Analytical structures of Gain-Scheduled fuzzy PI controllers

In this paper analytical input and output relation for Gain-Scheduled fuzzy PI controllers that use Zadeh AND operator with symmetric trapezoidal input fuzzy sets and skewed trapezoidal input fuzzy sets are derived. Overall input space division for symmetric and skewed trapezoidal input fuzzy sets with three membership functions in each input are derived for gain scheduled Fuzzy PI controllers. A self-tuning scheme for fuzzy logic controllers (FLCs) with output scaling factor (SF) is adjusted by fuzzy rules according to current trend of controlled process. The rule-base for tuning the output scaling factor is defined on error and change in error of the controlled variable using the symmetric trapezoidal and skewed trapezoidal membership functions (MFs). Tuning of the output scaling factor plays an important role in this self-tuning scheme. To show the effectiveness of gain scheduled fuzzy PI over fuzzy PI controller computer simulations for first order and second order time delay systems are considered.