ON-LINE ESTIMATION OF THE VENTILATION RATE OF GREENHOUSES J. Bontsema *, E.J. van Henten *, J.G. Kornet *, J. Budding ** and T. Rieswijk ** * Agrotehnology and Food Innovations B.V., Greenhouse Tehnology Group, Wageningen, The Netherlands, e-mail: jan.bontsema@wur.nl ** Priva B.V., De Lier, The Netherlands Abstrat: Using an unknown input observer, with an output linearising feedbak, an online estimator for the ventilation flow or rate is developed for natural ventilated greenhouses. The paper shows how to design, implement and tune suh an estimator in pratie and shows that it performs well. Furthermore the pratial value for the grower is disussed. opyright IFA Keywords: greenhouse limate, observer, ventilation rate, unknown input observer.. INTRODUTION In modern greenhouse hortiulture the limate in the greenhouse is ontrolled by a sophistiated greenhouse limate omputer. The role of the grower is to define among others temperature trajetories, arbon dioxide setpoints and relative humidity bounds, in suh a way that during the growing season the rop is maintained in an optimal ondition and the rop prodution is maximised. The limate omputer will then realise the by the grower desired limate. Beside the heat supply and the arbon dioxide supply, a main variable to ontrol the inside limate in a greenhouse is the natural ventilation through the windows in the roof of the greenhouse. However the ventilation is ontrolled by adjusting the window openings and is heavily depending on the outside wind onditions and the differene between inside and outside temperature. An easy method to estimate on-line the ventilation would give the grower valuable insight in the proess of his greenhouse limate. A model an desribe ventilation in a greenhouse, see f.i. (Jong, 99). These models are based on f.i. hourly averages of measurements of greenhouse limate variables, but these models are however applied on a timesale of minutes. Another approah is to alulate ventilation from stati mass or energy balanes. Sine in pratie the greenhouse limate is never in steady state, due to the external disturbanes, the error is large due to negleting the dynami storage term. If one uses a dynami mass or energy balane, this problem is solved, but on the other hand one is differentiating a measured variable, introduing amplifiation of the measurement noise. For off-line measurement one uses so-alled traer gas methods, see (Sherman, 99), however these methods an hardly be used in pratie during rop prodution. The objetive of this paper is to show how to estimate the ventilation rate in a greenhouse prodution system, using an observer tehniue for estimating unknown inputs of a system. Using a non-linear transformation, similar to output feedbak linearisation, the non-linear system is transformed into a linear one, whih makes it possible to use a linear observer design tehniue. After designing the linear observer, the inverse transformation is used to ahieve the final non-linear observer. In setion the observer theory is reapitulated, in setion 3 an unknown input observer is designed for a salar system, in setion 4 an observer is designed for a bilinear system using an output feedbak linearisation. In setion the greenhouse dynamis is
desribed and ompared with measurements from a real greenhouse. In setion 6 the proposed method is applied to the greenhouse system and in setion 7 the results of new method are ompared with the outome of a traer gas experiment. In setion 8 the pratial use of the method is disussed and in setion 9 some onlusions are drawn.. OBSERVER DESIGN It is assumed that the original proess has the following form: x = Ax+ Bu, y = x, n m x() = x, x R, u R, y R p An observer, the so-alled Luenberger observer, mentioned after his inventor has then the following form (Luenberger, 966; Luenberger, 97): xˆ = Axˆ+ Bu + L( y yˆ), yˆ = xˆ, xˆ() = xˆ () () The observer is atually a opy of the model of the original system, but sine the initial onditions of the system and observer are in general different, the outputs will be diiferent. The observer is therefore driven by the differene of the outputs of the system and the observer. If finally yt ˆ( ) yt () then xˆ( t) x() t. The uestion is how to determine L. For this we onsider the error between the state of the system and the state of the observer, et () = xt () xt ˆ( ), using () and () it follows that: et () = ( A Let ) () et ( ) = x xˆ (3) If L is hosen in suh a way that the matrix A-L has all its eigenvalues in the left half omplex plane, then independent from x xˆ, et (). Observers an also be defined for non-linear systems, the observer gain will then in general depend on the state (Dohain, 3). 