A simplified version of mamdani's fuzzy controller: the natural logic controller

This paper proposes the natural logic controller (NLC) that it comes through a very important simplification of the Mamdani's fuzzy controller (MFC) allowing easy-design for single-input-single-output (SISO) regulation problems. Usually, fuzzy controllers are built with two classical signals of process: The error and its rate of change. They use a moderate number of fuzzy subsets and fuzzy rules. The main features of the NLC approach are that use the minimal fuzzy partition (only two fuzzy subsets per variable) and it use the minimal fuzzy rule base (only two rules). The nonlinear resulting fuzzy controller is the simplest one with an analytically well-defined, input-output mapping and accepting a linear approximation at origin. It allows easy extension to more than two signals of process. Some properties of nonlinear mapping of NLC are analyzed and some results are also presents on testing stability when NLC is used on a linear process. A special attention is addressed to the two inputs NLC case, where stability can be tested using the circle criterion. Finally, two application examples are discussed in details.