Oscillatory Systems Research Articles

Phase slips in coupled oscillator systems.

Phase slips are a typical dynamical behavior in coupled oscillator systems: the route to phase synchrony is characterized by intervals of constant phase difference interrupted by abrupt changes in the phase difference. Qualitatively similar to stick-slip phenomena, analysis of phase slip has mainly relied on identifying remnants of saddle-nodes or "ghosts." We study sets of phase oscillators and by examining the dynamics in detail, offer a more precise, quantitative description of the phenomenon. Phase shifts and phase sticks, namely, the temporary locking of phases required for phase slips, occur at stationary points of phase velocities. In networks of coupled phase oscillators, we show that phase slips between pairs of individual oscillators do not occur simultaneously, in general. We consider additional systems that show phase synchrony: one where saddle-node ghosts are absent, one where the coupling is similarity dependent, and two cases of coupled chaotic oscillators.

Model order estimation for low-frequency oscillations in power systems by an advanced K-mean clustering approach

The estimation of low frequency modes present in the complex inter connected power system is very much crucial for taking remedial action to maintain power system stability and security. Modified total least square estimation of signal parameters via rotational invariance techniques (TLS-ESPRIT) is a popular mode estimation technique used for signal analysis, even in noisy conditions. But this technique requires a preliminary idea about the number of modes (Model order) present in the signal and its accuracy of estimation degrade when noise level increases. So the key contribution of this work is to develop a robust model order estimation technique, which will work efficiently in all range of signal and noise level. So, in this proposed work, an unsupervised sequential K-Mean++ clustering technique is implemented for the estimation of model order of low-frequency Phasor Measurement Unit (PMU) data by separating the significant eigenvalues of autocorrelation matrix (ACM) iteratively into signal and noise subspace. This two-layer K-Means++ algorithm promises a valid estimation of model order so that the insignificant eigenvalues are not clustered into the signal subspace. To validate the efficiency and robustness of the proposed method, a comparative study is carried out with the other techniques. Finally, the method is validated on two area data, real probing data obtained from Western Electricity Coordinating Council (WECC) network and oscillatory power data obtained for WSCC 9 and IEEE 39 bus system simulated on Real Time Digital Simulator (RTDS).

Hybrid wind-PV farm with STATCOM for damping & control of overall chaotic oscillations in two-area power system using hybrid technique

This manuscript proposes a hybrid wind-photovoltaic farm with static synchronous compensator(STATCOM) for damping and controlling general chaotic-oscillations in a two-area power system. The proposed hybrid method is the joint operation of Tasmanian Devil Optimization(TDO) and Aquila Optimizer (AO) and together called as TDO-AO technique. The major objective of the proposed technique is minimizing the error, optimizes the performance of the system and regulates the controller parameters of proportional-integral (PI). The STATCOM is used to regulate the voltage and improve the power-factor of the system, leading to better power quality and reduced losses. The TDO is used to optimize the location and size of the wind-PV farm. The AO is utilized to enhance the parameters of STATCOM. The hybrid wind-PV farm with STATCOM can provide a renewable source of energy and improve the stability and reliability of the power grid. While being optimally compensated, the system is vulnerable to 3-phase faults. Zero damping is one more disturbance, along with a change in reference voltage and electric torque. The disturbances are created to simulate the worst scenarios, so that the hybrid wind-PV farm may be rigorously evaluated for its effectiveness in reducing the total chaotic oscillations. In Wind-PV-STATCOM, the gate signal is managed by a controller that separately controls the AC and DC currents. Then, the performance of proposed method is implemented in MATLAB and it is contrasted with the existing methods. From the simulation analysis, the proposed method based settling time is 1.00 sec that is less than the existing one.

