PID Controller tuning and implementation aspects for building thermal control

Transcription

1 PID Controller tunng an mlementaton asects for bulng thermal control AFEZIS G. *, PAELIS P. *, RIPOLIAIS E.J. *, SAVRAAIS G.S. *, OLOOSA D. **, ALAIZAIS. * * Deartment of Electronc & Comuter Engneerng echncal Unversty of Crete echncal Unversty of Crete, ounouana Camus, 7300, Chana, Crete Greece ** Deartment of Natural Resources an Envronment Laboratory of Renewable Energy Resources Engneerng echnologcal Eucatonal Insttute of Crete 3, Romanou Str, 7300, Chana, Crete Greece {gkafetzs,etrosatels,vaggels,gstavr,koskal}@electroncs.tuc.gr htt:// Abstract: - he control of the noor envronmental arameters of bulngs s an oen roblem wth many ractcal ffcultes whch stem from the non-lnear, multvarable nature of the bulng moels. hs aer resents the tunng rocess of a conventonal PID controller for the thermal comfort control alcaton, n bulngs utlzng felbus systems. he PID controller has been chosen takng nto account ts wesrea eloyment an ts attractve features lke low comutatonal cost an smlcty of mlementaton. On the contrary, there s no stanar methoology for the extracton of ts arameters. herefore, emrcal methos shoul be utlze along wth tral an error technques on the target alcaton. he esgn roceure s llustrate an there s secal focus regarng the ractcal asects of the mlementaton on a laboratory nstallaton. Fnally, the results of the montore an comute varables of the exermental roceure are resente along wth relevant conclusons an scusson. ey-wors: - PID controller tunng, rocess reacton curve metho, thermal controller. Introucton One of the key esgn goals for bulng energy management systems (BEMS) s the reucton an mnmzaton of the energy consumton. Moreover, along wth the ower savng goals, the noor envronmental arameters shoul be ajuste roerly n orer to ensure comfort contons. herefore, a control algorthm s necessary to rove a balance between comfort an low energy consumton. Deste the scentfc rogress on the areas of bulng energy management systems an bulng networkng alcatons, the esgn of an otmal control algorthm resents ncrease ffculty. hs s ue to the nonlnear characterstcs of the bulng moel. Moreover, t s ffcult to effcently use a set of lnear state-sace equatons to escrbe ths famly of systems, as the exstng ones resent oor erformance an lack generalzaton. Several aroaches have been roose n orer to overcome the nonlnearty of the bulng s moel. hese nclue classc control aroaches an ntellgent system alcatons. Qu an Zaheerun [] roose the transformaton of H loo-shang tunng rules, to screte-tme tunng rules, n orer to mlement an aatve PI controller for HVAC (Heatng Ventlaton an Ar Contonng Systems). Wang, Lee, Fung, B an Zhang [2] suggeste a PID controller that resents hgh erformance for a range of lnear self-regulatng rocesses, along wth laboratory exermental results. Regarng ntellgent control, roltaks, olokotsa et al [3] suggeste a Fuzzy PD controller for thermal comfort n bulngs an Moshr an Rash [4] roose an aatve self-tunng fuzzy PID controller for the control of nonlnear HVAC systems. olokotsa et al [5] ntrouce a genetc algorthms otmze fuzzy controller for the noor envronmental management of bulngs. Huang an Lam [6], llustrate a genetc controller aroach for the tunng of a conventonal PID controller rules. hs aer escrbes the esgn, tunng an alcaton of a gtal PID controller for the ajustment of noor contons n the laboratory of Electrc Crcuts an Renewable Energy Sources at the echncal Unversty of Crete. he PID

