PREDICTIVE CONTROL OF AMBIENT AIR TEMPERATURE BY AUXILIARY CONTROL VARIABLE IN LARGE OCCUPIED SPACE

Transcription

1 PREDICTIVE CONTROL OF AMBIENT AIR TEMPERATURE BY AUXILIARY CONTROL VARIABLE IN LARGE OCCUPIED PACE L. Hach 1, Y. Katoh, J. Krima 1 Institte of Applied Physics and Mathematics, Faclty of Chemical Engineering, University of Pardbice, Pardbice, Czechia Department of Mechanical Engineering, Faclty of Engineering, Yamagchi University, Ube, Japan Abstract In the article is presented a control method of indoor air temperatre of larger occpied space. The desired temperatre is set on a standard PI-controller handling an inpt signal of CO -concentration parameter, which serves as axiliary control qantity. The space in which may gather many persons in relatively short time, represents controlled object with thermal conditions for which a predictive controller response is preferred. The controller handles the axiliary parameter as timedepending variable on pre-programmed basis and has a hygienic priority while setting controller s otpt. 1 Work Place afety And Indoor Air Contamination 1.1. Carbon Dioxide As Air Polltion Contaminant The goal of any indoor environment control incldes the keeping of air polltion contaminants far from hazardos concentration levels. These levels are known from medical stdies and ventilation rates shold psh carbon dioxide (CO ) concentrations below 1000 ppm acceptable to most individals [1], []. Negative health effects cased by carbon dioxide concentration level by longer time occpancy within enclosre spreads from tiredness to asphyxiation as it replaces oxygen in the blood. It is preferred tight or near hermetically closed conditions for mechanically ventilated space: the more tightness means more accrate indoor CO measrement, more effective control as well as energy savings. There is minimal hygienic limit of 7 m 3 /h.person nder exactly defined conditions [] for an nadapted person, while for adapted persons it is decreased to 9 m 3 /h.person. In good agreement are other recommendations ([4]) that shold essentially set control bondary limits. In terms of an air change (the nmber of times that the air in a room is flly changed within one hor), ACH vale is often prescribed, and the otdoor air rate can be obtained if the air change is mltiplied by the room volme. Becase there is also a certain correlation among the CO amont prodced by the gathered occpant(s) and its/their characteristics: adaptation degree (time period of presence), physical activity, age and clothing, the air rate estimation was frther detailed. 1.. CO -Concentration Monitoring The carbon dioxide (CO ) amont, generated by occpants in the controlled enclosed space, represents one of the three controllable qantities: inpt air rate m (kg.s -1 ), the operative temperatre t o ( o C) and CO concentration (ppm). Under assmption that people gathered in the room are the main sorce of air polltion (hman metabolism) compared to: - other internal sorces of carbon dioxide (technology devices, animals), - odor agents, released from bilding materials, the amont of both, the water vapor and CO amont cold be considered as reference indoor air parameters. If measred in indoor environment, they indirectly indicate approximately how mch otdoor air is entering an enclosed space in relation to the nmber of occpants nder assmption of knowing these qantities for the entering air. However, the qality of controlled qantities depends also on their measrement accracy, i.e. others appropriate sensors, their placement, control method and sampling time period; it is always a compromise between the control accracy demands and rationally chosen appropriate control system.

