Integrated system identification and PID controller tuning by frequency loop-shaping

A systematic design methodology for proportional-integral-derivative (PID) controllers is presented. Starting from data sets, a model of the system and its uncertainty bounds are obtained. The parameters of the controller are tuned by a convex optimization algorithm, minimizing a weighted difference between the actual loop transfer function and a target in an L₂/L_∞ sense. The target selection is guided by the identified model and its uncertainty. The problem of disjoint data sets and/or different models for the same system is also addressed. The method has proved successful in numerous practical cases showing both expediency in controller design and implementation and improved performance over existing controllers