Fractional-Order Partial Cancellation of Integer-Order Poles and Zeros

TL;DR

This paper introduces a fractional-order partial cancellation method for non-minimum phase zeros and unstable poles, improving control system stability and response by splitting integer-order zeros/poles into fractional-order pseudo zeros/poles.

Contribution

It presents a novel fractional-order approach to compensate non-minimum phase zeros and unstable poles, enhancing loop-shaping and stability margins in control systems.

Findings

Higher phase margin achieved

Reduced undershoot in step response

Steeper amplitude response around crossover

Abstract

The key idea of this contribution is the partial compensation of non-minimum phase zeros or unstable poles. Therefore the integer-order zero/pole is split into a product of fractional-order pseudo zeros/poles. The amplitude and phase response of these fractional-order terms is derived to include these compensators into the loop-shaping design. Such compensators can be generalized to conjugate complex zeros/poles, and also implicit fractional-order terms can be applied. In the case of the non-minimum phase zero, its compensation leads to a higher phase margin and a steeper open-loop amplitude response around the crossover frequency resulting in a reduced undershooting in the step-response, as illustrated in the numerical example.