Development and analysis of dynamical mathematical models of greenhouse climate: A review

Abstract

This paper summarizes the main developments achieved up to now on dynamical models of the greenhouse climate, regarding their structure, analysis, parameter estimation and model performance. The systems state-space approach is followed in order to describe main models’ structure features. The physical processes included in the dynamic equations of greenhouse climate are emphasized. The type of equations used, either differential equations, difference equations or transfer functions are described. The dynamic models of greenhouse climate are classified in mechanistic and black-box models. Mechanistic models are mainly focused on the knowledge of the greenhouse system whereas black-box models are more used for applications, including: control, optimization and design of the greenhouse system. Main results of this study are that models of greenhouse climate used mostly ordinary differential equations either to know more the system or to control and optimize it. Only few models used difference equations or ARX. Also more complex greenhouse climate models have been developed to get insight of the greenhouse system while models with few states are more useful for control and optimization purposes. The dynamic models of greenhouse climate have mostly founded on the first law of thermodynamics, namely (energy/ enthalpy) analysis and conservation of mass. Furthermore, although almost all the models have been calibrated and evaluated using measured data from the system, there is a lack of uncertainty and sensitivity analysis in the development of greenhouse climate models. In fact, none of the revised models were subjected to an uncertainty analysis. Some models of greenhouse environment have been reported with only a preliminary sensitivity analysis; a few of them with a formal local sensitivity analysis and none with a global sensitivity analysis.