Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth

Qiu-Yan He; Yi-Fei Pu; Bo Yu; Xiao Yuan

doi:10.1109/JAS.2020.1003009

Volume 7 Issue 5

Sep. 2020

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2020 > 7(5): 1425-1436

Qiu-Yan He, Yi-Fei Pu, Bo Yu and Xiao Yuan, "Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth," IEEE/CAA J. Autom. Sinica, vol. 7, no. 5, pp. 1425-1436, Sept. 2020. doi: 10.1109/JAS.2020.1003009

Citation:

Qiu-Yan He, Yi-Fei Pu, Bo Yu and Xiao Yuan, "Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth," IEEE/CAA J. Autom. Sinica, vol. 7, no. 5, pp. 1425-1436, Sept. 2020. doi: 10.1109/JAS.2020.1003009

Citation:

Qiu-Yan He, Yi-Fei Pu, Bo Yu and Xiao Yuan, "Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth," IEEE/CAA J. Autom. Sinica, vol. 7, no. 5, pp. 1425-1436, Sept. 2020. doi: 10.1109/JAS.2020.1003009

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Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth

doi: 10.1109/JAS.2020.1003009

Funds: This work was supported by the National Key Research and Development Program Foundation of China (2018YFC0830300) and National Natural Science Foundation of China (61571312)

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Author Bio:
Qiu-Yan He received the B.Eng. degree in electronic information engineering from Sichuan University in 2014, the M.Eng. degree in signal and information processing from Sichuan University in 2017. She is currently pursuing the Ph.D. degree at Sichuan University with research in fractional-order circuits and systems, fractional-order neural networks

Yi-Fei Pu received the Ph.D. degree from the College of Electronics and Information Engineering, Sichuan University in 2006.He is currently a Full Professor and a Doctoral Supervisor with the College of Computer Science and the College of Software Engineering, Sichuan University, and is the Chief Technology Officer of Chengdu PU Chip Science and Technology Company, Ltd. He has firstly authored about 20 papers indexed by SCI in journals, such as IEEE Transactions on Image Processing, IEEE Transactions on Neural Networks and Learning Systems, IEEE Access, Mathematic Methods in Applied Sciences, Science in China Series F: Information Sciences and Science China Information Sciences, and holds 11 Chinese inventive patents, as the first or single inventor. His research interests include the application of fractional calculus, fractional partial differential equation to signal analysis, and signal processing. He held several research projects, such as the National Nature Science foundation of China, and the Returned Overseas Chinese Scholars Project of Education Ministry of China

Bo Yu received the B.Eng. degree in electronic science and technology from Chengdu University of Information Technology in 2011, the M.Eng. degree from electronics and communication engineering from Sichuan University in 2016. He is currently a Lecturer with the College of Physics and Engineering, Chengdu Normal University. His current research interests include fractional-order circuits and systems

Xiao Yuan received the Ph.D. degree from University of Electronic Science and Technology of China, in 1998. He is currently an Associate Professor with the College of Electronics and Information Engineering, Sichuan University. His current research interests include the theory and applications of signal processing, especially the design of digital filter with arbitrary order, the applications of fractional calculus in image signal analysis and processing, and fractional-order circuits and systems, in particular with the mathematical principles of fractance approximation circuits. Dr. Yuan has authored and coauthored four books and about 120 papers
Corresponding author: B. Yu is with the College of Physics and Engineering, Chengdu Normal University, Chengdu 611130, China (e-mail: analogyb@foxmail.com)
Received Date: 2019-08-18
Revised Date: 2019-09-28
Accepted Date: 2019-11-06

Available Online: 2019-12-05

Abstract

Abstract

This paper discusses a novel rational approximation algorithm of arbitrary-order fractances, which has high order-stability characteristic and wider approximation frequency bandwidth. The fractor has been exploited extensively in various scientific domains. The well-known shortcoming of the existing fractance approximation circuits, such as the oscillation phenomena, is still in great need of special research attention. Motivated by this need, a novel algorithm with high order-stability characteristic and wider approximation frequency bandwidth is introduced. In order to better understand the iterating process, the approximation principle of this algorithm is investigated at first. Next, features of the iterating function and frequency-domain characteristics of the impedance function calculated by this algorithm are researched, respectively. Furthermore, approximation performance comparisons have been made between the corresponding circuit and other types of fractance approximation circuits. Finally, a fractance approximation circuit with the impedance function of negative 2/3-order is designed. The high order-stability characteristic and wider approximation frequency bandwidth are fundamental important advantages, which make our proposed algorithm competitive in practical applications.
- Fractal,
- fractance,
- fractional calculus,
- fractional-order systems

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References(49)

References

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Fractor is a burgeoning new circuit element with fractance (abbreviation of fractional-order impedance). The ideal fractor does not currently exist and its approximate physical realization is called a fractance approximation circuit. There are oscillation phenomena in the existing fractance approximation circuits. This paper discusses an improved rational approximation algorithm of arbitrary-order fractances, which has high order-stability characteristic and wider approximation frequency bandwidth.
Compared with the related algorithms, the predistortion exponent of this algorithm is not limited to be zero and has a value between -1 and 1. In order to better understand that why the algorithm is with high order-stability characteristic and wider approximation frequency bandwidth, features of the iterating function and frequency-domain characteristics of the impedance function calculated by this algorithm are researched in detail.
Approximation performance comparisons have been made between the corresponding circuit and other types of fractance approximation circuits. Moreover, a fractance approximation circuit with the impedance function of -2/3-order is designed to verify the practicality of the algorithm.

Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth

doi: 10.1109/JAS.2020.1003009

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通讯作者: 陈斌, bchen63@163.com

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