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

present a discrete-time D-LPV observer to estimate sensors and actuators states and faults, using the H∞ approach applied to the estimation error.

In [14], the authors present a pair of extended Luenberger observers (complete and reduced order) to estimate the compositions of a multicomponent mixture from temperature measurements of the distillation column plates. The observers' gains are calculated from the location of the closed-loop eigenvalues using a mathematical software.

In [15], a full-order nonlinear observer is presented to estimate the composition and temperatures of a distillation column. A nonlinear model obtained by the mass balance in each plate of the column is used, resulting in a set of high-order differential equations with nonlinear terms. The observer is validated in simulation to demonstrate his behavior and his robustness. The parametric representation or identification is another methodology used to estimate certain variables of the distillation columns, as presented in [16, 17].

The difficulty of designing and implementing the observers lies mainly in the nonlinear dynamics of the distillation column; thus, having a linear system would facilitate the design of observers and controllers to implement control strategies such as fault detection and diagnosis systems and automatic control and tolerant control in order to improve the performance and safety of the process, as well as the quality of the distilled product.

The Takagi-Sugeno fuzzy modeling is a tool to model and control complex systems using a nonlinear system decomposition in a multi-model structure formed by linear and not necessarily independent and fuzzy logic models [18, 19], where the representation of the nonlinear system is achieved by a weighted summation of the whole subsystems. The Takagi-Sugeno representation provides a solution to solve the problems in the design and implementation of control strategies for nonlinear systems.

In [20], the authors propose a methodology to design control techniques for systems represented in the Takagi-Sugeno form. In [21] the identification of a model of a binary distillation column, based on fuzzy models, taking into account 6 system inputs and 2 outputs for 64 rules is presented. The model is simulated using real data to validate its performance.

Authors in [22] present a controller of the molar composition of the distilled and bottom products for a binary distillation column using neural networks and fuzzy logic (ANFIS) based on a 2 2 MIMO system. In [23] an adaptive PID controller based on Takagi-Sugeno modeling to control the distilled and bottom products of a binary distillation column is presented.

Due to the close relationship between the fuzzy representation of nonlinear systems and the theory of linear matrix inequalities, different works based on both techniques have been developed, allowing to find solutions to the calculations corresponding to the observer and controller gains and the Lyapunov stability analysis. In [24], a methodology to design observers and controllers for a fuzzy system is proposed.

The main contribution of this work is the design of a fuzzy observer based on a Takagi-Sugeno model to estimate the molar compositions and temperatures of the light component in each plate of a binary distillation column. The observer performance is validated for applications such as system monitoring and fault detection.
