Fuzzy digital PID controller design based on robust stability criteria

Abstract

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, was developed. From input and output data of the process, a Fuzzy C-Means (FCM) clustering algorithm estimates the antecedent parameters and the rules number of a Takagi-Sugeno fuzzy model, whereas the least squares algorithm estimates the consequent parameters. A multiobjective genetic strategy is developed to tune the fuzzy digital PID controller parameters, so the gain and phase specified margins are obtained for the fuzzy control system. An analysis of necessary and sufficient robust stability conditions for fuzzy digital PID controller design, with the proposal of two theorems are presented. The digital fuzzy PID controller was implemented on a real time acquisition data platform, based on CompactRIO (NI cRIO-9073) and LabVIEW, from National Instruments, for temperature control of a thermic process. The experimental results for real time robust fuzzy digital PID control of the thermic process demonstrate the effectiveness and practical viability of the proposed methodology.