Discretization algorithm for fractional order integral by Haar wavelet approximation

Zhe Gao; Xiaozhong Liao

doi:10.1016/j.amc.2011.07.003

Discretization algorithm for fractional order integral by Haar wavelet approximation

Zhe Gao^*, Xiaozhong Liao

^*Corresponding author for this work

School of Automation

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

A discretization algorithm is proposed by Haar wavelet approximation theory for the fractional order integral. In this paper, the integration time is divided into two parts, one presents the effect of the past sampled data, calculated by the iterative method, and the other presents the effect of the recent sampled data at a fixed time interval, calculated by the Haar wavelet. This method can reduce the amount of the stored data effectively and be applied to the design of discrete-time fractional order PID controllers. Finally, several numerical examples and simulation results are given to illustrate the validity of this discretization algorithm.

Original language	English
Pages (from-to)	1917-1926
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	218
Issue number	5
DOIs	https://doi.org/10.1016/j.amc.2011.07.003
Publication status	Published - 1 Nov 2011

Keywords

Discretization algorithm
Fractional order PID controller
Fractional order calculus
Haar wavelet
Riemann-Liouville fractional order integral

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10.1016/j.amc.2011.07.003

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title = "Discretization algorithm for fractional order integral by Haar wavelet approximation",

abstract = "A discretization algorithm is proposed by Haar wavelet approximation theory for the fractional order integral. In this paper, the integration time is divided into two parts, one presents the effect of the past sampled data, calculated by the iterative method, and the other presents the effect of the recent sampled data at a fixed time interval, calculated by the Haar wavelet. This method can reduce the amount of the stored data effectively and be applied to the design of discrete-time fractional order PID controllers. Finally, several numerical examples and simulation results are given to illustrate the validity of this discretization algorithm.",

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AU - Gao, Zhe

AU - Liao, Xiaozhong

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N2 - A discretization algorithm is proposed by Haar wavelet approximation theory for the fractional order integral. In this paper, the integration time is divided into two parts, one presents the effect of the past sampled data, calculated by the iterative method, and the other presents the effect of the recent sampled data at a fixed time interval, calculated by the Haar wavelet. This method can reduce the amount of the stored data effectively and be applied to the design of discrete-time fractional order PID controllers. Finally, several numerical examples and simulation results are given to illustrate the validity of this discretization algorithm.

AB - A discretization algorithm is proposed by Haar wavelet approximation theory for the fractional order integral. In this paper, the integration time is divided into two parts, one presents the effect of the past sampled data, calculated by the iterative method, and the other presents the effect of the recent sampled data at a fixed time interval, calculated by the Haar wavelet. This method can reduce the amount of the stored data effectively and be applied to the design of discrete-time fractional order PID controllers. Finally, several numerical examples and simulation results are given to illustrate the validity of this discretization algorithm.

KW - Discretization algorithm

KW - Fractional order PID controller

KW - Fractional order calculus

KW - Haar wavelet

KW - Riemann-Liouville fractional order integral

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EP - 1926

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 5

ER -

Discretization algorithm for fractional order integral by Haar wavelet approximation

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Keywords

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