A robust fuzzy digital PID control methodology based on gain and phase margins specifications is proposed. A mathematical formulation based on gain and phase margins specifications, the Takagi-Sugeno fuzzy model of the process to be controlled, the structure of the digital PID controller, and the time delay uncertain system are developed. A multiobjective genetic strategy is defined to tune the fuzzy digital PID controller parameters, so the gain and phase margins specified to the fuzzy control system are found. An analysis of necessary and sufficient conditions for fuzzy digital PID controller design with robust stability, with the proposal of the two theorems, is presented. Experimental results show the efficiency of the proposed methodology in this chapter, applying a platform control in real time of a thermic process through tracking the reference and the gain and phase margins keeping closed the specified ones.
