Hugues Garnier

Identification of Continuous-time Models from Sampled Data

System identification is an established field in the area of system analysis and control. It aims to determine particular models for dynamical systems based on observed inputs and outputs. Although dynamical systems in the physical world are naturally described in the continuous-time domain, most system identification schemes have been based on discrete-time models without concern for the merits of natural continuous-time model descriptions. The continuous-time nature of physical laws, the persistent popularity of predominantly continuous-time proportional-integral-derivative control and the more direct nature of continuous-time fault diagnosis methods make continuous-time modeling of ongoing importance. Identification of Continuous-time Models from Sampled Data brings together contributions from well-known experts who present an up-to-date view of this active area of research and describe recent methods and software tools developed in this field. They offer a fresh look at and new results in areas such as: time and frequency domain optimal statistical approaches to identification; parametric identification for linear, nonlinear and stochastic systems; identification using instrumental variable, subspace and data compression methods; closed-loop and robust identification; and continuous-time modeling from non-uniformly sampled data and for systems with delay. The CONtinuous-Time System IDentification (CONTSID) toolbox described in the book gives an overview of developments and practical examples in which MATLAB can be brought to bear in the cause of direct time-domain identification of continuous-time systems.This survey of methods and results in continuous-time system identification will be a valuable reference for a broad audience drawn from researchers and graduate students in signal processing as well as in systems and control. It also covers comprehensive material suitable for specialised graduate courses in these areas.

Continuous-time model identification from sampled data: Implementation issues and performance evaluation

This paper deals with equation error methods that fit continuous-time transfer function models to discrete-time data recently included in the CONTSID (CONtinuous-Time System IDentification) Matlab toolbox. An overview of the methods is first given where implementation issues are highlighted. The performances of the methods are then evaluated on simulated examples by Monte Carlo simulations. The experiments have been carried out to study the sensitivity of each approach to the design parameters, sampling period, signal-to-noise ratio, noise power spectral density and type of input signal. The effectiveness of the CONTSID toolbox techniques is also briefly compared with indirect methods in which discrete-time models are first estimated and then transformed into continuous-time models. The paper does not consider iterative or recursive algorithms for continuous-time transfer function model identification.

Refined instrumental variable methods for identification of LPV Box-Jenkins models

The identification of linear parameter-varying systems in an input-output setting is investigated, focusing on the case when the noise part of the data generating system is an additive colored noise. In the Box-Jenkins and output-error cases, it is shown that the currently available linear regression and instrumental variable methods from the literature are far from being optimal in terms of bias and variance of the estimates. To overcome the underlying problems, a refined instrumental variable method is introduced. The proposed approach is compared to the existing methods via a representative simulation example.

Parameter and differentiation order estimation in fractional models

This paper deals with continuous-time system identification using fractional differentiation models. An adapted version of the simplified refined instrumental variable method is first proposed to estimate the parameters of the fractional model when all the differentiation orders are assumed known. Then, an optimization approach based on the use of the developed instrumental variable estimator is presented. Two variants of the algorithm are proposed. Either, all differentiation orders are set as integral multiples of a commensurate order which is estimated, or all differentiation orders are estimated. The former variant allows to reduce the number of parameters and can be used as a good initial hit for the latter variant. The performances of the proposed approaches are evaluated by Monte Carlo simulation analysis. Finally, the proposed identification algorithms are used to identify thermal diffusion in an experimental setup.

Identification and estimation of continuous-time, data-based mechanistic (DBM) models for environmental systems

Abstract Initially, the paper provides an introduction to the main aspects of existing time-domain methods for identifying linear continuous-time models from discrete-time data and shows how one of these methods has been applied to the identification and estimation of a model for the transportation and dispersion of a pollutant in a river. It then introduces a widely applicable class of new, nonlinear, State Dependent Parameter (SDP) models. Finally, the paper describes how this SDP approach has been used to identify, estimate and control a nonlinear differential equation model of global carbon cycle dynamics and global warming.

NUMERICAL ILLUSTRATIONS OF THE RELEVANCE OF DIRECT CONTINUOUS-TIME MODEL IDENTIFICATION

Abstract The aim of this paper is to establish a dependable approach to the identification of continuous-time models from sampled data. Some equation-error structure-based methods of the CONTSID (CONtinuous-Time System IDentification) Matlab toolbox that directly estimate continuous-time transfer function models from discrete-time data are compared with some classical discrete-time model identification techniques of the Matlab System IDentification (SID) toolbox. CONTSID is equipped with tools based on the developments over the past three decades and is noncommercial. The results of extensive numerical experiments presented in this paper suggest that direct approaches, that is, those in which continuous-time models are directly identified are superior to the indirect methods in which discrete-time models are first identified and then transformed into continuous-time models. It is also clear from this investigation that for identification problems in a wider context, that is, with choice between discrete-time and continuous-time models, it is desirable to have a set of tools, whose dependability is greatly enhanced by unifying all relevant approaches.

Refined Instrumental Variable Identification of Continuous-time Hybrid Box-Jenkins Models

This chapter describes and evaluates a statistically optimal method for the identification and estimation3 of continuous-time (CT) hybrid Box-Jenkins (BJ) transfer function models from discrete-time, sampled data. Here, the model of the basic dynamic system is estimated in continuous-time, differential equation form, while the associated additive noise model is estimated as a discrete-time, autoregressive moving average (ARMA) process. This refined instrumental variable method for continuous-time systems (RIVC) was first developed in 1980 by Young and Jakeman [52] and its simplest embodiment, the simplified RIVC (SRIVC) method, has been used successfully for many years, demonstrating the advantages that this stochastic formulation of the continuous-time estimation problem provides in practical applications (see, e.g., some recent such examples in [16, 34, 40, 45, 48]).

A PMF-based subspace method for continuous-time model identification. Application to a multivariable winding process

This paper presents a methodology for system identification of continuous-time state-space models from finite sampled input-output signals. The estimation problem of the consecutive time-derivatives and integrals of the input-output signals is considered. The appropriate frequency characteristcs of a linear filtering based on the Poisson moment functionals in regards to the derivative or integral estimation problem is shown. The proposed method combines therefore the Poisson moment functionals technique with subspace based state-space system identification methods. The developed algorithm is based on a generalized singular value decomposition to compensate the noise colouring caused by the linear prefiltering of the input-output data. Rules of thumb are presented to choose the design parameters and new regards to the selection of the Poisson filter cut-off frequency are introduced. Finally, the proposed method is applied to a multivariable winding processes. The experimental results emphasize the applicability of the developed methodology.

Identification of continuous-time errors-in-variables models

A novel direct approach for identifying continuous-time linear dynamic errors-in-variables models is presented in this paper. The effects of the noise on the state-variable filter outputs are analyzed. Subsequently, a few algorithms to obtain consistent continuous-time parameter estimates in the errors-in-variables framework are derived. It is also possible to design search-free algorithms within our framework. The algorithms can be used for non-uniformly sampled data. The asymptotic distributions of the estimates are derived. The performances of the proposed algorithms are illustrated with some numerical simulation examples.

Developments for the matlab contsid toolbox

Abstract The CONtinuous-Time System IDentification (CONTSID) toolbox is a successful implementation of the methods developed over the last twenty years for estimating continuous-time transfer function or state-space models directly from sampled data. This paper gives a short overview of the toolbox, describes the latest developments and illustrates them on a few examples. Finally, the future plans are briefly summarized.