High-Sampling Rate Dynamic Inversion—Filter Realization and Applications in Digital Control

This paper presents a stable inversion of nonminimum phase systems with highly efficient computation for high-sampling rate applications. The stable filter that inverts the dynamics of a nonminimum system is based on cascading a stable pole-zero cancellation infinite impulse response (IIR) filter with a high-order finite impulse response (FIR) filter which inverts the unstable zero dynamics. The high-order FIR filter is realized based on efficient IIR filter implementation first introduced by Powell and Chau then later modified by Kurosu. As a demonstrative example, the inversion filters are applied to feedforward tracking and repetitive control algorithms and realized by a field programmable gate array. The controllers are implemented at 100-kHz sampling rate to control the motion of a 4 degrees-of-freedom magnetically levitated shaft in experiment.