Analytical Structures for Fuzzy PID Controllers?

In this paper, analytical structures for fuzzy proportional-integral-derivative (PID) controllers are derived by using triangular membership functions for inputs, singletons, or triangular membership functions for output, minimum triangular norm, maximum or drastic sum triangular conorm, Mamdani minimum, drastic or Larsen product inference, nonlinear control rules, and center-of-sum defuzzification. It is shown that these analytical structures are not suitable for control purpose. In this context, it is extremely important to note that the analytical structures reported by Carvajal et al. are also not valid for control.