Economics-based optimal control of greenhouse tomato crop production

The design and testing of an optimal control algorithm, based on scientific models of greenhouse and tomato crop and an economic criterion (goal function), to control greenhouse climate, is described. An important characteristic of this control is that it aims at maximising an economic criterion, determined by the heating and CO ₂ supply cost on the one side and the of tomato yield on the other side. Unlike conventional control, the economic criterion, e.g. when energy taxes are included in it, directly leads to predictable energy savings. Whereas growers, using the conventional control, are inclined to optimise the climate for the crop, the economic criterion makes a trade off between yield and costs. The costs are mainly energy costs. As a result the energy efficiency improves.

In case of the greenhouse an existing model is modified and extended with a description of the air humidity and a heating pipe model. In case of the crop the number of states of the tomato model of de Koning has been reduced from several hundred to four based on 'reasoned aggregation', to make it suitable for control purposes. This results in a combined greenhouse crop model of nine states. The calibration of this model has been done sequentially. First the tomato model has been calibrated and then the greenhouse model using the output of the tomato model as an input. The different sub-models have been calibrated using independent data. The validation shows that the models predict the trend of the different states well. The value of the states displays a clear deviation, with the exception of the pipe temperature, which is accurately predicted.

The time-scales of the greenhouse crop system are very different. Simulations show that neglecting the fast greenhouse dynamics results in a considerable loss of performance. To take these different time-scales and the poor predictability of the weather into account, a time-scale decomposition is used. First a long term optimisation over a growing season is carried out, based on a long term weather prediction, neglecting the greenhouse dynamics. For the first time a solution of the long-term optimal greenhouse tomato crop production problem is presented. This solution is used to adapt the short-term criterion. In the short-term optimisation the greenhouse dynamics are taken into account. The computations are carried out using the 'receding horizon' principle combined with 'lazy man' weather predictions, and an optimal horizon of one hour. This way feedback is introduced into the system and the control becomes real-time implementable.

Economic results of experiments with the implemented optimal control algorithm show the applicability of the optimal control. The results were not inferior to the experimental results obtained with the conventional control in a second adjacent greenhouse compartment. The experiments seem unique because, to our best knowledge, never before the climate in a greenhouse has been completely determined by an optimal control algorithm designed on the basis of a greenhouse crop model and an economic criterion. The small difference between experimental and simulated results, despite model discrepancies, indicates the robustness of the algorithm. As an objective comparison of the optimal and conventional control is only possible based on a larger number of experiments, in this research the conventional and optimal control are compared by means of simulation. The simulations clearly show that a considerable amount of the energy consumption is needed for dehumidification (11%). Therefore it is important to choose the humidity bounds adequately. To be able to compare the results the penalty on crossing the 90% upper humidity bound is tuned such that the cumulative crossing for the conventional and optimal controller are equal.

The comparison shows that the optimal control of a greenhouse tomato crop production system without heat storage and autonomous availability of CO ₂ , when simulated over four characteristic days, improves the energy efficiency by 8.5%. Against a 5% drop of crop yield the energy consumption reduces by 12.5%. The optimal controller explicitly takes into account long-term effects. This may reduce the short term profit. However, assuming that the investments in bio-mass on the plant will finally pay off, extrapolation of the results from these four days shows an average gain in profit of 60%.