Equivalent variable domain fuzzy PID control with non-origin symmetry in the theoretical domain

The traditional variable domain fuzzy PID controllers need to contraction-expansion the internal domain of the fuzzy controllers, which has high design complexity and is difficult to implement. A control strategy is proposed to solve this problem. This control strategy does not change the internal domain of the fuzzy controller, but changes the input and output of the fuzzy controller to achieve the equivalent variable domain effect. In addition, in view of the limitation that the current method of the domain contraction-expansion is only applicable to the origin symmetric domain, a method is proposed to determine the position of the variable in the non-origin symmetry domain after the domain contraction-expansion. An equivalent variable-domain fuzzy PID controller is designed for a system that uses a servo motor and a ball screw as the drive mechanism. The feasibility of the equivalent variable domain fuzzy PID controller is verified by Matlab/Simulink simulation comparison experiments. And the experiments demonstrated that the equivalent variable domain fuzzy PID controller has faster response speed, stronger anti-interference ability and better control performance than the traditional fuzzy PID controller, PID controller and traditional variable domain fuzzy PID controller.