Optimization of distributed order fractional PID controller under constraints on robustness and sensitivity to measurement noise

This paper describes a novel approach towards optimal tuning of distributed order fractional PID controller parameters. A distributed order fractional PID controller (DPID) is approximated by a compound fractional controller with multiple fractional differintegrators connected in parallel. Orders of these differintegrators have been equally spaced, with the first one being the classical integrator of order 1, and the last one being the classical differentiator of order 1. A classical noise cancellation filter is considered as a part of controllers structure. The controller parameters, being the gains of all differintegrators, have been tuned. Proposed tuning procedure maximizes gain of classical integrator term under constraints on Maximum sensitivity, Ms, Maximum sensitivity to measurement noise, M
_n
and Maximum complementary sensitivity, M
_p
. Results are presented via a number of numerical simulations.