Robust Control Of Continuous Stirred Reactor System Based On T - S Fuzzy Model

In the practical industrial process, Continuous Stirred Tank Reactor(CSTR) is one of the important equipments. The chemical reaction process of a CSTR system involves nonlinearities, time-delays and uncertainties. It is difficult to apply the traditional control theory for modeling and controlling CSTR systems. Therefore,it has very important significance to research nonlinear time-delay models of CSTR systems. It is well known that Takagi-Sugeno(T-S) fuzzy models can approximate a nonlinear smooth function to any specified accuracy. As a result, analysis and synthesis methods in the linear control theory can be applied to nonlinear systems. So, T-S fuzzy model is one of important methods to research CSTR systems.So the T-S fuzzy model-based research of CSTR systems has important practical significance.This paper aims at identifying the non-dimensional model of CSTR systems to T-S fuzzy model. Thereby, the problems of stability analysis and H∞control of CSTR systems are investigated by employing Lyapunov-Krasovskii stability theory,the parallel distributed compensation method, and linear matrix inequality technique.Firstly, we introduce structure and working mechanism of CSTR systems, and then establish mathematical model of CSTR systems by utilizing the principle of material balance. Furthermore, a non-dimensional model is given.Secondly, the H∞control problem of T-S fuzzy uncertain linear time-delay systems is studied. By constructing appropriate Lyapunov-Krasovskii functional and applying delay-range-partition technique, convex technique and reciprocally convex technique to deal with its derivative, an H∞performance criterion in the form of linear matrix inequalities is given. From which the desired H∞feedback controller is designed by using the parallel distributed compensation(PDC) algorithm. Then a simulation is done by the Simulink and YALMIP Toolbox of MATLAB to verify the effectiveness of the theory results.Finally, the nonlinear model of CSTR system is identified to T-S fuzzy model.Then by employing the H∞performance criterion that is investigated previously,the desired robust H∞controller is designed. Then a simulation is done by the YALMIP Toolbox of MATLAB to verify the effectiveness of the theory results.