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ÿþEFITA 2003 Conference 5-9. July 2003, Debrecen, Hungary OPTIMAL MANAGEMENT OF GREENHOUSE ENVIRONMENTS José Boaventura Cunha and J. P. de Moura Oliveira, jboavent@utad.pt UTAD  Universidade de Trás-os-Montes e Alto Douro, Dep. Engenharias CETAV  Centro de Estudos e de Tecnologias do Ambiente e Vida 5001-911 Vila Real, Portugal Abstract: Greenhouse construction and operation have developed considerably during the last decade, mainly in northern European countries. These improvements took place in several areas, such as the development of new building techniques and actuators or the modelling of plant physiological processes and greenhouse climate. Presently, due to economic and environmental requirements, there is still a demand to achieve an optimal management of the greenhouse environment, in order to increase the efficiency of the crop production process. From the greenhouse grower point of view it is intended to maximise the profits, which is a very difficult objective to achieve in practice. This is because growers must make many complex decisions. These decisions are related to the capital investments they have required, the establishment of tactical plans involving the selection of crops, or the use of manual labour, and, a crucial issue, on how to operate the actuating equipments in order to achieve the greenhouse environment dynamical optimisation from an economic return point of view. The purpose of this article is to present methods and software tools for automating an optimal decision process for controlling the greenhouse climate, to illustrate their potential and to point to the problems that remain. Keywords: Dynamic optimisation, Greenhouse climate, Greenhouse models 1. Introduction The management of a greenhouse crop production process must be performed at different hierarchical levels and time bases, such as for the slow crop planning process and the faster processes of inside climate control. Today, practical applications are limited to the automation, in an optimal way, of the aerial and root environment control processes and large time scale decisions are made manually (Challa, 1999; Van Straten et al, 2000). The automation of an optimal decision process for regulating the climate inside a greenhouse is a very complex task. Below is described an optimal management and control greenhouse climate concept which emphasises its potentials and limitations. The analysis is directed towards the dynamic models that must be employed, the choice of cost functions and constraints, and the implementation of climate control algorithms. Basically, an optimal management and control greenhouse climate system have the components shown in figure 1 (Pohlheim and Hei² ner, 1997). 559 EFITA 2003 Conference 5-9. July 2003, Debrecen, Hungary Grower experience Grower experience Optimisation level Optimisation level Specified Specified Climate and control Climate and control trajectories trajectories constraints constraints Optimisation Weather Optimisation Weather + + Profit cost function - P Profit cost function - P Prediction Prediction xc xc Crop models Crop models Climate Control level Climate Control level Climate Climate Weather Weather Weather Weather models models models models ue ue Computed Computed Computed Computed trajectories trajectories trajectories trajectories Controller Controller Controller Controller Climate state Climate state Climate state Climate state Plant Response Plant Response Plant Response Plant Response + + uc uc xg xg ventilation,heating ventilation,heating ventilation,heating ventilation,heating ... ... ... ... Tair,,Rhair, CO2 Photosynthesis Tair,,Rhair,,CO2 Photosynthesis Tai r Rhai r CO2 Photosynthesis Tai r Rhai r, CO2 Photosynthesis ... ... ... ... ... ... ... ... Greenhouse- Plant system Greenhouse- Plant system Figure 1. Greenhouse management and control system architecture This management and control concept requires the use of at least two hierarchical levels, referred as the control and optimisation levels. Also, grower experience must be used to specify crop planning, plant requirements, among other management decisions. Here, we only treated system operations linked with the climate control and optimisation levels. The implementation of this type of architecture requires prior knowledge of the influence of the environmental factors over the production quality and productivity in order to perform the economic optimisation strategy, usually the grower profits maximisation. To achieve this goal, an