Neurofluid coupling during sleep and wake states

BackgroundIn clinical populations, the movement of cerebrospinal fluid (CSF) during sleep is a growing area of research with potential mechanistic connections in both neurodegenerative (e.g., Alzheimer's Disease) and neurodevelopmental disorders. However, we know relatively little about the processes that influence CSF movement. To inform clinical intervention targets this study assesses the coupling between (a) real-time CSF movement, (b) neuronal-driven movement, and (c) non-neuronal systemic physiology driven movement. MethodsThis study included eight young, healthy volunteers, with concurrently acquired neurofluid dynamics using functional Magnetic Resonance Imaging (MRI), neural activity using Electroencephalography (EEG), and non-neuronal systemic physiology with peripheral functional Near-Infrared Spectroscopy (fNIRS). Neuronal and non-neuronal drivers were assessed temporally; wherein, EEG measured slow wave activity that preceded CSF movement was considered neuronally driven. Similarly, slow wave oscillations (assessed via fNIRS) that coupled with CSF movement were considered non-neuronal systemic physiology driven. Results and conclusionsOur results document neural contributions to CSF movement were only present during light NREM sleep but low-frequency non-neuronal oscillations were strongly coupled with CSF movement in all assessed states – awake, NREM-1, NREM-2. The clinical/research implications of these findings are two-fold. First, neuronal-driven oscillations contribute to CSF movement outside of deep sleep (NREM-3); therefore, interventions aimed at increasing CSF movement may yield meaningful increases with the promotion of NREM sleep more generally – a focus on NREM S3 may not be needed. Second, non-neuronal systemic oscillations contribute across wake and sleep stages; therefore, interventions may increase CSF movement by manipulating systemic physiology.

Power system oscillation damping controller design: a novel approach of integrated HHO-PSO algorithm

Power system oscillation damping controller design: a novel approach of integrated HHO-PSO algorithm

Development of the equivalent Great Britain 36-zone power system for frequency control studies

This paper presents a dynamic model of the equivalent Great Britain (GB) 36-zone power system, which can be used for reliable and realistic assessment of emerging load frequency control mechanisms. Flexible architecture of the presented dynamic test system permits a broad range of security of supply and small-signal stability studies for design of future power grids. It can be particularly useful for academic research, but also for undertaking feasibility studies in power industries. The proposed dynamic test system, which is obtained through network reduction of the original full-scale GB transmission power system developed by National Grid Electricity System Operator (NGESO) Company, provides detailed information about the GB power system. In this regard, the required data and modelling approaches to develop the 36-zone system are provided in detail. The presented dynamic test system represents the system topology, impedance characteristics and electromechanical oscillations of the original GB power system however, it is not an exact equivalent of the master GB system. Illustrative dynamic models of the key system components, including synchronous generators, automatic voltage regulators, power system stabilizers, hydro and steam turbines models along with speed governing systems are presented. Dynamic behavior of 36-zone test system in response to infeed loss contingencies is investigated. Particularly, the impact of changes in the system inertia on the system electromechanical modes is examined using the modal analysis approach. In this context, the mode shape concept is employed to determine dominant generators and contribution of different zones in the low frequency oscillations. Moreover, time-domain simulations are undertaken to validate the modal analysis results. Additionally, the condition of different zones from the viewpoint of frequency nadir and maximum rate of change of frequency for various contingencies and extreme cases are examined.

Dynamical system of a time-delayed ϕ6-Van der Pol oscillator: a non-perturbative approach

A remarkable example of how to quantitatively explain the nonlinear performance of many phenomena in physics and engineering is the Van der Pol oscillator. Therefore, the current paper examines the stability analysis of the dynamics of ϕ6-Van der Pol oscillator (PHI6) exposed to exterior excitation in light of its motivated applications in science and engineering. The emphasis in many examinations has shifted to time-delayed technology, yet the topic of this study is still quite significant. A non-perturbative technique is employed to obtain some improvement and preparation for the system under examination. This new methodology yields an equivalent linear differential equation to the exciting nonlinear one. Applying a numerical approach, the analytical solution is validated by this approach. This novel approach seems to be impressive and promising and can be employed in various classes of nonlinear dynamical systems. In various graphs, the time histories of the obtained results, their varied zones of stability, and their polar representations are shown for a range of natural frequencies and other influencing factor values. Concerning the approximate solution, in the case of the presence/absence of time delay, the numerical approach shows excellent accuracy. It is found that as damping and natural frequency parameters increase, the solution approaches stability more quickly. Additionally, the phase plane is more positively impacted by the initial amplitude, external force, damping, and natural frequency characteristics than the other parameters. To demonstrate how the initial amplitude, natural frequency, and cubic nonlinear factors directly affect the periodicity of the resulting solution, many polar forms of the corresponding equation have been displayed. Furthermore, the stable configuration of the analogous equation is shown in the absence of the stimulated force.

