# Design of a NARX-ANN-Based SP Controller for Control of an Irrigation Main Canal Pool
## 4 Results and Discussions  
For the evaluation of the performance of the modified SP control system with the NARX-ANN-based models, a comparative experimental analysis was carried out with another SP with a conventional structure, that included an internal linear model (13) and did not include the gain tuning block \(K(t)\). Both control systems were designed to fulfill the same specifications, considering the following real operation scenarios of our canal pool. **Scenario (1):** Experimental performance evaluation of the water distribution control system with both designed controllers when a positive setpoint change \(\Delta r(t)\) is applied from 3.10 to 3.55 m (setpoint tracking). Table 1 and Figure 11 illustrate the comparative experimental time responses to that setpoint change yielded by the water distribution control system with the two controllers, where \(MP\) is the overshoot, \(E_{ee}\) is the steady-state error, \(T_{  
From Figure 11 and Table 1 it is observed that the control system with the NARX-ANN-based SP controller designed reaches the new reference water level practically without overshoot and with zero steady state error--like the conventional SP--but the rise time and the settling time are approximately the 50% of the times yielded by the conventional SP. After time 3500 s, the responses provided by both control systems have reached the new setpoint with zero steady state error and, therefore, their steady time responses are similar. We highlight that the same responses attained after 3500 s is consequence of the integral terms included in the structures of controller (17) and the PI controller (18), which is a common term in both control systems. However, the main difference is produced in the transient, in which our proposal achieves the final value much faster than the conventional SP controller. Specifications used to design the conventional PI controller embedded in the SP structure are quite conservative. In theory, much faster responses could be achieved using this control system by tuning controller (18) with higher values of the gain crossover frequency \(\omega_{c}\). However, the value of \(\omega_{c}\) used here--though it is not too fast--yields a robust controller (18) that maintains a stable closed-loop response in all the range of operation of the canal, and not only in the nominal operation point at which the controller has been designed. In fact, the highly nonlinear dynamics of the canal makes aggressive linear controllers (controllers that yield very fast damped responses) designed based on a linearized model around an operation point become unstable when the canal operates in a point far away from the linearized one. However, our nonlinear control system based on our TD-NARX-ANN nonlinear model allows a much faster response in the nominal operation point without neither unstabilizing or excessively degrading the closed-loop response of the canal when operating at points far away from nominal. This is caused by the fact that our TD-NARX-ANN nonlinear model captures better than linear model (11) the nonlinear behaviour of our canal pool allowing us to design a controller that takes into account at some extent such nonlinearity. These results confirm that the NARX-ANN-based SP controller designed improves the management of the water flow through the canal pool and satisfies the users water demand in a shorter time. Figure 12: Experimental comparative output signals of the controllers designed. **Scenario (2):** Experimental performance evaluation of the water distribution control system with both designed controllers against the rejection of an external load disturbance \(D(t)\). In this case, an increment of 10% in the lateral discharge \(q_{1}(t)\) of the canal pool to satisfy the users water demand was considered as an external load disturbance \(D(t)\).