir humidity control system The control outputs of interests re room ir temperture (θ ) nd reltive humidity (φ). In order to mintin room ir temperture nd humidity in desirble rnges, trditionl PID controllers hve been used to reduce component costs. The control inputs tht vry ccording to the control ctions re the supply ir flowrte (f s ) nd the rte of moist ir produced in the humidifier (h), which will be discussed in more detil Room temperture control system Tking the PID control lgorithm into ccount, one of control inputs, relted to the room ir temperture (θ ) cn be given by, t de() t fs() t kpe() t ki e( ) d k 0 d fs0() t (17) dt where f s0 (t) is the mnul reset. In electronic controllers, the mnul reset is often referred to s trcking input. The error e(t) cn be defined by, e(t) = (tl P ) r, (18) where r is the setpoint vlue of the room ir temperture, nd L P (= 2.4 [min]) is the dedtime. The PID prmeters (the proportionl gin k p, the integrl gin k i, nd the derivtive gin k d ) cn be determined by the well-known tuning method. The inherent disdvntge of the I ction, which esily cuses instbilities, cn be reduced by vrying the reset f s0 (t) to compenste for therml lods upsets (disturbnces). In some cses of HVAC systems, the reset f s0 (t) cn be estimted by knowledge of the plnt dynmics. Eqution 17 cn be given in discrete-time system when control input nd error signl re respectively ssumed to be f s (k) nd e(k) t time kt (T is the smpling period). k ej ( 1) ej ( ) k f ( k) kek ( ) kt ek ( ) ek ( 1) f ( t) d (19) 0 s p i s j0 2 T

10 218 Advnces in PID Control This is clled the position lgorithm becuse f s (k) typiclly represents the position of n ctutor (Tkhshi 1969). From Eqution 1, the operting point t its stedy-stte cn be written: w q Q (w s = c p f s ). (20) s s 0 L 0 The reset (f s0 ) of the supply ir flowrte cn be obtined by, f s0 ql() t qth() t ( 0() t r()) t () t. (21) c ( ( t) ( t)) p r s In Eqution 21, the supply ir temperture ( s ), the outdoor temperture ( 0 ), nd the setpoint ( r ) cn esily be mesured. However, therml lods cnnot be specified in dvnce. Thus, it is recommended tht occupnts must roughly estimte therml lods to improve the control performnce t dequte smpling intervl. For exmple, three of the rough estimtes for compenstion cn be used s: the mximum (75%), the medium (50%), nd the minimum (25%), where 100 % mens the mximum supply ir flowrte [m 3 /min].at ny given point of opertion, the reset (f s0 ) to offset therml lods cn be esily clculted using Eqution 21. Thus, it cn be concluded tht the controller with lower I ction is superior to tht with no I ction, nd is lso clled PD controller Room humidity control system To control the room ir reltive humidity, nother one of control inputs tht vry ccording to the control ctions is the rte of moist ir produced in the humidifier h(t). The control input cn be given by, de () t ht () k e() t k e( ) d k h() t dt where h 0 (t) is the reset. The error e h (t) cn be defined by, t h ph h ih 0 h dh 0, (22) e h (t) = r (t L Ph ) (23) where r is the setpoint vlue of the room ir reltive humidity nd L Ph (= 2.4 [min]) is the dedtime. The hygrometer in the room cn detect the room ir reltive humidity ( ), but not the bsolute humidity (x). Therefore, the reltive humidity is used in the error e h (t) for the clcultion of the control input h(t). However, the humidity model cn be described by the reltionl expression of the bsolute humidity. And, the derivtion of the humidity model prmeters from the experimentl results in terms of the reltive humidity my be extremely difficult. As result, PID prmeters (proportionl gin k ph, integrl gin k ih, nd derivtive gin k dh ) must be determined by tril nd error under the considertion tht the bsolute humidity cnnot be directly mesurble. In this study, for the ske of simplicity, it is ssumed tht the bsic reltion of the humidity model is invrint even if the vrible in the humidity model is chnged the bsolute humidity into the reltive humidity. For this reson, the trditionl tuning method (Ziegler nd Nichols 1942) for the first-order lg plus