Observation of thermal acoustic modes of a droplet coupled to an optomechanical sensor

The bulk acoustic modes of liquid droplets, well understood from a theoretical perspective, have rarely been observed experimentally. Here, we report the indirect observation of acoustic vibrational modes in a picoliter-scale droplet, extending up to ∼40 MHz. This was achieved by coupling the droplet to an ultra-sensitive optomechanical sensor, which operates in a thermal-noise limited regime and with a substantial contribution from acoustic noise in the ambient medium. The droplet vibrational modes manifest as Fano resonances in the thermal noise spectrum of the sensor. This is among the few reported observations of droplet acoustic modes and of Fano interactions in a coupled mechanical oscillator system driven only by thermal Brownian motion.

Design of the electric vehicle powertrain systems based on μ-analysis

Aiming at the oscillation in the electric vehicle powertrain systems, a control strategy based on the structural singular value [Formula: see text] is proposed. To solve the problem of robustness under parameter uncertainty, the traditional [Formula: see text]-synthesis needs to obtain all-pass characteristics through the weight function in the nominal system, which reduces the perturbation suppression ability of the system. Unlike the previous use of [Formula: see text]-analysis as a system performance criterion, this paper starts from the essence of parameter uncertainty problems and designs controllers based on the relationship between parameter uncertainty and nominal systems, using structural singular value [Formula: see text] as a performance constraint. The result shows that the [Formula: see text]-analysis not only takes into account the robustness and disturbance rejection ability but also reduces the controller order. In addition, the oscillation suppression effect in the presence of transmission backlash is verified, and the [Formula: see text]-analysis can suppress the oscillation better than the [Formula: see text]-synthesis.

Tuning of PID/PIDD2 Controllers for Second-Order Oscillatory Systems with Time Delays

PID control is the longest history and the most vital basic control mode that has been widely applied in the production process. The oscillatory dynamics of the process have various features, and parameter tuning is complicated. To reduce the complexity of the parameter tuning process and improve the performance of the system, in this research, we propose a new tuning method for the PID/PIDD2 controllers for second-order oscillatory systems with time delays under the constraint of certain robustness. In comparison to existing PID for second-order oscillatory systems with time delays, simulation findings demonstrate that the tuning method of the proposed PID/PIDD2 controllers trades off robustness and disturbance rejection performance.

Impact of a Redox Flow Battery on the Frequency Stability of a Five-Area System Integrated with Renewable Sources

Energy storage devices are imperative to damp out the oscillations caused by sudden magnified disturbances occurring in a power system. The presence of a small rating of storage device in each area can alleviate the system oscillations effectively. Therefore, in this work, redox flow batteries (RFBs) have been integrated in each area of a five-area interconnected system for effective load frequency control (LFC). The RFB pumps up the active power into the system quickly to meet the short-time overload; in turn, the efficacy of the LFC in the system is boosted. Despite the presence of the RFB in the power system, a secondary controller is necessary to quench the deviation of frequency and tie-line power caused by the power mismatch between demand and generation. In this perspective, a cascade controller incorporated with a fractional operator (FO) has been endorsed and designed through a nascent selfish herd optimizer technique to evaluate the transient response of the system. Besides this, the unprecedented performance of fractional-order cascade controllers has been compared with one-stage classical controllers with and without a fractional operator. Further, the robustness of the proposed controller has been inspected through subjecting it to a random load in the presence/absence of an RFB and parametric variation. Finally, the proposed model has been simulated in the OPAL-RT-4510 platform to validate the performance of the proposed controller that has produced in the MATLAB environment.

Coupled Oscillators in an Agroecosystem: Integrating Direct and Indirect Effects.

AbstractAgricultural pests are increasingly appreciated as subjects of ecology. One particular case, a pest in coffee production, is analyzed here using the conceptual framework of complex systems, increasingly acknowledged as having an obvious home in the field of ecology, notorious for its complex structures. The particular case analyzed here arguably falls under the control of the complexity of the ecological system rather than of a simple magic bullet of population regulation. The system, which has been under study in southern Mexico for the past quarter century, is analyzed through the lens of neutral oscillations of the classical nondissipative Lotka-Volterra system. Based on three consumer/resource pairs (populations of [1] an ant, [2] a scale insect, [3] a beetle predator of the scale insect, [4] a fungal pathogen of the scale insect, and [5] a fly parasitoid of the ant), this five-dimensional system is well known qualitatively. Coupling all agents through both direct effects and trait-mediated indirect effects, the behavior of the neutral oscillation form of the system reveals a complex set of behaviors, including harmonized invariant sets, chaos, and/or quasiperiodicity. Such behaviors are well-known subjects in the science of complex systems and, it is argued, are ultimately sufficient to effect a degree of regulation on the pest, independent of explicit density-dependent feedback. Control of the system is thus seen as arguably actuated through its complexity, independent of any classic dissipative force.

