On the Possibility of Unstable Pole-Zero Cancellation in Feedback Systems

摘要

It is a very well-known classical fact that in feedback systems the non-minimum phase zeros of the process transfer function limit the performance of the closed-loop system. The radical of this limitation is that the non-minimum phase zeros of the process transfer function cannot be cancelled anywise (e.g. by providing a controller with the same unstable poles) since such a cancellation leads to internal instability. The aim of this paper is to show that fractional-order controllers can partly cancel the non-minimum phase zeros of the process (as well as unstable poles of the process) and remove the limitations put on the performance of the feedback system by such non-minimum phase zeros. The proposed strategy is applied to the inverted pendulum problem and it is shown that the performance of the feedback system (which employs the LQG controller) is signiˉcantly improved by using the proposed unstable fractional-order pole-zero cancellation strategy.