MODELING AND CONTROL OF LIVESTOCK VENTILATION SYSTEMS AND INDOOR ENVIRONMENTS

Transcription

1 MODELING AND CONROL OF LIVESOCK VENILAION SYSEMS AND INDOOR ENVIRONMENS Zhuang Wu, Per Heselberg 2, Jakob Stoustrup 3 Department of Control Engneerng, Aalborg Unversty, Fredrk Bajersvej 7C, DK-9220, Aalborg East, Denmark 2 Department of Buldng echnology and Structural Engneerng, Aalborg Unversty, Sohngaardsholmsvej 57, DK-9000, Aalborg, Denmark 3 Department of Control Engneerng, Aalborg Unversty, Fredrk Bajers Vej 7C, DK-9220, Aalborg East, Denmark ABSRAC he hybrd ventlaton systems have been wdely used for lvestock barns to provde optmum ndoor clmate by controllng the ventlaton rate and ar flow dstrbuton wthn the ventlated buldng structure. he purpose of ths paper s to develop models for lvestock ventlaton systems and ndoor envronments wth a major emphass on the predcton of ndoor horzontal varaton of temperature and concentraton adapted to the desgn of approprate controllng strategy and control systems. he Lnear Quadratc (LQ) optmal control method takng nto account of the effect of necessary constrants and random dsturbances s desgned through system lnearzaton. he well desgned control systems are able to determne the demand ventlaton rate and arflow pattern, mprove and optmze the ndoor hermal Comfort (C), Indoor Ar Qualty (IAQ) and energy use. KEYWORDS Lvestock Ventlaton, hermal Comfort, Indoor Ar Qualty, LQ Optmal Control. NOMENCLAURE c p Heat capacty q Volume flow rate ρ Ar densty subscrpts P Pressure Zone H Average heght of nlet vent and leakage o Outsde A Area of openngs and leakage n Flow n U Heat transfer coeffcent of buldng envelope out Flow out V ref Wnd speed NPL Neutral Pressure Level m& Mass flow rate wall Buldng envelope INRODUCION Hybrd ventlaton systems have been wdely used for lvestock buldngs. Lvestock ventlaton s concerned wth comfort nterpreted through anmal welfare, behavor and health, and most mportantly, t s concerned wth factors such as converson rato, growth rate and mortalty (J.A.Clark, 984). Most exstng analyses for the lvestock ventlaton system assume that the ndoor ar temperature and concentraton s unform. However, the actual ndoor envronment at any controllng sensor (especally when the sensors are located horzontally) wll depend on the ar flow dstrbuton that s usually depcted as a map of the

2 0 domnant ar paths. herefore, the control system for large scale lvestock barns neglectng the horzontal varatons could obvously result n sgnfcant devatons from the optmal envronment for the senstve pgs or chckens n the lvestock barn. In ths paper, the lvestock ndoor envronment and ts control system wll be regarded as a feedback loop n whch the controller provde the optmal actons to the actuators takng nto account of the necessary dsturbances and random noses based upon the developed ndoor clmate model and ventlaton equpment models. he purpose of ths paper s to desgn an approprate controllng strategy to mprove the ndoor anmal hermal Comfort (C) and Indoor Ar Qualty (IAQ) through an optmal energy approach. MAHEMAICAL MODELLING he fan asssted natural ventlaton prncple wll be nvestgated n ths work. As seen n Fgure (a), (b) and (c), the system conssts of evenly dstrbuted fans and fresh ar openngs on the walls. From the vew of drecton A and B, Fgure (A) and (B) provde a descrpton of the domnant ar flow map of the buldng ncludes the arflow nteracton between each conceptual zone by applyng the mult-conceptual zone method. In each zone, t s possble to montor the zonal clmate and concentraton and effect of the control sgnals through the actuators movements: nlet vents and exhaust fans. he necessary smplfyng assumptons for developng models are as follows: he nteractve arflow between nternal zones, whch s nfluenced by the nlet ar jet trajectory, thermal buoyancy forces and convectve heat are assumed to be constant. Heat gan from anmals and solar radaton are assumed to be constant. he rate of the heat loss by evaporaton s neglected. he thermal propertes of the arflow are assumed to have bulk average values. Arflow nvolves no mass accumulaton nsde the buldng. he heat transfer coeffcent of buldng envelope s assumed to be constant. he pressure s assumed to be constant on each buldng surface (same value of pressure coeffcent C p s used for all openngs on the same sde of the buldng). A hydrostatc pressure dstrbuton s assumed n the space. Openng characterstcs are assumed ndependent on flow rate, pressure dfference and outsde temperature (constant dscharge coeffcent C d are used for all openngs). B (a) (c) B A (b) Fgure : Synoptc of Large Scale Lvestock Barn and the Domnant Arflow Map of the Barn A Models of Indoor Clmate A conceptual mult-zone method wll be employed to analyze and develop the ndoor clmate model. he lvestock buldng wll be dvded nto several macroscopc homogeneous conceptual zones horzontally so that the nonlnear dfferental-algebrac Eqn. and Eqn. 2

