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In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
Oscillations in a power system can be categorized into free oscillations and forced oscillations. Many algorithms have been developed to estimate the modes of free oscillations in a power system. Recently, forced oscillations caught many…
Sustained oscillations (SOs) are commonly observed in systems dominated by converters. Under specific conditions, even though the origin of SOs can be identified through negative damping modes using conventional linear analysis, utilizing…
As power systems become more and more interconnected, the inter-area oscillations has become a serious factor limiting large power transfer among different areas. Underdamped (Undamped) inter-area oscillations may cause system breakup and…
Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal…
This paper presents an analytical approach to explore the damping effect of inner loops on grid-forming converters. First, an impedance model is proposed to characterize the behaviors of inner loops, thereby illustrating their influence on…
Assuming that a constant potential energy function has meaning for a dissipated harmonic oscillator, then an important issue is the time dependence of the turning points. Turning point studies demonstrate that the common model of external…
Models of physical systems are used to explain and predict experimental results and observations. The Modeling Framework for Experimental Physics describes the process by which physicists revise their models to account for the newly…
This letter proposes an analytical approach to formulate the power system oscillation frequency under a large disturbance. A fact is revealed that the oscillation frequency is only the function of the oscillation amplitude when the system's…
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state…
We study the problem of finding the resistors in a resistor network from measurements of the power dissipated by the resistors under different loads. We give sufficient conditions for local uniqueness, i.e. conditions that guarantee that…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to determine the minimal additive forcing…
The damped harmonic oscillator is a workhorse for the study of dissipation in quantum mechanics. However, despite its simplicity, this system has given rise to some approximations whose validity and relation to more refined descriptions…
Model bias is an inherent limitation of the current dominant approach to optimal quantum control, which relies on a system simulation for optimization of control policies. To overcome this limitation, we propose a circuit-based approach for…
During their operation, due to shifts in environmental conditions, devices undergo various forms of detuning from their optimal settings. Typically, this is addressed through control loops, which monitor variables and the device…
We investigate the impact of nonlinear damping on the dynamics of a nanomechanical doubly clamped beam. The beam is driven into nonlinear regime and the response is measured by a displacement detector. For data analysis we introduce a…
Poorly damped oscillations pose threats to the stability and reliability of interconnected power systems. In this work, we propose a comprehensive data-driven framework for inferring the sources of forced oscillation (FO) using solely…
Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degrees-of-freedom models have been used to account for experimentally observed nonlinear…
The work concerns the spectral, entropy and bifurcation analysis of the dynamics of a reverse-flow system. The existence of chaotic oscillations was demonstrated in a wide range of changes in the parameters of the model. The model of such a…