Problem Of Oscillations Research Articles

On the Problem of Nonlinear Oscillations of a Conservative System in the Absence of Resonance

On the Problem of Nonlinear Oscillations of a Conservative System in the Absence of Resonance

A Microgrid Stability Improvement Method by Applying Virtual Adaptive Resistor Paralleling with a Grid-Connected Inverter

An increase in renewable energy generation in the microgrid can cause voltage oscillation problems. To address this issue, an equivalent circuit of the microgrid was established, including a synchronous generator, grid-connected inverter, and constant power load. Then, the impact of different renewable energy generation ratios, different direct current (DC) voltage loops, and phase-locked loop control bandwidths of the grid-connected inverter on microgrid stability were analyzed. The results indicate that an increase in the renewable energy generation ratio leads to a decrease in the stability margin of the microgrid. A microgrid stability improvement method involving the parallel connection of a virtual resistor with the grid-connected inverter was proposed. The resistance value of the virtual resistor was obtained through an adaptive algorithm. This method ensures the stable operation of the microgrid under different renewable energy generation ratios.

Advanced Sliding Mode Design for Optimal Automatic Generation Control in Multi-Area Multi-Source Power System Considering HVDC Link

The multi-area multi-source power system (MAMSPS), which uses a variety of power sources including gas, hydro, thermal, and renewable energy, has recently been implemented to balance the growing demand for electricity and the overall capacity for power generation. In this paper, an integral sliding mode control with a single-phase technique (ISMCSP) is applied to two areas, with each area including gas–wind–thermal power systems with HVDC system. Firstly, a two-area gas–wind–thermal power system with HVDC (TAGWTPSH) is the first model in this scheme to consider the parameter uncertainties of a MAMSPS. Secondly, sliding mode design law with a single-phase technique is introduced to alleviate chattering and oscillation problems. Then, power system stability is ensured by the Lyapunov control theory based on the new LMIs technique. Thirdly, the ISMCSP’s effectiveness in a MAMSPS is also assessed under random load patterns and parameter variations regarding settling time and over-/undershoot. The ISMCSP was created to alter the fundamental sliding mode control, and therefore the suggested approach performs better than recently published approaches. This is demonstrated by the frequency overshoot deviation value in frequency deviations: 0.7 × 10−3 to 2.8 × 10−3 for the TAGWTPSH with the suggested ISMCSP. In the last case, for random changes in load from −0.4 to +0.5 p. u, the proposed ISMCSP method still stabilizes the frequency of the areas meeting the standard requirements for AGC.

Novelty in Intelligent Controlled Oscillations in Smart Structures

Structural control techniques can be used to protect engineering structures. By computing instantaneous control forces based on the input from the observed reactions and adhering to a strong control strategy, intelligent control in structural engineering can be achieved. In this study, we employed intelligent piezoelectric patches to reduce vibrations in structures. The actuators and sensors were implemented using piezoelectric patches. We reduced structural oscillations by employing sophisticated intelligent control methods. Examples of such control methods include H-infinity and H2. An advantage of this study is that the results are presented for both static and dynamic loading, as well as for the frequency domain. Oscillation suppression must be achieved over the entire frequency range. In this study, advanced programming was used to solve this problem and complete oscillation suppression was achieved. This study explored in detail the methods and control strategies that can be used to address the problem of oscillations. These techniques have been thoroughly described and analyzed, offering valuable insights into their effective applications. The ability to reduce oscillations has significant implications for applications that extend to various structures and systems such as airplanes, metal bridges, and large metallic structures.

A Novel Analytical Approximate Solution for Strongly Nonlinear Third-Order Jerk Equations Using a Modified Iteration Method

Nonlinear jerk equations, characterized by a third-order time derivative, play a crucial role in modeling various physical phenomena across disciplines like mechanics, circuits, and biology. Accurately solving these equations is essential for understanding and predicting the behavior of such systems. However, obtaining analytical solutions for nonlinear jerk equations can be challenging, necessitating the development of robust and accurate approximation methods. This work explores, for the first time, the application of the modified iteration approach to solve third-order jerk equations. By comparing the obtained approximate solutions with both exact and existing analytical solutions for established engineering problems, we demonstrate the superior accuracy and rapid convergence of the proposed method. The significantly reduced error percentages highlight the effectiveness of the modified iteration approach in providing precise solutions for nonlinear jerk equations, paving the way for its application in a wide range of oscillation problems within nonlinear sciences and engineering.