3 relatng the zonal temperature and zonal concentraton C r, can be derved by applyng the theory of conservaton of energy and mass. By substtutng wth the zone number nto Eqn. and Eqn. 2, we could derve four coupled dfferental equatons for ndoor thermal comfort n terms of zonal temperature and ndoor ar qualty n terms of zonal ar concentraton respectvely. For Eqn., the rate of energy Q & transferred by mass flow can be calculated by Eqn. 3. Q &,,, ndcate the heat exchange due to the ar flow across the conceptual boundary of zone and zone, whle for the mddle zones whch have heat exchange wth neghbor zones on each sde, two more parts Q &,,, wll be added to Eqn.. he value of nteractve mass flow between nternal zones s the sum of nfluence from ar jets, heat plume, thermal buoyancy and ar exchange rate. Q & nlet,, outlet,, leakage, represent the heat transfer by mass flow through nlet, outlet and leakage of the zone respectvely. he convectve heat loss through the buldng envelope s denoted by Q & conve and descrbed as U Awall ( o ). he heat source of the zone Q & ncludes the heat gan from anmal heat producton, solar source, radaton and heatng system. For Eqn. 2, the rate of concentraton s ndcated as C r n, where C r represents the concentraton level and the ar exchange rate n s calculated by Eqn. 4. For the mddle zones whch have mass flow nteracton wth neghbor zones on both sdes, two more parts C r, n,, Cr, n, should be added to Eqn. 2. he rate of contamnant generaton s denoted by G and the zonal volume s denoted by V. d Q & () M c p, =,, n, out, leakage, conve, source, dt dc dt r, = Cr, nout Cr, o nn Cr, n, Cr, n, G V (2) Q & = m& c p (3) m& 3600 n = ρ V (4) Models of Inlet Vent and Motor Fan System q n ΔP ρ o qout ρ = 0 (5) ΔP 2 ΔP q = Cd A sgn( ΔP) ρ (6) ΔP = C 2 o ρ ovref P ρ o g ( H NPL H ) (7) 2 P Eqn. 5 gves the relatonshp between the volume flow rate and pressure dfference across the openngs based on mass balance equaton wth sngle zone method. he ventlaton flow rate can be determned from Eqn. 6 and the pressure dfference s the combng drvng forces of

4 thermal buoyancy and wnd as Eqn. 7. herefore, Eqn. 5 wll then result n a lnear equaton from whch we can solve for the nternal pressure P. Wth fan law, the straghtforward relatonshp between total pressure dfference, volume arflow rate and motor speed s clarfed n a nonlnear statc equaton (P.Heselberg, 2004). Performance Smulaton he open loop dynamc performances of zonal varaton for ndoor temperature and CO 2 concentraton wthn a day based on the developed C model and IAQ models are demonstrated n Fgure 2(a) and (b). he system started from operatng ponts whch mantan the system behavor (ndoor clmate and ndoor ar qualty) at the requred condton wth exceptonally low horzontal varaton. he system s stmulated by a serous of step changes of the ndoor zonal heat source and zonal contamnant load durng the entre tme horzon. he smulaton s mplemented wth stochastc external temperature, ambent concentraton and wnd speed dsturbances generated from random sources through low-pass flters. (a) (b) (c) (d) (e) (f) (g) (h) Fgure 2: Open loop Dynamc Performance for (a) Zonal emperature and (b) Zonal CO 2 Concentraton; Step Changes of (c) Heat Source (f) Contamnant Source; Stochastc Wnd Speed (e) and external temperature (d) for C model; Stochastc Wnd Speed (h) and Ambent CO 2 Concentraton (g) for IAQ model.

