Oscillatory Systems Research Articles

Nonequilibrium quantum heat transport between structured environments

We apply the hierarchical equations of motion technique to analyzing nonequilibrium heat transport in a spin-boson type model, whereby heat transfer through a central spin is mediated by an intermediate pair of coupled harmonic oscillators. The coupling between each pair of oscillators is shown to introduce a localized gap into the effective spectral densities characterizing the system–oscillator–reservoir interactions. Compared to the case of a single mediating oscillator, we find the heat current to be drastically modified at weak system-bath coupling. In particular, a second-order treatment fails to capture the correct steady-state behavior in this regime, which stems from the λ 4-scaling of the energy transfer rate to lowest order in the coupling strength λ. This leads naturally to a strong suppression in the steady-state current in the asymptotically weak coupling limit. On the other hand, the current noise follows the same scaling as in the single oscillator case in accordance with the fluctuation-dissipation theorem. Additionally, we find the heat current to be consistent with Fourier’s law even at large temperature bias. Our analysis highlights a novel mechanism for controlling heat transport in nanoscale systems based on tailoring the spectral properties of thermal environments.

Development of discrete asymptotic algorithm for the optimal trajectory and control in oscillatory systems with liquid damper

Development of discrete asymptotic algorithm for the optimal trajectory and control in oscillatory systems with liquid damper

Assessment of Dynamic States of Railway Vehicles: Structural Mathematical Modeling

Introduction. The speed rise of railway transport and an increase in the loads on the axles of wheelsets necessitate the modernization of the existing fleet. Scientific studies in the field of rolling stock dynamics are aimed at taking into account the oscillatory processes that occur during the movement of railway vehicles in a traditional design. The attachment of supplementary elements was considered at the coupling level of two cars and the attachment of a third trolley in the center of gravity of the railway platform. The scientific literature has not paid enough attention to the construction of mathematical models that make it possible to assess the dynamic states of such constructive solutions. The objective of this study is to create a method for evaluating the dynamic conditions of a car. The situation is considered when an additional set of mass-inertial and elastic elements is introduced into its structure, and the general dynamic condition of the vehicle depends on the adjustment of their parameters.Materials and Methods. The basic research tool is the structural mathematical modeling, which is based on an approach where the source design scheme is a mechanical oscillatory system in the form of a solid body on elastic supports with supplementary typical elements introduced into its structure. The dynamic analogue of the calculation scheme used is the block diagram of the automatic control system, the use of which provides detailing the connections between typical elastic and mass-inertia elements.Results. A method for estimating the dynamic states of railway vehicles is proposed. It is based on the construction of mathematical models, taking into account the introduction of an additional structure of mass-inertia and elastic elements. The impact of additional parameters on the dynamic condition of the vehicle is investigated. Analytical relations have been obtained that provide reducing the dynamic loads on the major structural elastic elements when changing the corresponding parameters of a technical object. The transfer function of interpartial relations is given, which provides controlling the interaction between the coordinates of the vehicle movement under the action of two kinematic disturbances of the in-phase type.Discussion and Conclusion. The generated mathematical model provides for assessment, monitoring and control of the dynamic state of the vehicle under conditions of kinematic disturbances. The research results can be used to modernize existing vehicles and create new ones with improved dynamics.

Embedded exponential Runge–Kutta–Nyström methods for highly oscillatory Hamiltonian systems

Exponential/extended Runge–Kutta–Nyström (ERKN) methods have been validated by numerous theoretical and numerical results to be more efficient and suitable than classical Runge–Kutta–Nyström (RKN) methods in dealing with highly oscillatory Hamiltonian systems. Once numerical solutions are required to achieve a prescribed local error tolerance for practical problems, the embedded ERKN pairs with adaptive stepsize are needed. Given the higher efficiency of high-order methods than low-order methods, this paper focuses on high-order embedded ERKN pairs. Using the particular mapping from RKN methods into ERKN methods, we establish an approach to constructing high-order embedded ERKN pairs. By diagonalizing the frequency matrix, an implementation algorithm with less calculation amount than the direct calculation procedure is proposed for high-dimensional problems. In addition, the dispersion and dissipation of the ERKN pairs ERKN4(3) and ERKN8(6) are analyzed. Furthermore, the application of ERKN pairs to an important highly oscillatory problem, i.e., the wave equation prescribed with different boundary conditions is discussed. For the periodic boundary condition, a special implementation algorithm incorporated with FFT techniques is presented, which decreases the calculation amount in one time step from O(N2) to O(Nlog⁡N). Finally, numerical results with the FPU problem, the Klein–Gordon equation in the nonrelativistic limit regime, and a two-dimensional wave equation demonstrate the superiority of ERKN pairs over classical RKN pairs.

