# Design of a NARX-ANN-Based SP Controller for Control of an Irrigation Main Canal Pool
## 1 Introduction
Consequently, it is used in the application of different linearization methods [20] or the obtention of linear mathematical models by using systems identification tools [23; 40]. The linear mathematical models yielded by these procedures do not characterize accurately the nonlinear dynamic behavior of the water distribution in irrigation main canal pools and, accordingly, their application to the controller's design does not yield satisfactory results in many cases [6; 18]. In general, nonlinear processes can only be adequately characterized by nonlinear models [41]. Thus, in spite of the abundant research in this field, the development of nonlinear control-oriented models of irrigation main canal pools remains an open problem. Recently, artificial neural networks (ANNs) are being used to describe effectively and accurately the dynamic behavior of processes with nonlinear dynamic behaviors. They are computational models that process information inspired by the behavior observed in biological neurons [42; 43; 44]. ANNs receive increasing acceptance and are applied in diverse fields because they use non-physics-based algorithms, handle appropriately nonlinear relationships, and incorporate user experience into their structure [45; 46; 47]. Therefore, they constitute a powerful tool for obtaining adequate dynamic models of nonlinear and time-varying processes that can be applied to the design of controllers based on nonlinear process models, including SP and model predictive controllers (MPC), see e.g., [48; 49; 50; 51; 52]. An important and useful class of discrete-time nonlinear models is the Nonlinear Autoregressive with eXogenous Inputs (NARX) model, which was introduced by [PERSON] in 1980s as a new representation of a wide class of discrete nonlinear systems [41]. Different ANN architectures have been considered as subsets of the NARX model [43]. The NARX-ANN and TD-NARX-ANN (Time Delay-NARX-ANN) are recurrent dynamic neural network architectures used to model different nonlinear dynamic systems that are characterized by a good learning, fast convergence, and well generalization [53; 54]. Diverse authors have proposed the use of NARX-ANN and TD-NARX-ANN for modelling different nonlinear processes and implementing their control systems. A NARX-ANN model for the prediction of the daily direct solar radiation was used in [55]. A NARX-ANN based modeling approach to establish a robust water management tool to aid urban water managers in controlling the development of shallow water tables induced by artificial recharge activity was presented in [56]. A NARX-ANN model for accurate discharge prediction through lateral orifices of irrigation main canals was employed in [57]. A NARX-ANN to predict moisture sorption kinetics and consequently equilibrium moisture content of shiitake mushrooms over a wide range of relative humidity and temperature was developed in [58]. A NARX model reference adaptive control system of a magnetic levitation process was introduced in [59]. A NARX-based model predictive controller for grain dryers was designed in [60]. A NARX-based model predictive controller for turboshaft direct fuel control of an aircraft engine to improve its response ability in the presence of degraded conditions was implemented in [61]. A novel control system for a shunt active power filter based on a NARX-ANN was proposed in [62]. Based on a NARX model, two intelligent controllers to guarantee the desired growth conditions of crops, such as humidity and temperature, in a greenhouse were implemented in [63]. A general-purpose genetic algorithm (GA)-optimized NARX-ANN-based controller for control of nonlinear chemical and biochemical processes was introduced in [64]. A NARX-ANN-based predictive controller of personalized heating systems was designed in [65]. A NARX-ANN-based Smith predictor controller for time-delay compensation of nonlinear processes was developed in [46; 66].