economic cost function is employed and solved through an optimisation algorithm, in order to generate the optimal climate reference trajectories that maximise profits. Generally, the objective is to maximise a cost function that is dependent on the difference between the gross economic return and the operation costs of the climate conditioning equipment, taking into account actuators and crop physical and physiological constraints. In this way, the optimisation algorithm must use information about the predicted yield value and the operating costs necessary to achieve that yield. This paper addresses several software tools needed to implement the described management strategy, namely the crop growth and greenhouse climate models. The performance of these models must be adequate to compute the climate trajectories, which are regulated by the controller in order to achieve the maximum profit. 2. Greenhouse climate management and control The maximisation of the grower net income requires the definition of a performance criterion to simulate the profits achieved for different control actions over time. The maximisation of the function P(u) can be done with this propose (Pohlheim and Hei²ner, 1997; Van Straten, et. al., 2000), tf (1) P(u) = FB xc tf - FC x,u dt ( ) ( ) ( ) +" to where: P is the profit achieved within the time period [to, tf], FB denotes the benefits obtained from marketing the yield at time tf, and FC the costs related with the greenhouse operation. The matrix x=[xc xg] and u=[ue uc] contains the state variables of the crop development, xc, (dry weight, etc.), the 560 EFITA 2003 Conference 5-9. July 2003, Debrecen, Hungary greenhouse climate, xg, (air temperature, etc.), the external inputs, ue, (solar irradiation, etc.), and the control inputs, uc, for heating, cooling, CO2 enrichment, among others. In this context, the optimal management objective is to compute the optimal control actuating signals, uop, in order to maximise the economic cost function, uop(t) = arg (2) max P(u) u subject to constraints in the inside greenhouse climate variables and control inputs, umin < u(t) < umax, and xg min < xg (t) < xg max (3) This approach for computing suitable control inputs in real-time is similar to the MBPC - model based predictive controller approach (Camacho, 1994), where the cost performance function can be optimised by diverse methods, such as by using linear programming algorithms (Philip Gill, et al., 1991). To apply this optimal control approach to horticultural practice requires the use of software models to compare the outcomes for different scenarios. This implies the use of dynamic models to predict inside greenhouse climate, crop development and weather in order to infer the optimal control solution of a set of control sequences. 2.1. Greenhouse Climate Models The greenhouse climate could be described by energy and mass flows equations (Boulard et al., 1993, Bot, 1991), which are generated by the differences in energy and mass content between the inside and outside air or by the control or exogenous energy and mass inputs, dTag 1 = qinh - qout,h + ph (4) ( ) dt Caph , dcm 1 = qi nm - qout,m + pm (5) ( ) , dt V where: Tag is the air temperature, Caph the thermal capacity, qin,h and qout,h the energy inflow and outflow, ph the energy production per unit of time, cm the mass concentration, qin,m and qout,m the mass inflow and outflow and pm the mass produced per unit of time referred to the greenhouse volume V(m3). However, since these models are difficult and time consuming to tune in practice, it is possible to use parametric models to describe the dynamics of the greenhouse climate system (Boaventura Cunha et al., 2000). Assuming that the greenhouse climate can be described as a linear system around a particular operating point, the commonly used parametric ARX model (Ljung, 1987), eq.(6), can be employed: A(q-1)xg (kT ) = B(q-1)u(kT - nT ) + ( kT) (6) where: T is the sampling interval (in general 1min), q-1 is the backward-shift operator, n is the number of delays from input to output, and A and B are polynomials in q-1. In order to select a model, a set of possible models, with different orders (degrees of polynomials A and B) and delays must be first chosen, and then the best model selected. There are several criteria that can be employed, but the one most commonly used is Aikaike s Information theoretic Criterion (AIC), (Akaike, 1974). Previous research (Boaventura Cunha et al., 1997, 2000), has shown that second-order models, based on the previous equations and