Design, Performance, and Stability Analysis of a Formula-based Fuzzy Pi Controller

In this paper, a new formula-based fuzzy proportional-integral (FPI) controller is proposed. This controller is based on the conventional proportional-integral (PI) controller. The proposed FPI controller has a linear structure similar to that of the conventional controller, and the operation of the proposed controller is based on analytical formulas. The structure is designed by using three membership functions as input variables and five membership functions as output variables. Thus, the proposed controller is a discrete-time fuzzy version of the conventional PI controller. For performing stability analysis, sufficient conditions for the bounded-input bounded-output (BIBO) stability of overall closed-loop control are derived by using the small gain theorem. The performance of the FPI controller in setpoint tracking, disturbance rejection, and noise suppression is evaluated. Computer simulations of the control of the outlet flow concentration of a nonlinear non-thermic catalytic continuous stirred-tank reactor (CSTR) were performed by using the National Instrument software LabVIEW ; the simulation results obtained for the proposed FPI controller and its counterpart fuzzy PI (NI FPI) controller using Fuzzy Logic toolkit were compared. The performance of the proposed formula-based FPI controller is considerably better than that of the NI FPI controller. Our simulation results demonstrate the effectiveness of the proposed FPI controller.