Development and Testing of an Inside Temperature Model for a Microcomputer-Controlled Greenhouse

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DEVELOPMENT AND TESTING OF AN INSIDE TEMPERATURE MODEL FOR A MICROCOMPUTER-CONTROLLED GREENHOUSE P . Otto*, K. Sokollik*, :;: Jllllf ' l/llII

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Wernstedt* and M. Diezemann **

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Abstract. The articl e present s a model set up on the basi s of me~ured data fo r the automat i c control of the ins ide c l imat e of gr eenhouses hav ing an area of about 4000 m . The mode l consists of tw sul:xrn::le l s, one for t he vari abl es 'tanperature' and ' Global radiat i on ' rel ating t o the outside climate, and t he other f or the var i ous heat ing systems. The latest methods of design of experiments (stat i cs , dynamics) and par ameter estimat i on t aking i nto conside ration model restrictions have been used fo r devel oping t he model . Ve ri f i cati on of t he mod~l i n pract i ce was car r i ed out by desi gning a tolerance r ange cont rol coupl ed with a predicti on of t he values of t he quant i ties relat ing to t he outsi de cl imate . The r esul ts obtai ned are s atisfactory and are being presented in this w rk. Keywords. Agriculture; greenhouse; heat systems; difference equations; ident i f i cation ; temperature control.

INTRODUCTION In the present energy situation the economical use of heating energy in greenhouses, which figure among large consumers, has become a task of pre-eminent importance. That's why not only the presetting of time-variant climatic conditions (set points) bringing on a maximum yield, but also the adjustment of these set points including all available ways of control with minimum amount of energy are extremely important. This purpose is served by realizing a conr trol strategy which based on an inside temperature prediction model and taking into account the relatively high lag time and dead times of the subsystems of the greenhouse, permits to take control decisions in such a good time that an essential saving of heating energy is achieved. Thus, the centre of our investigations was the development of a simple greenhouse inside temperature model which may be used in combination with a tolerance band control algorithm on microcomputer basis. Although greenhouses are to be regarded as time-variant systems we have done without an adaptive control conception in contrast to the approach described by Udink ten Cate (1981), since one main reason for the timevariant behaviour is already included by the prediction of the outside climate pa-

2045

rameters, and since the adaptation of the greenhouse mo del is possible as well. The model has been designed for a greenhouse type G 300, a fourspan standard design with a cultivated area of 3740 m2 • Its heating systems consist of a tube heating and 18 warm-air fan heaters and are designe d for a flow temperature of the heating water of up to 12 0 °c (Otto and others, 1981). DESCRIPTION OF THE SYSTEM The greenhouse may be regarded as an air conditioning system with adjustable and non-adjustable influence factors (input variables) and with inside climate parameters (output variables) which depend on them and which are of importance for yie~ information. The central point of our further considerations will be the inside temperature being this inside climate parameter which is determining for the amount of vegetable yielded in a greenhouse. Only those variables affecting the inside temperature will be taken into account as influence factors. These are the following: -number of the warm-air fan heaters in operation adjustable

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-position of the valve of the tube heating -flow temperature of the heating medium

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input var i a bl es

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2046

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non-adjustable input variables There is no need to include the ventilation flaps, since the heating systems are only operated in closed state. All other outside climate quantities are being regarded as stochastic disturbance variables. The prediction of inside temperature values presupposes the knowledge of prognostication values for the outside climate parameters which are to be obtained by means of a corresponding prediction model. Consequently, the greenhouse inside temperature model is composed of two submodels, as shown by the structure represented in fig.1. -outside temperature -global radiation

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Fig. 2. Course af the outside temperature

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fan heaters tube heating flow temperature venlilation flaps

OUTSIDE CLIMATE QUANTITIES

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Fig. 1. Structure for the inside temperature model SIGNAL MODELS FOR THE OUTSIDE CLIMATE QUANTITIES 'TEMPERATURE' AND 'GLOBAL RAD IATION' The influence factors 'temperature' and 'global radiation' varying according to the season and to the time of the day, they are subject to so-called annual and daily temperature courses which are composed of periodical shares. Therefore, the respective signal courses may be described by time series on the basis of sine and cosine functions, respectively. The results of a regression analysis have shown that the daily courses of the outside temperature (TA) and of the global radiation (GS) can already be approximated by means of simple time series models according to Eq.1 and Eq.2, as can be seen from fig.2 and fig.3,(Wernstedt, Mezynski,1979). 2

