Nonlinear input mapping in fuzzy control systems

The input scaling factors in a fuzzy control system are often used as a transformation from the real input data to the desired space. Sometimes, they are tuned for better performance just as the coefficients in a PID controller. Theoretically, they are constant and should be adjusted for better performance while the operating point is changed. In this paper, the authors suggest nonlinear mapping functions to substitute the role of input scaling factors. The results show how the nonlinear mapping function work and the performance could be better by proper adjustment. It is also noticed that such mapping will change the shapes of the membership functions. That means one need not tune every membership function of linguistic variables, and just choosing a proper nonlinear mapping function could achieve the same effects. The authors use an inverted pendulum system to verify the results.