On the distributed order PID controller

This paper proposes a generalized fractional controller that covers the complete range of differintegrators of order −1 to order 1. This controller is named distributed order PID controller (DOPID) due to the fact that it broadens the structure of the conventional PID controller. Furthermore, a new method for implementation of distributed order PID controller (DOPID), as well as analysis of its properties in both time and frequency domain are proposed. As DOPID controller represents generalized classical PID controller, it is approximated by a compound fractional controller with multiple fractional differintegrators, with multiple gains, connected in parallel. Orders of these differintegrators have been equally spaced, with the first one being the first order classical integrator, and the last one being the first order classical differentiator. Noise cancellation filter is considered explicitly in the controller's structure.