PI Fuzzy Virtual Actuator Design for Takagi-Sugeno Systems

The paper presents conditions suitable in design of Takagi-Sugeno proportional/integral fuzzy virtual actuators for the nonlinear continuous-time systems, controllable by the Takagi-Sugeno fuzzy output controllers in parallel distributed form. Considering measurable premise variables independent on the system inputs, the problem is formulated as an enhanced disturbance suppression concept, implying asymptotic stability of the closed-loop system after activation of the Takagi-Sugeno fuzzy virtual actuator. Demonstrating the separation principle for Takagi-Sugeno fuzzy virtual actuator design, the sufficient design conditions are outlined in the terms of linear matrix inequalities in adapted bounded real lemma structures. The method generates the Takagi-Sugeno fuzzy virtual actuator also in a parallel distributed form, to compile the sub-model closed-loops after the fuzzy virtual actuator activation by inference through the membership functions. Takagi-Sugeno fuzzy virtual actuator is performed as an autonomous algorithm that may be activated with dependence on the fault detection and isolation subsystem response.