2 controller s chosen ue to ts smlcty, low comutatonal overhea an excetonal behavour to a we range of alcatons. he controller eveloe n ths work, s mlemente on a ersonal comuter whch communcate wth the sensors an actuators usng the Euroean Installaton Bus (EIB) nfrastructure. he system nuts are receve from a set of sensors whch montor the noor an outoor contons. Such sensors are noor an outoor temerature, relatve humty, mean raant temerature (MR) an ar see. he outut of the system controls two ar-contonng unts of 36,000 btu each, use for both heatng an coolng. he esgn objectve s to ajust the noor temerature to a esre set value, on the resence of external sturbances. Moreover, the resultng system shoul be able to comensate for the sensor naccuraces, resent fast convergence to the set ont, mnmum oscllaton amltue an mnmum overshoot or unershoot. Secton 2 resents a bref ntroucton to the classc PID controller. Secton 3 eals wth the escrton of the Zegler Nchols methoology for the controller s arameters tunng. On secton 4, the tunng rocess along wth the exermental results of the laboratory alcaton of the controller, are resente. Fnally, on the ffth secton there s a short scusson about the contrbuton of ths work. 2. Conventonal PID Controller he conventonal PID controller s the most oular controller n nustry. Its we eloyment s justfe ue to ts effectveness along wth smlcty of esgn an mlementaton. Deste ts avantages, the esgn of such a controller s not escrbe by a general methoology an focuses on emrcal methos. 2. Analyss of the controller he PID controller conssts of three arts: the Proortonal gan (P), the ntegral gan (I) an the fferental gan (D). her general transfer functon s gven by: 2 G c (s) = + s + s + + s or () s s where the gans, an are the gans for roortonal, ntegral an ervatve art resectvely. he general block agram of a lant wth a PID controller attache to t, s gven on the followng fgure: Fg., Block agram of lant wth a PID controller An equvalent transfer functon s gven below: U ( s) Gc ( s) = = c + s + E( s) s (2) where = s the ntegral constant, = s the ervatve constant an c. he above transfer functon can be transforme on the contnuous-tme oman gvng the followng equaton: t u( = c + τ ) τ + t 0 (3) If the samlng tme has low value ths equaton o can be transforme to a screte-tme fferental equaton. he fferental term (D) s relace by a frst orer exresson of fference an the ntegral term (I) by a sum gvng the equaton on the screte-tme oman: k = + o u ( c ) + ( k )) (4) = o o 2.2 Characterstcs of the PID controller 2.2. P controller he P art gan, s roortonal to the nut error value. It offers lmte erformance as t s unable to elmnate the steay state error. It s common to use the exresson, Proortonal Ban (PB), to escrbe the acton of the roortonal gan. he 00% equvalent equaton s gven by: PB[%] = (5) I controller he outut of the ntegral art s roortonal to the calculate sum of errors an emonstrates a way of slow reacton control. Moreover, t manages to elmnate the steay state error by generatng resectve actuaton oututs an at the same tme works aganst the oscllatory behavour of the lant.

3 2.2.3 D controller he ervatve art gan s roortonal to the rate of change of the control error. It leas to fast resonse stable systems at the cost of steay state error ntroucton an oscllatory behavour. 3. PID Parameters Extracton he PID controller esgn objectve s to etermne a set of gans (or gans along wth tme constants) (,, ) or (,, ), n orer to fulfll the c erformance requrements. hese gans are to be calculate n such a way that the transent resonse, tolerance to sturbances an steay error secfcatons are met. In ractce, t s not ossble to acheve all of these requrements. Many researchers have tre to overcome these ffcultes an obtan a global esgn metho of PID controllers. As a result many methos for tunng sngle-loo an mult-loo PID controllers have been roose. Some of these are: Zegler-Nchols, Cohen an Coon, Ho-Hang-Cao an Internal moel control. In ths aer Zegler- Nchols metho s revewe an use to calculate the PID controller s arameters. 3. Zegler-Nchols metho In 943 Zegler an Nchols [7] roose a metho known as rocess reacton curve metho. In ths metho, the oen loo unt ste resonse of the lant (the controller s sconnecte from the system) s measure an aroxmate by small straght lnes usually gven a form as shown n fgure 2. Controller P PI PID c τ 0.9 τ.2 τ Parameters τ 0.3 τ τ able Controllers Parameters by Zegler-Nchols metho It has to be note that a major savantage of the Zegler-Nchols metho, s the unesre effect of oscllatory behavour on a set of systems. 4. Exermental Proceure 4. General he PID controller use, s ale for the control of laboratory s temerature an t has the basc characterstcs of PID controllers, as they were gven n the secton 2. Fgure 3 shows the block agram of PID controller an ts transfer functon s gven by eq. (4) angent Process Reacton Curve Fg. 3, PID block agram Fg. 2, Plant unt ste resonse he tangent, n the ont of the curve where the frst ervatve receves ts maxmum value s rawn (ont of nflecton). he τ, an arameters are calculate below: Delay tme τ = t t0 (6) resonse tme = t 2 t (7) y y0 an gan = (8) u u 0 he rules of Zegler- Nchols metho for the extracton of PID arameters are as shown n able. he nuts of the controller are three: the current temerature error, the sum of all ast temerature errors an the temerature error fference, c. he error s efne as the fference of the setont, whch s the esrable acheve temerature, from the resent measure temerature, = set ont - measure tem. he set ont was selecte at C as t was consere to be a sutable temerature for the summer season. he sum of errors s efne as the sum of all ast temerature errors lus the current error. he error fference s efne as the fference between the current error an the revous error, ce ( = k ).

