Analysis and design of fuzzy-PID controller with generalized linear membership function

A kind of membership function, called as generalized linear membership function(GLMF), is designed in the paper, and the triangular and trapezoid ones are as its special cases. It is derived that the fuzzy-PID Controller with GLMF is equivalent to the sum of a nonlinear PID controller and a compensation value, based on the analytical structure of the controller. With the definition of fuzzy Lyapunov function, the stabilization condition is given to adjust the performance of the fuzzy system. Finally, the characters of the designed fuzzy system, derived by theoretical analysis, are manifested by the simulation results of several examples.