Development of a type-2 fuzzy proportional controller

Studies have shown that PID controllers can be realized by Type-1 (conventional) fuzzy logic systems (FLSs). However, the input-output mapping of such fuzzy PID controllers are fixed. The control performance will, therefore, vary if the system parameters are uncertain. This paper aims at developing a type-2 FLS to control a process whose parameters are uncertain. A method for designing Type-2 triangular membership functions with the desired generalized centroid is first proposed. By using this type-2 fuzzy set to partition the output domain, a type-2 fuzzy proportional controller is obtained. It is shown that the type-2 fuzzy logic system is equivalent to a proportional controller that may assume a range of gains. Simulation results are presented to demonstrate that the performance of the proposed controller can be maintained even when the system parameters deviate from their nominal values.