Linear matrix inequalities tool to design predictive model control for greenhouse climate

Abstract

Modeling and regulating the internal climate of a greenhouse have been a challenge as it is a complex and time variant system. The main goal is to regulate the internal climate considering the difference between nighttime and diurnal phases of the day. To depict the comportment of the greenhouse, a multi model approach based on two multivariable black box models have been proposed representing the diurnal and nighttime phases of the day. The least-squares method is utilized to identify the parameters of these two models based on an experimental collected data. We have shown that these two models are more representative than one model to describe the dynamic behavior of the greenhouse. The second contribution is to control the internal temperature and hygrometry respecting constraints on actuators and controlled variables. For this purpose, a constrained model predictive control scheme based on the multi-modeling approach have been developed. The optimization problem of the control law is transformed to a convex optimization problem includes linear matrix inequalities (LMI). The simulation results show that the adopted control method of indoor climate allows rapid and precise tracking of set points and rejects effectively the external disturbances affecting the greenhouse.