11 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets 219 dedtime system s shown in Eqution 6 (the plnt prmeters is described by Equtions 7 nd 8) cn be used. Since the supply ir temperture ( s ) cn be ffected by the rte of moist ir produced in the humidifier (h), the reset of the supply ir flowrte (f s0 ) rising from moist ir vritions must be ccounted. This mens tht good control performnce for heting mode cn be expected. The reset h 0 (t) for the humidifier cn be obtined from Equtions 5, 9, 11, nd 12 s follows: First, tking the humidity model (Eqution 5) t the stedy-stte nd the setpoint vlue x r of the bsolute humidity into ccount, the following eqution cn be obtined by, n fs( xs xr) p 0. (24) Second, substituting Eqution 24 into Eqution 9, 11 nd 12, Eqution 24 cn be rewritten by, f x h x n p 0 s c r 0 fs h 0 n fs0.25x0 0.75xr xr p0 fs h0 n 0.25x0 fs 0.25xrfs p 0 h0 n 0.25xrfs 0.25x0 fs p 0 s0 r 0 h () t 0.25 f ( x x ) np (25) However, s will be seen in Eqution 25, the first term is smll in comprison to the second term nd h 0 (t) my be negtive. The djustble reset h 0 (t) cn be found to be nerly zero under most circumstnces in the present work. Tble 2 provides PID prmeters tuned by the trditionl ultimte sensitivity method (Ziegler nd Nichols 1942) nd the empiricl modified PID method. The ultimte sensitivity method is simple nd intuitive. It hs been still widely used, either in its originl form or in some modifiction. Since it only gives bll-prk vlues, it is necessry to mke mnul tuning to obtin the desired performnce. Our empiricl modified PID controller cn help improve the time response of control system becuse therml lods nd operting conditions re chnging continuously in HVAC systems. In modified PID prmeters for room ir temperture control, the proportionl gin (k p ) is bout 80 % of tht of the conventionl tuning method. The integrl gin (k i ) is one-fourth of tht of the conventionl tuning method. The derivtive gin (k d ) is nerly the sme s tht of the conventionl tuning method. In modified PID prmeters for room ir reltive humidity control, ll gins (k ph, k ih, nd k dh ) re nerly one-tenth of those of the conventionl tuning method.

12 220 Advnces in PID Control 3. Simultion results in dily opertion To illustrte the control performnce of the room temperture nd humidity control systems, severl simultion runs re mde. Representtive outdoor temperture nd therml lods profiles for one-dy (between 08:00 in the morning nd 08:00 in the next morning) re ssumed s shown in Figure 4. These profiles re bsed on the experimentl dt obtined from the Ntionl Institute for Environmentl Studies in Tsukub, Jpn. In the right hnd side of Figure 4, the dshed line depicts the rtificil estimted vlue of the therml lod. At the strt-up (t 08:00 in the morning), the feedbck control system tkes over nd controls the room ir temperture nd reltive humidity. These simultion runs re crried out under the sme conditions mentioned bove. Figure 5 depicts the djustble reset (f s0 ) of the supply ir flowrte for dily opertion clculted using Eqution 21. The computtionl intervl of 1 hour (60 min) for djusting the reset is used in this control. These simultion runs re mde on MATLAB which is n effective tool for field engineers in control engineering. The following control configurtions re used in our room temperture nd humidity control. These bbrevitions re common throughout the reminder of this pper. k p k i (T i ) k d (T d ) Conventionl PID (4.57) (1.16) Modified PID (10.9) 10 (1.15) () Temperture control k ph k ih (T ih ) k dh (T dh ) (4.65) 1.41 (1.16) (b) Humidity control (T i, T ih : integrl times, T d, T dh : derivtive times for temperture nd humidity controls, respectively) Tble 2. PID prmeters. Fig. 4. Outdoor temperture nd therml lods profiles.

13 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets 221 Fig. 5. Reset of supply ir flowrte. Number of control outputs of interest Room temperture nd humidity control This refers to the room ir temperture nd reltive humidity control. Setpoints of control outputs Regrding the room ir temperture r : 1. Fixed setpoint The setpoint r is fixed t 24 C for dily opertion. 2. Vrible setpoint The setpoint r re vried within the rnge, tht r is set t the vlue ( 0 4) C where 0 is the outdoor temperture, nd r is limited to the minimum 20 C nd the mximum 28 C. Regrding the room ir reltive humidity φ r : The setpoint φ r is usully fixed t 55 % for dily opertion. Control strtegies for the reset 1. Conventionl PID control This refers to conventionl PID control with the fixed reset (f s0 = 50 %). 2. Modified PID control This refers to modified PID control with the djustble reset (Figure 5). Performnce indices The control performnce should be evluted by defining three performnce indices. 1. ISE (the integrl of squred error) 24 2 ISE = edt 0 2. ICI (the integrl of control input) ICI = 24 0 fsdt 3. IPID (the integrl of control input produced in PID controller only) IPID = 24 ( f 0 s fs0 ) dt

