Fractional state variable filter for system identification by fractional model

Cois, Olivier; Oustaloup, Alain; Poinot, Thierry; Battaglia, Jean-Luc

doi:10.23919/ecc.2001.7076300

Cited by 87 publications

(39 citation statements)

References 6 publications

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“…In our identification procedure, we take T = t i for t i ∈ [1. 8,8]. The obtained estimations and the associated relative estimation errors are shown in Figure 2 and Figure 3.…”

Section: Simulation Resultsmentioning

confidence: 99%

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Identification of fractional order systems using modulating functions method

Liu

Laleg‐Kirati

Gibaru

et al. 2013

2013 American Control Conference

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Abstract-The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

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“…In our identification procedure, we take T = t i for t i ∈ [1. 8,8]. The obtained estimations and the associated relative estimation errors are shown in Figure 2 and Figure 3.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…In [7], the use of methods based on fractional orthogonal bases has been introduced. Other techniques can be also found for example in [8], [9], [10] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Identification of fractional order systems using modulating functions method

Liu

Laleg‐Kirati

Gibaru

et al. 2013

2013 American Control Conference

View full text Add to dashboard Cite

show abstract

“…Special care needs to be given to the estimation of the coefficients of the FDM to reduce the effect of perturbations and/or noise on the input and output data. An effective way to estimate the coefficients of a continuous-time (fractional order) model is through a SVF [40][41][42]. From a signal analysis point of view, the SVF consists of multiple band-pass filters used to obtain the behavior of differentiation at low frequencies, while reducing the effect of noise at high frequencies.…”

Section: Least Squares-based State-variable Filter Methodsmentioning

confidence: 99%

Dynamic Prediction of Power Storage and Delivery by Data-Based Fractional Differential Models of a Lithium Iron Phosphate Battery

et al. 2016

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A fractional derivative system identification approach for modeling battery dynamics is presented in this paper, where fractional derivatives are applied to approximate non-linear dynamic behavior of a battery system. The least squares-based state-variable filter (LSSVF) method commonly used in the identification of continuous-time models is extended to allow the estimation of fractional derivative coefficents and parameters of the battery models by monitoring a charge/discharge demand signal and a power storage/delivery signal. In particular, the model is combined by individual fractional differential models (FDMs), where the parameters can be estimated by a least-squares algorithm. Based on experimental data, it is illustrated how the fractional derivative model can be utilized to predict the dynamics of the energy storage and delivery of a lithium iron phosphate battery (LiFePO 4 ) in real-time. The results indicate that a FDM can accurately capture the dynamics of the energy storage and delivery of the battery over a large operating range of the battery. It is also shown that the fractional derivative model exhibits improvements on prediction performance compared to standard integer derivative model, which in beneficial for a battery management system. Keywords: fractional differential model (FDM); energy storage and delivery; system identification; battery management system (BMS); least squares-based state-variable filter (LSSVF) method

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“…Only few papers deal with system identification using fractional statespace representation [6,10]. They are based on the minimization of an output error criterion by nonlinear programming techniques.…”

Section: Introductionmentioning

confidence: 99%

“…Then, they deduced the fractional model after estimating its rational approximation. Cois et al [6] proposed several extensions of equation error methods, such as the state variable filters and the instrumental variable (IV), to fractional system identification. Aoun et al [7] synthesized fractional orthogonal bases generalizing various bases (Laguerre, Kautz,...) to fractional differentiation orders for identification issues.…”

Section: Introductionmentioning

confidence: 99%