Fractional Order PID Controller Tuning by Frequency Loop-Shaping: Analysis and Applications

The purpose of this paper is to compute the parameters of the fractional Proportional Integral Derivative (PID) controller to achieve a closed loop sensitivity bandwidth approximately equal to a desired bandwidth using frequency loop shaping technique. This work provides the influences of the order of a fractional integrator which is used as a target on loop shaping, stability and robustness performance. A comparison between classical PID controllers and fractional PID controllers is presented. Some advantages of fractional PID controllers over classical PID controllers have been discussed. The proposed models used in this work are to compute the classical PID parameters. The novelty in this work is to develop a generalized mathematical form for the fractional PID.