A 'Big leaf, big fruit, big substrate' model for experiments on receding horizon optimal control of nutrient supply to greenhouse tomato

A dynamic model was set up to describe the mineral content, fruit dry matter content, and biomass of greenhouse tomato, for use in an experiment aiming at controlling the fertigation so as to reach the best compromise between disinfection costs of the recycled water and income from fruit fresh weight production, while ensuring that the dry matter of the fruits is above a given quality standard. The model describes the effect of mineral shortage on growth, and has a simple mechanism to relate dry matter content to the total ion concentration in the substrate. Optimal control requires a quantitative model in state-space form. In order to reduce on-line computation time, the number of states was kept within reasonable limits by lumping leaves, fruits and substrate into three compartments. Therefore the model is labelled `big leaf, big fruit, big substrate¿ or 3Bigs model. Using parameters from literature and some calibration on previous experiments, quite acceptable fits were obtained for biomass, and dry matter and K, N, and Ca contents of the fruits. The model was subsequently used in a receding horizon optimal control experiment. Ion-concentrations in the drain as measured by ion-specific electrodes are fed back to correct the state of the model before the next values of the required drain flow and the fertilizer fluid aliquots are computed. Although it was not possible to operate the controller for more than six weeks, it could be observed that the controller behaviour was consistent with expectations in view of the given model and goal function. The fresh weight yield and the dry matter constraint dominate the behaviour. The results also suggest that currently used ion concentrations are higher than necessary for uninhibited growth.