A unified general type-2 fuzzy PID controller and its comparative with type-1 and interval type-2 fuzzy PID controller

Abstract

For the type reduction of general type-2 fuzzy sets based on α-plane representation was converted to type reduction of several interval type-2 fuzzy sets, so it was time consuming in real applications. In this paper, a unified general type-2 fuzzy PID (UGT2-FPID) controller using the upper and lower bounds of one α-plane is proposed, which has higher real time. The UGT2-FPID controller contains another two adjust parameters, and the analytical structure of UGT2-FPID controller is obtained by adapting input combination method. Furthermore, this paper discusses the parameter adjustment methods to achieve better controlling effects by the mathematical expressions of UGT2-FPID controller. The robustness and effectiveness of proposed general type-2 fuzzy PID controller are tested by two production process objects. The simulation results show that the controlling effects of proposed general type-2 fuzzy PID controller are better than PID, type-1 fuzzy PID, and interval type-2 fuzzy PID controller even if there are exit uncertainties, like controlled object structure changing, controller disturbance, or output noise.