Acceptable nitrate concentration of greenhouse lettuce: two optimal control policies

Greenhouse lettuce with high nitrate levels is unmarketable in the European Union. To avoid the loss of a crop, an economical environmental control strategy, based on a suitable crop model, is required. A recently developed dynamic lettuce growth model, in conjunction with a simple greenhouse model, is used here to develop a strategy for hydroponic greenhouses where temperature and nitrate supply rate can be controlled. Two cases are considered: (1) fixed spacing, as in traditional systems and (2) potted or floating plants, where continuously variable spacing can be used as a third control variable. The optimization criteria are formulated for a market-quota situation, and optimal control methodology is used to find the optimal strategies. Two simplifying assumptions are made, (1) the weather is constant throughout the growing period and (2) photosynthesis and growth are not inhibited. The results show that the optimal policy for the variable spacing systems is independent of the age of the crop. The canopy density (leaf area index) is maintained constant by continuously increasing the spacing, the optimal heating temperature alternates, and the optimal ventilation temperature is constant. If, under the prevailing light level, the minimum temperature cannot ensure a sufficiently low crop nitrate content, the supply rate of nitrate must be reduced. The optimal control policy for fixed spacing systems is to start with the highest permissible temperature and with abundant nitrate supply. At certain points in time, a switch down to the temperature of unventilated and unheated greenhouse, and later to the lowest feasible temperature, may be required. Finally, a switch to the lowest permissible nitrate supply rate may also be needed. Two variants of the variable-spacing system (fixed and free final state of the crop) are analysed first. Next, the fixed-spacing system (with fixed and free final state) is explored. An algorithmic solution method is outlined for each of the cases and sample results are compared.