# Design of a NARX-ANN-Based SP Controller for Control of an Irrigation Main Canal Pool
## 1 Introduction  
Water is a vital and essential resource for human life, environment, as well as for sustainable development [1]. However, millions of people currently live in conditions of extreme water scarcity [2]. Water scarcity is the consequence of two particularities: physical scarcity, and economic scarcity [3, 4]. Physical scarcity is determined as the insufficiency of natural resources to supply a region's demand for water, while economic scarcity is demarcated as the consequence of poor investment in science, technologies, and infrastructures [5, 6]. In irrigation systems, most of the water resources are transported by the networks of irrigation canals [7, 8, 9]. In most countries, irrigation canals are manually operated [10, 11, 12]. Currently, one of the reliable solutions to face the problems related to water scarcity in irrigated agriculture is the automatic control, which is considered a powerful tool to improve the operation and efficiency of water distribution in the irrigation main canals [13, 14]. The application of conventional PID (proportional integral derivative) controllers is one of the most widespread solutions to control the water distribution in irrigation main canal pools, see e.g., [15, 16, 17]. However, this control strategy usually does not yield satisfactory results because irrigation main canal pools are complex systems that are characterized by nonlinear dynamic behaviors with dominant time delays [18, 19, 20], and PIDcontrollers are not adequate for this class of processes [21; 22; 23; 24]. Therefore, the design and implementation of controllers aimed at increasing operability and safety in irrigation main canal pools, represents an important and challenging research field [25; 26; 27]. One of the most widely used controllers for processes with dominant time delays (processes in which the time delay is much greater than the largest of the time constants) is the Smith predictor (SP) [28; 29; 30]. It is characterized by having a linear mathematical model of the process to be controlled in its structure, and it shows a low effectiveness in rejecting load disturbances [31; 32]. The SP has been the subject of intensive research and modifications aimed at improving its performance, robustness, and disturbance rejection features, as well as enabling its application in diverse processes (unstable, time-varying, nonlinear, etc. ), see e.g., [33; 34; 35]. The SP has been applied to water distribution control in different irrigation main canal pools. Among the first proposals are those made by [PERSON] [36], [PERSON] [9], [PERSON] [37] and [PERSON] [38]. They are characterized by combining the conventional structure of the SP with PI or PID controllers, which do not guarantee an effective water distribution control. The adaptive SP was proposed also to improve the effectiveness of water distribution control in irrigation main canal pools with large variations in their operating conditions [18; 26]. Furthermore, in recent years, the SP has been combined with fractional order controllers to increase the robustness of the control of irrigation canal pools, see e.g., [19; 34]. One of the essential problems that present these SP-based control systems is their poor performance due to the use (in the SP structure) of linear mathematical models of the water distribution dynamic behavior in irrigation main canal pools [6]. They also have a low rejection of load disturbances, which originates insufficient accuracy in water distribution control. Irrigation main canals are nonlinear complex processes [8; 9]. The physical dynamics of the water distribution in irrigation main canal pools has traditionally been modeled by the Saint-Venant equations, nonlinear hyperbolic partial differential equations with complex constraints, whose analytical solution is very complicated in the case of an arbitrary geometry [39; 40]. These equations are derived from mass and momentum balances and are very difficult to use for the design of a controller [8].