Residue Matching: A Method to Determine Intersample Vibrations in Systems With State Feedback

Abstract

In this paper, we present a new method to determine the continuous-time response of sampled-data systems with uniform sampling, zero-order hold, and full-state feedback. In such systems, a continuous-time plant is controlled using a discrete-time control law. Traditionally, sampled-data systems are designed in discrete time, resulting in, given by the nature of this kind of modelling, unmodelled intersample behaviour. We show that the Laplace transform of the otherwise piecewise-continuous state response can be expressed in closed form that fully represents the intersample dynamics. A practical technique is also provided to decouple individual vibration components and reconstruct response functions in the time domain. The proposed approach is also able to capture intersample vibrations compared to common methods, which may lead to inaccurate results in specific cases. The presented new formulae are derived analytically and verified by simulations through numerical examples and experiments on a DC motor drive.