Finite time stable inversion in discrete frequency domain: Accuracy analysis, improvement and application to wafer stage

Abstract

Stable inversion represents a classic approach to achieve the exact inverse input for non-minimum-phase (NMP) systems. Solutions deduced based on state–space equations and transfer functions have been frequently proposed, however they are basically developed in the infinite-time horizon and are inherently time-domain computation methods. Considering the practical finite-time tracking tasks, this paper investigates the finite-time stable inversion problem. In particular, the discrete-frequency-domain solution which enables frequency-domain computation is studied. As the main contribution of the paper, the accuracy issues of the discrete-frequency-domain solution are revealed and an easy-to-use procedure is provided to improve the inversion accuracy by utilizing pre-actuation and post-actuation methods. Simulation and experiment both verify the effectiveness of the developed discrete-frequency-domain stable inversion technique.