Stability Analysis of Parallel Fuzzy P + Fuzzy I + Fuzzy D Control Systems

The study presented in this paper is in continuation with the paper published by the authors on parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP + FI + FD) controller. It addresses the stability analysis of parallel FP + FI + FD controller. The famous small gain theorem is used to study the bounded-input and bounded-output (BIBO) stability of the fuzzy controller. Sufficient BIBO-stability conditions are developed for parallel FP + FI + FD controller. FP + FI + FD controller is derived from the conventional parallel proportional plus integral plus derivative (PID) controller. The parallel FP + FI + FD controller is actually a nonlinear controller with variable gains. It shows much better set-point tracking, disturbance rejection and noise suppression for nonlinear processes as compared to conventional PID controller.