Design of unmanned aerial vehicle formation keeping controller based on improved consistency algorithm design

This article conducts in-depth research on the problems of large gain convergence oscillation and simultaneous application of translational rotation in traditional consistency algorithms. First, based on the traditional consistent formation algorithm, a virtual long machine is introduced, and a new norm is defined to extend the original consistent algorithm to solve the problem of large gain convergence oscillation in the Linearizability algorithm. Secondly, in response to the issue of the inability to maintain the formation caused by the application of translational rotation in traditional consistent formation processes, the maximum distance is introduced as feedback to the reference controller to modify the reference input trajectory to ensure good tracking of the formation during translational rotation. Finally, a joint semi physical simulation was conducted using the open-source flight control Ardupilot and the open-source simulation platform Airsim to further validate the feasibility of the improved algorithm. The results of this study indicate that the proposed algorithm has significant improvements in solving the problems existing in traditional consistency protocols and has good feasibility in practical applications.

Super-resolution lensless on-chip microscopy based on array illumination and scattering multiplexing with polystyrene microspheres layer

The resolution of lensless on-chip microscopy is mainly limited by the pixel size of the image sensor. Many super-resolution techniques have emerged to solve the problem of insufficient imaging resolution. Most existing pixel super-resolution technologies rely on precise electric translation stage for hundreds of high-precision displacements, or on expensive tunable lasers to generate diffraction diversity. Conventional ptychography iterative engine (PIE) is considered an effective method for improving imaging resolution, but it is prone to oscillations in the early stage of iteration. In this paper, we propose a ptychography imaging technique based on scattering multiplexing, which involves coating the surface of the image sensor with a layer of polystyrene microspheres, and utilizing a 4 × 3 LED array to sequentially illuminate the sample. An innovative ptychography reconstruction algorithm based on dual amplitude gradient descent (DAGD) is designed for the reconstruction from the holograms, which effectively avoids the problems of slow convergence speed and obvious oscillation. Compared with other similar technologies, our system has no moving parts and uses inexpensive partially coherent light illumination. It only records 12 holograms and reaches the imaging resolution of 1.23 μm, which is 1.36 times pixel super-resolution compared with the pixel size of the sensor.

Partially extended oscillation and nonoscillation theorems for half‐linear Hill‐type differential equations with periodic damping

This study addressed the oscillation problems of half‐linear differential equations with periodic damping. The solution space of any linear equation is homogeneous and additive. Generally, by contrast, the solution space of half‐linear differential equations is homogeneous but not additive. Numerous oscillation and nonoscillation theorems have been devised for half‐linear differential equations featuring periodic functions as coefficients. However, in certain cases, such as applying Mathieu‐type differential equations to control engineering, which is a typical example of the Hill equation, some oscillation theorems cannot be applied. In this study, we established oscillation and nonoscillation theorems for half‐linear Hill‐type differential equations with periodic damping. To prove the results, we used the Riccati technique and the composite function method, which focuses on the composite function of the indefinite integral of the coefficients of the target equation and an appropriate multivalued continuously differentiable function. Furthermore, we discuss the special case of the oscillation constant of a damped half‐linear Mathieu equation.

The Schwinger pair production method in the framework of non-commutative phase space coordinates and its applications

In noncommutative phase space (NCPS), we investigate the pair creation rate for the problem of scalar and spinorial particles emerging from a vacuum under the influence of uniform external electromagnetic fields using the Schwinger formal technique. It is demonstrated that under specific conditions, where the speed of light c approaches the Fermi velocity [Formula: see text] and [Formula: see text] (with [Formula: see text] representing the cyclotron frequency), the behavior of the Dirac oscillator problem in a uniform electromagnetic field within NCPS is akin to the monolayer graphene problem in NCPS. In addition, the production probability per unit volume per unit time is discussed, along with the limits of parameter deformations.

An Optimized Power-Angle and Excitation Dual Loop Virtual Power System Stabilizer for Enhanced MMC-VSG Control and Low-Frequency Oscillation Suppression

Modular Multilevel Converter Virtual Synchronous Generator (MMC-VSG) technology is gaining widespread attention for its ability to enhance the inertia and frequency stability of the power grid integrated with converter-interfaced renewable energy sources. However, the excitation voltage regulation in the MMC-VSG can generate equivalent negative damping torque and cause low-frequency oscillation problems similar to those in synchronous machines. This article aims to improve the system’s damping torque and minimize low-frequency oscillations by introducing a Virtual Power System Stabilizer (VPSS) into the power control loop. Building on the study of dynamic interactions between various control links of the MMC, this research establishes a reduced-order model (ROM) and a Phillips–Heffron state equation for the MMC-VSG single machine infinite bus system, using a hybrid modeling approach and a zero-pole truncation method. It also analyzes the mechanism of low-frequency oscillations in the MMC-VSG system through the damping torque method. The analysis reveals that the negative damping torque produced during the excitation voltage regulation process causes changes in the virtual power angle, which in turn increases the risk of low-frequency oscillation in the MMC-VSG. To address this issue, the article proposes an optimized control method for the MMC-VSG dual power loop architecture (power-angle/excitation) VPSS. This strategy compensates for the inadequate damping torque of a single loop VPSS and effectively suppresses low-frequency oscillations in the system.

