Advances in System Identification Using Fractional Models

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Rachid Malti ◽  
Stephane Victor ◽  
Alain Oustaloup
Keyword(s):  
System Identification ◽  
Least Squares ◽  
Prior Knowledge ◽  
Time Domain ◽  
Simultaneous Estimation ◽  
Thermal System ◽  
Fractional Model ◽  
Output Error ◽  
Equation Error ◽  
Fractional Models

This paper presents an up to date advances in time-domain system identification using fractional models. Both equation-error- and output-error-based models are detailed. In the former models, prior knowledge is generally used to fix differentiation orders; model coefficients are estimated using least squares. The latter models allow simultaneous estimation of model coefficients and differentiation orders using nonlinear programing. As an example, a thermal system is identified using a fractional model and is compared to a rational one.

scholarly journals System Identification Using Fractional Models: State of the Art

2007 ◽  
Author(s):  
Rachid Malti ◽  
Ste´phane Victor ◽  
Olivier Nicolas ◽  
Alain Oustaloup
Keyword(s):  
System Identification ◽  
Time Domain ◽  
State Of The Art ◽  
Simultaneous Estimation ◽  
Time Domain Simulation ◽  
Identification Methods ◽  
Non Linear Programming ◽  
Equation Error ◽  
Fractional Models ◽  
General Aspects

This paper presents a state of the art of actual achievements in time-domain system identification using fractional models. It starts with some general aspects on time and frequency-domain representations, time-domain simulation, and stability of fractional models. Then, an overview on system identification methods using fractional models is presented. Both equation-error and output-error-based models are detailed. In the former models, prior knowledge is generally used to fix differentiation orders; model coefficients are estimated using least squares. The latter models allow simultaneous estimation of model’s coefficients and differentiation orders, using non linear programming. A real thermal example is identified using a fractional model and compared to a rational one.

Initialization of Identification of Fractional Model by Output-Error Technique

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Abir Khadhraoui ◽  
Khaled Jelassi ◽  
Jean-Claude Trigeassou ◽  
Pierre Melchior
Keyword(s):  
Numerical Simulation ◽  
Least Squares ◽  
Fractional Order ◽  
Fractional Integration ◽  
New Approach ◽  
Fractional Model ◽  
Output Error

A bad initialization of output-error (OE) technique can lead to an inappropriate identification results. In this paper, we introduce a solution to this problem; the basic idea is to estimate the parameters and the fractional order of the noninteger system by a new approach of least-squares (LS) method based on repeated fractional integration to initialize OE technique. It will be shown that LS method offers a good initialization to OE algorithm and leads to acceptable identification results. The performance of the proposed method is shown through numerical simulation examples.

Output error MISO system identification using fractional models

2021 ◽  
Vol 24 (5) ◽  
pp. 1601-1618
Author(s):  
Abir Mayoufi ◽  
Stéphane Victor ◽  
Manel Chetoui ◽  
Rachid Malti ◽  
Mohamed Aoun
Keyword(s):  
System Identification ◽  
Optimization Algorithm ◽  
Simulation Analysis ◽  
Good Efficiency ◽  
Output Error ◽  
Single Output ◽  
Multiple Input ◽  
Fractional Models ◽  
Definition Of ◽  
Initialization Procedure

Abstract This paper deals with system identification for continuous-time multiple-input single-output (MISO) fractional differentiation models. An output error optimization algorithm is proposed for estimating all parameters, namely the coefficients and the differentiation orders. Given the high number of parameters to be estimated, the output error method can converge to a local minimum. Therefore, an initialization procedure is proposed to help the convergence to the optimum by using three variants of the algorithm. Moreover, a new definition of structured-commensurability (or S-commensurability) has been introduced to cope with the differentiation order estimation. First, a global S-commensurate order is estimated for all subsystems. Then, local S-commensurate orders are estimated (one for each subsystem). Finally the S-commensurability constraint being released, all differentiation orders are further adjusted. Estimating a global S-commensurate order greatly reduces the number of parameters and helps initializing the second variant, where local S-commensurate orders are estimated which, in turn, are used as a good initial hit for the last variant. It is known that such an initialization procedure progressively increases the number of parameters and provides good efficiency of the optimization algorithm. Monte Carlo simulation analysis are provided to evaluate the performances of this algorithm.

scholarly journals Recursive set membership estimation for output–error fractional models with unknown–but–bounded errors

2016 ◽  
Vol 26 (3) ◽  
pp. 543-553 ◽  
Author(s):  
Messaoud Amairi
Keyword(s):  
A Priori ◽  
Ellipsoid Algorithm ◽  
Fractional Systems ◽  
Output Error ◽  
Set Membership ◽  
Equation Error ◽  
Fractional Models ◽  
Bounded Error ◽  
Optimal Bounding Ellipsoid ◽  
New Formulation

Abstract This paper presents a new formulation for set-membership parameter estimation of fractional systems. In such a context, the error between the measured data and the output model is supposed to be unknown but bounded with a priori known bounds. The bounded error is specified over measurement noise, rather than over an equation error, which is mainly motivated by experimental considerations. The proposed approach is based on the optimal bounding ellipsoid algorithm for linear output-error fractional models. A numerical example is presented to show effectiveness and discuss results.

Thermal system identification using fractional models for high temperature levels around different operating points

2012 ◽  
Vol 70 (2) ◽  
pp. 941-950 ◽  
Author(s):  
Asma Maachou ◽  
Rachid Malti ◽  
Pierre Melchior ◽  
Jean-Luc Battaglia ◽  
Bruno Hay
Keyword(s):  
High Temperature ◽  
System Identification ◽  
Thermal System ◽  
Fractional Models ◽  
Temperature Levels ◽  
Operating Points
Sign in / Sign up

Export Citation Format

Share Document