## 4 Example
### Experiments
the control horizon should be done also carefully and there is also a threshold which should not be crossed in order to avoid control performance deterioration. Figure 5: Responses of the control system with FMPC1 algorithm and \(\lambda=0.001\) to changes in the setpoint to \(\overline{C}_{B1}=1\) mol/L and \(\overline{C}_{B2}=1.25\) mol/L and to the change of the disturbance by 10% in the 6 th minute of the experiment; \(s=35\)—black lines, \(s=10\)—green dashed lines, \(s=5\)—magenta lines, \(s=1\)—blue lines. To sum up, during designing of an algorithm it is advisable to check if the control horizon can be decreased (and optimization problem solved by the algorithm simplified). However, it should be done carefully, because for too short control horizon control performance can got worse. Figure 6: Responses of the control system with FMPC2 algorithm and \(\lambda=0.001\) to changes in the setpoint to \(\overline{C}_{B1}=1\) mol/L and \(\overline{C}_{B2}=1.25\) mol/L and to the change of the disturbance by 10% in the 6 th minute of the experiment; \(s=35\)—black lines, \(s=5\)—green dashed lines, \(s=2\)—magenta lines, \(s=1\)—blue lines. The mechanisms of disturbance measurement utilization were used in the next experiments. Both FMPC algorithms generated similar responses. The first method of disturbance measurement utilization (red lines in Figures 7 and 8) is based on the same approach as in the standard DMC algorithm, the second one employs the nonlinear process model (magenta lines in Figures 7 and 8). Disturbance compensation near \(C_{B}=1.25\) mol/L is almost the same in the case of both methods; differences in responses are really small. It is because the model of disturbance influence on the control plant for the first method was obtained near this output value. Figure 7: Responses of the control system with FMPC1 algorithm and \(\lambda=0.0001\) to changes in the setpoint to \(\overline{C}_{B1}=1\) mol/L and \(\overline{C}_{B2}=1.25\) mol/L and to the change of the disturbance by 10% in the 6 th minute of the experiment; mechanism of disturbance measurement utilization: not used—blue lines, based on the linear model—red lines, based on the nonlinear model—magenta lines. Application of both methods of disturbance measurement utilization near \(C_{B}=1\) mol/L causes reduction of the maximal control error by around 50% comparing to the case when disturbance measurement was not exploited (blue lines in Figures 7 and 8). Both methods offer very good disturbance compensation. However, in the case of the one based on the nonlinear model (magenta lines in Figures 7 and 8) the output value achieves the setpoint slightly faster than the one based on the linear model (red lines in Figures 7 and 8) while changes of the control signal are smaller. Figure 8: Responses of the control system with FMPC2 algorithm and \(\lambda=0.0001\) to changes in the setpoint to \(\overline{C}_{B1}=1\) mol/L and \(\overline{C}_{B2}=1.25\) mol/L and to the change of the disturbance by 10% in the 6 th minute of the experiment; mechanism of disturbance measurement utilization: not used—blue lines, based on the linear model—red lines, based on the nonlinear model—magenta lines.