International Journal of Chemical Engineering and Applications, Vol. 1, No. 1, June 2010 ISSN: 2010-0221 38 Abstract—In this paper, a fuzzy model predictive control strategy is proposed for multivariable nonlinear control problem in a distillation column. This method is based on piecewise linear fuzzy model of the process to be controlled, which is used for predicting the outputs. An optimization technique is developed to minimize the difference between the model predictions and the desired prediction horizon. Comparisons are made with conventional controllers. The results confirmed the potentials of the proposed strategy of piecewise linear fuzzy control. Index Terms— Distillation column, MIMO systems, Model Predictive Control, Takagi-Sugeno fuzzy model. I. INTRODUCTION Model Predictive Control (MPC) is a powerful tool for the control of multivariable systems. It has become a popular research topic during last few decades [1] and unlike many other advances techniques. The main reason for this success is the ability of MPC to control multivariable systems under various constraints in an optimal way. Continuous and batch processes in chemical and petrochemical plants are inherently nonlinear and many of them are highly nonlinear. For highly nonlinear system, a linear MPC algorithm may not give satisfactory dynamic performance. Several researchers [10] have developed nonlinear model predictive control (NMPC) algorithms that accept various kinds of nonlinear models such as nonlinear ordinary differential equations, partial differential equations, integro-differential equations and delay equations models. Such models can be accurate over a wide range of operating conditions. However, these models, usually based on the first principles, are difficult to develop for many industrial cases. Moreover, an NMPC incorporating a nonlinear process can be precisely described by a set of linear submodels in someway, and then the design of a model predictive controller can be greatly simplified. Reference [3] introduced a novel fuzzy logic-based modeling methodology, where a nonlinear system is divided into a number of linear or nearly linear subsystems. A Manuscript received April 9, 2010. R. Sivakumar is with St. Joseph’s College of Engineering, Anna University, Chennai ( phone: +91 9444309944; fax: +91 44 2450 0861; e-mail: rsivakumar1@gmail.com). K. Suresh Manic is with St. Joseph’s College of Engineering, Anna University, Chennai (e-mail: ksuresh_me@yahoo.com) V. Nerthika is a research scalar in the Department of Chemical engineering, Anna University, Chennai (e-mail: nerthi82@gmail.com) R. Akila is a research scalar in the Department of Chemical engineering, Anna University, Chennai (e-mail: akilarajamanickam@yahoo.com) K. Balu is with Department of Chemical Engineering, Anna University, Chennai (e-mail: kbalu@annauniv.edu) quasi-linear empirical model is then developed by means of fuzzy logic for each subsystem. The model is a rule-based fuzzy implication (FI). The whole process behavior is characterized by a weighted sum of the outputs from all quasi-linear FIs. The methodology facilitates the development of a nonlinear model that is essentially a collection of a number of quasi-linear models regulated by fuzzy logic. It also provides an opportunity to simplify the design of model predictive controllers. However some issues limit the possible application of MPC to multivariable systems with significant delays and nonlinear systems. These limitations can be deal with fuzzy MPC (FMPC). However, tremendous difficulties have been found in tuning controller parameters since the algorithm requires frequent model updating in control. A T–S type model is the basis of their fuzzy model. However, they essentially treated the fuzzy model as a set of conventional piecewise linear models. Thus, the uniqueness of a Takagi–Sugeno-type model exhibiting soft transition through any operating regions is lost, causing deterioration in the closed-loop dynamic performance of a system. The recent interest in fuzzy logic controllers can be attributed to their ability to exploit the tolerance for imprecision and uncertainty to achieve robustness and low-cost solution. The advantages of fuzzy logic are used with MPC to provide the solution for complex problems. In this paper a FMPC algorithm is developed and applied to binary distillation column. First, a fuzzy model of distillation column is developed and can be used as a predictor in MPC [5]. Then the objective functions and optimizer based on fuzzy rules are developed. Model based controllers use an internal model to predict future outputs. These future outputs can be calculated by means of different optimization methods, depending on the system and objective functions. In this paper, Takagi- Sugeno fuzzy model is used for distillation column and branch-and-bound algorithm is used for optimization. II. PROCESS DESCRIPTION A. System Modelling A typical two product distillation column is taken as study model shown in Fig. 1 shows the most important loops of a binary distillation. Acceptable operation of a binary distillation column normally requires the following control objects: • Control of the composition of the distillate • Control of the composite of the bottom products • Control of the liquid hold-up in reflux drum • Control of the liquid hold-up at the base of the column The first two control objectives characterize the two Application of Fuzzy Model Predictive Control in Multivariable Control of Distillation Column R. Sivakumar, K. Suresh Manic, V. Nerthiga, R. Akila, K. Balu