Fractional-order unstable pole-zero cancellation in linear feedback systems

• Fractional-order unstable pole-zero cancellation in feedback systems is proposed.
• Proposed method decreases the time-domain undershoots in step response.
• Proposed method increases the phase and gain margin.
• Proposed method makes the open-loop system less non-minimum phase.
• Illustrative examples confirm the efficiency of the proposed cancellation method.

As a very well-known classical fact, non-minimum phase zeros of the process put some limitations on the performance of the feedback system. The source of these limitations is that non-minimum phase zeros cannot be cancelled by unstable poles of the controller since such a cancellation leads to internal instability. The aim of this paper is to propose a method for fractional-order cancellation of non-minimum phase zeros of the process and studying its properties. It is specially shown that the proposed cancellation strategy increases the phase and gain margin without leading to internal instability. Since the systems with higher gain and phase margin are easier to control, the proposed method can be used to arrive at more effective controls, which is also verified by the simulation results.