Derivation and analysis of three-input inference for fuzzy PID controllers

The fuzzy PID controller based on three-input inference is analyzed. Defining linear fuzzy regions in a linguistic error state space, a general Linear-like Fuzzy Logic Controller output is obtained. The solutions for two- and one-input fuzzy outputs are obtained as special cases of the three-input solution. The outputs of each controller are decomposed into linear and nonlinear terms with simple expressions. The multi-phase solution that exists in the fuzzy output solution is expressed with least number of non-linear terms. The linear output is used to identify the apparent linear PID gains of each controller type. The behavior of the apparent gains is similar to linear gain terms in a conventional PID controller. Thus three types of fuzzy controllers are tuned for obtaining overall performance.