Interval Type-2 Fuzzy PID Controller Using Disassembled Gradational Optimization

This paper presents an interval type-2 fuzzy proportional–integral–derivative (IT2F-PID) controller that is designed using a new disassembled gradational optimization (D-GO) method. A PID controller is first optimized using the D-GO method and then connected to a type-1 fuzzy logic system (T1-FLS). The parameters of the T1-FLS are optimized, and the T1-FLS is blurred into the interval type-2 fuzzy logic system (IT2-FLS). Finally, the IT2F-PID controller is formed. The proposed method is compared with the concurrent and general optimization methods. The simulation results show that the D-GO method reduces the optimization time by over 90% compared with the general method, and decreases the integral-of-time-absolute-error (ITAE) by 30%. Beyond that, compared with the concurrent optimization method, the D-GO method reduces time by over 25%, and the ITAE value by about 95%. In the normal case, model uncertainty, target uncertainty, and external disturbance, the control ability of the IT2F-PID controller designed using the D-GO method is verified via simulations using a nonlinear forced closed-loop system. The results show that the overshoot is reduced by 80% and the fluctuation is reduced by 67% compared with a traditional PID controller and an IT2F-PID controller built using the general method.