2 CO -sensor placement division of controlled space into zones The CO -sensor placement was one of decisive tasks in order to get sfficiently reliable and representative measrement vales. There are several rles regarding the temperatre as well as CO sensors placement with respect to the vertical and horizontal temperatre profiles. The CO concentration map basically copies the similar one of water vapor small deviations throghot the enclosre. temming from individal sorces occpants, it qickly spreads arond (Fig.1), ths the concept of microclimate near the sorce was nsefl for positioning the CO -sensor there, not to mention the mobility near the sensor. Rather, pon the indoor air velocity profile estimation were proposed places, in which lesser flctations of CO concentration levels were expected, frthermore minimal inflences of inlets/otlets inclding openings (doors, windows), ths minimizing possible CO -measrement of otdoor air. As the low air velocities one wold expect in central part of the enclosre, on the other site, the basic reqirements dictate to avoid the sensor placement in any bondary layer zone, regardless of character flows (laminar, transient or trblent one). Finally, on the margins of the occpied zone the sensors were placed, ths avoiding false signals with expectation of obtaining vales withot any nnecessary delay TVOC-Monitoring and Removal Efficiency Where other odor agents (released from bilding material, frnitre and eqipment, etc.) are decisive for otdoor air rate, its minimm vale shold be sed: R G TVOC TVOC 3.6 i, TVOC e, TVOC (1) In Eq. (1) symbols denote: R TVOC minimm otdoor air rate per nit srface area (dm 3.s -1.m - ), G TVOC TVOC rate prodction within the interior per nit srface area (µg.h -1.m - ), ρ i,tvoc TVOC interior concentration limit (µg.m -3 ), ρ e,tvoc TVOC concentration in otdoor air (µg.m -3 ), TVOC total volatile organic coomponds (ppm). Then, the reqired otdoor air rate is the sm of the two air rates (if they occr), i.e. based on CO estimation in previos chapter and calclated from TVOC level. In addition, if air recirclation is sed, the otdoor air rate mst not be lower than 10 % of spplied air into the room. Odor sbstances material removal efficiency Basically, there are three ways of deodorization: chemical, mechanical and biological (introdcing plants). There are several known organic as well as anorganic grops of material capable of odor sbstances removal. The most sbtitle grop is based on carbon variations: from activated carbon, charcoal to varios synthetic materials. The material prodced in shapes of blocks, roles, etc., is one of filter active components in air ventilation system. Controlling with Axiliary Control Variable.1. P-Controller (IO) Adjstment Takahashi ettings In the following chapter is introdced the conventional P-controller designed to maintain reqired operative temperatre t o in the middle-sized library room. The IO (single-inpt-singleotpt) controller s temperatre sensor is placed at the internal wall ot of reach of direct snshine or possible mobile heat sorce (compter or any other heat generating device). It provides basic signal of indoor air temperatre t a, while the three other temperatre sensors stick to the external wall, opposite and side wall of the room. Their vales are smmarized and represent the average radiant temperatre of srronding walls t mrt - the mean radiant temperatre as an area mean parameter. Together with indoor air temperatre is calclated operative temperatre (EN IO 7730): t O a tmrt At 1 A ()

3 Where t o is the operative temperatre [ o C], t a is the air temperatre [ o C], t mrt is the mean radiant temperatre [ o C], A is a factor accordance to the relative air velocity (A = 0.5 for var = 0. m/s, A = 0.6 for var = m/s, A = 0.7 for var = m/s). The aim of the control task was to maintain the desired operative temperatre 93 K, resp. 94 K (0 or 1 C) within the occpied zone 3, while the infiltration was assmed to be 0,9 h -1, still above the limit for a non-smoking space as is stated in most national hygienic standards and normatives, 5. Takahashi control algorithm 6 with respect to proportional-sm processing of control deviation e shold minimize the integral fnctional J formed from its sqares differences: J( ) 1 T e e where symmetrical positive-definitive matrix 3 x 3, e deviation vector, e() = w() - y(). 0 There is an inpt vector e() into controller of deviations of operative temperatre and airflow rate and on the controller otpt () single actator that serves to change the fan heater otpt, otdoor airflow rate and flap for recirclating air remain constant, Fig. 1: (3) 5 4 Otdoor air spply dct Tested space Occpied zone Air otlet Figre 1: The reference space controlled by (a) operative temperatre sensor and (b) operative temperatre sensor with CO -sensor. 1 operative temperatre sensor, CO -sensor, 3 heater nit, 4 flap of air recirclation nit, 5 air rate sensor, 6 central control nit, MIMO-controller (mlti-inpt-mlti-otpt). For the control algorithm is tilized time-discretisation form with proportional and sm part (P), i.e. its continos formla follows from: 1 ro e e d (4) Ti 0 where integration is sbstitted throgh sm of control deviation e: k k r ek ei o with - sampling period (s). Recommended vales of both parameters of P-controller proportional constant and time constant 6: 0,9. n 0,135. n. r0 K (6) 0,7. n. Ti r0 K I - integral constant (s) - sampling period (s) n - transient time (s) r 0 - proportional constant (gain) of controller (-) - time lag (s) K - system gain (-) T i i0 (5)

