An approach for the robustness comparison between piecewise linear PID-like fuzzy and classical PID controllers

摘要

The comparison of the stability robustness between the classical PID controller and two piecewise linear PID-like fuzzy controllers to the variations of the parameters in the second order plant is provided in this paper. The definition of a stability robust controller (to the parameter variations of the plant model) is presented. Then Kharitonov's theorem is applied to find the regions of robustness to the parameter variations for the control systems with different controllers. Based on the size of regions of robustness, the relative robustness factor is defined, and the robustness comparison is provided. For every classical PID controller with gain coefficients determined and fixed, it is shown that we can always design the piecewise linear PID-like fuzzy controllers to be more robust than the specific classical PID controller. The results of robustness comparison is further confirmed in the simulation included for the second order uncertain plant.