On embedded FIR filter models for identifying continuous-time and discrete-time transfer functions: the RPM approach

Abstract

For identifying a continuous-time (CT) transfer function model, data filtering is a solution which provides the necessary unmeasurable input--output derivative approximations. In discrete-time (DT) system identification, the well-known ARX model can be used successfully if the estimate is performed with suitable prefiltered data. This article describes the reinitialised partial moment (RPM) model which embeds implicitly a finite impulse response filter in both CT and DT domains. With knowledge of the important role of data prefiltering in standard methods, this RPM model embedded filter gives particular properties to this original tool. Although both the CT RPM model and the DT RPM model present an embedded filter, the formulation and the implementation in the CT and the DT domains are different. Therefore, the aim of this article is to present a tutorial on the RPM models and to give an overview of all the applications.

Keywords:

• continuous-time model
• discrete-time model
• reinitialised partial moments
• RPM filter
• RPM model
• system identification
• transfer function model

Notes

1. Output error methods and equation error methods in the sense of the classification introduced by Landau (1976) and Ljung and Söderström (1983).

2. For the first-order system defined by (6) and with the assumption of a zero-mean white noise, .

3. Notice that both CT and DT design parameters, in (10) and in (56), are linked by .

4. Here the OE, PEM and N4SID algorithms refer to the Matlab procedures with the same names in the System Identification Toolbox.