Time variability and periodicities of cross‐regional hydroclimatic causation in the contiguous United States

AbstractIdentifying and understanding various causal relations are fundamental to climate dynamics for improving the predictive capacity of Earth system modeling. In particular, causality in Earth systems has manifest temporal periodicities, like physical climate variabilities. To unravel the characteristic frequency of causality in climate dynamics, we develop a data‐analytic framework based on a combination of causality detection and Hilbert spectral analysis, using a long‐term temperature and precipitation dataset in the contiguous United States. Using the Huang–Hilbert transform, we identify the intrinsic frequencies of cross‐regional causality for precipitation and temperature, ranging from interannual to interdecadal time scales. In addition, we analyze the spectra of the physical climate variabilities, including El Niño‐Southern Oscillation and Pacific Decadal Oscillation. It is found that the intrinsic causal frequencies are positively associated with the physics of the oscillations in the global climate system. The proposed methodology provides fresh insights into the causal connectivity in Earth's hydroclimatic system and its underlying mechanism as regulated by the characteristic low‐frequency variability associated with various climatic dynamics.

Self-induced non-synchronous resonance phenomena and stability in reduced aero-elastic system

The paper is aimed at the parametric dynamic analysis of the two degrees of freedom (DoF) phenomenological model of aero-elastic interaction between a friction-damped flexible mounted body and a flowing fluid. A coupled system of a linear structure oscillator and the van der Pol based wake oscillator is introduced. Firstly, the complex eigenvalue problem is used for the comprehensive analysis of frequency lock-in, veering and crossing areas from the structural mode stability point of view. Further, an in-depth analysis of the fully nonlinear model based on the numerical continuation method is presented. The analysis focuses on non-synchronous vibration in the resonance areas. Attention is paid to the investigation of transition mechanisms to frequency lock-in and frequency veering in the structural response. In experimental studies, the amplitude and frequency jumps are observed. Here, we show that the origin of these jump phenomena results from the mutual coexistence of two stable solutions, which form a hysteresis region, which can be found in experimentally gained data. Moreover, the influence of structure friction-damping on nonlinear response is evaluated. The proposed phenomenological model is validated concerning two different experimental-based investigations.

A novel method for estimating properties of attentional oscillators reveals an age-related decline in flexibility.

Dynamic attending theory proposes that the ability to track temporal cues in the auditory environment is governed by entrainment, the synchronization between internal oscillations and regularities in external auditory signals. Here, we focused on two key properties of internal oscillators: their preferred rate, the default rate in the absence of any input; and their flexibility, how they adapt to changes in rhythmic context. We developed methods to estimate oscillator properties (Experiment 1) and compared the estimates across tasks and individuals (Experiment 2). Preferred rates, estimated as the stimulus rates with peak performance, showed a harmonic relationship across measurements and were correlated with individuals' spontaneous motor tempo. Estimates from motor tasks were slower than those from the perceptual task, and the degree of slowing was consistent for each individual. Task performance decreased with trial-to-trial changes in stimulus rate, and responses on individual trials were biased toward the preceding trial's stimulus properties. Flexibility, quantified as an individual's ability to adapt to faster-than-previous rates, decreased with age. These findings show domain-specific rate preferences for the assumed oscillatory system underlying rhythm perception and production, and that this system loses its ability to flexibly adapt to changes in the external rhythmic context during aging.

System identification and centralised causal impedance matching control of a row of two heaving point absorber wave energy converters