4 4.2 Extracton of the PID arameters he Zegler-Nchols metho was use as escrbe n secton 2, for the extracton of the c, an arameters. At frst, whle the controller was sconnecte from the system (oen loo), a unt ste nut was ale by settng the two ar contons to oerate constantly at full ower for an amount of tme suffcent for the system to reach a steay state. Moreover, no other sort of HVAC control was erforme on the nstallaton. he ero n whch the measurements were taken was, at the en of July At the same tme, temerature measurements were receve every 2 mnutes. he tme of 2 mnutes was chosen so as to yel ense measurements an rove goo aroxmaton of the temerature curve. he curve exort roceure was ale for a number of ays n orer have a large set of measurements. As t can be eucte from fgure 3, the laboratory temerature stablzes slghtly above 22 C after 20 mnutes. hs haens because of the constant contrbuton of coolng to the laboratory sace wthout any sgnfcant loss ue to external sturbances. emerature oc Measurements (every 2 mnutes) Fg. 4, emerature curve as functon of tme (each samle on x axs corresons to a two mnutes nterval) As suggeste by the Zegler-Nchols metho, the ont n whch ervatve s maxmum was foun an the tangent at ths ont was rawn as shown n fgure 5. emerature oc oc Zegler-Nchols metho angent: y = -.55x Measurements (every 2 mnutes) Fg. 5, emerature curve wth tangent at the ont of nflecton Accorng to the metho, the elay tme τ calculate value was 2 mn, whle the resonse tme was 2.44 mn. he resonse tme ranges from τ u to the moment where the tangent ntersects the steay-state art of the temerature curve, corresonng to 22.2 C. he gan s efne by the fference of the steay-state temerature from the ntal one an s calculate as: = = 8.55 (9) Subsequently, the c,, values are comute from the equatons on table where the τ,, an are substtute by ther corresonng calculate values. he results are ecte on the table 2. c P PI PID able 2 Controllers arameters After the extracton of the PID arameters, the equaton 4 takes the followng form: = + k o u ( ) + ( k )) (0) 4 = o o he next ste was the selecton of the samlng tme o to be 8 mn. hus, the fnal transfer functon of the controller s gven by: = 8 + k u( ) + ( k )) () 4 8 = o

