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In this paper, as an introduction, the nonlinear model of a distillation column is presented in order to understand the fundamental paper that the column heating actuator has in the distillation process dynamics as well as in the quality and safety of the process. In order to facilitate the implementation control strategies to maintain the heating power regulated in the distillation process, it is necessary to represent adequately the heating power actuator behavior; therefore, three different models (switching, nonlinear and fuzzy Takagi–Sugeno) of a DC-DC Buck-Boost power converter, selected to regulate the electric power regarding the heating power, are presented and compared. Considering that the online measurements of the two main variables of the converter, the inductor current and the capacitor voltage, are not always available, two different fuzzy observers (with and without sliding modes) are developed to allow monitoring the physical variables in the converter. The observers response is compared to determine which has a better performance. The role of the observer in estimating the state variables with the purpose of using them in the sensors fault diagnosis, using the analytical redundancy concept, likewise, from the estimation of these variables other non-measurable can be determined; for example, the caloric power. The stability analysis and observers gains are obtained by linear matrix inequalities (LMIs). The observers are validated by MATLAB® simulations to verify the observers convergence and analyze their response under system disturbances.

Distillation is the process most commonly used in industry to separate chemical mixtures; its applications range from cosmetic and pharmaceutical to petrochemical industries. The equipment required to perform the distillation process is known as distillation column. Since initial investment and maintenance costs for distillation columns are very high it is necessary to have an appropriate mathematical model that allows improving the comprehension of the column dynamics, especially its thermal behaviour, in order to enhance the control and safety of the process. This chapter presents a general panorama of the mathematical modelling of distillation columns, having as a specific case of study the comparison of a space-state non-linear model and a Takagi-Sugeno fuzzy model for a batch distillation column using a binary mixture (Ethanol-Water).

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