Similar to offshore wind turbines, multiple point absorber wave energy converters (WECs) will be installed in an array configuration, to increase the total capacity, and to benefit from the economies of scale. Whereas wind turbines always interact destructively due to wake effects, WECs can interact constructively, since hydrodynamic interactions between the WECs occur through radiation and diffraction of waves, changing the direction of the incoming wave energy. This paper presents the dataset and results of the experimental modelling of a row of two ‘WECfarm’ heaving point absorber WECs at the wave basin of Aalborg University (AAU). Impedance matching enables maximum power transfer between two oscillatory systems, from the waves to the Power Take-Off (PTO) of the WEC. While literature covers this impedance matching approach for single, isolated WECs, the research discussed in this paper is unique by applying the experimental modelling of the impedance matching approach on a row of two WECs. Radiation system identification tests are executed to determine the intrinsic impedance of the isolated WECs, and the 2 × 2 impedance matrix of the two-WEC array. A causal impedance matching resistive and reactive controller are designed, implemented and tested for a selection of operational sea states. For centralised control, hydrodynamic interactions are taken into account by considering the complete impedance matrix, whereas for decentralised control no hydrodynamic interactions are taken into account by considering only the diagonal of the impedance matrix. The power absorption performance of the isolated WECs, the two-WEC array with decentralised control, and the two-WEC array with centralised control, are compared. Constructive interaction is identified, yielding enhanced power absorption for the array compared to the WECs isolated. Therefore, the layout of the WEC array and the control of the PTO should be optimised simultaneously, to maximise the power absorption of the array as a whole.

Design of novel UPFC based damping controller for solar PV integrated power system using arithmetic optimization algorithm

Abstract Integrating renewable energy sources like solar power into traditional power systems poses challenges. One such challenge is the effect of renewable power plants, which use power electronics, on the grid’s stability. Specifically, these plants can impact small-signal stability by either damping or exacerbating low-frequency oscillations. This paper introduces a novel Unified Power Flow Controller (UPFC) based damping controller specifically designed for Solar Photovoltaic (PV) integrated power systems. It employs an Arithmetic Optimization Algorithm (AOA) to optimize the UPFC damping controller parameters and mitigate low-frequency oscillations in the power system. The objective function minimizes the Integral Time Absolute Error (ITAE) of speed deviations under varying loading conditions. The proposed technique is utilized simultaneously to control the modulation index of series and phase angle of shunt converters of UPFC. The MATLAB/simulation results obtained effectively from the proposed technique which is actualized and identify both detrimental and beneficial impacts of increased PV penetration for small signal stability performance. The study reveals both the small-signal stability of the system and its response to large disturbances that alter the active power balance and frequency stability. The results of the analysis demonstrated with single and multimachine environment by comparing with the other optimizations like PSO, DE, DE-PSO and GWO, the proposed one is effective for damping out the oscillations. The effectiveness of the proposed damping controller is further confirmed through real-time validation using the OPAL-RT setup.

Research results of resonant vibration equipment for compaction of concrete mixtures on a physical model

Introduction. The purpose of this article is to confirm the results of research on resonant vibration equipment for compacting concrete mixtures obtained using a mathematical model. The object of research is an oscillatory system of resonant vibration equipment consisting of two masses interconnected by elastic and dissipative elements. In addition, the first mass is connected to a fixed base through elastic and dissipative elements.Materials and methods. The main provisions of the theory of similarity and statistical processing of experimental data are used in the research. The required number of repeated experiments was determined statistically, and the reproducibility of the experiment was verified by the Cochran criterion. Results. The criteria and indicators of similarity of processes occurring in the system of resonant vibration equipment have been developed, formulas for the transition from the parameters of nature to the parameters of the physical model have been proposed. The technical characteristics of the physical model are presented.During the experiment, oscillograms of the movements of the vibrator and the working body which are shifted relative to each other by an angle of π/2 were obtained. At the same time, the amplitude of vibrations of the vibrator significantly exceeds the amplitude of vibrations of the working body.Discussions and conclusions. The presented dependences of the amplitudes obtained on mathematical and physical models qualitatively repeat each other. In the studied frequency range of the driving force, the maximum error is 12%. This confirms the results obtained on the mathematical model of resonant vibration equipment.

Identification of oscillatory systems with unknown continuous input actions

Identification of oscillatory systems with unknown continuous input actions

Fractional-order identification system based on Sundaresan’s technique

This paper investigates the Sundaresan technique for modeling fractional order systems. Sundaresan, Prasad, and Krishnaswamy published this method in 1978 for modeling oscillatory and non-oscillatory systems based on the second-order integer transfer function. This technique is based on the transient response parameters. A problem of convergence of the derivative of the response in the frequency domain makes it impossible to follow Sundaresan’s solution in his original paper with integer order when it is a fractional order case. The paper proposes an equation that outlines this problem. Due to the limited knowledge of the inverse Mittag-Leffler function, a reduced form of this equation is explicit to avoid the inverse problem. Results with simulated and real curve shapes show that the method works well, with a good approximation to the curve, both with simulation and real system curves.

