Design and Analysis of a Typical Fuzzy Controller with General Linear Membership Function

Based on the analytical structure of a typical fuzzy controller with sum-product operators, gravity of center defuzzifier and single point output, the default of trapezoid membership function is analyzed in detail, and then a new kind of membership function called general linear membership function (abbr. GLMF) is designed in the paper. GLMF includes characters of triangle and trapezoid shaped membership function which are widely used in practical application. With the derivation of analytical structure of fuzzy controller with GLMF, It is proved that the fuzzy controller is the sum of a global two-dimensional multilevel relay and a local nonlinear PI or PD controller with nonlinear gain. Finally, a typical single inverted pendulum system is used in simulation to manifest the effectiveness of the design.