An efficient fixed-point realization of inversion based repetitive control

The paper presents a fixed-point realization of non-minimum phase system inversion for inversion based control algorithms such as feedforward, repetitive controller, and iterative learning control. Based on the author's previous work on efficient dynamic inversion using stable pole-zero cancelation and non-minimum phase zero inversion using Kurosu filter, this paper employs the use of the Delta Operator filter realization to mitigate quantization effects in fixed-point computations. The Kurosu filter based inversion, where the difference of two IIR filters are used to approximate a high order FIR filter and switches are used to perform time reversals for phase compensation, is computationally efficient and well suited for low level fixed-point realization by digital signal processors or field programmable gate arrays. However, substantial quantization noise is evident in high sampling rate implementation. The Delta Operator realization increases computational complexity only slightly while providing substantial reduction of quantization noise. The method is employed in the feedforward and repetitive control of a piezoelectric actuator and the experimental results are presented to demonstrate its effectiveness.