Implementation of constant phase elements using low-Q band-pass and band-reject filtering sections

Petržela, Jiří; Šotner, Roman; Guzan, Milan

doi:10.1109/ae.2016.7577274

Cited by 18 publications

(5 citation statements)

References 13 publications

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“…Knowledge of the mentioned positions itself can lead to cascade connection of bilinear filters, while coupling of zeroes and poles pairs result into cascade of biquadratic filtering two-ports. A systematic approach of how to use generalized band-pass and band-reject filtering section for CPE approximation is described in paper [48].…”

Section: Discussionmentioning

confidence: 99%

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Petržela

2020

Entropy

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This paper provides readers with three partial results that are mutually connected. Firstly, the gallery of the so-called constant phase elements (CPE) dedicated for the wideband applications is presented. CPEs are calculated for 9° (decimal orders) and 10° phase steps including ¼, ½, and ¾ orders, which are the most used mathematical orders between zero and one in practice. For each phase shift, all necessary numerical values to design fully passive RC ladder two-terminal circuits are provided. Individual CPEs are easily distinguishable because of a very high accuracy; maximal phase error is less than 1.5° in wide frequency range beginning with 3 Hz and ending with 1 MHz. Secondly, dynamics of ternary memory composed by a series connection of two resonant tunneling diodes is investigated and, consequently, a robust chaotic behavior is discovered and reported. Finally, CPEs are directly used for realization of fractional-order (FO) ternary memory as lumped chaotic oscillator. Existence of structurally stable strange attractors for different orders is proved, both by numerical analyzed and experimental measurement.

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Section: Discussionmentioning

confidence: 99%

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Petržela

2020

Entropy

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“…Oustaloup approximation: The fractional derivative s α can be approximated within a desired frequency range using rational functions in s with various methods such as Newton, Muir, Oustaloup, Matsuda, power series expansion (PSE), continuous fractions expansion (CFE), and others [1,31,32,33]. Once a rational function is obtained, it can be implemented in hardware using ladder networks, tree structures, transmission lines, or filtering sections [1,33,34,35]. The required circuit components for implementation may include resistors, inductors, capacitors, and negative impedance converters.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Exploring Four Direct Synthesis Scenarios for Fractional-Order Controllers

Muñiz-Montero,

Muñoz-Pacheco,

Arizaga-Silva

et al. 2023

Preprint

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The noticeable lag in the development of fractional-order controllers through direct synthesis, compared to their PID counterparts, underscores a clear challenge. To counteract this trend and explore novel control structures, a dual approach involving hardware synthesis and parameter optimization is imperative. This study primarily focuses on hardware synthesis, investigating four scenarios that combine various integer and fractional-order models for both the plant and the desired closed-loop transfer function. Anchored in Oustaloup’s fractional-order derivative approximation, the approach utilizes biquadratic filters and adder amplifiers for synthesis. The method’s validity is demonstrated through numerical simulations of two examples and experimental characterization of one of them. The latter involves the use of two AN231E04 Field Programmable Analog Arrays. The ensuing response effectively showcases the dynamic behavior of a three-term fractional system with an order of 2α=49.2, a natural frequency ω n =49 rad/s, and a damping factor of ζ=− 0.1. The results underscore the practical viability of the proposed approach, laying a foundation for its application in real-world scenarios.

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“…Practically, since the entire frequency spectrum cannot be satisfied, approximation models by Valsa [29] were used where the RC ladder network is truncated at a certain extent, making the circuit valid for a certain limited range of frequencies [13]. Approaches in the implementation of such circuits where then attempted throughout the years for industrial controllers [6,12], design of signal processing filters [22], and microelectronic circuits [1].…”

Section: General Theory Of Insulation Resistancementioning

confidence: 99%

Novel Polarization Index Evaluation Formula and Fractional-Order Dynamics in Electric Motor Insulation Resistance

Gonzalez¹,

Petráš

Ortigueira

2018

FCAA

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One of the common test metrics prescribed by IEEE Std 43 for testing motor insulation is the Polarization Index (P.I.) which evaluates the “goodness” of the machine’s insulation resistance by getting the ratio of the insulation resistance measured upon reaching t2 > 0 minutes (IRt2) from t1 > 0 minutes (IRt2) for t2 > t1 > 0, after applying a DC step voltage. However, such definition varies from different manufacturers and operators despite of decades of research in this area because the values of t1 and t2 remain to be uncertain. It is hypothesized in this paper that the main cause of having various P.I. definitions in literature is due to the lack of understanding of the electric motor’s dynamics at a systems level which is usually assumed to follow the dynamics of the exponential function. As a result, we introduce in this paper the fractional dynamics of an electric motor insulation resistance that could be represented by fractional-order model and where the resistance follows the property of a Mittag-Leffler function rather than an exponential function as observed on the tests done on a 415-V permanent magnet synchronous motor (PMSM). As a result, a new PMSM health measure called the Three-Point Polarization Index (3PPI) is proposed.

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Implementation of constant phase elements using low-Q band-pass and band-reject filtering sections

Cited by 18 publications

References 13 publications

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Exploring Four Direct Synthesis Scenarios for Fractional-Order Controllers

Novel Polarization Index Evaluation Formula and Fractional-Order Dynamics in Electric Motor Insulation Resistance

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