14 222 Advnces in PID Control Fig. 6. Simultion results of conventionl PID. Room temperture nd humidity control Typicl dily simultion results show tht the conventionl PID nd the suitbly modified PID controllers cn mintin the room ir temperture nd reltive humidity close their respective setpoints irrespective of vrible therml lods. The method of determining PID prmeters for the modified controller is prcticl for room temperture nd humidity control systems. Fixed setpoint Figure 6 nd 7 show the responses to the fixed setpoint of the room ir temperture for the cses of the conventionl PID nd the modified PID controls, respectively. In Figure 6, there re sudden chnges in θ nd φ during the initil few hours, which then settle to setpoints. We cn expect tht, since the trnsient responses of θ nd φ will lso chnge rpidly, θ nd φ re very close to their setpoints even though θ 0 nd q L re vried. The supply ir flowrte illustrtes instbilities loclly due to humidifier working. When looking over results of Figures 6 nd 7, it should be noted tht the responses (θ nd φ) of the conventionl PID control nd the modified PID control re somewht different.

15 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets 223 Fig. 7. Simultion results of Modified PID. Conventionl PID Modified PID ISE ICI IPID Tble 3. Comprison of control performnce indices to fixed setpoint. Becuse the reset for the modified PID control cn be djusted very often, it becomes difficult to mintin θ nd φ t the setpoints, so θ fluctutes round the setpoint. It is cler tht the results for modified PD control cnnot represent n improvement over those for the conventionl PID control. For smll vlues of the integrl gin (k i ) for the modified PID control, θ creeps slowly towrds the setpoint. However, s will be seen in the ner future, this disdvntge my be clerly solved.

16 224 Advnces in PID Control Fig. 8. Vrible setpoint profile. Tble 3 shows tht the results of the vlidtion simultions in terms of three performnce indices. For the ISE (trcking ccurcy), it is evident tht the shrply chnge of the reset ggrvtes the trcking ccurcy of θ for the modified PID control, but it is enhnced by incresing the integrl gin (k i ). Further investigtion into the totl mount of control inputs (ICI nd IPID) cn led to some interesting results. It is recognized tht the ICI is exctly the sme for the two control strtegies. The physicl interprettion of this fct is tht there is no difference of supply ir flowrtes between two control strtegies. However, for the IPID, the modified PID control clerly represents n improvement over the conventionl PID control. As mtter of fct, the merit of the modified PID control becomes obvious when the mximum cpcity of the controller is limited. Vrible setpoint Figure 8 depicts the setpoint profile (( 0 4) [C]) of room ir temperture depending on the outdoor temperture on typicl dy. The responses to the vrible setpoint for the cses of the conventionl PID nd the modified controls re shown in Figure 9 nd 10, respectively. The room ir temperture nd humidity follow their respective setpoint profiles even though therml lods re vrible. It is pprent from Figure 9 tht the solid res indicte rpidly oscillting vlues due to hunting when the humidifier is positioned between 0 % nd 100 %. Subsequently, the room ir temperture cn be oscillted with the occurrence of such huntings. The sme trend is lso pprent in the supply ir flowrtes. It cn be seen from Figure 10 tht suitbly tuned modified controller cn mintin the room ir temperture nd humidity close to their respective setpoints suppressing such huntings. The effectiveness of the modified PID control cn be confirmed. By compring these responses with those of Figure 6 nd 7, it is cler tht the humidifier is turned on very often nd the hunting of the room ir temperture my occur simultneously. Fig. 9 nd 10 demonstrte loclly rpid oscilltion of the humidifier when the indoor reltive humidity φ becomes below the setpoint 55 %. This is due to the fct tht the humidifier is very sensitive to control inputs. There re lso mny technologicl problems to be solved when we mke positive use of the humidifier in cooling opertion.