4 bstitting R = K / n, K p = r 0, and K I = r 0. / I follows: K P 0,9 1 K R I K I 0,7. R The settings with P-controller were sed while simlating heating p the space dring daylight period, and adeqate change of the average temperatre of the external wall, Fig.. These transient responses were modeled in MATLAB software with its imlink toolbox 7. (7) t w ( C) P imlation parameters Max time step 300 Tolerance 1e- Nm. method Rnge- Ktta 3 rd order top time 4000 Acceleration no imlation parameters Max time step 300 Tolerance 1e- Nm. method Rnge- Ktta 3 rd order top time 4000 Acceleration no 0.45 Figre : Average srface temperatre t w transient response for heating p the otdoor wall of reference space (nit-step heat load). P point of inflexion. t mrt ( C) P 0.6 Figre 3: Mean radiant temperatre t mrt transient response for heating p the reference space (nit-step heat load). P point of inflexion. From the transient responses yields differences between the operative air temperatre and the mean radiant temperatre in the tested room mch smaller than 4 C. With assmption of low velocities of the indoor air within the occpied zone (< 0. m.s -1 ), the simplified design operative temperatre t o : t O i mrt 1 t t (8) was sed instead of Eq. () as the main inpt onto MIMO-controller (Chap..). The simlation test of the tested room response, inclding periodic (sins) daytime temperatre swing cased by exposing the external wall to the external heat load, allows to determine its thermodynamic characteristics crcial to the investigated space 3. Provided that the air in the space

5 is perfectly stirred (as is sally assmed in models of that kind), the simlation model order n enables to estimate the system time constant together with the dead time (lag): inf (9) n 1 system time constant, time lag and n system order. The comparison of temperatre amplitdes on exterior- and interior-faced otdoor wall, nder otdoor climate-driven thermal distrbances, is sefl for evalating gains, if thermal eqilibrim wold not be sfficiently reached. For the external wall, the overall damping coefficient was: t wo, i vwo 0.19( ) t wo, e, (10) t wo, e - two amplitdes of temperatre harmonic swing on otdoor-faced external wall (K), t wo, i - two amplitdes of temperatre harmonic swing at room-faced inner srface of the external wall (K)... MIMO-Controller with Axiliary Control Variable With the CO -control concept is decisive the CO concentration of otdoor air rate while heater maintains the desired operative temperatre t o (eventally indoor air temperatre t a ). To the rise of CO concentration level mst be adeqate increase of otdoor air rate. It cold be done by increasing fan revolving or often by flap position control (Fig. 1), recommended ventilation rates are given for inst. in EN 1551:007, Annex B. For this the inpt vector e() into MIMO (mltiple-inpt-mltiple-otpt) controller contains deviations of operative temperatre t o, airflow rate m and CO concentration C, and on the controller otpt similar vector of actators () that serve heater Q, fll fresh-air (otdoor) airflow rate m and flap position l a for recirclating air (Fig. 1, Chap..1). The basic CO -profile in the tested room was estimated as the space is occpied dring daylight hors by nmber of occpants with patterns of gathering larger nmber of occpants in certain time periods as is seen in Table 1: Table 1: 1-day reference space probability occpation Average no of occpants 7-9 A.M A.M. 11 A.M. -1 P.M. Time (hor) P.M. P.M. 5-7 P.M. 7-9 P.M. 9 P.M.- 7 A.M The apriori information abot CO -concentration level together with the internal heat sorces (metabolism heat rate) was employed to minimize afterwards controller s actions throgh simltaneos comparison with actal CO -vale. Their difference is set as the axiliary variable forming the term of deviation vector e(). The primary controller inpt represents the operative temperatre of the tested space with approximated transfer fnction of the 3 rd -order and different time constants: K p td F3 ( p) e 1 p11 p 1 p 3 (9) where K is system gain and 1,, 3 are time constants of the reference room. Employing system order redction rles [7], the 4 th -order eqation wold sbstitte the same model with the 4-time mltiple time constant s and with dead time td : K p td F4 ( p) e 4 1 p (10) The reference space transfer fnction F 4 (p) with the transfer fnction of otdoor airflow rate, resp. CO -concentration level fill deviation vector e().

