scholarly journals Compact Wide Frequency Range Fractional-Order Models of Human Body Impedance against Contact Currents

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Todd J. Freeborn ◽  
Ahmed S. Elwakil ◽  
Brent Maundy
Keyword(s):  
Least Squares ◽  
Fractional Order ◽  
Human Body ◽  
Nonlinear Least Squares ◽  
Wide Frequency Range ◽  
Frequency Range ◽  
Model Simulations ◽  
Integer Order ◽  
Body Impedance ◽  
Constant Phase Elements

Three circuit models using constant phase elements are investigated to represent the human body impedance against contact currents from 40 Hz to 110 MHz. The parameters required to represent the impedance are determined using a nonlinear least squares fitting (NLSF) applied to the averaged human body impedance dataset. The three fractional-order models with 4, 6, and 7 parameters are compared to an already existing integer-order, 11-parameter model. Simulations of the fractional-order models impedance are presented and discussed along with their limitations.

scholarly journals Design of Cascaded and Shifted Fractional-Order Lead Compensators for Plants with Monotonically Increasing Lags

2020 ◽  
Vol 4 (3) ◽  
pp. 37
Author(s):  
Guido Maione
Keyword(s):  
Fractional Order ◽  
Transfer Functions ◽  
Wide Frequency Range ◽  
Frequency Range ◽  
Robust Controller ◽  
Simulation Experiments ◽  
Rational Transfer ◽  
Serial Connection ◽  
Efficiency Performance ◽  
Two Stages

This paper concerns cascaded, shifted, fractional-order, lead compensators made by the serial connection of two stages introducing their respective phase leads in shifted adjacent frequency ranges. Adding up leads in these intervals gives a flat phase in a wide frequency range. Moreover, the simple elements of the cascade can be easily realized by rational transfer functions. On this basis, a method is proposed in order to design a robust controller for a class of benchmark plants that are difficult to compensate due to monotonically increasing lags. The simulation experiments show the efficiency, performance and robustness of the approach.

Fractional-order circuit models of the human body impedance for compliance tests against contact currents

2017 ◽  
Vol 78 ◽  
pp. 238-244 ◽  
Author(s):  
V. De Santis ◽  
V. Martynyuk ◽  
A. Lampasi ◽  
M. Fedula ◽  
M.D. Ortigueira
Keyword(s):  
Fractional Order ◽  
Human Body ◽  
Body Impedance ◽  
Compliance Tests

scholarly journals Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 422 ◽  
Author(s):  
Jiri Petrzela
Keyword(s):  
Fractional Order ◽  
Resonant Tunneling ◽  
Chaotic Behavior ◽  
Phase Error ◽  
Wide Frequency Range ◽  
Chaotic Oscillator ◽  
Tunneling Diodes ◽  
Constant Phase Elements ◽  
Very High ◽  
Structurally Stable

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.

Modeling of a Fractional Order Element Based on Bacterial Cellulose and Ionic Liquids

2021 ◽  
Vol 143 (7) ◽  
Author(s):  
R. Caponetto ◽  
S. Graziani ◽  
E. Murgano ◽  
C. Trigona ◽  
A. Pollicino ◽  
...  
Keyword(s):  
Ionic Liquids ◽  
Frequency Domain ◽  
Bacterial Cellulose ◽  
Fractional Order ◽  
Wide Frequency Range ◽  
Complex Frequency ◽  
Frequency Range ◽  
Time Stability ◽  
Order Element ◽  
Lumped Circuit Model

Abstract In this paper, a novel fractional-order element (FOE) is modeled in a wide frequency range. The FOE is based on a green biopolymer, i.e., bacterial cellulose (BC), infused with ionic liquids (ILs). The modeling is performed in the frequency domain and a lumped-circuit model is proposed. The model is an evolution with respect to a simpler one already introduced by the authors, for a narrower frequency range. Results show that ILs generate a quite complex frequency domain behavior, which can be described in the framework of FOEs. Furthermore, results on the time stability of the device under investigation are given.

An Integer-Order Transfer Function Estimation Algorithm for Fractional-Order PID Controllers

2020 ◽  
Vol 11 (3) ◽  
pp. 133-150
Author(s):  
Kishore Bingi ◽  
Rosdiazli Ibrahim ◽  
Mohd Noh Karsiti ◽  
Sabo Miya Hassan ◽  
Vivekananda Rajah Harindran
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Curve Fitting ◽  
Estimation Method ◽  
Estimation Algorithm ◽  
Fractional Order Systems ◽  
Function Estimation ◽  
Frequency Range ◽  
Integer Order ◽  
Fractional Order Differentiator

Fractional-order systems and controllers have been extensively used in many control applications to achieve robust modeling and controlling performance. To implement these systems, curve fitting based integer-order transfer function estimation techniques namely Oustaloup and Matsuda are most widely used. However, these methods are failed to achieve the best approximation due to the limitation of the desired frequency range. Thus, this article presents a simple curve fitting based integer-order transfer function estimation method for fractional-order differentiator/integrator using frequency response. The advantage of this technique is that it is simple and can fit the entire desired frequency range. Using the approach, an approximation table for fractional-order differentiator has also been obtained which can be used directly to obtain the approximation of fractional-order systems. A simulation study on fractional systems shows that the proposed approach produced better parameter approximation for the desired frequency as compared to Oustaloup, refined Oustaloup and Matsuda techniques.

scholarly journals Frequency Response Based Curve Fitting Approximation of Fractional–Order PID Controllers

2019 ◽  
Vol 29 (2) ◽  
pp. 311-326 ◽  
Author(s):  
Kishore Bingi ◽  
Rosdiazli Ibrahim ◽  
Mohd Noh Karsiti ◽  
Sabo Miya Hassam ◽  
Vivekananda Rajah Harindran
Keyword(s):  
Frequency Response ◽  
Frequency Domain ◽  
Fractional Order ◽  
Curve Fitting ◽  
Order Approximation ◽  
Frequency Range ◽  
Approximation Techniques ◽  
Integer Order ◽  
The Best Approximation ◽  
Fractional Order Pid

Abstract Fractional-order PID (FOPID) controllers have been used extensively in many control applications to achieve robust control performance. To implement these controllers, curve fitting approximation techniques are widely employed to obtain integer-order approximation of FOPID. The most popular and widely used approximation techniques include the Oustaloup, Matsuda and Cheraff approaches. However, these methods are unable to achieve the best approximation due to the limitation in the desired frequency range. Thus, this paper proposes a simple curve fitting based integer-order approximation method for a fractional-order integrator/differentiator using frequency response. The advantage of this technique is that it is simple and can fit the entire desired frequency range. Simulation results in the frequency domain show that the proposed approach produces better parameter approximation for the desired frequency range compared with the Oustaloup, refined Oustaloup and Matsuda techniques. Furthermore, time domain and stability analyses also validate the frequency domain results.

scholarly journals Approximated Fractional Order Chebyshev Lowpass Filters

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Todd Freeborn ◽  
Brent Maundy ◽  
Ahmed S. Elwakil
Keyword(s):  
Least Squares ◽  
Fractional Order ◽  
Nonlinear Least Squares ◽  
Least Squares Optimization

We propose the use of nonlinear least squares optimization to approximate the passband ripple characteristics of traditional Chebyshev lowpass filters with fractional order steps in the stopband. MATLAB simulations of(1+α),(2+α), and(3+α)order lowpass filters with fractional steps fromα = 0.1 toα = 0.9 are given as examples. SPICE simulations of 1.2, 1.5, and 1.8 order lowpass filters using approximated fractional order capacitors in a Tow-Thomas biquad circuit validate the implementation of these filter circuits.

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