Optimal sliding mode control for frequency stabilization of hybrid renewable energy systems

AbstractThe constant changes in the load power lead permanently to a power mismatch between the power generation and the power consumption. So, the system frequency due to the power imbalance deviates from the nominal value. Consequently, a control loop should be implemented to stabilize the system frequency whenever a load change occurs. This paper presents a new super‐twisting sliding mode control methodology for obtaining an optimal frequency performance in a multi‐pool system. The paper presents a three‐pool system for frequency deviation problems using an optimal gain Super Twisting Sliding Mode Controller (STSMC), which regulates the frequency change and the line power change to zero in a minimal time. The extent of the excellence of the study proposed is evaluated by comparing it with three Benchmark classical controllers, which are the Tilt‐Integral‐Derivative (TID), Proportional‐Integral‐Derivative (PID), and Fractional‐Order PID (FOPID). The parameters of the four controllers are determined by a proposed physical meta‐heuristic optimization technique called Transient Search Optimizer (TSO), inspired by the dynamic behaviour in the electrical circuits comprising storage elements such as capacitors and inductors during the switching actions. The system simulation is performed, and the STSMC proved overwhelming superiority over other controllers, as it deals better with the transient interval of the system response. Renewable Energy sources (RESs) like photovoltaic and wind energy systems are established, and the STSMC is tested with industrial and residential load models. Finally, energy storage devices such as batteries and superconducting magnetic energy storage are implemented to suppress the rapid fluctuations in the system response, and it succeeded in doing that as the system oscillations are greatly damped with the energy storage devices.

Application of Laplace-based variational iteration method to analyze generalized nonlinear oscillations in physical systems

In this paper, the variational iterative method (VIM) with the Laplace transform is utilized to solve the nonlinear problems of a simple pendulum and mass spring oscillator, which corresponds to the Duffing equation. Finding the Lagrange multiplier (LM) is a significant phase in the VIM, and variational theory is frequently employed for this purpose. This paper demonstrates how the Laplace transform can be utilized to locate the LM in a more efficient manner. The frequency obtained by Laplace-based VIM is the same as that defined in the already existing methods in the literature in order to ensure the clarity of the results. Numerous analytical techniques can be used to solve the Duffing equation, but we are the first to do it using a Laplace-based VIM and a distinctive LM. The fundamental results of my paper are that LM is also the same in the Elzaki transformation. In the vast majority of instances, Laplace-based VIM only requires one iteration to arrive at an answer with high precision and linearization, discretization or intensive computational work is required for this purpose. Comparing analytical results of VIM by Laplace transform to the built-in Simulink command in MATLAB which gives us the surety about the method’s applicability for solving nonlinear problems. Future work on the basic pendulum may examine the effects of nonlinearities and damping on its motion and the application of advanced control mechanisms to regulate its behavior. Future research on mass spring oscillators could examine the system’s response to random or harmonic input. The mass spring oscillator could also be used in vibration isolation to minimize vibrations from one building to another.

Investigation of the Existence of Limit Cycles in Multi Variable Nonlinear Systems with Special Attention to 3X3 Systems

The proposed work addresses the dynamics of a general system and explores the existence of limit cycles (LC) in multi-variable Non-linear systems with special attention to 3x3 nonlinear systems. It presents a simple, systematic analytical procedure as well as a graphical technique that uses geometric tools and computer graphics for the prediction of limit cycling oscillations in three-dimensional systems having both explicit and implicit nonlinear functions. The developed graphical method uses the harmonic balance/harmonic linearization for simplicity of discussion which provides a clear and lucid understanding of the problem and considers all constraints, especially the simultaneous intersection of two straight lines & one circle for determination of limit cycling conditions. The method of analysis is made simpler by assuming the whole system exhibits the limit cycling oscillations predominantly at a single frequency. The discussions made either analytically/graphically are substantiated by digital simulation by a developed program as well as by the use of the SIMULINK Toolbox of MATLAB Software.

