Design of Robust Fuzzy Regulators with Optimal Initial Conditions Compensation

 In almost all cases, the goal of the design of automatic control systems is to obtain the parameters of the controllers, which are described by differential equations. Takagi-Sugeno (T-S) fuzzy models can perfectly represent the nonlinear system. In general, the controller is artificially built and it is possible to update its initial conditions. In the design of optimal quadratic regulators, the initial conditions of the controller can be changed in an optimal way and they can improve the performance of the controlled system. Following this idea, an LMI-based design procedure to update the initial conditions of PI controllers, considering the nonlinear plant with polytopic uncertainties, described by T-S fuzzy models, is presented. The importance of the proposed method is that it also allows other specifications, such as, the decay rate and constraints on control input and output. Keywords automatic control, initial conditions, IVC, quadratic regulator, PI controller, optimal control, LMIs, polytopic uncertainty.