2. Takagi-Sugeno fuzzy model for a batch distillation column

The objective of a batch distillation process is to separate two or more elements from a mixture, where the most volatile element is obtained as the distilled

mixture and the extraction of the distilled product are carried out continuously. In the batch distillation, the mixture is initially deposited in the boiler; at the end of the

The batch operation is mainly used to separate small amounts of mixture, to obtain different qualities of the distilled product from the same mixture, or to

A batch distillation column is not operated using constant parameters; the control actions are continuously adjusted according to the state of the distillation; therefore, monitoring and controlling all the variables of the process are essential to improve the quality and quantity of the distilled product, as well as to guarantee the safety of the process and the operators. To fulfill or facilitate this objective, it is necessary to implement control techniques such as models, observers, and controllers.

In the literature, modeling and control techniques such as estimators, observers, fault detection systems, and control systems are applied to distillation columns in order to obtain a better analysis and understanding of the dynamics of the process, improving the quality of the distilled product and enhancing the user safety, among other tasks. Distillation column simplified models present the basic principles of the process and its operation taking into account several considerations to describe the dynamics of the system in a simpler but understandable form. Authors in [2] present a simplified model of a binary distillation column, based on the liquid-vapor equilibrium of the binary mixture and the mass balance considering all the elements of the

Authors in [3] design a model based on the existence of the liquid and vapor molar fluids that vary in each column plate; the compositions of the bottom product and the distilled product are estimated using a dynamic model based on the mass and component balances. In [4] a low-order model of an ideal multicomponent distillation using the theory of nonlinear wave propagation is presented. Authors in [5] present a low-order model for a reactive multicomponent distillation column, in addition to designing a predictive control to obtain the best quality of the distilled product. Rigorous models are more complete because they represent plate by plate the element balance of phases in each element of the distillation column (boiler, condenser, and plates). In these models, the mathematic expressions are determined by a series of differential equations given by mass, light component, or energy balances depending on the application, the control strategy, or the operation type. An important advantage of the rigorous modeling is the high resolution of the dynamics, having the disadvantage of combining a greater number of variables and expressions that make difficult the design, simulation, and implementation of controllers.

In [6], a model based on neural networks is presented in order to optimize the energy efficiency in a binary distillation column. Authors in [7] present a model of a binary distillation column based on neural networks. The neural network training and validation are performed using real data from a nine-plate pilot plant for a mixture of methanol and water. Authors in [8] present the simulation and optimization of a rigorous model for a batch reactive distillation column. Authors in [9] present the design and simulation of a discrete Kalman filter to estimate the molar

Generally, the light component composition measurement is performed offline using expensive instruments, so the implementation of state observers to estimate online this composition has become a frequent and important task. Authors in [10–12] present high-gain observers to estimate the light component composition in all the distillation column plates from the measurement of the temperature of

Due to the different distillation types and their mathematical representation, there are different types of observers for different applications. In [13] the authors

compositions of the light component in a batch distillation column.

some plates and the column actual inputs.

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process, the distillate and bottom product are extracted.

Distillation - Modelling, Simulation and Optimization

separate multicomponent mixtures.

distillation column as plates.
