## 3 Simulation Results and Discussion
Figure 4: BSM1-controlled variables’ responses under NMPC and economic-oriented tracking controllers (Hybrid-EMPC or HEMPC). (**a**) Nitrates and nitrites concentration in the second vector (\(S_{\text{NO2}}\)) response (**b**) dissolved oxygen in the last aerobic reactor (\(S_{\text{O5}}\)) response. NMPC: non-linear model predictive controller; OCI: overall cost index. Figure 5: Control signals applied to the BSM1 plant operating under NMPC and HEMPC controllers. (**a**) Internal recycle flow (\(Qa\)) (**b**) oxygen transfer coefficient (\(Kla\)). Figure 6: BSM1-controlled variables’ responses under NMPC and EMPC controllers. (**a**) Nitrates and nitrites concentration in the second vector (\(S_{\text{N02}}\)) response (**b**) dissolved oxygen in the last aerobic reactor (\(S_{\text{O5}}\)) response. EMPC: economic-oriented model predictive controller. Figure 7: Control signals applied to the BSM1 plant operating under NMPC and EMPC controllers. (**a**) Internal recycle flow (\(Qa\)) (**b**) oxygen transfer coefficient (\(Kla\)). The performance indices calculated for the overall operation period with the proposed controllers are presented in Tables 2 and 3, respectively. The influent profile described in the BSM1 for dry weather (Figure 2) is used to evaluate the plant performance over an operation period of four days, the first day with constant influent. The influent quality index defined in [22] to measure the pollution load of the influent is _IQ_ = 55,945.14 kg-pollutants/day. The indices computed for the default BSM1 strategy are included also for comparison. Table 2 contains the indices associated with the variables considered in the economic-oriented model predictive controller optimization, to show that performance indices vary according to the relative importance given to each objective in the optimization. In general, all the EMPC designs improve the pumping energy with respect to the NMPC and PI default strategies based on set-point tracking. A reduction in the energy costs (_AE + PE_) of 13% with respect to the NMPC is achieved, with the pure EMPC focused on the optimization of the energy costs (EMPC-OCI). Ammonium concentration in the effluent reduces by 21% when the EMPC is focused on the minimization of the off-specification ammonium concentration in the effluent. Comparing with the default BSM1 PI strategy, a reduction of the energy costs of 13% is achieved also with the EMPC-OCI, produced especially by a decrease in the pumping energy of up to 23%. Table 3 is presented to show that additional process variables are affected by the economic optimization, and it is possible to include them in the optimization. The _OCI_ index reported in Table 3  
Figure 8: Instantaneous pumping (**a**) and aeration energy (**b**) for the BSM1 plant operating under selected controllers. Figure 9: Ammonium concentration in the effluent for selected controller designs. corresponds to the BSM1 performance index, which includes aeration energy, pumping energy, mixing energy and sludge production costs. In order to compare with the previous work of [PERSON] and [PERSON] [PERSON] and [PERSON] (2016), Table 4 presents the changes in the performance indices, with respect to the operation with the BSM1 default PI strategy in the same simulation scenario. The comparison is made with selected designs with analogous tuning parameters. The EMPC proposed in this work enhances the economic performance mainly by reducing the pumping energy in all the cases, and the aeration energy in the EMPC-OCI design, which are the operation costs considered in the economic function. In the [PERSON] and [PERSON] and [PERSON] (2016) formulation, the BSM1 overall cost index (_OCI_) is optimized; it includes aeration and pumping energy, but also the mixing energy and the costs of sludge disposal. Then, an operation with small energy consumption with respect to the default PI strategy is achieved in general, but pumping aeration costs are larger than those obtained with the methodology proposed here.