## 3 Simulation Results and Discussion  
Several simulations are carried out to study the process behavior with the different controllers and their effect on process economics and removal efficiency. The performance indices provided by the BSM1 platform are used to evaluate the process performance, with the different controllers in the operating period under characteristic dry weather influent variations. The evolution of the most relevant process variables along the operating horizon is presented in the following figures. First, the comparison between the standard NMPC, which is focused on the set-point tracking, and the HEMPC (HEMPC-OCI: \(w_{1}\) = 1, \(w_{2}\) = 0, HEMPC-NH: \(w_{1}\) = 0, \(w_{2}\) = 1) is presented. The controlled variables are shown in Figure 4, and the corresponding control signals (manipulated variables) are shown in Figure 5. The NMPC exhibits an acceptable set-point tracking even though an offset is observed, especially in the nitrates concentration (\(S_{\mathrm{NNO2}}\)). Although better set-point tracking could be attained using more elaborated techniques to deal with the plant-model mismatch problem, it is not a critical issue because the objective of the proposed control strategies is to improve the economic aspects in the operation. In the operation under HEMPC-OCI, the \(S_{\text{NO2}}\) and \(S_{\text{O5}}\) responses present higher variation between the operational limits than the NMPC and HEMPC. The evolution of the control inputs with the different controllers is presented in Figure 5, where it is possible to see that the weights given to the economics in \(J_{ECO}\) (Equation (8)) in the controller algorithm significantly affect the control signal. The recycle flow (\(Q_{a}\)) is especially affected, showing more intensive movements in the NMPC in order to reach the set point than in the hybrid controllers. In the case of the HEMPC-OCI, a lower recycle rate minimizes the pumping energy. In the case of HEMPC-NH, it could be interpreted in the sense that the lower values of the recycle are favorable for ammonium elimination. A similar trend is appreciated in the aeration energy, but in lower magnitude. In the case of the pure-EMPCs (Figures 6 and 7), the effect of the weighting of the energy costs and the penalization for off-specification ammonium concentration in the effluent in the economic cost function is more notorious than in the hybrid controllers, since the values of the manipulated variables are uniquely determined by the optimization of the economic performance index \(J_{ECO}\). Then, significance differences can be observed in the response of the controlled variables when using each controller. Particularly, the oxygen concentration increases with the EMPC-NH to improve the ammonium elimination, and decreases with the EMPC-OCI due to the minimization of the aeration energy. The minimization of the pumping and aeration energy carried out by the EMPC-OCI produces lower values of both manipulated variables, as expected. On the other hand, it can be seen that the minimization of the off-specification ammonium concentration in the effluent performed by the HEMPC-NH requires more aeration (_KLa_), but minimum values of the recycle flow (\(Qa\)). The instantaneous values of the aeration energy and the pumping energy along the operation period are presented in Figure 8 for the most representative EMPC and HEMPC designs, and the corresponding ammonium concentration in the effluent is presented in Figure 9. In general, higher weights of the _OCI_ (EMPC-OCI, HEMPC-OCI) improve economics, but increase the violations of the limit of ammonium in the effluent, since \(S_{\text{O5}}\) levels are reduced to minimize aeration costs. On the other hand, the minimization of the violation fines of the required effluent quality (HEMPC-NH, EMPC-NH) increases the _OCI_. However, that increase in the _OCI_ is associated with the aeration energy to reduce the levels of ammonium, since the internal recycle flow decreases when ammonium concentration is minimized, as observed in the figures.