TA=9, 05-2, 05 cos Tt + 0,05 cos

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Fig. 3. Course of the global radiation

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I inside temperature

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The short-term prediction which is necessary for the intended control strategy requires a permanent adaptation of the mo dels . This may be achieved by assigning to the standard courses, which have been fixed a priori and which correspond to present wheather condit ions, the polynomial time series set-ups obtained by a recursive filtration of the actually measured values or as a result of a weighted recursive regression. Prediction will then be made on this basis. SUBMODELS FOR THE MAIN PARAMETERS INFLUENCING INSIDE TEMPERATURE Profound investigations have revealed that the application of experimental-statistical models is a dv antageous compare d to theoretical model conceptions especially as for their applicability for microcomputers (otto and others, 1981). The basic idea of the experimental total mo del starts out from the assumption that the outside temperature is consi dered to be the reference quantity for the inside temperature, of which it represents a primary component, too. All other influence

2047

Tes ti ng o f an I n sid e Te mp e r a tur e Mo d e l

factors produce the temperature difference which is responsable for the temperature gradient between inside and outside in the sum. On the basis of the cooling and heating curves plotted it was stated that the influence exerted by the heating systems and by the outside climate quantities may be determined in the form of lag elements including dead times. Thus, the basic structure of the experimental inside temperature model can be represented as in fig. 4. InSI(le tpmperalure TA

global

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Fig. 4. Submodels for the inside temperature mo del The model parameters for the heating systems were identified on the basis of active experiments with optimal test signal sequences carried out in a greenhouse (Otto, Wernstedt, 1978). The number of the warm-air fan heaters and the entrance valve of the tube heating had been changed according to test signal sequences obtained from modified PlackettBurman plans. This permitte d a suboptimal estimation (in the senae o~ D-optimality) of the interpolation no des of a non-linear weight function mo c el ( Hammerstein structure with a non-linearity of second order). Parameter estimation for the flow temperature mo del (table 1) was then made in an analogous way. The submo dels for global radiation and outside temperature have been calculated on the basis of drift measurements, with the heating systems being out of operation. Estimate d Parameters for the Submodels Subsystem V T (min ) LH 23,4 0 ,32 SH 12 0 0 , 03 28 TV 0, 095 GS 23,5 0, 05 1 25 TA TABLE 1

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EXPERIMENTAL GLOBAL MODEL It must be said that the parameters calculated still show some errors, which is due to the extremely unfavourable statistical characteristics of the data for global radiation and outside temperature (strong correlation and slight modifications during the observarion period resulting in badly conditioned information matrices) and also to the fact that the influence exerted by the outside temperature cannot be completely eliminated (no constant test conditions). This was confirmed by the results of an active test plan ca~ried out over a 48-hour time period, in which all stages of the adjustable influence factors 'warm-air fan heaters' and 'tube heating' which may occur in normal operation, as well as flow temperature changes have been realized within a process-close workable control range. In fig. 5 the inside temperature courses both calculated and measured are being compared with each other in dependence of the various influence factors. estimated inside temperature measured inside temperatu-e outside temperatu-e global radiation flow temperature

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Fig. 5. Comparison of the measure d and estimate d inside temperature in dependence of the input variables The evaluation of the results obtained permits the following statements: 1. The course of the estimated inside temperature presents, according to its tendency, a relatively good conformity with the measured values, which can be regarded as a confirmation of the model structure assumed. 2. The relatively large, but almost constant deviations suggest that especially those parameters (gains) responsable for the static behaviour still show

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2048

some errors. ). Particularly large deviations also turn up when global radiation is effective. Here, the gain constant had to be basically cheoked up. 4. At the reversing points of the tube heating deviations are found making clear that because of the frequent reversals also the dynamics of the tube heating has to be taken into consideration using a transfer element of the form -pTt (3) GSH(p) - V • eT 1 + p SH The aim of our further investigations was to specify the model parameters on the basis of the available data using already known and newly developed identification methods. PARAMETER ESTIMATION USING THE METHOD OF DIRECT REGRESSION The most simple identifioation method for specifying the model parameters is that of direct regression. The set-up for a oorresponding difference equation model reads: outside temperature global radiation

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b 2 ·z -1 + -1 U2 (z) 1+a 2 z

warm-air fan heaters

flow temperature (4)

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The parameters partially turn out to be nonsensioal for system theory (e.g. false signs for some coupled parameters), what is conditioned by the strong auto- and cross oorrelation of the influence factors and the bad condition of the information matrix resulting from this (otto and others, 1981). Furthermore, it is an essential disadvantage that only the ooupled parameters oan be estimated and that it is practically scarcely possible to establish a oonnection with the gains and the time constants of the particular submodels.

