Fractional-Order Partial Cancellation of Integer-Order Poles and Zeros
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OriginalversjonVoss, B., Weise, C., Ruderman, M. & Reger, J. (2022). Fractional-Order Partial Cancellation of Integer-Order Poles and Zeros, 55 (25), 259-264. https://doi.org/10.1016/j.ifacol.2022.09.356
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.