Sampling and Sampled-Data Models: The Interface Between the Continuous World and Digital Algorithms

Abstract

M odern signal processing and control algorithms are invariably implemented digitally, yet most real-world systems evolve in continuous time. Hence, the interaction between sampling and the behavior of continuous-time systems is an important ingredient in all real-world signals and systems problems.The literature on sampled-data systems goes back several decades [1]- [5]. Modern systems allow much faster sampling rates than were previously possible, which suggests that it is timely to reexamine sampled-data models [6]- [8]. Such a re-examination is the main goal of this article. A tutorial overview is provided of several related topics, including » exact and approximate sampled-data models arising from an underlying continuous-time system » connections between sampled-data models and the underlying continuous-time systems at fast sampling rates » intersample behavior.

Decoupling P-NARX models using filtered CPD

“…The use of shifted input samples contributes to retrieving a nonphysical model, in this case of the forced Duffing oscillator. One such mechanism is the introduction of sampling zeros (Goodwin et al, 2013).…”

Computationally efficient identification of continuous-time Lur’e-type systems with stability guarantees

“…Identification of continuous-time models from discrete data points is a challenging task due to the unobserved intersample behavior of the true system. Analysis tools for errors due to intersample behavior and practical guidelines for the design of the excitation signal are presented (Goodwin, Aguero, Cea Garridos, Salgado, & Yuz, 2013;Rao & Unbehauen, 2006;Schoukens, Relan, & Schoukens, 2017;Soderstrom, Fan, Carlsson, & Bigi, 1997). As we are dealing with a medical application, there is no freedom in the design of the excitation signal; it is the signal that is also used during conventional operation.…”

On partially minimum-phase systems and disturbance decoupling with stability

“…is full rank by definition of the continuous-time relative degree r 2 and because ∆ is invertible (see [29] for details) so concluding, from the Implicit Function Theorem, the existence of δ ∈]0, T * [ so that (30) admits a unique solution of the form (32) around the continuous-time solution (31). Disturbance decoupling and stability of the zero-dynamics are ensured by multi-rate sampling as proven in [29] combined with the arguments of Theorem 2.…”

“…In this context, the problem under study is even more crucial because of the further unstable zero-dynamics intrinsically arising due to sampling [27]. As a consequence, the minimum-phase property of a given nonlinear continuous-time system is not preserved by its sampled-data equivalent [28,29,30,31]. To overcome those issues, several solutions were proposed based on different sampling procedures [32,33,34,35,36,32,35].…”