scholarly journals Practical Applications of Diffusive Realization of Fractional Integrator with SoftFrac

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1767
Author(s):  
Jerzy Baranowski ◽  
Waldemar Bauer ◽  
Rafał Mularczyk
Keyword(s):  
Fractional Calculus ◽  
Fractional Integral ◽  
Low Frequency ◽  
Phase Lag ◽  
Low Frequencies ◽  
Practical Applications ◽  
Fractional Integrator ◽  
The World ◽  
Frequency Behavior ◽  
Domain Integration

Fractional calculus has found multiple applications around the world. It is especially prevalent in the domains of control and electronics. One of the key elements of fractional applications is the fractional integral (or integrator) which is a backbone of famous PIλD controller. It gives advantages of traditional PID with a limited phase lag. The are, however, issues with implementation, which will allow good low-frequency behavior. In this paper, we consider a diffusive realization of a fractional integrator with the use of quadratures. We implemented this method in numerical package SoftFrac, and we illustrate how different quadratures work for this purpose. We show superiority of bounded domain integration with logarithmic transformation and explain issues with behavior for extremely low frequencies.

Control-Oriented Modeling of Lithium-Ion Batteries

2020 ◽  
Author(s):  
Brody Riemann ◽  
Jie Li ◽  
Kasim Adewuyi ◽  
Robert Landers ◽  
Jonghyun Park
Keyword(s):  
Low Frequency ◽  
Lithium Ion ◽  
Battery Management ◽  
Computationally Efficient ◽  
Low Frequencies ◽  
Battery Modeling ◽  
Capacitance Effect ◽  
Frequency Domains ◽  
Frequency Behavior ◽  
Time And Frequency Domains

Abstract Battery Management Systems (BMSs) require control-oriented models. Physics-based electrochemical models describe detailed battery phenomena, but are too computationally intensive for use in BMSs. Single Particle Models (SPMs) are often used for control-oriented battery modeling since they are physics-based and computationally efficient; however, they are only valid over very low frequency ranges and C-rates. Empirical Equivalent Circuit Models (ECMs) are also used in BMSs since they are computationally efficient and describe battery behavior over wide frequency ranges; however, they provide no physical understanding of the battery and often employ fractional order terms. This work provides a control-oriented battery model that combines the benefits of SPM and ECM models, while overcoming their limitations. The proposed model incorporates some of the battery physics found in electrochemical models, can easily be used in both the time and frequency domains, and describes battery behavior over its entire frequency range. A linearized SPM models battery physics at very low frequencies. For low frequencies, integer-order linear systems are used to approximate diffusion physics, and high frequency behavior is modeled by the double layer capacitance effect. The model is validated in the time and frequency domains via a comparison to Pseudo 2-Dimensional (P2D) model simulations and experimental data.

Modulation of seismic noise near the San Jacinto fault in Southern California: Origin and observations of the cyclical time dependence and associated crustal properties

2020 ◽  
Author(s):  
Vladislav G Martynov ◽  
Luciana Astiz ◽  
Debi Kilb ◽  
Frank L Vernon
Keyword(s):  
Seismic Noise ◽  
Southern California ◽  
Low Frequency ◽  
Ocean Waves ◽  
Seismic Attenuation ◽  
Phase Lag ◽  
Low Frequencies ◽  
San Jacinto Fault ◽  
San Jacinto Fault Zone ◽  
Seismic Quality Factor

Summary We examine the cyclic amplitude variation of seismic noise recorded by continuous three-component broadband seismic data with durations spanning 91 to 713 days (2008–2011) from three different networks: Anza seismic network, IDA network and the Transportable seismic array. These stations surround the San Jacinto Fault Zone (SJFZ) in southern California. We find the seismic noise amplitudes exhibit a cyclical variation between 0.3 and 7.2 Hz. The high frequency (≥ 0.9 Hz) noise variations can be linked to human activity and are not a concern. Our primary interest is signals in the low frequencies (0.3–0.9 Hz), where the seismic noise is modulated by semi-diurnal tidal mode M2. These long-period (low frequency) variations of seismic noise can be attributed to a temporal change of the ocean waves breaking at the shoreline, driven by ocean tidal loading. We focus on the M2 variation of seismic noise at f = 0.6 Hz, travelling distances of ∼92 km through the crust from offshore California to the inland Anza, California, region. Relative to the shoreline station, data from the inland stations show a phase lag of ∼ –12°, which we attribute to the cyclic change in M2 that can alter crustal seismic attenuation. We also find that for mode M2 at 0.6 Hz, the amplitude variations of the seismic quality factor (Q) depend on azimuth and varies from 0.22 per cent (southeast to northwest) to 1.28 per cent (northeast to southwest) with Q = 25 for Rayleigh waves. We propose the direction dependence of the Q variation at 0.6 Hz reflects the preferred orientation of sub-faults parallel to the main faulting defined by the primarily N45° W strike of the SJFZ.

