Two-rule-based linguistic fuzzy controllers

This paper presents a new methodology to design two- or three-input-single-output fuzzy logic controllers (FLCs). The main features of the proposed methodology are: 1) the rule-bases are not complete and consist of only two rules relating fuzzy descriptions of not-self correcting errors to the sign of control actions, and 2) appropriate choices of input and output membership functions together with a fuzzy reasoning method lead to completeness of the controllers. The paper also focuses on the use of a quasilinear-mean (q-l-m) operator as soft implementation of the logical connective "and". FLCs derived in this way are characterized by input-output mappings which are smooth, easy-to-analyze, and easy-to-implement. This paper also includes a comparison with conventional three-term controllers and N×N-rule-based FLCs. Some simulation results are also proposed.