Dynamic analysis of magnetic spring-based nonlinear oscillator system

This paper aims to study the dynamics of the single-degree-of-freedom magnetic spring-based oscillator system. The proposed oscillator system contains a nonmagnetic shaft, a floating permanent magnet (PM), and two fixed permanent magnets (PMs). All PMs are placed in such a way that they can repel each other. At first, the proposed system's magnetic properties and magnetic restoring force are studied. Experimental and numerical analyses have been carried out to validate the analytical investigation of the magnetic restoring force. The linear and nonlinear coefficients of the oscillator system are analysed from the magnetic restoring force. Moreover, how the gravitational force affects the equilibrium position is studied by varying the height of the oscillator. The magnetic restoring forces for different oscillator heights are also analysed. In addition, the system dynamics, such as damping ratio, eigenvalues and natural frequencies of the oscillator system, are investigated with and without electromechanical coupling. Finally, the proposed system's energy generation capacity is examined using electromechanical coupling.

The Similarity Law of Cavitation Number on Cavitation Instability in Liquid Rocket Inducer

Abstract The influence of inducer rotation speed on the propagation characteristics of rotating cavitation and on the unsteady characteristics of cavitation in rotating cavitation and cavitation surge were examined using a three-bladed inducer, which is named THK inducer, to develop the rocket engine turbopump that can operate stably over a wide operating range. The novel point of the paper is focusing on the cavitation itself, which is the cause of cavitation instabilities. The paper conducted two types of experiments using an inducer and single hydrofoils, and the dimensional and nondimensional unsteady characteristic, which is the frequency of unsteady cavitation and the Strouhal number, were evaluated. Three types of rotating cavitation and cavitation surge were observed in the inducer. For a given cavitation number, the Strouhal number of rotating cavitation and the frequency of unsteady cavitation in cavitation surge are independent of the inducer rotation speed, respectively. The characteristic of rotating cavitation corresponds to that of cavitations arising in hydrofoils, but its characteristic of cavitation surge does not correspond. The dynamic characteristic of cavitation compliance in cavitation surge is similar to that of several rocket engine turbopumps. Therefore, it was proved that rotating cavitation is a cavity oscillation and cavitation surge is a system oscillation. Additionally, in a flow field with the same flow coefficient and different impeller rotation speed, the unsteady characteristics of cavitation instabilities are equal if the cavitation number is equal, which is named the “similarity law of cavitation number on cavitation instability.”

LABVIEW IN THE RESEARCH OF FRACTAL PROPERTIES OF THE TOPOLOGY OF NETWORKS AND STOCHASTIC PROCESSES

The advancement and utilization of computer technologies for studying and diagnosing the technical state of dynamic systems are closely linked to scientific and technological progress. Among these technologies, fractal technologies hold a prominent position [1]. Time series data, which record changes in controlled parameters over time, are commonly used for diagnosing technical objects and systems. The use of fractals will also be of interest in assessing the resonant frequency characteristics of oscillatory systems [3]. The informational characteristics of topologically distributed networks (e.g., computer, cellular) significantly depend on their geometry, node placement, and inter-node distances. The fractal dimension, a fundamental characteristic of networks, plays a crucial role in this context [2]. The research paper presents a methodology for modeling and synthesizing large networks using the node density function, which follows a power function with a fractal dimension. This characteristic aligns with Zipf's law of population distribution around urban centers. The paper also provides fractality degree indices for the network diagram. Software tools such as LabVIEW play a significant role in scientific research and experiment automation.

Quantum evolution represented by Brownian motion.

We propose a stochastic Schrödinger equation in which the momentum is coupled to a white Gaussian noise. In the stochastic representation, the kinetic energy representing the self-interaction of momentum is reduced to a linear term of momentum. As such, the quantum evolution operator factorizes into two contributions due to the momentum and the potential, respectively. The exact quantum propagator thereby becomes an expectation of the stochastic one in which the amplitude results from the potential with a fluctuating position: The particle moves with a constant velocity, subjected to a complex Brownian motion. We demonstrate that the stochastic Schrödinger equation can be feasibly used to derive the quantum propagators for the linear potential and the harmonic oscillator system. Novel semiclassical and other approximations may be developed from the new representation of quantum mechanics.

On mitigation of oscillations of a mechanical system with two degrees of freedom in the vicinity of external resonances

On mitigation of oscillations of a mechanical system with two degrees of freedom in the vicinity of external resonances