3. UNKNOWN INPUT OBSERVER Observers originally were designed to estimate the non measured states. In reent years observer design is also used to estimate unknown inputs of a system. For simpliity we onsider a salar system: where ut () assumed that x () t = ax() t + bu() t yt () = xt () (4) is an unknown input. Furthermore it is ut () is a slowly varying signal, so ut (). Defining z = x and z = u, the system an be written as: d z a b z z = z () This system is similar to the one desribed by en. l (). Using an observer, with observer gain L = l it is easy to alulate that the transfer funtion from the unknown u ( ) to the estimated û ( ẑ ) is given by: Defining: z Gs () bl = s + ( a+ l ) s+ bl (6) a+ l ω = bl, ξ = (7) ω the transfer funtion is in standard seond order form. We an therefore give a good reipe for tuning the observer. For a good estimate of the unknown input signal, whih we assumed to be slowly varying, the transfer funtion, for low freuenies should have a gain lose to and a phase lag lose to zero. One an obtain suh a result by hoosing ξ =.77 and ω to times the dominant freueny in the signal to be estimated. 4. OBSERVER FOR BILINEAR SYSTEMS A speial lass of non-linear systems are the so-alled bilinear systems, whih have in the euations a produt between the states and inputs. onsider the following salar system: x () t = ax() t + bx() t u() t yt () = xt () (8) Defining a new input vt () = xtut () (), en. (8) is transformed, by a non-linear transformation into a linear system with the new input vt (). This nonlinear transformation is atually an output feedbak linearisation. For this transformed system the standard observer as desribed in setion 3 an be used for the unknown input vt (), giving an estimation vt ˆ( ) of vt (). The estimation û is then vˆ given by the bak transformation uˆ =. xˆ. GREENHOUSE DYNAMIS The energy balane for a Venlo-type greenhouse is given by (Henten, 994) dt = Qpipe Qvent Qtrans +Q rad (9)
where T is the temperature inside the greenhouse,,, Q and Q are respetively the heat Qpipe Q vent trans rad supply by the heating pipes, the energy loss due to natural ventilation, energy loss through the greenhouse over and the heat load due to the global radiation of the sun. is the ombined heat apaity of the greenhouse, the rop and the onstrution of the greenhouse. The heat supply is desribed by: with pipe, Q = T T ) pipe pipe, ( pipe () the heat transfer oeffiient between the heating pipes and the greenhouse. T is the temperature of the heating pipes. The energy loss due to the ventilation is: with pipe Q = φ ( T T ) () vent vent out the heat apaity of, φ vent is the ventilation flux and Tout is the outdoor temperature. The energy loss through the greenhouse over is given by: Q = ( T T ) trans ov out () where ov is the heat transfer oeffiient of the greenhouse over. Finally the heat load due to global radiation is: Q rad = I (3) with rad is the fration of the global radiation, responsible for the heat load on the greenhouse. I is the global radiation. This energy balane is simulated using measured data for the ontrol and external disturbanes. These data were reorded on a ommerial greenhouse in the western part of the Netherlands. The rop was a fully produing tomato rop. For the ventilation flux a model of (Jong, 99) is used. In this model the ventilation flux is funtion of the wind speed and diretion, the inside and outside temperature, the window opening and the onfiguration of the ventilation windows. Furthermore this ventilation model is only valid for greenhouses of Venlo-type. The ontrols on day 7 (Marh th, 4) are shown in figure. rad pipe temp. () window opening (%) sreen 8 6 4. Fig.. The external disturbanes ating on the greenhouse on day 7. The external disturbanes are shown in figure. radiation (W/m) Temp. outside () Windspeed (m/s) 6 4 4 Fig.. The external disturbanes ation on the greenhouse on day 7. The results of the simulated temperature in the greenhouse are shown in figure 3. The opening of the so-alled energy saving sreen, whih is not well modelled, auses the large deviation between simulated and measured temperature around o lok in the morning. However in our researh we did not fous on a perfet fit of the model on the measured data, also for the reason that we don t want that the model is too muh aommodated to the ventilation model of (Jong, 99). inside temperature () 3 9 8 7 6 simulation measurement 4 3 time (hours) Fig. 3. Simulated and measured temperature of the greenhouse on day 7.
