## 3 Results and Discussion  
### Tuning  
The system response observed in the outlet H\({}_{2}\)S concentration is shown in Figure 1, for maintained oscillation (Figure 1a) and step response (Figure 1b) methods. According to the MO method, the ultimate gain (K\({}_{\text{U}}\)) was 0.14 and ultimate period (P\({}_{\text{U}}\)) was 148 s. The K\({}_{\text{U}}\) was ten time higher than the value obtained using nitrate (K\({}_{\text{U}}\) = 0.015) and the Pu was almost half the value obtained using nitrate (P\({}_{\text{U}}\) = 343 s) [16]. Thus, a lower value of P\({}_{\text{U}}\) produced an increase in the integral gain with a stabilizing effect on the oscillations during the response of the control variable [26]. On the other hand, an increase of the K\({}_{\text{U}}\) value increases all the gains (proportional, integral and derivative), which, may have a delayed effect on the control. However, these correlationsmay not be accurate, because the gains are dependent on each other and the change in one of them may produce changes in the effect of the other two [26]. The \(\mathrm{K_{U}}\) and \(\mathrm{P_{U}}\) allowed to calculated the specific controller gains, which are shown in Table 3.  
Moreover, the graphical procedure for the step-response method is represented in Figure 1b. After the step perturbation, the outlet \(\mathrm{H_{2}S}\) concentration increased from 66.7 to 138.6 ppmv (RE 94.0%). Therefore, the \(\mathrm{H_{2}S}\) concentration versus time allowed to obtain gain (K), delay time (L) and constant time (T), parameters that were used in the gain's calculation (Table 3). A comparison of the calculated gains (Table 3) by ZN and AMIGO with the values obtained by tuning during the nitrate operation [16] showed significant variation. Specifically, the proportional and integral gains for the PID and PI controllers showed a variation of 76.37 - 98.11%, while in the derivative gain, values observed an increase of 141.34 - 145.01%. However, the marked difference between the obtained parameters did not have a negative influence on the process control, despite previously being described in literature, where gain values variations lower than 50% rarely have significant effects on the response of the  
However, while recording the nitrite inlet flow (Figure 2b) for each controller, it is important to remark the oscillatory response observed in the manipulated variable for the PID-MO respect to the other controllers. Thus, an unstable system is expected with this behavior, maintained or increased over time. A comparison of the calculated errors (Table 4) indicates a significant reduction between the errors calculated for the PI and PID controllers tuned by MO, respect to the step-response tuning. Table 5 shows the offset, stabilization time (time until setpoint is reached), and average, maximum and minimum outlet H\({}_{2}\)S concentration. The offsets, average, maximum and minimum H\({}_{2}\)S concentrations were similar in the six controllers; likewise, the lower stabilization time was for the PI and PID control tuned by the MO method. In general, the errors calculated in nitrite operation are higher than those calculated in nitrate operation [27], probably because of an increase of sensitivity in nitrite operation. In relation with stabilization time, a similar value of 0.41 was obtained by [PERSON] et al. [16] using nitrate and PID controller tuned by MO. As a comparative result, PID-MO and PI-MO were selected to evaluate a variable H\({}_{2}\)S IL profile (Figure 3), controlling the H\({}_{2}\)S outlet concentration at a set point of 100 ppmv. Under the action of the PID-MO controller (Figure 3a), the system became unstable at the lowest value of the studied H\({}_{2}\)S IL profile. The amplitude of the observed oscillations in nitrite flowrate