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Research Papers

Estimation of the Order and Parameters of a Fractional Order Model From a Noisy Step Response Data1

[+] Author and Article Information
Mahsan Tavakoli-Kakhki

Faculty of Electrical Engineering,
K. N. Toosi University of Technology,
P.O. Box 16315-1355,
Tehran 19697, Iran
e-mail: matavakoli@kntu.ac.ir

Mohammad Saleh Tavazoei

Electrical Engineering Department,
Sharif University of Technology,
P.O. Box 11155-4363,
Tehran, Iran
e-mail: tavazoei@sharif.edu

A short version of this paper has been presented in the 6th IFAC Workshop on Fractional Differentiation and its Applications, Grenoble, France, Feb. 4–6, 2013.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 24, 2013; final manuscript received November 28, 2013; published online February 24, 2014. Assoc. Editor: YangQuan Chen.

J. Dyn. Sys., Meas., Control 136(3), 031020 (Feb 24, 2014) (7 pages) Paper No: DS-13-1214; doi: 10.1115/1.4026345 History: Received May 24, 2013; Revised November 28, 2013

This paper deals with integral based methods to estimate the order and parameters of simple fractional order models from the extracted noisy step response data of a process. This data can be obtained from both open-loop and closed-loop tests. Numerical simulation results are presented to verify the robustness of these proposed methods in the presence of the measurement noise.

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Figures

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Fig. 1

Estimation of α and T by fractional order integration

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Fig. 5

The control system considered in Sec. 5

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Fig. 6

Estimation of α and T by fractional order integration from closed-loop data

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Fig. 7

Noisy unit step response of G(s) in Eq. (36) with SNR=20

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Fig. 8

fγ(t) for different values of integral order γ in Example 1

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Fig. 9

Noisy unit step response of G(s) in Eq. (41) with SNR=20

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Fig. 10

fγ(t) for different values of integral order γ in Example 3

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Fig. 11

Values of integral 1k∫0tg(τ)dτ in Example 3

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Fig. 12

Noisy control signal in Example 4

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Fig. 13

hγ(t) for different values of integral order γ in Example 4

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