Robust Tracking Control for the Non-isothermal Continuous Stirred Tank Reactor

Abstract

A non-isothermal continuous stirred tank reactor (CSTR) is the most important element of chemical industrial equipment which is characterized by a highly nonlinear behavior. It is a multi-input multi-output (MIMO) nonlinear systems exposed to disturbances. The operation of the non-isothermal CSTR can be disturbed by its uncertain parameter such as variation in heat reaction. Therefore, the two difficult problems in CSTR control are tracking trajectory and disturbance attenuation. In this paper, a robust H∞ fuzzy tracking control via Takagi-Sugeno (T-S) model is designed to robustly stabilize the non-isothermal CSTR system for both concentration and temperature affected by disturbances. T-S fuzzy model approach is proposed to derive the nonlinear model of the CSTR to several local linear models. A parallel distributed compensation control law is used to stabilize the closed-loop system. Linear matrix inequality conditions are derived for analyzing regional robust stability and performance based on Lyapunov function, and an H∞ criterion is employed to guarantee the attenuation of disturbances. In trajectory tracking framework, an integral action is introduced as a new state variable. Finally, a comparative study between H∞ controller and linear quadratic regulator (LQR) controller is made. Simulation results show that the proposed H∞ controller ensures an asymptotic stability and guarantees highly robustness against changes in reaction heat with a good trajectory tracking. The H∞ controller gives better performance than the classical LQR controller.

Keywords

• takagi-sugeno fuzzy model
• parallel distributed compensation
• h-infinity
• linear quadratic regulator
• continuous stirred tank reactor
• bioprocess