Describing function method for stability analysis of PD and PI fuzzy controllers

A fuzzy logic controller saturates outside the universe of discourse region. This saturation gives rise to a universal nonlinearity for this type of controller. In this paper, the effects of this nonlinearity are analyzed for the most usual fuzzy controllers: PD and PI fuzzy controllers. It is shown that due to this saturation some pathological behaviors such as oscillations or unstable limit cycles can occur. The methodology employed in the analysis is based on the describing function, which is determined for PD and PI fuzzy controllers. One example illustrates the relevance of the proposed methodology.