Investigation of the dynamics of transverse oscillations of a vertical rod under gravity, friction, and thermal expansion

The paper considers the mathematical formulation of the problem of transverse oscillations of a vertical rod under gravity, friction and external pulse effect, leading to thermal expansion of the rod. The dynamics of the system under consideration corresponds to the behavior of a fuel element (FE) in a pulsed reactor and is related to the dynamic stability of the processes occurring in it.The FE dynamics is described by inhomogeneous linear differential equation of the fourth order with non-constant coefficients. Initial boundary conditions are not smooth since they correspond to the instant heating of the part of the FE surface exposed to neutron pulse radiation. The general solution of the homogeneous linear equation can be found using the concept of generalized functions expressed as a series expansion in terms of coordinate eigenfunctions dependent on p parameter. The p parameter is related with the FE mass and at some certain values results in bifurcation points of the boundary value problem for eigenfunctions. The partial solution can be found in several ways: using the Fourier transform, the method of Green's function, and in terms of series expansion by eigenfunctions.Eigenfunction expansion coefficients in an explicit form have been obtained and the numerical solution accuracy has been estimated for some important particular cases. The results of the obtained exact solutions appear to be very close to the results of the ANSYS numerical estimations. In the future the obtained exact solutions will be used as input data to simulate self-consistent system dynamics of more than 400 FE. Therefore, the advantage of the exact solution in practical use is that its calculation is much faster as compared with the finite element method done with ANSYS.

PDM-Coulombic effects of non-inertial cosmic string on a Klein-Gordon oscillator

This paper addresses the problem of a three-dimensional Klein-Gordon oscillator with position-dependent mass in a non-inertial cosmic string background. We provide solutions to this problem and analyze the eigensolutions, considering the influence of non-inertial effects and the presence of position-dependent mass (PDM) on the eigenvalues. Expressions are obtained for the bound state energies and wave functions.

Reformulation of Time-Dependent Density Functional Theory for Nonperturbative Dynamics: The Rabi Oscillation Problem Resolved.

Rabi oscillations have long been thought to be out of reach in simulations using time-dependent density functional theory (TDDFT), a prominent symptom of the failure of the adiabatic approximation for nonperturbative dynamics. We present a reformulation of TDDFT which requires response quantities only, thus enabling an adiabatic approximation to predict such dynamics accurately because the functional is evaluated on a density close to the ground state, instead of on the fully nonperturbative density. Our reformulation applies to any real-time dynamics, redeeming TDDFT far from equilibrium. Examples of a resonantly-driven local excitation in a model He atom, and charge-transfer in the LiCN molecule are given.

Multilevel Parareal Algorithm with Averaging for Oscillatory Problems

Multilevel Parareal Algorithm with Averaging for Oscillatory Problems

Stability Analysis Method of a Hierarchical Control Structure Microgrid Based on a Small-Signal Model and Hopf Bifurcation Theory

To the oscillation and stability problem caused by multi-scale and broadband electromagnetic dynamics among many isomerized power electronic devices in a microgrid, a small-signal model of hierarchical control structure microgrid and stability analysis method based on oscillation trajectories are proposed. Moreover, a hierarchical control structure is used as the research object in microgrid, and the analysis is performed based on the small-signal model and Hopf bifurcation theory. First, the small-signal model of the hierarchical control structure microgrid is established, combining the dominant eigenvalue and participation factor analysis methods, to analyze the influence of the controller and related sensitive parameters on the dynamic performance of the system. Then, based on the small-signal model and Hopf bifurcation theory, a stability analysis method based on oscillation trajectories is proposed. The relationship between different oscillation modes and limit cycles in the microgrid system and the influence of the sag control parameter values on the oscillation trajectory and stability domain of the system are researched on. Combining Hopf bifurcation theory and oscillation trajectory to delineate the stable domain of parameter trajectories, the influence of secondary control on the system stability is analyzed under different oscillation trajectories and load disturbances, revealing the corresponding relationship between the state trajectories of different oscillation modes and system stability of a hierarchical control structure microgrid. Based on the proposed oscillating trajectories, the stability analysis method has sufficient universality for studying the impact of system stability, establishing the parameter selection standards for the design of microgrids. Finally, according to the verification results, the correctness and applicability of above methods are verified.