5 It proves to be evdent from the smulaton results, that the conceptual mult-zone models for C and IAQ contan sgnfcant nformaton on horzontal varaton whch s not able to be captured by the sngle zone model wth mean temperature and concentraton, under the crcumstances that the zonal dsturbances changes. DESIGN OF CONROL SYSEM he entre lvestock ventlaton system and ndoor envronment s a Multple Input and Multple Output (MIMO) dynamc nonlnear process and strongly coupled ntrnsc system. It s exposed to external dsturbances and nose and has actuators wth saturaton. Consequently, t s necessary to explore the applcaton of advanced control algorthms, such as the optmal control, predctve control etc. to satsfy the equlbrum between the ndoor ar qualty, thermal comfort and energy consumpton. Lnear Quadratc (LQ) optmal control s a good method for ventlaton control system analyss before applyng other more complex control schemes. he LQ control deals wth a lnear state space model whch s derved from the system lnearzaton around the equlbrum ponts, where the hermal Neutral Zone and anmal demand concentraton are selected to be the reference values. he performance functon for LQ control s: mn N k = 0 [ x ( k) Q x( k) u ( k) Q u( k) ] x ( N) Q x( ) 2 N N (8) where k denotes the sample tme, x s measurable states or controlled varables (zonal temperature and zonal concentraton) matrx, and u s control sgnal or manpulated varables (nlet vents and fan speed) matrx, N denotes the tme horzon, the weghtng matrces Q and Q N are postve defnte and Q 2 s postve sem-defnte, and they are defned as dagonal matrces. he dagonal elements are the nverse value of the square of the maxmum allowed devatons n the states and the control sgnals (G.F.Frankln et al., 998). By usng Dynamc Programmng, we could obtan a lnear tme varyng controller, where the dynamc gan s determned by the Rccat Equatons. he optmal control sgnals are generated from ths lnear feedback MIMO controller takng nto account of the dsturbances varables (external temperature, heat source, ambent concentraton and contamnant load). hen, ths generated control sgnals are nput to the process to predct the zonal temperature and concentraton. he sensor and motor dynamcs s relatvely fast compared wth the entre system response and could be neglected. (a) (b) Fg. 3 Close Loop Dynamc Performance wth Feedback Gan for (a) Zonal emperature, (b) Zonal CO 2 Concentraton.

6 Fgure 3 llustrates the close loop dynamc performances of the ndoor temperature and ar concentraton wth a lnear feedback gan for anmal thermal comfort and ndoor ar qualty by applyng the same varaton of the dsturbances for open loop smulaton as shown n Fgure 2. A certan amount of tral and error s requred wth an nteractve computer smulaton before a satsfactory desgn s obtaned, for example, one of possbltes s to adjust the weghtng matrx. hrough comparng the close loop and open loop of the smulaton results, we could recognze that the system wth controller has much shorter response tme to reach the steady state and has the capablty to reject the ndoor and outdoor dsturbances oscllaton and nose relatvely by adjustng the ar flow rate through eght nlet vents and four exhausted fans. DISCUSSION Amng at mprovement of performances and optmzaton of energy, the man achevement of ths work s the successful applcaton of the LQ optmal controller for lvestock ventlaton systems analyzed by a conceptual mult-zone method. he results prove to be frutful that the desgned control scheme s feasble and flexble to satsfy the purpose. Some parameters of the mathematcal models wll be dentfed through experment n a real scale lvestock barn equpped wth hybrd ventlaton systems. he nterfacal mxng parameters whch descrbe the arflow nteracton of nternal zones wll be calbrated wth expermental measurement by usng gas tracer. Advanced control methods, dynamc dsturbances models, estmator for weather condton, augmented control sgnals for more actuators such as the operaton of the heatng system for cold weather, ar-condtonng systems for warm weather, shade screen for solar radaton wll be appled n future and the result wll be compared wth those obtaned wth currently used classcal PID controller. AKNOWLEDGEMEN he authors would lke to acknowledge fnancal support from the Dansh Mnstry of Scence and echnology (DMS) and Center for Model Based Control (CMBC) wth Grant number: / BIBLIORAPHY G.F.Frankln, J.D.Powell and M.L.Workman (998). Dgtal Control of Dynamc Systems. 3 rd edton. Readng Mass.: Addson-Wesley. J.A.Clark (98). Envronmental Aspects of Housng for Anmal Producton. Butterworth Henemann. England. J.P.Bourdouxhe, M.Grodent and J.Lebrun (998). Reference Gude for Dynamc Models of HVAC Equpment. Amercan Socety of Heatng, Refrgeratng and Ar-Condtonng Engneers. Atlanta. K.Zhou, J.C.Doyle and K.Glover (996). Robust and Optmal Control. Prentce-Hall. New Jersey. P.Heselberg (2002). Prncples of Hybrd Ventlaton. IEA Energy Conservaton n Buldngs and Communty Systems Program, Annex 35: Hybrd Ventlaton n New and Retroftted Offce Buldng. P.Heselberg (2004). Natural and Hybrd Ventlaton. Aalborg Unversty. Denmark.