METHOD OF ASSESSING THE CHANGE IN DESIGN PARAMETERS OF PRECISION ROTARY SYSTEMS BY THE PHASE SHIFT OF THE VIBRATION STATE

The article examines the issue of precision rotary systems (PRS) and the relationship between their dissipative characteristics and changes in design parameters, which is applicable for assessing the quality of their assembly and diagnosing objects in general. We identified a dynamic model, the dissipative parameters of which sufficiently accurately reflect the local properties of the structure. The question of assessing the quality of assembly by dissipative parameters comes down to the choice of the diagnostic sign that is most suitable for this case and the method of its measurement. Such a sign is a phase shift between the disturbance force and the vibration velocity. From this point of view, phase-frequency measurement methods are generally more accurate, which allows using the advantages of precise hardware methods to obtain information to the fullest extent. The proposed variation ratio, which connects the changes in a real object’s phase vector of the mechanical impedance (PVMI) and the deviation of the dissipative parameters of its mathematical model, makes it possible to diagnose the dissipative parameters with a sufficient accuracy degree. The considered numerical example of a partial assembly of precision rotary systems confirms the accuracy of the calculation. Thus, the proposed variation ratio, which connects the changes in the PVMI of a real object and the deviation of the dissipative parameters of its mathematical model, allows for the diagnosis of the dissipative parameters with a sufficient accuracy degree. The considered numerical example of a partial assembly of the PRS confirms the accuracy of the calculation. This fact is of particular importance in manufacturing aviation and space technology products. We should also note that the existing analysis methods do not provide an opportunity to form an idea about the nature of the total measured signal and its structure. Therefore, the work solves the task of developing a method for diagnosing the controlled technical condition of a rotary electromechanical system based on the selection of the most informative ranges of the output signal to increase the reliability of diagnosis. Keywords: oscillatory system, dissipative properties, mathematical model, phase angle, impedance, sensitivity matrix.

METHOD OF ASSESSING THE CHANGE IN DESIGN PARAMETERS OF PRECISION ROTARY SYSTEMS BY THE PHASE SHIFT OF THE VIBRATION STATE

The article examines the issue of precision rotary systems (PRS) and the relationship between their dissipative characteristics and changes in design parameters, which is applicable for assessing the quality of their assembly and diagnosing objects in general. We identified a dynamic model, the dissipative parameters of which sufficiently accurately reflect the local properties of the structure. The question of assessing the quality of assembly by dissipative parameters comes down to the choice of the diagnostic sign that is most suitable for this case and the method of its measurement. Such a sign is a phase shift between the disturbance force and the vibration velocity. From this point of view, phase-frequency measurement methods are generally more accurate, which allows using the advantages of precise hardware methods to obtain information to the fullest extent. The proposed variation ratio, which connects the changes in a real object’s phase vector of the mechanical impedance (PVMI) and the deviation of the dissipative parameters of its mathematical model, makes it possible to diagnose the dissipative parameters with a sufficient accuracy degree. The considered numerical example of a partial assembly of precision rotary systems confirms the accuracy of the calculation. Thus, the proposed variation ratio, which connects the changes in the PVMI of a real object and the deviation of the dissipative parameters of its mathematical model, allows for the diagnosis of the dissipative parameters with a sufficient accuracy degree. The considered numerical example of a partial assembly of the PRS confirms the accuracy of the calculation. This fact is of particular importance in manufacturing aviation and space technology products. We should also note that the existing analysis methods do not provide an opportunity to form an idea about the nature of the total measured signal and its structure. Therefore, the work solves the task of developing a method for diagnosing the controlled technical condition of a rotary electromechanical system based on the selection of the most informative ranges of the output signal to increase the reliability of diagnosis. Keywords: oscillatory system, dissipative properties, mathematical model, phase angle, impedance, sensitivity matrix.

