Recursive Discrete-Time Models for Continuous-Time Systems Under Band-Limited Assumptions

TL;DR

This paper develops recursive discrete-time models for continuous-time nonlinear feedback systems under band-limited assumptions, providing theoretical error bounds and experimental validation methods.

Contribution

It introduces a recursive modeling approach for nonlinear feedback systems with delay, along with theoretical error bounds and a measurement methodology for validation.

Findings

Recursive models effectively simulate nonlinear feedback systems.

Theoretical error bounds are established for band-limited signals.

A measurement methodology for output error validation is proposed.

Abstract

Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many applications) described as y(t) = g1(u(t), y(t)), one has to solve at each time step a nonlinear algebraic loop for y(t). If a delay is present in the loop, i.e., y(t) = g2(u(t), y(t -1)), fast recursive simulation models can be developed and the need to solve the nonlinear differential-algebraic equations is removed. In this paper, we use the latter to model the nonlinear feedback system using recursive discrete-time models. Theoretical error bounds for such kind of approximated models are provided in the case of band-limited signals, and furthermore, a measurement methodology is proposed for quantifying and validating the output error bounds experimentally.