PARAMETER ESTIMATION INCLUDING A PRI OR I KNOWLEDGE

tube heating b S·z -1 + Z(z) + -1 US(z) 1+a z S After having effected the common transformat ions we get the following model set-up for the difference equation: x(k)-

• a 1 a 2a)a 4 a S u 1 (k-i) - outside temperature u 2 (k-i) - global radiation u)(k-i) - number of the warm-air fan heaters u (k-i) - flow temperature 4 uS(k-i) - valve position of the tube heating - inside temperature x(k-i) z(k) - disturbance; n(k) -filtered disturbance Although a very good reproduction of the measured inside temperature course may be obtained by means of the parameters asoertained through regression, this model is not suitable for prediction.

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(S)

Some a priori information about the model parameters being already available from the preliminary investigations carried out, it was rather practicable for evaluating the test plan to use an algorithm specifically developed for model estimation with strongly correlated input signals. This algorithm employs the optimization method of ROSENBROCK together with penalty shifting functions (Polak, 1971; Selfert, 1984). Since in this case, the goal funotion is newly calculate d in each searching step it is possible to substitute into Eq. S the parameters of the subsystems for the coupled parameters and to directly estimate them. Eq. S then becomes:

Testing of an Inside Temperature Model

x(k) • u1(k-1)b1+u2(k-2)b1(a2+a3+a4+a5) + ••• -X(k-5)(a1a2a3a4a5) • (6) It is also possible to formulate a set-up using the single difference equations of the subsystems if suitable initial values for the partial output quantities can be given. For example, for a 2/1-system the set-up could read: x 1 (k-1) - x 2 (k-1)-0 x 1 (k) - a 11 x 1 (k-1)+b 11 u 1 (k-1) (7 ) x 2 (k) m a 21 x 2 (k-1)+b 21 u 2 (k-1) x(k) = x 1 (k) + x 2 (k) • Contrary to Eq. 6, the number of the parameters to be estimated decreases by about two thirds. From some theoretical considerations appropriate limitations for the possible range of values of the parameters to be estimated have been set and fixed in the form of inequat ions. Table 2 shows the tolerance bands used and the improved parameters. TABLE 2 Tolerance Ranges of the Parameters new parameter values Tolerance ranges VTA 0,9< VTA< 1 0,95 VGS 0,1< VGS< 0,75 0,109 0,262 VLH 0,25
20,4 10,5 29,3 44,5

20 < TTA < 35 10
min min min min

In fig. 6 there are represented the execution procedure and the results of evaluation of the test. - - estimated TI

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Fig. 6. Course of the measured and estimated values of the inside temperature (including a priori information) As the experimental model does not require the type of heating, the covering used and the like to meet some special requirements, but only takes the connections between input variables and inside temperature into account, the approach described here is

2049

also applicable to any other greenhouse. For getting the data which are necessary for the parameter search algorithm it is recommended to use optimal test signal sequences for the adjustable input quantities. A SIMPLE TOLERANCE BAND CONTROL SYSTEM FOR TESTING INSIDE TEMPERATURE MODEL The following considerations and also properties of the process examined are of importance for designing a suitable inside temperature control: 1. The time constants of the process are relatively large (10 to 57 min), thus making it difficult to react quickly to set point deviations. 2. The possibilities of location of the heating systems are very limited. 3. There exist a vertical and a horizontal temperature gradient in the greenhouse. 4. The tube heating is not suitable for short interventions in the control action by reason of the small influence exerted on rapid inside temperature changes. Therefore, we suggest to determine by a verification model calculation the control instruction suitable to eliminate the set point deviation to be expected, using already calculated inside temperature prognostication values. The future outside climate quantities may be ascertained by means of the signal models already desoribed. Thus, the total model permits to calculate the prognostication value for the inside temperature, with the regulated quantities being kept constant. After a tolerance band check-up, the kind and the contribution of the regulated quantities are determined by a verification calculation. BeSides, the instantaneous value of the objective quantity is being kept within a rought tolerance band. The band widths have to be fixed in consideration of plant-physiological aspects. The set point of the inside temperature may be kept constant or adjusted in dependence of the light. Fig. 7 shows a rough schema of the control conception. If a set point deviation is detected dur.mg the prognostication period, the algorithm will first calculate the number of warmair fan heaters which have to be switched

