Maximum sensitivity based fractional IMC–PID controller design for non-integer order system with time delay

• A novel fractional controller structure is investigated based on internal model control scheme.
• An analytical method is proposed for the controller parameters tuning using maximum sensitivity.
• The proposed fractional IMC-PID controller has a good robustness with respect to process variation and model uncertainty.
• The controller parameters can be easily determined by a given robust degree (maximum sensitivity).

A simple approach with a small number of tuning parameters is a key goal in fractional order controller design. Recently there have been a number of limited attempts to bring about improvements in these areas. In this paper, a new design method for a fractional order PID controller based on internal model control (IMC) is proposed to handle non-integer order systems with time delay. In order to reduce the number of tuning parameters and mitigate the impact of time delay, the fractional order internal model control scheme is used. Considering the robustness of the control system with respect to process variations and model uncertainty, maximum sensitivity is applied to the tuning of the parameters. The resulting controller has the structure of a fractional order PID which is cascaded with a filter. This is named a fractional IMC–PID controller. Numerical results are given to show the efficiency of the proposed controller.