Low Frequency Noise Behavior in Semiconductors

1997 ◽  
Vol 11 (20) ◽  
pp. 899-907
Author(s):  
S. V. Melkonyan ◽  
F. V. Gasparyan ◽  
V. M. Aroutiunyan
Keyword(s):  
Spectral Density ◽  
Characteristic Frequency ◽  
Low Frequency ◽  
Frequency Noise ◽  
Low Frequency Noise ◽  
Low Frequencies ◽  
Frequency Behavior

The low frequency behavior of the generation-recombination noise in the homogeneous semiconductors is investigated. The form of Lorentz law for spectral density of noise at low frequencies is made more precise. It is shown that at superlow frequencies the spectrum of generation-recombination noise changes into the 1/f-law. The characteristic frequency of this change depends on the temperature and dimensions of the sample.

scholarly journals The Vertical Structure of Low-Frequency Motions in the Nearshore. Part I: Observations

2016 ◽  
Vol 46 (12) ◽  
pp. 3695-3711 ◽  
Author(s):  
Thomas C. Lippmann ◽  
Edward B. Thornton ◽  
Timothy P. Stanton
Keyword(s):  
Water Column ◽  
Vertical Structure ◽  
Energy Levels ◽  
Low Frequency ◽  
Companion Paper ◽  
Phase Lag ◽  
Current Profile ◽  
Low Frequencies ◽  
Sensor Position ◽  
Alongshore Current

AbstractField observations of oscillating currents in the surfzone of a natural beach show significant vertical structure in energy, phase, and rotation at low frequencies around 0.005 Hz, where most of the energy is associated with vorticity motions. Energy levels in the cross-shore component of the flow seaward of the sandbar decay near the bottom. Shoreward of the bar crest, the flow decays nearly linearly over the water column. Conversely, a weaker alongshore component of the flow increases near the bottom seaward of the sandbar and is roughly depth-uniform inside the bar crest. Near this 0.005-Hz frequency band, the coherence between the uppermost and successive vertically separated sensors drops off quickly, with as much as a 70%–80% coherence drop over the water column (ranging from 2.5 to 4 m). The phase relative to the uppermost sensor shifts approximately linearly over depth, with as much as 50° phase lag at the bottom that can lag or lead the surface. Rotary coefficients also vary across the surfzone and are generally nonzero with rotational directions (cyclonic or anticyclonic) and orientation that depend on sensor position relative to the sandbar and alongshore current profile. The rotary coefficients are generally not uniform with depth and can change sign in the vertical. The observed behavior is qualitatively predicted by boundary layer theory (discussed in the companion paper by Lippmann and Bowen). The nonuniform vertical structure has implications to the interpretation of field data and horizontal nearshore mixing.

scholarly journals Recombination Radio Lines at Very Low Frequencies

2002 ◽  
Vol 199 ◽  
pp. 349-350
Author(s):  
A.A. Konovalenko ◽  
S.V. Stepkin ◽  
D.V. Shalunov
Keyword(s):  
Low Frequency ◽  
Radio Lines ◽  
Low Frequencies ◽  
Radio Recombination Lines ◽  
Decameter Wavelength ◽  
The World

Investigations of carbon low frequency radio recombination lines measured with the world biggest decameter wavelength array UTR-2 are described.

scholarly journals The Effect of Efferent Stimulation on the Phase and Amplitude of Extracellular Receptor Potentials in the Lateral Line System of the Perch (Perca Fluviatius)

1983 ◽  
Vol 102 (1) ◽  
pp. 223-238 ◽  
Author(s):  
I. J. RUSSELL ◽  
D. A. LOWE
Keyword(s):  
Lateral Line ◽  
Low Frequency ◽  
Receptor Potential ◽  
Mechanical Stimulus ◽  
Lateral Line System ◽  
Phase Lag ◽  
Low Frequencies ◽  
Line System ◽  
Lateral Line Nerve ◽  
Centre Frequency

