An Optimal Fuzzy Control Method for Nonlinear Time-Delayed Batch Processes

An optimal fuzzy controller design scheme is proposed to address the influence of time delay and disturbance on the control performance of nonlinear batch processes. First, a two-dimensional (2D) equivalent Takagi-Suguno (T-S) fuzzy error model is formulated. By introducing a quadratic performance index function and adopting 2D Lyapunov-Krasovskii theory, the existence condition of the optimal fuzzy control law is given. Furthermore, its solvable condition, which depends on time-delay bounds, is constructed in terms of linear matrix inequalities, and its gain is obtained by using an optimization algorithm. This design has the advantages of faster tracking and better tracking performance. Finally, two different algorithms (with and without optimization) are used to control the water level of a triple-capacity water tank. The results show that the presented strategy is more effective and feasible.