Theoretic derivation of control actions for three-rule fuzzy PID controllers

Three-rule fuzzy PID controllers are developed which employ only a single input variable to generate the fuzzy proportional action. The nonlinear mapping between the input and output of the fuzzy system is represented explicitly, and the control actions are defined in terms of the design parameters. Important properties of the nonlinear relationship are discussed to provide an analytical basis for the systematic design of the controllers. Numerical simulation is presented to show the performance of the proposed controllers