5. Conclusions

In this work a fuzzy observer to estimate the molar composition of the light component in each plate of a binary distillation column is presented. The observer is based on a Takagi-Sugeno fuzzy model of eight rules, taking as premise variables the light component composition in the condenser and in the boiler, as well as the reflux signal.

The gains are calculated by means of LMIs in order to guarantee the stability for each of the closed loop linear subsystems.

The fuzzy observer is validated in simulation by using real data from an 11-plate binary distillation column for an ethanol-water mixture, considering seven RTD temperature sensors and a 300-watt heating resistor. In order to validate the fuzzy observer convergence, different tests were carried out with ideal and different initial conditions between the nonlinear system and the fuzzy observer, as well as disturbances in the light component composition in the nonlinear system.

The observer under different initial conditions has a convergence time of 45 sec. It is also shown that the observer's convergence time under disturbances in the composition of the plate 1 is 1 sec.

Applying from two to seven perturbations to the nonlinear system, it is demonstrated that the observer is robust under multiple perturbations, enabling its implementation as a residual generator in a fault detection system.

Author details

25

Mario Heras-Cervantes<sup>1</sup>

Héctor Javier Vergara Hernández<sup>2</sup>

Juan Anzurez-Marin<sup>1</sup> and Elisa Espinosa-Juárez<sup>1</sup>

1 UMSNH, DEPFIE, Morelia, Michoacán, México

2 TecNM/IT Morelia, Morelia, Michoacán, México

provided the original work is properly cited.

\*Address all correspondence to: actelleza@gmail.com

, Gerardo Marx Chávez-Campos<sup>2</sup>

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

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

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

,

\*,

, Adriana del Carmen Téllez-Anguiano<sup>2</sup>

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