17 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets 225 Fig. 9. Simultion results of conventionl PID. Conventionl PID Modified PID ISE ICI IPID Tble 4. Comprison of control performnce indices to vrible setpoint. Tble 4 represents the control performnce indices obtined by typicl dily simultion results. A comprison with Tble 3 shows tht there is very little difference in performnce between the fixed setpoint nd the vrible setpoint. For the ISE, the ISE for the modified PID is lrger thn tht for the conventionl PID. This mens tht the I ction is effective for not only elimintion of offset (stedy-stte error) but lso disturbnce ttenution. Trcking ccurcy nd disturbnce ttenution will be enhnced by selecting high integrl gin. For the ICI, it is striking tht the ICI vlues re exctly the sme for two control strtegies. For the IPID, the modified PID control gives slightly better results thn the conventionl PID control. It is concluded tht the modified PID control should be lso incorported by limiting the mximum control input vilble to the controller.

18 226 Advnces in PID Control Fig. 10. Simultion results of Modified PID. 4. Conclusions In this pper, the room temperture nd humidity control systems with the conventionl PID control using fixed reset or the modified PID control using djustble resets which compenste for therml lods upset re exmined. The simultion results for one-dy opertion bsed on prcticl outdoor temperture nd therml lods profiles provide stisfctory control chrcteristics. The results of vlidtion simultions re demonstrted in terms of three performnce indicies (s three integrls of squred error (ISE), control input (ICI), nd control input in PID controller only (IPID)). The results obtined in this study re summrized in the following: 1. The room ir temperture nd humidity illustrte instbilities loclly due to humidifier working. 2. By chnging the setpoint of the room ir temperture on the bsis of the outdoor tempertures profile, the control performnce cn be remrkbly improved. 3. In dily opertion, when the reset is djusted t every hour, the shrply chnge of the reset ggrvte the response of the room ir temperture. The response cn be improved by proper selection of the computtionl period.

19 Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets The proposed control strtegy for the djustble reset cnnot be effective for energysvings, but hs possibility in cse tht there exists limittion of the mximum control input vilble to the controller. Finlly, the results given in this pper were motivted by the desire to obtin stisfctory performnce with djustble reset better thn tht with fixed reset. Consequently, it is concluded tht there is little inherent dvntges in designing the modified PID controller with djustble reset. However, since this modified PID control lightens the totl mount of control input produced in the controller, it cn be good cndidtes for the next HVAC controllers. The work reported here is being continued to vlidte severl conclusions obtined by experimentl results. 5. Acknowlegdment This reserch ws prtilly supported by the Ntionl Institute for Environment Studies in Tsukub. The uthors would like to cknowledge stffs of Controls Group for their contribution to this study. 6. Nomenclture C = overll het cpcity of ir-conditioned spce (kj/k) C d = overll therml cpcity of humidifier spce (kj/k) c p = specific het of ir (kj/kg K) α = overll trnsmittnce-re fctor (kj/min K) α d = overll trnsmittnce-re fctor outside humidifier (kj/min K) = indoor ir temperture (C) r = setpoint of indoor ir temperture (C) s = supply ir temperture (in humidifier) (C) sr = setpoint of supply ir temperture (in humidifier) (C) c = supply ir temperture (in cooling coil) (C) 0 = outside temperture (C) = density of ir (1.3 kg/m 3 ) c p = specific het of ir (kj/kg K) f s = supply ir flowrte (m 3 /min) f s0 = reset of supply ir flowrte of room (m 3 /min) w s = c p f s, het of supply ir flowrte (kj/min K) V = room volume ( m 3 ) V d = room volume of humidifier (m 3 ) x = indoor bsolute humidity (kg/kg (DA)) x s = bsolute humidity of supply ir (kg/kg (DA)) x si = return ir bsolute humidity t the inlet of ir-hndling unit (kg/kg (DA)) x 0 = outdoor bsolute humidity (kg/kg (DA)) = indoor reltive humidity (%) r = setpoint of indoor reltive humidity of room (%) h = rte of moist ir produced in humidifier (kg/min) = therml lod from internl het genertion (kj/min) q L