6 3 Closed Loop Control with Axiliary Variable 3.1. Axiliary Variable Performance as Fnction of Transfer Fnctions The control concept with axiliary qantity of CO concentration level shows Fig. 4: y x + w(τ) + F F H x R F R F RH _ x R x RH y H + z(τ) + Figre 4. Block scheme of closed control loop with axiliary control qantity y H of CO concentration. F - transfer fnction of controlled reference space, F H - transfer fnction of controlled axiliary reference space (CO, TVOC), F R P-controller transfer fnction, F RH - transfer fnction of axiliary controller. Transfer fnctions for all for otpts, i.e. [y (τ), y H (τ)] for the tested room space, resp. [x (τ), y H (τ)] for the MIMO-controller were set in order to compose a simlation model of the tested space with the controller. Takahashi rles for the MIMO-controller parameters adjstment remain the same as is described in Chap..1. Distrbance vector z() acts together with controller otpt x R and control qantity (program) w with controlled qantity y. Transfer fnction of axiliary controller F RH (p) yields from known transfer fnction of PI-controller: F RH p K C 1 1 (11) Ti p where K C is controller gain and T i time integration constant. The transfer fnction of the reference space of the 3rd order (Eq. (9) with the CO -concentration transfer fnction F H (p) is: p p FH F p y p (1) y H Ths, the axiliary control qantity yields: FH yhp y p (13) F Transfer fnctions of other nits in block scheme of closed control loop in Fig. 4 are obtained throgh disconnecting the circit in three different circit points (at y, y H and x ). By their sbstittion back into the condition of closed control loop z x R = x wold be assessed inflence of distrbance variable: p p p F p p 1 F pf p F pf p (14) y z R The Eq. (14) finally indicates the inflence of axiliary control variable on the qality of the control process: the denominator became bigger with the term F H (p).f RH (p), so the control deviation nit becomes smaller in the thermal eqilibrim state. 3.. Reslts and Conclsion There was presented a control method with a partially time-predictive variable of occpant(s) prodction of carbon dioxide as main sorce polltion. From the hygienic directives (for inst. []) the limits of CO content (in the modeled case of 1800 mg.m -3 (1000 ppm(v))) cold be served throgh fixed airflow rate as well as flap position in air recirclation nit. More efficient approach wold control both, the fresh-air flow rate and the recirclated air. To the controlled operative temperatre was sitably associated the variable pon which are estimated internal heat sorces, odoros particles H RH

7 and primarily, the carbon dioxide concentration stemming from occpant(s) hman metabolism. The measrement of CO -qantity is carried ot with reglar sampling time to on-line modify defalt vales (Table 1), ths it is providing actal vales pon which is based mltilevel control: standard temperatre control of operative (alternatively indoor air) temperatre and simltaneosly keeping the limits of CO concentration level. The later parameter the axiliary variable is part of a control process depicted in Fig. 5, green dashed line: t a (-) z % imlation parameters Max time step 300 Tolerance 1e- Nm. method Rnge- Ktta 3 rd order top time 1400 Acceleration no Figre 5: Indoor air temperatre nit-step response for load change of the distrbance variable heating p of the modeled space. It shows the transient response of the modeled space to nit-step inpt of the heating load of the air heater with axiliary control variable. The difference is shown in the plot in comparison to the transient response on the nit-step of the same distrbance variable (heat load) withot axiliary control fnction. It represents nearly %-improvement of the deviation from desired indoor air temperatre in the eqilibrim state and it is accordingly percentage fraction of the saved energy. References [1] Gnnarsen, L., Fanger, P.O. (199) Adaptation to indoor air polltion, Environment International, 18:43-54, [] AHRAE 6.1 (007) Ventilation for acceptable indoor air qality, Atlanta, GA, American ociety of Heating, Refrigerating and Air-Conditioning Engineers. [3] Hach, L. and Katoh, Y. Thermal responses in control loop in indirect control of indoor environment of non-air-conditioned space with qasi-steady-state model. JME International Jornal eries C-Mechanical ystems Machine Elements and Manfactring, 46(1):197{11, 003. [4] CR 175:1998 Ventilation for bildings Design criteria for the indoor environment. Technical report of Eropean Committee for tandardization. [5] ANI/AHRAE tandard , Thermal Environmental Conditions for Hman Occpancy, Atlanta: American ociety of Heating, Refrigerating, and Air conditioning Engineers, Inc., UA, 199. [6] Takahashi Y.: Digital Control, 3rd edition, Iwanami Pbl., Tokyo, (In Japanese), March [7] Marshall,. A., An approximate method for redcing the order of a linear system, Control, 1966, pp [8] The Mathworks, Inc Matlab User Gide, reprint, Natick, Massachsetts, UA.

8 Contact information: Lbos Hach Institte of Applied Physics and Mathematics, Faclty of Chemical Engineering, University of Pardbice, Pardbice, Czechia