criteria, describe the dynamics of the system well, and that the parameters are time-varying. More explicit, to simulate and predict the air temperature and humidity, Tas and Rhas, the models described by the following equations (7) and (8) can be used, 561 EFITA 2003 Conference 5-9. July 2003, Debrecen, Hungary îø Tag kT -Tao kT ùø ( ) ( ) ïøúø îø B1,t B2,t B3,t B4,t ùø Rad kT ( ) ïøúø (7) ðøûø Tas kT = ( ) 1 + a1,tq-1 + a2,tq-2 ïø(Tpipe -Tag ) × heat(kT )úø ïøúø ïøúø (Tag - Tao) × vent(kT ) ðøûø (Rhg îø - Rho ) × vent(kT ) ùø ïøúø Tag kT îø B1,h B2,h B3, h B4, h ùø ( ) ïøúø ðøûø (8) Rhas kT = ( ) 1+ a1,hq-1 + a2,hq-2 ïøúø Rhg (kT )- Rho (kT) ïøúø ïø(Tpipe -Tag ) × heat(kT ) úø ðøûø where: ai denotes the transfer functions denominator parameters, Bi the polynomials in the delay operator, Tao the outside air temperature, Rad the outside solar radiation, Tag and Rhg the measured inside air temperature and humidity, Tpipe the temperature of the heating pipes and vent, heater the ventilation and heating inputs. Several methods have been proposed to estimate the time-varying parameters of polynomials A and B, Aström et al. (1989). For the case where the real parameters are slow time variants, as in this type of process, a recursive least squares algorithm with exponential forgetting can be used (Boaventura Cunha et al., 1997; 2000). 2.2. Crop Models Crop growth models are essential tools in the greenhouse management and climate control, since the control outputs are generated by balancing the benefits associated with the marketable produce against the costs related with its production. Basically, plant growth models are classified in descriptive and explanatory models. The first category of models does not reflect the physiological mechanisms present in plant responses, whereas explanatory models are based on a quantitative description of the physiological processes. Descriptive models have a small number of state variables and short computing times, which are advantageous if they are to be used in real-time greenhouse climate control, and the model parameters can be easily estimated by employing recursive least squares algorithms. However, descriptive models have the limitation of not providing acceptable results when used on other species or locations (Marcelis et al., 1997). In the second category of crop growth models, several plant physiological responses are described using subsystems. The development of such a model requires sufficient understanding of the biological processes, and to benefit from its application an appropriate validation must be performed (Van Henten and Van Straten, 1994). The major components of this type of models are crop light interception, photosynthesis and respiration processes and often they provide simulations of dry matter production rather than fresh matter production (Marcelis and Gizen., 1998; Spitters et al., 1989). dWd t ( ) = c² (c±Æphot -Æresp) (9) dt dWd t ( ) in which is the crop growth rate, Æphot is the gross carbon dioxide uptake due to dt canopy photosynthesis, Æresp is the maintenance respiration rate related with the amount of carbohydrates consumed, c± is a conversion factor from assimilated CO2 into sugar equivalents and c² a factor that accounts for the respiratory and synthesis losses during the conversion of carbohydrates to structural material. 562 EFITA 2003 Conference 5-9. July 2003, Debrecen, Hungary The gross canopy photosynthesis and maintenance respiration rates of the crop and the response of canopy photosynthesis are described in several articles (Goudrian and Monteith, 1990; Spitters et al., 1989 and Acock et al., 1978). 2.3. Weather Prediction Models The optimisation module needs good predictions of the outside weather during short and long time horizons. For time horizons of minutes to a day, it is possible to compute good predictions using ARMA - auto regressive moving average models combined with ANN - artificial neural networks to describe the time series for the outside temperature and humidity (Boaventura Cunha et. al, 2000; J. P. Coelho et. al, 2002). To predict the solar irradiation at the same time scales, it is also convenient to use Sun geometric equations. However, for time periods of two to ten days it must also be used climate predictions made by the meteorologist companies and for longer time periods there are not available feasible predictions. One simple way of solving this limitation is to admit that for long time prediction horizons, where the computed predictions are not accurate, the weather will behave in the same