20 228 Advnces in PID Control q B = fn lod (59.43 kj/min) q d = lod by humidifier ( ( c )h kj/min) p = evportion rte of occupnt ( kg/min) P = totl pressure of mixed ir (101.3 kp) p w = prtil pressure of wter vpor t the inlet of ir-hndling unit (kp) p ws = prtil pressure of sturted vpor t temperture c (kp) h 0 = reset of rte of moist ir produced in humidifier (kg/min) n = number of occupnts in the room (-) K P = plnt gin of room temperture dynmics T P = time constnt of room temperture dynmics L P = dedtime of room temperture dynmics K Ph = plnt gin of room humidity dynmics T Ph = time constnt of room humidity dynmics = dedtime of room humidity dynmics L Ph 7. References Kshr. M. et l. (2000). Physicl Model of n Air-Conditioned Spce for Control Anlysis, ASHRAE Trnsctions, Vol. 106, Prt II: pp Åström. K. & Hägglund. T. (1995). PID controllers: Theory, design nd tuning, pp nd , Instrument Society of Americ. Hrtmn. T. (2003). Improving VAV Zone Control, ASHRAE Journl, pp Tir. U. (2004). Sve-Energy Type Temperture-Humidity Simultneous Control using Model Predictive Control Method, Journl of Society of Instrument nd Control Engineering, Vol. 43-9, pp Ymkw. Y. et l. (2010). Compenstion of Mnul Reset to Offset Therml Lods Chnge for PID Controller, ASHRAE Trnsctions, Vol. 116, Prt 1, pp Zhng. Z. & Nelson. R.M. (1992). Prmetric nlysis of building spce conditioned by VAV system, ASHRAE Trnsctions, Vol. 98, Prt 1, pp Mtsub. T. et l. (1998). Stbility Limit of Room Air Temperture of VAV System. ASHRAE Trnsctions, Vol. 104, Prt II: pp Ymkw. Y. et l. (2009). Stbility of Temperture Control System in VAV Systems, ASHRAE Trnsctions, Vol. 115, Prt 1, pp Ozw. K. et l. (2003). A Tuning Method for PID Controller Using Optimiztion Subject to Constrints on Control Input. ASHRAE Trnsctions, Vol. 109, Prt 1, pp ASHRAE. (1989) ASHRAE Hndbook Fundmentls, Americn Society of Heting, Refrigerting nd Air-Conditioning Engineers, Inc. Wexler. A. & Hylnd. R.W. (1983). ASHRAE Trnsctions 89(2A): 500. Tkhshi. Y., M. J. Rbins & D. M. Auslnder. (1969). Control nd dynmic systems, New York, Addison-wesley Ziegler. J. G. & Nichols. N. B. (1942). Optimum settings for utomtic controllers, Trnsctions of the Americn Society of Mechnicl Engineers, Vol. 64-8: pp. 759

21 Advnces in PID Control Edited by Dr. Vlery D. Yurkevich ISBN Hrd cover, 274 pges Publisher InTech Published online 06, September, 2011 Published in print edition September, 2011 Since the foundtion nd up to the current stte-of-the-rt in control engineering, the problems of PID control stedily ttrct gret ttention of numerous reserchers nd remin inexhustible source of new ides for process of control system design nd industril pplictions. PID control effectiveness is usully cused by the nture of dynmicl processes, conditioned tht the mjority of the industril dynmicl processes re well described by simple dynmic model of the first or second order. The efficcy of PID controllers vstly flls in cse of complicted dynmics, nonlinerities, nd vrying prmeters of the plnt. This gives pulse to further reserches in the field of PID control. Consequently, the problems of dvnced PID control system design methodologies, rules of dptive PID control, self-tuning procedures, nd prticulrly robustness nd trnsient performnce for nonliner systems, still remin s the res of the lively interests for mny scientists nd reserchers t the present time. The recent reserch results presented in this book provide new ides for improved performnce of PID control pplictions. How to reference In order to correctly reference this scholrly work, feel free to copy nd pste the following: Tknori Ymzki, Yuji Ymkw, Kzuyuki Kmimur nd Shigeru Kurosu (2011). Air-Conditioning PID Control System with Adjustble Reset to Offset Therml Lods Upsets, Advnces in PID Control, Dr. Vlery D. Yurkevich (Ed.), ISBN: , InTech, Avilble from: InTech Europe University Cmpus STeP Ri Slvk Krutzek 83/A Rijek, Croti Phone: +385 (51) Fx: +385 (51) InTech Chin Unit 405, Office Block, Hotel Equtoril Shnghi No.65, Yn An Rod (West), Shnghi, , Chin Phone: Fx: