Articles
Development and performance of a greenhouse climate model for optimal control based on vapor pressure deficit
Article number
1437_12
Pages
85 – 94
Language
English
Abstract
Vapor pressure deficit (VPD) is a variable that can be used to control greenhouse climate since its manipulation might reduce water consumption of the crop and at the same time maintain elevated gas exchange rates between the crop and the air.
In this work a two-state dynamic model, including air temperature and air humidity, was developed to determine vapor pressure deficit of the air.
The unsteady-state energy balance within the greenhouse includes the incoming energy from solar radiation, the energy released into the air due to condensation on greenhouse surfaces, the energy exchange through glazing, and heat losses due to ventilation and crop transpiration, and through the ground.
The transient mass balance for air humidity considers the incoming mass flow due to crop transpiration, the loss of humidity due to ventilation, and the gain of humidity due to condensation.
The mathematical model was programmed in MATLAB-SIMULINK with a C-MEX file s-function to speed up the simulations.
The numerical integration was performed by a Runge-Kutta type integration routine with variable step-size (ode45 function) and a relative tolerance of 10‑8 and absolute tolerance of 10‑10. Data for the input variables of the model were collected from an experimental greenhouse of the Biosystems Lab at the University of Chapingo, Mexico.
From an uncertainty analysis and a global sensitivity analysis, the most influential model parameters were identified.
Those parameters were used to carry out a model calibration with a nonlinear least squares procedure.
The performance of the model predictions against measurements, for temperature and humidity, was evaluated using MSE, RMSE, MAE, and model efficiency (EF) statistics.
Since both the calibrated and evaluated models predicted low air VPD values <0.5 kPa and high VPD values of >0.8 kPa, >1.2 kPa for all the days and more rarely >2 kPa control strategies are required to improve the greenhouse environment.
In this work a two-state dynamic model, including air temperature and air humidity, was developed to determine vapor pressure deficit of the air.
The unsteady-state energy balance within the greenhouse includes the incoming energy from solar radiation, the energy released into the air due to condensation on greenhouse surfaces, the energy exchange through glazing, and heat losses due to ventilation and crop transpiration, and through the ground.
The transient mass balance for air humidity considers the incoming mass flow due to crop transpiration, the loss of humidity due to ventilation, and the gain of humidity due to condensation.
The mathematical model was programmed in MATLAB-SIMULINK with a C-MEX file s-function to speed up the simulations.
The numerical integration was performed by a Runge-Kutta type integration routine with variable step-size (ode45 function) and a relative tolerance of 10‑8 and absolute tolerance of 10‑10. Data for the input variables of the model were collected from an experimental greenhouse of the Biosystems Lab at the University of Chapingo, Mexico.
From an uncertainty analysis and a global sensitivity analysis, the most influential model parameters were identified.
Those parameters were used to carry out a model calibration with a nonlinear least squares procedure.
The performance of the model predictions against measurements, for temperature and humidity, was evaluated using MSE, RMSE, MAE, and model efficiency (EF) statistics.
Since both the calibrated and evaluated models predicted low air VPD values <0.5 kPa and high VPD values of >0.8 kPa, >1.2 kPa for all the days and more rarely >2 kPa control strategies are required to improve the greenhouse environment.
Publication
Authors
I.L. López-Cruz, E. Fitz-Rodríguez, R. Salazar-Moreno, A. Rojano-Aguilar
Keywords
dynamic model, model calibration, model evaluation, optimal control, tomato
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