5 4.3 Exermental results of the PID controller alcaton he PID controller s ale for the ajustment of noor temerature. he varables whch were montore an calculate were: nternal temerature, external temerature, MR (Mean Raant emerature), PMV (Precte Mean Vote) [8] an A/C uty cycle (controller outu, efne by the ercentage of system cycle tme, the unts oerate. he measurements laste two ays, startng from 2/07/2005 :52 an ene at 22/07/2005 5:48. he samlng tme was set to 8 mnutes. he ero of ar-contonng oeraton coul receve a value rangng from 0 to 8 mnutes corresonng to a 00% uty cycle. It has to be note that urng the measurement ero the values of the varables may fluctuate. Fgures 6, 7, 8 an 9 ect the measurements of the montore varables. PMV emerature (oc) :52 4:7 6:7 8:7 20:8 22:8 0:8 2:8 4;9 6:9 8:9 0:9 2:20 4:20 5:48 me (hour:mnutes) PMV (Precte Mean Vote) Fg. 8, Precte Mean Vote (PMV) Internal emerature an A/C uty cycle PMV Internal em Set ont oc 35 Internal emerature Int em :52 4:7 6:7 8:7 20:8 22:8 0:8 2:8 4:9 6:9 8:9 0:9 2:20 4:205:48 me (hour:mnutes) emerature (oc) Set ont oc A/C Duty Cycle (%) A/C Duty cycle 20 :52 4:7 6:7 8:7 20:8 22:8 0:8 2:8 4:9 6:9 8:9 0:9 2:20 4:205:48 me (hour:mnutes) Fg. 9, Internal emerature vs A/C uty cycle emerature (oc) 27 :52 4:7 6:7 8:7 20:8 22:8 0:8 2:8 4:9 6:9 8:9 0:9 2:20 4:205:48 me (hour:mnutes) Fg. 6, Internal emerature Internal emerature - External emerature - MR Internal em MR External em 25 :52 4:7 6:7 8:7 20:8 22:8 0:8 2:8 4:8 6:8 8:9 0:9 2:20 4:205:48 me (hour:mnutes) Fg. 7, Internal emerature vs External emerature an MR 5. Dscusson he exermental results verfe that the controller satsfes the orgnal esgn objectves. As shown on the fgure 6, the system reaches the area near the set ont n 48 mnutes (6 cycles). he maxmum unershoot s at 27.4 C yelng a 2.% fference from the esre set value. he oscllaton amltue oesn t excee 2.5% of the set value whch s accetable for the alcaton (less than 0.5 C). hs behavor s ue to the tye of control on the coolng unts. As revously state, the coolng unts were controlle by turnng them on for a roorton of a esre ero, set at 8 mnutes. After they were turne off an untl the begnnng of the new system cycle, the temerature woul rse, thus yelng the oscllatons. Moreover, the oscllatory behavor s eenent on external sturbances such as oen oors an wnows an the varaton of the external temerature of course. An engneerng traeoff was mae on the choce of the system cycle (an the samlng tme subsequently). A very small value of the system cycle reuces the oscllaton amltue an yels a fast resonse, because of the amlfcaton of the ervatve art gan. hs subjects the mechancal arts of the unts to stressful

6 contons. Moreover, the steay-state error s not elmnate as the ntegral gan s reuce. he average comute noor temerature was calculate from the measurements to be.073 C. he stanar evaton was C. he nternal comfort s eventually reserve takng nto account the PMV curve from fgure 8, as ts largest art reses on the (0-0.5) range whch s eal for the summer ero. hs aer resente the exermental results rven tunng rocess for a conventonal PID controller for noor thermal comfort control alcaton. he PID controller arameters for the lant n stuy were erve usng the emrcal rocess reacton curve metho suggeste by Zegler an Nchols. he resultng controller was teste for a long amount of tme an was roven to be stable an robust. Moreover, t reache the esre set ont resentng low oscllaton amltue an low unershootng. Furthermore, machne stress an low energy consumton were taken nto account for the choce of the system cycle. he results taken from the laboratory nstallaton valate the roer esgn an functonalty of the result system an rove a stable bass for future research. to otmze controller arameters for HVAC systems, Energy an Bulngs, Vol. 3, Issue, 997, [7] J. B. Zegler an N. B. Nchols, Otmum settngs for automatc controllers, rans. ASME, vol. 64, 942, [8] P.O.Fanger, hermal comfort, Mc Graw-Hll, New York, 972. References: [] Qu G., Zaheerun M., Real-me tunng of PI controllers n HVAC systems, Internatonal Journal of Energy Research () 2004,.33-7 [2] Wang Q.G., Lee.H., Fung H.W, B Q., Zhang Yu, PID tunng for mrove erformance, IEEE ransactons on Control Systems echnology, Vol.7, Issue 4, July 999, [3] roltaks E.I., olokotsa D., alatzaks., Stavrakaks G., Stuy an Imlementaton of a Fuzzy PD hermal Comfort Controller for Embee Felbus Systems Alcatons, WSEAS rans. on Crcuts an Systems, Vol. 3, Issue 9, Nov. 2004, [4] Moshr F., Rash F., Self-tunng Base Fuzzy PID Controllers: Alcaton to Control of Nonlnear Multvarable Systems, Lecture Notes n Comuter Scence, LNCS Srnger - Verlag, August 2004 [5] olokotsa D., Stavrakaks G.S., alatzaks., Agors D., Genetc algorthms otmze fuzzy controller for the noor envronmental management n bulngs mlemente usng PLC an local oeratng networks, Engneerng Alcatons of Artfcal Intellgence, Volume 5, Issue 5, Setember 2002,.47-4 [6] Huang W., Lam H.N., Usng genetc algorthms