Comparative Study of Type-2 and Type-1 Fuzzy PI Controllers on Sensor Noise Suppression in a Control Loop

Abstract

The main contribution of this work is to reveal that footprint of uncertainty (FOU) of type-2 (T2) fuzzy logic sets (FLS) have a great impact on the system performance and the uncertainty caused by sensor noise can be effectively suppressed by merely changing the values of FOU. As a case study, in this paper, a novel technique for sensor noise suppression, i.e. minimizing the effects of measurement uncertainty, by T2 proportional-integral (PI) fuzzy logic controller (FLC) has been investigated in simulation for a discrete nonlinear and unstable system in closed loop using MATLAB environment. For T2 PI FLC, FOU was varied to find its optimum value to provide the best sensor noise suppression. The investigations conducted have shown that the FOU of 90% offered the best sensor noise suppression and in the considered case an improvement of 13-19% has been successfully observed over its counterpart type-1 (T1) PI FLC. T1 PI FLC was considered as a special case of T2 PI FLC with zero FOU and Genetic Algorithm (GA) was used to tune controller gains for minimum integral of absolute error (IAE) in T1 PI i.e. T2 PI FLC with zero FOU. The simulation results clearly demonstrated that the T2 PI FLC is better able to handle the uncertainty due to sensor noise present in the control system in comparison to T1 PI FLC.