2050

P . Otto et ell .

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Fig. 7. Schema of the control conception for testing inside temperature model on or off for eliminating this deviation. If the maximally possible response of this regulated quantity reveals to be insufficient, there will also be determined the necessary reduction or rise of the flow temperature. The tube heating will be reversed into the other state only if a second even larger tolerance band is exceeded or not reached, respectively. If the instantaneous inside temperature is lying within the range detrimental to plants, all regulating elements will be set to the corresponding maximum (minimum). The verification of the model and the control algorithm was carried out by means of an example simulated on a computer type EC 1040. The width of the first tolerance band had been chosen to be ± 1.8 degrees and ± 3.0 degrees for the second one (see fig. 8).

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t 10

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ing systems are represente d for a simulation period of 36 hours. CONCLUSION An experimental process model for predicting the inside temperature in a greenhou~ has been set up. On the basis of this model it is possible, with regard to the relatively long dead times and inertias et the greenhouse subsystems, to take control decisions for the heating systems in such a good time that energy savings can be achieved. The verifications made of the total model have proved that the structure assume d is right and that good conformity between system and model behaviour can be obtained when using the model parameters being specified for the respective greenhouse. The model's suitability tor controlling the inside temperature was verified by means of a simulated example of a simple tolerance band control. Further investigations concerning the control realize d by microcomputers are being conducted in close cooperation between the Ilmenau Institute of Technology, Section of Technical and Biome d ical Cybernetics and the IfG GroBbeeren of the Academy of Agricultural Sciences of the GDR, with some first results already being achieved by Mahlendorf und Engmann ('1981), Engmann, Mahlendorf and Diezemann (1984). REFERENCES U., Mahlendorf, R. and Diezemann, M.(1984). Control strategie for a microcomputer-controlle d greenhouse (Part 2: Modebased development of control algorithm and simulation). Preprints of the 9. IFAC-Congress, Budapest, Hungary 1984 Mahlendorf, R. and En gm ann , U. (1981). Pulsbreitenmodulierte Innentemperaturregelung mit Signalvorhersage auf K 1510. Forschungsbericht TH Ilmenau, unveroff. Otto, P. and Wernstedt, J. (1978). Entwurf und Anwendung von Testsignalfolgen zur Identifikation nichtlinearer dynamischer Systeme. msr, 21 (1978) Otto, P., Soko11ik, K., Se ifert, A., Wernste dt, J. and Diezemann, M. (1981). Entwicklung eines Innentemperaturmodells fUr den Einsatz in Gewachshausern zur Anwendung von Mikrorechnern. Forschungsbericht TH Ilmenau, unveroffentllcht Polak, E. (1971). comautational Methods in 07timization. Aca emIc Press, New York London Seifert, A. and Wernstedt, J. (1984). Development and testing of methods of parameter estimation of dynamic systems in consideration of restrictions. Preprints of the 9. IFAC- Congress, pest, Hungary 1984 Udink ten Cate, A.J. and van de Vooren,~. (1981). Adaptive Systems in Greenhouse Climate Control. VIII. IFAC Congress, Kyoto 1981, Late Papers, 72.1,pp.9-15 Wernstedt, J. and von Mezynski, W.(1979). Entwicklung von Signalmo dellen - Methoden und Anwendungen. 24. IWK der TH Ilmenau (1979), H. 1, pp. 183-186 En~ann~

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Fig. 8. Course of the inside temperature for the tolerance band control The prognostication values for the inside temperature were calculated by means of the experimental total model by using the measured outside climate values. In fig.8 the inside temperature course and the control decisions taken for the single heat-