way as in the previous year. 3. Conclusions The dynamic optimisation method described has a similar concept of a model based predictive controller using linear and non-linear models and an economic cost function. To be feasible in practical applications, the optimal control inputs time computation must be much lower than the sampling time of the sensor readings, which is normally 1 minute. Today, with the available microprocessors, this does not constitute a problem. The major drawback for the implementation of this concept is related with the prediction models quality. Since the models will influence the management scenarios, the propagation of model errors in time due to their imprecision, as for the case of the outside climate, do not enable to achieve in practice a rigorous optimisation. Another factor that pose problems to the implementation of this concept is related to the difficulty of handling fluctuations in market prices. Also, growers and greenhouse automation companies must be convinced of the advantages of this optimal management approach before it can be implemented in practice. Despite the above restrictive considerations, optimal management and control systems have a tremendous potential to reduce the effort of the grower on decision tasks related with the economic performance of the greenhouse operation. REFERENCES Acok B., D. A. Charles Edwards, D. J. Fitter, D. W. Hand, L. J. Ludwig., J. Warren Wilson and C. Withers (1978). The contribution of leaves from different levels within a tomato crop to canopy net photosynthesis: an experimental examination of two canopy models, Journal of Experimental Botany, Vol. 29 pp. 815-827. Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Automation and Control, AC- 19, 716-723. Aström, K. J. And B. Wittenmark (1989). Adaptive control, Addison - Wesley, Massachusetts. Bot, G.P.A. (1991). Physical modelling of greenhouse climate. Proceedings of the IFAC/ISHS Workshop, pp: 7- 12. Boulard, T. and A. Baille, (1993). A simple greenhouse climate control model incorporating effects on ventilation and evaporative cooling. Agricultural and Forest Meteorology, 65, pp:145-157. Camacho, E.F., Bordons, C., (1994). Model predictive control in the process industry, Springer, Sevilla, 1994. Goudriaan J., J. L. Monteith (1990). A mathematical function for crop growth based on light interception and leaf area expansion. Annals of Botany, vol.66, pp.695-701. 563 EFITA 2003 Conference 5-9. July 2003, Debrecen, Hungary Hugo Challa (1999). Integration of explanatory and empirical crop models for greenhouse management support, Proceedings of Models -Plant Growth, Acta Hort. 507, pp:107-115. J. Boaventura Cunha., C. Couto and A.E.B. Ruano, (1997). Real-time parameter estimation of dynamic temperature models for greenhouse environmental control. Control Eng. Practice, Vol. 5, N.10, pp. 1473-1481. J. Boaventura Cunha, Carlos Couto, A.E.B. Ruano (2000). A greenhouse Climate Multivariable Predictive Controller, Acta Horticulturae N. 534, ISHS, pp:269-276. J. P. Coelho, J. Boaventura Cunha, P. B. de Moura Oliveira (2002). Solar radiation Prediction methods applied to improve greenhouse climate control, World Congress of Computers in Agriculture and Natural Resources, 13-15 March, 2002, pp:154-161. Ljung, L. (1987). System identification - theory for the user, PTR Prentice-Hall, New Jersey. Marcelis, L.F.M., Heuvelink, E., Goudriaan, J., (1997), Modelling biomass production and yield of horticultural crops: a review, Sc. Horticulturae, pp: 83-104. Marcelis, L.F.M., Gijzen, H, (1998). Evaluation under commercial conditions of a model prediction of the yield and quality of cucumber fruits, Scientia Horticulturae, pp: 171-181. Philip Gill, W. Murray, M. Wright (1991). Numerical linear algebra and optimisation, Addison Wesley, USA, 1991, p:426. Pohlheim, H. and A. Hei²ner (1997). Optimal control of greenhouse climate using evolutionary algorithms, International Scientific Colloquium, Germany, pp:1-8. Spitters, C.J.T., H. van Keulen e D.W.G. van Kraalingen, 1989, A simple and universal crop growth simulator: SUCROS87, Rabbinge, Ward, van Laar (eds.), Simulation and system management in crop production, Pudoc, Wageningen. Van Henten, E. J., Van Straten, G., 1994, Sensitivity Analysis of a Dynamic Growth Model of Lettuce, J. agric. Engng Res., pp: 19-31. Van Straten, H. Challa, F. Buwalda (2000). Towards user accepted optimal control of greenhouse climate, Computers and Electronics in Agriculture vol. 26, pp:221-238. 564

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