6. OBSERVER FOR THE VENTILATION RATE ˆ vˆ φ = (9) ( ˆ T Tout ) The model for the greenhouse temperature as defined in setion 6 an be rewritten as: dt pipe, + This proedure has been applied in a simulation, over = T where the ventilation flow in the simulation model is alulated aording (Jong, 99), T, meas is in this ase of ourse the simulated temperature. The ( T Tout ) φvent + (4) results are given in figure 4. ( T + T + I) pipe, pipe over out rad Defining () = ( pipe, Tpipe + overtout + rad I) vt () = ( T T ) φ, a = out vent pipe, + over b =, euation (4) an be rewritten as: Note that dt () and alulated and estimated ventilation flow (m/s). x -3.. estimated ventilation flow alulated ventilation flow = at + bv() t + d() t () Fig. 4. The estimated and alulated ventilation flow of a greenhouse on day 7. is a measured disturbane and the transformation vt () = ( T Tout ) φvent has the non-linear system of en. (4) transformed into the linear one of en. (). For the system of en. () the method of setion 3 an be applied. The estimator for the ventilation flow or atually for the transformed ventilation flow is then given by: dtˆ = atˆ ˆ () ˆ + bv + d t + l ( T, meas T ) (6) dvˆ = l ˆ ( T, meas T ) where is the measured inside T, meas temperature, whih is available form the greenhouse limate omputer. From the measurements from the ommerial greenhouse it turned out that a reasonable hoie for the parameters a and b is: From the figure it follows that we have a perfet estimator, only in the beginning there is some deviation, mainly due to the fat that the observer starts at a different initial value than the simulation model. In the following figure the estimated ventilation flow, based on the real measurements of day 7 is given and ompared with the alulated ventilation flow aording to (Jong, 99). estimated and alulated ventilation flow... 3 x -3 estimated alulated 4 a =.9 and b= 3.3 (7) The gains of the estimator or observer are obtained aording setion 3 as l =.39 and l = 8.3333 (8) From en. (7), whih in pratie will be alulated on-line aording to the sample instants for the measurements in the greenhouse as defined on the limate omputer, ˆ φ an be alulated by transforming bak ˆv : 3 4 6 7 8 Fig.. The estimated and alulated ventilation flow of a greenhouse on day 7. Although there is more differene between the estimated and alulated ventilation flow ompared to the simulation, the order of magnitude is the same, whih gives good onfidene that the new method is orret. Note that the outome of the new method need not to be the same as the alulations from (Jong, 99), sine the latter is also only a model and not reality.
The new method an be seen as a result of sensor fusion, sine the measurements of a set of four sensors, respetively a radiation sensor and three temperature sensors (pipe, inside and outside) are used to alulate a new variable, namely the ventilation flow. On the other hand the new method an also be seen as an intelligent or soft sensor, besides measurements also knowledge in the form of the energy balane of the greenhouse is used. In the next setion the new method is ompared to soalled traer gas experiments. 7. TRAER GAS EXPERIMENTS At the hortiultural researh station in Naaldwijk, the Netherlands, two lassial traer gas experiments with arbon dioxide were performed to evaluate the proposed method. For these experiments an empty greenhouse with a onrete floor was used in order not to have disturbing soures and sinks of arbon dioxide. With losed windows pure O was supplied up to a onentration of ppm or higher. Then the supply is stopped and the windows are opened. This has been repeated for several window openings. The measurements of the seond experiments are shown in figure 6. O (ppm) Window opening (%) 3 3 4 4 8 6 4 3 3 4 4 time (minutes) Fig. 6. The measured O -onentration and the window openings at the leeward side. For an empty greenhouse and no supply of arbon dioxide, the arbon dioxide balane is written as: do, in = ( O, in O, out ) φvent () Where O and O are the inside and outside,in arbon dioxide onentration and Assuming that is a onstant. is onstant, what is a reasonable assumption during the experiments, the differential euation for the differene between inside and outside arbon dioxide onentration, O, is: d O,out O,out The solution of this euation is: = Oφvent () O () t = O () e t φ() vdv () The average ventilation flow on the i th sampling interval is then given by: φ ( t ) = ln O ( t ) ln O ( ti ) (3) i i In figure 7 the estimated ventilation flux aording to the new method and the alulated flux aording to the traer gas method are ompared. O (ppm) 3 x -3 Vent. flux (m.s-) vent. rate (hour-) - 3-3 Time (seonds) Fig. 7. The deay of the O -onentration in ase of a window opening of %, the estimated ventilation flux by an observer ( ) and the estimated flux based on the O deay (---). The figure at the bottom shows the ventilation rate. Both methods give similar results, whih show that estimating the ventilation flux, or rate using the unknown input observer with output linearising feedbak is a good method. 8. PRATIAL USE OF THE ESTIMATION The method gives an estimation of the ventilation flux, from whih the ventilation rate easily an dedued. The ventilation rate says how often the inside in a greenhouse is refreshed in one hour. Growers prefer to know the ventilation rate instead of the ventilation flux. The method gives a good estimate for the ventilation rate, but this is not always interesting for the grower. He would also like to have insight in how muh energy he loses by ventilation, how muh arbon dioxide is lost by ventilation and how muh moisture has been removed by ventilation. One one has estimation for the ventilation flow, this is easily alulated. In figure 8 the estimated ventilation rate on June 9 th 4 is shown, together with the applied window openings.
Vent. rate, hour- Window opening (%) 4 3 Time (hour) 8 6 4 Time (hour) Fig. 8. The estimated ventilation rate (upper part) and the window openings at the east side ( ) and at the west side (--) (lower part). From figure 8 it an be seen that the windows were opened in the beginning of the night and when the sun starts to shine. When the solar radiation is at its maximum, the windows at both sides of the roof of the greenhouse are maximally opened. It is also lear that the ventilation rate is high at these moments. Radiation Energy O Moisture 6 4 4 x -6 4 x - 4 Time (hour) Fig. 9. The global radiation, loss of energy, loss of O and removed moisture on June 9 th 4. From figure 9 it follows that the energy loss is large at moments when the ventilation rate is large. In ase of high radiation this is neessary in order to redue the heat load from the sun and also at this moment large ventilation has a good effet on removing the exess of moisture, so the rop will have a good transpiration. On the ontrary the ventilation has a negative effet on O onentration, while at high radiation levels, a lot of O is needed for a good prodution of the rop. 9. ONLUSIONS An unknown input observer with an output feedbak linearisation is a good and simple method for estimation the ventilation flow or rate in natural ventilated greenhouses. The method does not depend on wind measurements (inaurate, (Knoll, 4)), window onfiguration and works for all types of greenhouses. The method is easy to implement and to tune for the partiular greenhouse. Furthermore the new method gives the grower valuable insight is the energy and mass flows aused by ventilation. The new method for estimation the ventilation rate is an example of sensor fusion and also an example of an intelligent or soft sensor. AKNOWLEGMENTS This researh is sponsored by the Duth Ministry of Eonomial affes under projet number EETK and by the Duth Hortiultural ounil (Produktshap Tuinbouw) under projet number 73. REFERENES Dohain, D. (3). State and parameter estimation in hemial and biohemial proesses: a tutorial. Journal of Proess ontrol, 3, 8-88. Henten, E. J. v. (994). Greenhouse limate management : an optimal ontrol approah, PhD Thesis Wageningen University. Jong, T. d. (99). Natural ventilation of large multispan greenhouses, De Jong, PhD Thesis Wageningen University. Knoll, B. (4). Personal ommuniation. Luenberger, D. G. (966). Observer for Multivariable Systems. IEEE Transations on Automati ontrol, A-, 9-97. Luenberger, D. G. (97). An Introdution to Observers. IEEE Transations on Automati ontrol, A-6, 96-6. Sherman, M. H. (99). Traer-Gas Tehniues for Measuring Ventilation in a Single Zone. Building and Environment,, 36-374. Furthermore at night the ventilation was used to remove moisture, but as an be seen also energy will be lost.