Grid synchronised three phase VSI-based hardware emulator to realise low frequency electromechanical oscillations in power systems and their effects on physical distance relay

Grid synchronised three phase VSI-based hardware emulator to realise low frequency electromechanical oscillations in power systems and their effects on physical distance relay

Numerical simulation of fractional-order Duffing system with extended Mittag-Leffler derivatives

In this paper, we studied the dynamics of a nonlinear fractional-order Duffing system combined with Mittag-Leffler derivatives in order to provide dynamic behaviors different from existing ones. The Mittag-Leffler derivative is a generalized version of the exponential kernel derivative. To achieve this goal, we introduced a modified extension to higher-order Mittag-Leffler derivatives to overcome the initialization problem. Moreover, we discussed some properties and relationships of the studied derivatives. Then we presented numerical schemes to handle fractional extensions of the considered oscillatory system including the Mittag-Leffler and the Caputo derivatives. Numerical simulations are carried out and the resulting simulation dynamics of the studied fractional oscillatory system are compared.

Improving PID Controller Performance in Nonlinear Oscillatory Automatic Generation Control Systems Using a Multi-objective Marine Predator Algorithm with Enhanced Diversity

Power systems are pivotal in providing sustainable energy across various sectors. However, optimizing their performance to meet modern demands remains a significant challenge. This paper introduces an innovative strategy to improve the optimization of PID controllers within nonlinear oscillatory Automatic Generation Control (AGC) systems, essential for the stability of power systems. Our approach aims to reduce the integrated time squared error, the integrated time absolute error, and the rate of change in deviation, facilitating faster convergence, diminished overshoot, and decreased oscillations. By incorporating the spiral model from the Whale Optimization Algorithm (WOA) into the Multi-Objective Marine Predator Algorithm (MOMPA), our method effectively broadens the diversity of solution sets and finely tunes the balance between exploration and exploitation strategies. Furthermore, the QQSMOMPA framework integrates quasi-oppositional learning and Q-learning to overcome local optima, thereby generating optimal Pareto solutions. When applied to nonlinear AGC systems featuring governor dead zones, the PID controllers optimized by QQSMOMPA not only achieve 14%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} reduction in the frequency settling time but also exhibit robustness against uncertainties in load disturbance inputs.

Enhancing model identification with SINDy via nullcline reconstruction.

Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse Identification of Nonlinear Dynamics (SINDy). This paper illustrates the importance of accurately determining the system's limit cycle position in phase space for identifying sparse and effective models. We introduce a method for identifying the limit cycle position and the system's nullclines by applying SINDy to datasets adjusted with various offsets. This approach is evaluated using three criteria: model complexity, coefficient of determination, and generalization error. We applied this method to several models: the oscillatory FitzHugh-Nagumo model, a more complex model consisting of two coupled cubic differential equations with a single stable state, and a multistable model of glycolytic oscillations. Our results confirm that incorporating detailed information about the limit cycle in phase space enhances the accuracy of model identification in oscillatory systems.

Multi-type synchronization for coupled van der Pol oscillator systems with multiple coupling modes.

In this paper, we investigate synchronous solutions of coupled van der Pol oscillator systems with multiple coupling modes using the theory of rotating periodic solutions. Multiple coupling modes refer to two or three types of coupling modes in van der Pol oscillator networks, namely, position, velocity, and acceleration. Rotating periodic solutions can represent various types of synchronous solutions corresponding to different phase differences of coupled oscillators. When matrices representing the topology of different coupling modes have symmetry, the overall symmetry of the oscillator system depends on the intersection of the symmetries of the different topologies, determining the type of synchronous solutions for the coupled oscillator network. When matrices representing the topology of different coupling modes lack symmetry, if the adjacency matrices representing different coupling modes can be simplified into structurally identical quotient graphs (where weights can be proportional) through the same external equitable partition, the symmetry of the quotient graph determines the synchronization type of the original system. All these results are consistent with multi-layer networks where connections between different layers are one-to-one.

PMSM Speed Active Disturbance Rejection Control Based on Modified Extended State Observer

In order to address the issues of significant input variations and complex disturbances in speed control of permanent magnet synchronous motors (PMSM), a Modified Active Disturbance Rejection Controller (ADRC) based on an improved Modified Extended State Observer (ESO) is proposed in this paper. In this new method, a nonlinear cascaded structure of observers is adopted. By utilizing the TD filter, high‐frequency noise can be attenuated while preserving the dynamic characteristics of the signal. Moreover, system oscillations caused by minor errors are effectively suppressed. The introduction of propeller and wave models enhances the realism of simulated marine environmental disturbances. Research results indicate that, compared to a single Extended State Observer, the cascaded MESO exhibits better disturbance rejection and noise resistance in complex marine environments, and the proposed MADRC outperforms both PI controllers and ADRC in dealing with marine environmental disturbances. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.