4. Results and discussion

The fuzzy observer validation is performed using real data from a distillation process; the main characteristics are shown in Tables 1 and 2.

The process operates during 50 min, taking the initial compositions xð Þ¼ 0 [0.8555, 0.8525, 0.8480, 0.8412, 0.8309, 0.8148, 0.7896, 0.7483, 0.6767, 0.5369, 0.2300] in steady state.


## Table 1.

Process parameters.


Table 2. Mixture parameters.

The system input signals used in the validation stage are the reflux signal, considering an opening percentage of 20%, starting at the 5 min and lasting 30 min, and the heating power.

Figure 4 shows the light component compositions calculated by the nonlinear model in the 11 plates of the distillation column; this simulation is carried out considering no disturbances in the system.

Figure 5 shows the composition estimated by the observer with initial conditions different from the nonlinear model. The composition initial conditions of the observer are <sup>x</sup>^\_ð Þ¼ <sup>0</sup> [0.8555, 0.8525, 0.8480, 0.8412, 0.8309, 0.8148, 0.7896, 0.7483, 0.6767, 0.5369, 0.2300]. The convergence time of the observer is 48 sec.

Figure 6 shows the result of the fuzzy observer simulation considering a disturbance in the plate 6 composition.

Figure 7 shows the plate 6 composition estimated by the fuzzy observer and the comparison with the nonlinear model to verify the observer's convergence.

Figure 8 shows the simulation of the compositions estimated by the fuzzy observer under seven perturbations in the composition of plates 4, 6, and 8.

In Figure 9, a comparison between the light component compositions in plates 4, 6, and 8 is shown to verify the convergence of the fuzzy observer with the nonlinear model.

Figure 4. Light component composition, nonlinear model.

It can be noted that the light component composition estimation has a minimum

error compared with the composition obtained from the nonlinear model using real data; besides, the convergence time is suitable for an online failure detection

system or different control tasks.

Plates 4, 6, and 8 light component estimations under disturbances.

Figure 6.

Figure 7.

Figure 8.

23

Plate 6 light component estimation under disturbance.

DOI: http://dx.doi.org/10.5772/intechopen.83479

Fuzzy Logic Modeling and Observers Applied to Estimate Compositions in Batch Distillation…

Plate 6 light component estimation comparison.

Figure 5. Light component estimated by the observer. Different initial conditions.

Fuzzy Logic Modeling and Observers Applied to Estimate Compositions in Batch Distillation… DOI: http://dx.doi.org/10.5772/intechopen.83479

Figure 6. Plate 6 light component estimation under disturbance.

The system input signals used in the validation stage are the reflux signal, considering an opening percentage of 20%, starting at the 5 min and lasting 30 min,

Figure 4 shows the light component compositions calculated by the nonlinear model in the 11 plates of the distillation column; this simulation is carried out

Figure 5 shows the composition estimated by the observer with initial conditions

Figure 7 shows the plate 6 composition estimated by the fuzzy observer and the

In Figure 9, a comparison between the light component compositions in plates

different from the nonlinear model. The composition initial conditions of the observer are <sup>x</sup>^\_ð Þ¼ <sup>0</sup> [0.8555, 0.8525, 0.8480, 0.8412, 0.8309, 0.8148, 0.7896, 0.7483, 0.6767, 0.5369, 0.2300]. The convergence time of the observer is 48 sec. Figure 6 shows the result of the fuzzy observer simulation considering a distur-

comparison with the nonlinear model to verify the observer's convergence. Figure 8 shows the simulation of the compositions estimated by the fuzzy observer under seven perturbations in the composition of plates 4, 6, and 8.

4, 6, and 8 is shown to verify the convergence of the fuzzy observer with the

and the heating power.

considering no disturbances in the system.

Distillation - Modelling, Simulation and Optimization

bance in the plate 6 composition.

nonlinear model.

Figure 4.

Figure 5.

22

Light component composition, nonlinear model.

Light component estimated by the observer. Different initial conditions.

Figure 7. Plate 6 light component estimation comparison.
