# Design of a NARX-ANN-Based SP Controller for Control of an Irrigation Main Canal Pool
## 5 Conclusions  
The contribution of this work is a modification of the well-known Smith predictor controller in which the internal linear model has been substituted by the combination of a NARX-ANN-based model and a TD-NARX-ANN-based model, in order to take into account the dynamic nonlinearities in the effective control of water distribution in an irrigation main canal pool. By application of system identification procedures, NARX-ANN and a TD-NARX-ANN with recurrent architectures have been obtained which describe with high accuracy the non-linear dynamic behavior of the water distribution in the studied canal pool. The NARX-ANN structure with an input layer with 13 memory blocks for the input and output signals, three neurons in the hidden layer and one neuron in the output layer provided the best models performance. A third model which is linear and is represented by a time-delay first order transfer function was obtained using an identification procedure. The validation results of the three models illustrate that the FIT performance indexes of the NARX-ANN-based models are higher than that of the linear model. In the context of hydraulic engineering, one of the contributions of this paper consists therefore of the fact that accurate nonlinear models based on the NARX-ANN could be obtained for an irrigation main canal pool under different real operation conditions using real-time data and system identification procedures. The results attained are very promising and show that there is great potential for the use of NARX-ANN-based models in depicting the dynamic behavior of irrigation main canal pools. We remark that improving the accuracy of these nonlinear dynamic models has a significant impact on improving the performance of water distribution control systems. Besides modifying the SP conventional structure by substituting the linear mathematical models by the non-linear NARX-ANN-based models, a gain tuning block of gain \(K(t)\) has been added that estimates the load disturbance \(\hat{D}(t)\), which is summed to the controller output signal \(u(t)\) in order to reject the negative effect of the load disturbance \(D(t)\) on the control system and, thus, increase the controller performance. The experimental results obtained on the real operation scenarios of the studied canal pool illustrate that our modified NARX-ANN-based SP controller improves the control system performance and therefore satisfies the users water demands in time. The benefits that are obtained with the increment of water distribution control performance in the main irrigation canal pools are reverted to a better management and rational use of the available hydraulic resources, as well as to a greater environment protection due to the reduction of the current operation water losses. The proposed NARX-ANN-based SP controller constitutes a simple and attractive option for the accurate water distribution control in the irrigation main canal pools and, therefore, it reveals that there is a great potential in the application of the artificial intelligence to design non-linear control systems for this class of hydraulic processes, as well as to design prediction and decision support systems to optimize the operation of irrigation systems. This research will be expanded in the future to obtain non-linear NARX-ANN-based models of the remaining canal pools of the ZCAMC, and to use these models in the design and implementation of an integral intelligent water distribution control system for the complete irrigation main canal. Conceptualization, [PERSON] and [PERSON]; methodology, [PERSON] and [PERSON]; software, [PERSON]; validation, [PERSON]; formal analysis, [PERSON] and [PERSON]; writing, review and editing, [PERSON], [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.