1. Microphonic and summating potentials were recorded extracellularly from lateral line organs in the suborbital canal of the perch in response to sinusoidal movements of canal fluid. 2. These potentials were changed in amplitude, shape and phase, relative to the mechanical stimulus, by electrical stimulation of efferent fibres in the lateral line nerve. 3. The receptor potential amplitude/stimulus intensity relationships for the microphonic and summating potentials saturated at high levels of stimulation, and at progressively lower amplitudes with increasing frequencies of mechanical stimulation. Efferent stimulation tended to reduce this rate of saturation. 4. Amplitude versus frequency relationships plotted at different stimulus intensities for the microphonic potential showed that the lateral line organs were most sensitive to frequencies between 35–65 Hz (centre frequency), and at these frequencies efferent stimulation caused the greatest increase in amplitude. 5. Analysis of the second order and third order harmonic components of the microphonic showed that these were reduced by efferent stimulation and that the strongest reduction occurred at the centre frequency. 6. The phase of the receptor potential led that of the mechanical stimulus at very low frequencies by nearly 90°. This changed to zero phase at the centre frequency and to a phase lag at higher frequencies. Efferent stimulation caused no change in phase of the microphonic relative to the control state at the centre frequency, but caused a progressive phase lead and lag as the frequency was decreased and increased respectively about the centre frequency. 7. In the linear response range, the lateral line organs responded as critically damped low frequency resonators to the velocity of the stimulus. Efferent stimulation appeared to alter the damping of this resonance. The possibility is discussed that efferent stimulation can alter the mechanical properties of the lateral line hair cells.

scholarly journals Annular Variability and Eddy–Zonal Flow Interactions in a Simplified Atmospheric GCM. Part I: Characterization of High- and Low-Frequency Behavior

2009 ◽  
Vol 66 (10) ◽  
pp. 3075-3094 ◽  
Author(s):  
Sarah Sparrow ◽  
Michael Blackburn ◽  
Joanna D. Haigh
Keyword(s):  
Low Frequency ◽  
Circulation Model ◽  
Zonal Flow ◽  
Life Cycles ◽  
Quasi Equilibrium ◽  
Global Circulation Model ◽  
Low Frequencies ◽  
Flow Interactions ◽  
Slow Evolution ◽  
Frequency Behavior

Abstract Experiments have been performed using a simplified, Newtonian forced, global circulation model to investigate how variability of the tropospheric jet can be characterized by examining the combined fluctuations of the two leading modes of annular variability. Eddy forcing of this variability is analyzed in the phase space of the leading modes using the vertically integrated momentum budget. The nature of the annular variability and eddy forcing depends on the time scale. At low frequencies the zonal flow and baroclinic eddies are in quasi equilibrium and anomalies propagate poleward. The eddies are shown primarily to reinforce the anomalous state and are closely balanced by the linear damping, leaving slow evolution as a residual. At high frequencies the flow is strongly evolving and anomalies are initiated on the poleward side of the tropospheric jet and propagate equatorward. The eddies are shown to drive this evolution strongly: eddy location and amplitude reflect the past baroclinicity, while eddy feedback on the zonal flow may be interpreted in terms of wave breaking associated with baroclinic life cycles in lateral shear.

A note on fractional integral operator associated with multiindex Mittag-Leffler functions

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1931-1939 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Fractional Integral ◽  
Fractional Integration ◽  
Fractional Integral Operator ◽  
Integration Formula ◽  
Special Cases

Recently Kiryakova and several other ones have investigated so-called multiindex Mittag-Leffler functions associated with fractional calculus. Here, in this paper, we aim at establishing a new fractional integration formula (of pathway type) involving the generalized multiindex Mittag-Leffler function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

scholarly journals Earless toads sense low frequencies but miss the high notes

2017 ◽  
Vol 284 (1864) ◽  
pp. 20171670 ◽  
Author(s):  
Molly C. Womack ◽  
Jakob Christensen-Dalsgaard ◽  
Luis A. Coloma ◽  
Juan C. Chaparro ◽  
Kim L. Hoke
Keyword(s):  
High Frequency ◽  
Species Differences ◽  
Low Frequency ◽  
Auditory Brainstem ◽  
Low Frequencies ◽  
Hearing Sensitivity ◽  
Sensory Pathways ◽  
Airborne Sound ◽  
Vibrational Sensitivity ◽  
Species Specific

Sensory losses or reductions are frequently attributed to relaxed selection. However, anuran species have lost tympanic middle ears many times, despite anurans' use of acoustic communication and the benefit of middle ears for hearing airborne sound. Here we determine whether pre-existing alternative sensory pathways enable anurans lacking tympanic middle ears (termed earless anurans) to hear airborne sound as well as eared species or to better sense vibrations in the environment. We used auditory brainstem recordings to compare hearing and vibrational sensitivity among 10 species (six eared, four earless) within the Neotropical true toad family (Bufonidae). We found that species lacking middle ears are less sensitive to high-frequency sounds, however, low-frequency hearing and vibrational sensitivity are equivalent between eared and earless species. Furthermore, extratympanic hearing sensitivity varies among earless species, highlighting potential species differences in extratympanic hearing mechanisms. We argue that ancestral bufonids may have sufficient extratympanic hearing and vibrational sensitivity such that earless lineages tolerated the loss of high frequency hearing sensitivity by adopting species-specific behavioural strategies to detect conspecifics, predators and prey.

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