Identification of a Linear Continuous Time Stochastic Model of the Heat Dynamics of a Greenhouse

Abstract

In order to use a model-based optimal control strategy for the heat supply to greenhouses, a reasonable description of the heat dynamics is required. This paper describes the identification of a linear stochastic model for the heat dynamics of a greenhouse which takes the global radiation, the outdoor air temperature and the heat supply as input variables. The model is a linear and lumped parameter model formulated in state-space form in continuous time. The formulation contains physically interpretable parameters and, for their identification, data from an experiment conducted in winter have been used. During the experiment, the heat supply was controlled by a pseudo-random binary signal (PRBS) in order to avoid a correlation between the heat supply and other variables, and in order to ensure that the dynamic characteristics of the greenhouse were present in the data. A number of alternative model structures have been considered, and by using statistical methods a model with three thermal capacities is suggested. This model predicts the air temperature 2 min ahead with a standard deviation of 0·062 K. Physical knowledge as well as statistical methods are used to validate the model. The estimated parameters of the model show reasonable agreement with prior physical knowledge. Additionally, the model has been verified by simulating the air temperature using an independent set of data.