Open-Loop Optimal Temperature Control in Greenhouses

Earlier research has revealed that considerable energy savings can be achieved by maintaining an average temperature in the greenhouse in stead of maintaining rigid pre-defined temperature 'blue-prints'. A model based optimal control approach has proven to be a suitable framework to tackle these kind of control problems and it has been shown that these algorithms can be implemented on-line. But, when on-line optimal temperature control is considered, interesting questions arise, some of which are still unresolved. The issue tackled in this paper concerns the relation between the resolution of the control strategy, (sample time) and energy savings of the control strategy. One would expect that an accurate and frequent anticipation to changing outdoor climate conditions might result in reduced energy consumption. It was indicated in the literature that a sample-time of 0.25 h or I hour should be sufficient, but these choices were hardly motivated. In this research, the relation between the control resolution and energy savings was quantitatively investigated using a dynamic greenhouse climate model and measurements of Dutch outdoor climate conditions containing high-frequency components. The results indicate that for an open-loop optimal control problem concerning the realization of an average temperature during a fixed period of one day using a minimum amount of energy with full a-priori knowledge of the outdoor weather, a resolution of the heating profile between half an hour and a hour suffices to produce accurate results in terms of energy conservation. These results were not much affected by parameter variations (heat capacity of the air, the solar heating efficiency) or opening and closing of thermal screens.