The path planning algorithm for UUV based on the fusion of grid obstacles of artificial potential field

The artificial potential field approach (APFA) has the advantages of short computation time and easy implementation, widely used in path planning. The problems of local oscillation and susceptibility to local minima for APFA are considered in three dimensions (3D) path planning application of unmanned underwater vehicle (UUV), and the artificial potential field grid method (APFG) is proposed. The core principles of APFG include three key methods: firstly, obstacles are rasterized in a 3D map, and repulsive points are attached to the grid surface to alter the range of repulsive influence, thereby compensating for the issue of longer planned paths caused by the idealized modeling in traditional APFA; secondly, the repulsion function of the grid surface is modified to ensure that the potential field is parallel to the grid surface, thus addressing the problem of local oscillation in UUV path planning. Additionally, the introduction of virtual target points helps prevent the UUV from getting trapped in local optima, effectively overcoming the drawbacks of local oscillation and convergence to local minima in 3D path planning for UUV. The simulations show that APFG effectively overcomes the shortcomings of local oscillations and the tendency to fall into local minima for UUV in 3D path planning, and the path planning is smooth and efficient.

Embedment of WENO-Z reconstruction in Lagrangian WLS scheme implemented on GPU for strongly-compressible multi-phase flows

It is a notoriously challenge problem for Lagrangian particle methods to solve compressible flows with strong discontinuities and large volume variations. To overcome the problems of numerical oscillations, an accurate and stable Lagrangian Weighted-Least-Square (LWLS) method embedded with WENO-Z scheme (LWLS-WENO-Z) is proposed. To further enhance the numerical accuracy and stability, the particle shifting technique, the multi-level local-refinement technique, and the interface repulsive force are appropriately employed in the numerical scheme. Moreover, the smooth and stable coupled particle method between the LWLS and Roe's Riemann solver (LWLS-RR) is considered for the comparisons, further demonstrating the merit of the proposed LWLS-WENO-Z scheme. To reduce the simulation time, parallel computing with a CUDA-based program for the proposed scheme is implemented on a single GPU. In the numerical experiments, several 1D/2D benchmarks are solved to test the accuracy of the proposed method. Particularly, the challenge 2D underwater explosion and the cavitation bubble collapse and jetting are numerically investigated. Compared to other reference solutions, the present coupled particle method demonstrates robustness and superior accuracy in simulating these strongly-compressible multi-phase flows.

Research on large-signal stability of SOFC-lithium battery ship DC microgrid

Aiming at the solid oxide fuel cell (SOFC) applied to the ship DC microgrid in the face of pulse load disturbance is prone to make the SOFC voltage drop too large leading to the DC grid oscillation problem. In this paper, a stability criterion method for SOFC-Li battery DC system based on hybrid potential function is proposed. Firstly, a mathematical model of shipboard DC microgrid with SOFC-Li battery is established and the accuracy of the model is verified. Then, the stability criterion of the system based on the hybrid potential function under large disturbances is constructed. Subsequently, the effects of system stability under impulse load conditions were analysed under different parameters. Based on the constructed criterion, simulation verification of the stability boundary conditions of the SOFC system operating independently or jointly with a lithium battery system is carried out. The experimental results show that the proposed stability criterion and control strategy are effective in accurately predicting the system stability boundary. The experimental results verify the effectiveness of the proposed method in improving the stability of the system and provide a theoretical basis for further research on the dynamic characteristics of SOFC systems under complex load conditions.

Amplitude reconstruction of acoustic emission signals on the base of its mathematical modeling as a stochastic process

The problem of random oscillations generated by inner defect within the neighborhood of the boundary of the elastic massive body under the pre-failure stage is considered. The investigation is based on results of the invariants’ method in acoustic emission (AE) theory consisting in the stability conditions of the mean of statistic distribution parameters of signal characteristics under the same pre-failure stage. The mathematical model of arising wave process of displacement oscillations in the massive body is constructed and the correctness of its using is studied. The problem in question is reduced to the investigation of a boundary integral equation in special stochastic process classes. The task of reconstructing from AE signals and describing the nature of the random process of defect radiation at the free boundary of the body is set. Some numerical are presented.

Double-Closed-Loop Model Predictive Control Based on a Linear Induction Motor

The conventional PI control, which has been extensively employed in the high-performance control of linear induction motors, has the benefit of a straightforward concept, quick dynamic response, and simple control. Nevertheless, the linear induction motor is more susceptible to outside disturbances and mismatched parameters since it is a highly linked, high-order, nonlinear, time-varying, complex system. Because of this, this paper proposes a double-closed-loop control of the linear induction motor, whose speed and current loops are the model-predictive speed controller and the model-predictive current controller, respectively, to solve the problems of speed overshoot and oscillation when the linear induction motor is operated under PI control. The findings demonstrate the benefits of the suggested control strategy, which significantly enhances the linear induction motor’s speed control performance. These benefits include improved dynamic performance, limited overshooting, and robust resistance to load disturbance.