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

Abstract

Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discretetime 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 (DAE) 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, furthermore a measurement methodology is proposed for quantifying and validating the output error bounds experimentally.

A simplified model of a fueldraulic actuation system with application to load estimation

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Identification of block-oriented nonlinear systems starting from linear approximations: A survey

“…It is commonly assumed for nonlinear feedback systems to have at least one sample delay in either the forward or the backwards path of the feedback loop to avoid the presence of nonlinear algebraic loops during simulation. It is shown in (Relan & Schoukens, 2016) under bandlimited assumptions that the approximation error made by introducing such a delay in the model can be kept arbitrary low by selecting a sufficiently high sampling frequency.…”

Grey-box state-space identification of nonlinear mechanical vibrations

“…The imaginary parts of the coefficients are seen to be more than one order of magnitude smaller than the real parts. The frequency dependence of the real parts is also found to be reduced when increasing the sampling frequency, as a result of the decrease of the error inherent to the discrete-to continuous-time conversion [Pintelon & Schoukens (2001); Relan & Schoukens (2016)]. Using the averaged values of the coefficients calculated at 2441 Hz (doing so at 12205 Hz leads to very similar values, see Table 2), Fig 8 displays the synthesis of the nonlinear restoring force c 1 y 2 nl (t) + c 2 y 3 nl (t) in the system.…”