Our understanding of model-based climate control encompasses all the approaches where new climate set-points are determined using either information output from the model or the knowledge contained in the model itself. Optimal control is probably the most widely used method to exploit available models and determine 'optimal' crop environmental conditions.90-92 Climate control application of crop models within the framework of optimal control also requires a model of the greenhouse climate because the control variables directly modify the climate. The plant behaviour is driven indirectly through its responses to modifications of the environment.
In one of its simplest forms, the climate optimisation problem is defined as follows: using a crop dry matter accumulation model and an algebraic expression of the greenhouse climate model, find the day- and night-time temperatures that maximise a cost function, balancing the relative growth rate and the heating costs (CO2 enrichment can also be included). Gal et al.,93 Seginer,94'95 Seginer et al.96 and Critten97 showed that the optimal solution can be expressed as a direct function of the external climate conditions for each time instant independently. In practice this allows for the offline computation of lookup tables that indicate what actions should be taken under current conditions. Seginer et al.22 have studied the temperature optimisation problem, only based on plant need. They used a dynamic model of the carbon balance of the crop with a temporary carbohydrate pool to derive the day and night temperatures that maximise the relative growth rate, for a given daily radiative flux. The results are that young crops need higher temperatures than old ones where the maintenance respiration rate is higher and that for a given situation, several couples of day and night temperature are optimal. Tchamitchian et al.98 and Tap et al.99 have used a dynamical greenhouse model instead of an algebraic one to introduce the damping of temperature caused by the structures in the greenhouse. Solving the climate problem, either for tomato or for lettuce, respectively, proved to be a rather difficult numerical problem.
Coupling a dynamical model of the greenhouse climate to a lettuce growth model, van Henten100 used the singular perturbation approach101 to tackle the problem of models with different magnitudes of time constants. A new development in this area (Tap, personal communication) applies the same method to a simplified tomato crop model. Daily optimisation of the climate (so-called fast processes) under the constraint of long-term optimisation of the crop production (so-called slow processes) can then be solved.
Although many theoretical applications of models to climate control have been studied, none or very few have been put to test in practice. A technical reason is that, at the time of writing, optimal control produces time-varying set-points which cannot be implemented on commercial greenhouse climate computers.
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