Identification of Fractional Order Models: Application to 1D Solid Diffusion System Model of Lithium Ion Cell

Allafi, Walid; Zajic, Ivan; Burnham, Keith J.

doi:10.1007/978-3-319-08422-0_9

Cited by 4 publications

(5 citation statements)

References 13 publications

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“…Alavi et al [49] combined Victor's IVSVF method and a gradient-based optimization to identify parameters of electrochemical impedance models. Allafi et al [99] applied a simplified refined IVSVF to identify a fractional transfer function (FTF) model of a Li-ion battery. In contrast to the instrumental variable method, Jacob et al [100] recently proposed a Bayesian approach to identify the parameters of generic fractional-order systems and then applied this approach to battery models.…”

Section: System Identificationmentioning

confidence: 99%

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

Zou

Zhang

et al. 2018

Journal of Power Sources

430

155

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Electrochemical energy storage systems play an important role in diverse applications, such as electrified transportation and integration of renewable energy with the electrical grid. To facilitate model-based management for extracting full system potentials, proper mathematical models are imperative. Due to extra degrees of freedom brought by differentiation derivatives, fractional-order models may be able to better describe the dynamic behaviors of electrochemical systems. This paper provides a critical overview of fractional-order techniques for managing lithium-ion batteries, lead-acid batteries, and supercapacitors. Starting with the basic concepts and technical tools from fractional-order calculus, the modeling principles for these energy systems are presented by identifying disperse dynamic processes and using electrochemical impedance spectroscopy. Available battery/supercapacitor models are comprehensively reviewed, and the advantages of fractional types are discussed. Two case studies demonstrate the accuracy and computational efficiency of fractional-order models. These models offer 15-30% higher accuracy than their integer-order analogues, but have reasonable complexity. Consequently, fractional-order models can be good candidates for the development of advanced battery/supercapacitor management systems. Finally, the main technical challenges facing electrochemical energy storage system modeling, state estimation, and control in the fractional-order domain, as well as future research directions, are highlighted.

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Section: System Identificationmentioning

confidence: 99%

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

Zou

Zhang

et al. 2018

Journal of Power Sources

430

155

View full text Add to dashboard Cite

show abstract

“…where the over-parametrised polynomial B(D β ) and vector F(t) are given in (15) and (16), with ḡ i (t) = g i (x). Since measured data is used for parameter estimation, the output of the model in (19) is considered to be corrupted by a noise process.…”

Section: Problem Reformulation Based On Hwfc Modelmentioning

confidence: 99%

“…Since the 1980s, as computing technology matured, the necessary tools to implement fractional-order systems for modelling, estimation and control were developed. Fractional-order systems have subsequently found wider applications in engineering, [12] physics [13,14] and control [15,16]. For example, the battery system is employed in energy storage applications and described by a fractional-order model, known as Randle's equivalent circuit (REC) [17].…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation of the fractional‐order Hammerstein–Wiener model using simplified refined instrumental variable fractional‐order continuous time

Allafi

Zajic

Uddin

et al. 2017

IET Control Theory & Applications

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This study proposes a direct parameter estimation approach from observed input-output data of a stochastic singleinput-single-output fractional-order continuous-time Hammerstein-Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input-output data by considering the system to be a multi-input-single-output linear fractional-order continuoustime model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input nonlinear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein-Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein-Wiener output model.

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“…Fractional calculus has received an increasing attention to model the dynamical behaviour of real systems, processes, and materials [1], [2] as a more suitable mathematical tool than the integer-order calculus. The nonlinear fractionalorder models have been used to describe complex nonlinear processes, for example, the nonlinear fractional order Randle's equivalent circuit model for describing the battery system [3].…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation of Hybrid Fractional-Order Hammerstein-Wiener Box-Jenkins Models Using RIVCF Method

Allafi

Zhang

Dinh

et al. 2018

2018 26th International Conference on Systems Engineering (ICSEng)

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Identification of Fractional Order Models: Application to 1D Solid Diffusion System Model of Lithium Ion Cell

Cited by 4 publications

References 13 publications

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

Parameter estimation of the fractional‐order Hammerstein–Wiener model using simplified refined instrumental variable fractional‐order continuous time

Parameter Estimation of Hybrid Fractional-Order Hammerstein-Wiener Box-Jenkins Models Using RIVCF Method

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