# Energy-Water Management System Based on MPC for a Greenhouse in a Mapuche Indigenous Community
## 1 Introduction
The authors of [11] proposed a genetic algorithm solution to optimize the sizing of PV irrigation systems while minimizing implementation costs and irrigation deficits. The results displayed better convergence than those of traditional optimizers, but the optimized system was characterized by low-efficiency energy usage. The authors of [12] designed a PV irrigation system that was optimized with a genetic algorithm and considered the irrigation demand, total system cost (implementation and operation), and income obtained from selling crops based on the total crop yield. The results showed that the proposed method reduced the overall system size, thereby increasing the economic feasibility. The authors of [13] proposed a technological-economic optimization model to minimize the life cycle cost of a PV irrigation system while minimizing the probability of energy deficiency. Additionally, the authors of [14] applied a centralized MPC to optimize water and energy considering the relevant water requirements and energy costs. Finally, the authors of [15] proposed a decision support system that maximized profit by determining the optimal combination of desalinated and brackish water for irrigation. Taking into account these previous works, the main contributions of the present work are as follows:  
* Neural networks and phenomenological models are used to predict the climatic variables that usually affect crop yields. * A new controller design that integrates elements from energy and water management systems is proposed. This integrated control strategy is established to control crops in greenhouses in the short and medium terms. * A climate regulator is implemented based on the openness of windows. Notably, the proposed controller design is based on concepts from model predictive control, and the optimal control actions are performed. Additionally, the proposed design includes fuzzy optimization for handling multiple control objectives and constraints by considering the uncertainty of the predicted climatic variables. The novelties of this work are as follows:
* The integrated EWMS is applied for the operation of a semiclosed greenhouse. Previous works only applied EWMSs to open-field crops. * Fuzzy optimization is included in the designed model predictive control scheme in the EWMS. As mentioned above, with fuzzy optimization, the model predictive control strategy can handle multiple control objectives and constraints, even when the system is affected by uncertainties. This paper is structured as follows. Section 2 presents the details of the base methods considered as the background for the implementation of autoregressive models for the disturbance signals and the design of the model predictive controller. Section 3 describes the problem statement for applying the EWMS to greenhouse crops. Section 4 details how the predictions of the different climate variables that affect the greenhouse are handled. Section 5 presents the formulation of the MPC for implementing the EWMS over the short and medium terms. Section 6 describes the case study considered in this research, and Section 7 provides the corresponding simulation results. Finally, this work ends with Section 8, where the main conclusions based on the simulation results are discussed.