# Design of a NARX-ANN-Based SP Controller for Control of an Irrigation Main Canal Pool
## 2 ANN-Based System Identification of an Irrigation Main Canal Pool  
The research presented in this paper is based on the Zaza-Ciego de Avila Main Canal (ZCAMC), which is one of the most important hydraulic constructions in Cuba [67]. This canal is in the central zone of the country and connects the Zaza reservoir (with a capacity of 1,020,106 m\({}^{3}\)) with the south of the Ciego de Avila County. The surface irrigated is about 148,200 ha that is used for the cultivation of rice, sugar cane, citrus fruits, soybeans, horticulture, as well as for the development of fishing and livestock. The canal delivers a total volume of 900,106 m\({}^{3}\) of water/year that alleviates the overexploitation of the phreatic level in the region [68]. This canal is a 44.5 km long cross-structure with variable water discharge between 33.0 and 23.0 m\({}^{3}\)/s, overall canal height from 4.80 to 3.87 m, and normal water depth varying from 4.30 to 3.10 m. It has a trapezoidal cross-section, the bottom width varies from 6 to 3.2 m, and the average slope is 0.07 m/km [6]. It has four pools separated by undershot gated cross-structures. This canal is mostly operated in a downstream end regulation mode [8; 26]. All the pools of this canal are electrified and equipped with downstream end water level and gate position sensors, SIMATIC S7-300 PLCs, motors for the gates' positioning, and systems for data acquisition, processing, and storage. Likewise, this canal has a remote supervisory control and data acquisition system (SCADA) with communication by radio and field buses that provide real time data of the controlled variables. Figure 1 is a view of ZCAMC. Mathematical models have a vital role in systems analysis and design [41]. The controller design habitually requires a dynamic mathematical model that accurately characterizes the behavior of the processes to be controlled [69; 70]. Therefore, one of the significant challenges of the controller design methodology is to obtain a suitable mathematical model of the process. Several mathematical models have been developed for the irrigation main canal pools, see e.g., [8; 40; 50]. Since the irrigation main canal pools have complex nonlinear dynamics, linear approximation models of their dynamic processes are often developed [8; 9], which have been often attained by applying system identification procedures, see e.g., [9; 18; 23]. System identification is the approach used to infer and construct process models from a set of experimental input-output data [41; 69]. Since 1986, neural networks have been applied in the system identification of non-linear dynamic processes [42]. Data and results reported in this paper were obtained from the first pool in the ZCAMC. It is a trapezoidal cross section main canal pool 12.5 km long, operated by using the distant downstream operation method [6; 70]. This pool is equipped with an industrial personal computer, and a SIMATIC S7-300 PLC. The downstream end water level is controlled by four upstream undershoot gates situated at the beginning of the pool. Figure 2 is a  
Figure 1: A view of Zaza-Ciego de Avila Main Canal (ZCAMC). schematic representation of this canal pool, in which the four control gates are represented by an equivalent gate. The available measurements are the downstream end water levels \(y_{1}(t)\), and the gate positions \(u_{1}(t)\). Thus, the controlled variable is the downstream end water level \(y_{1}(t)\), and the manipulated variable is the position of the upstream equivalent gate \(u_{1}(t)\). In this paper, using the system identification procedures [69] and the real-time experimental data attained through the SIMATIC S7-300 PLC system in open loop operating points, three models are obtained that describe the nominal dynamic behavior of the water distribution in the studied canal pool.