Representation Of Time Delay Research Articles

A Sampling Load Frequency Control Scheme for Power Systems with Time Delays

In this study, we investigate the effectiveness of a robust sampled‐data H∞ load frequency control (LFC) scheme for power systems with randomly occurring time‐varying delays. By using the input‐delay technique, the sampled‐data LFC model is reformulated as a continuous time‐delay representation. Then, Bernoulli‐distributed white noise sequences are used to describe randomly occurring time‐varying delays in the sampled‐data LFC model. Some less conservative conditions are achieved by utilizing the Lyapunov–Krasovskii functional (LKF) and employing Jensen inequality and reciprocal convex combination lemma to ensure the considered power system has mean‐square asymptotic stability under the designed control scheme. The derived results are based on linear matrix inequalities (LMIs) that can readily be solved using the MATLAB LMI toolbox. The criteria obtained are used to analyze the upper bounds for time delays, and a comparison study to validate the efficacy of the presented method is presented.

Novel Control-Oriented Models for Liquid Transport in Falling Film Evaporator Tubes

The paper presents novel control-oriented transport models for evaporating liquid films in the tubes of a falling film evaporator. In this context, our goal consists in qualitatively mapping the experimentally observed input-output behavior. Two transport models are proposed, where the difference between them is that one allows overtaking of liquid particles and the other does not. The transport models are equipped with two new models of evaporation which are different from the commonly assumed uniform evaporation. The models are initially developed from the conservation laws in the form of partial differential equations. Using the method of characteristics we then obtain the input-output relations for the proposed models in the form of time-delay equations. The time-delay representation is advantageous for simulation and for the future control design. In a simulation study, we observe the principal properties of the models and find that they correspond well with the experimentally observed input-output behavior.

Transformation from a Pure Time Delay to a Mixed Time and Phase Delay Representation in the Auditory Forebrain Pathway

Birds and mammals exploit interaural time differences (ITDs) for sound localization. Subsequent to ITD detection by brainstem neurons, ITD processing continues in parallel midbrain and forebrain pathways. In the barn owl, both ITD detection and processing in the midbrain are specialized to extract ITDs independent of frequency, which amounts to a pure time delay representation. Recent results have elucidated different mechanisms of ITD detection in mammals, which lead to a representation of small ITDs in high-frequency channels and large ITDs in low-frequency channels, resembling a phase delay representation. However, the detection mechanism does not prevent a change in ITD representation at higher processing stages. Here we analyze ITD tuning across frequency channels with pure tone and noise stimuli in neurons of the barn owl's auditory arcopallium, a nucleus at the endpoint of the forebrain pathway. To extend the analysis of ITD representation across frequency bands to a large neural population, we employed Fourier analysis for the spectral decomposition of ITD curves recorded with noise stimuli. This method was validated using physiological as well as model data. We found that low frequencies convey sensitivity to large ITDs, whereas high frequencies convey sensitivity to small ITDs. Moreover, different linear phase frequency regimes in the high-frequency and low-frequency ranges suggested an independent convergence of inputs from these frequency channels. Our results are consistent with ITD being remodeled toward a phase delay representation along the forebrain pathway. This indicates that sensory representations may undergo substantial reorganization, presumably in relation to specific behavioral output.

Time delay for one-dimensional quantum systems with steplike potentials

This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schr\"odinger Hamiltonian $H=\ensuremath{-}\ensuremath{\Delta}+V$ with a potential $V(x)$ converging to different limits ${V}_{\ensuremath{\ell}}$ and ${V}_{r}$ as $x\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ and $+\ensuremath{\infty}$, respectively. Due to the anisotropy, they exhibit a two-channel structure. We first establish the existence and properties of the channel wave and scattering operators by using the modern Mourre approach. We then use scattering theory to show the identity of two apparently different representations of time delay. The first one is defined in terms of sojourn times while the second one is given by the Eisenbud-Wigner operator. The identity of these representations is well known for systems where $V(x)$ vanishes as $\ensuremath{\mid}x\ensuremath{\mid}\ensuremath{\rightarrow}\ensuremath{\infty}$ $({V}_{\ensuremath{\ell}}={V}_{r})$. We show that it remains true in the anisotropic case ${V}_{\ensuremath{\ell}}\ensuremath{\ne}{V}_{r}$, i.e., we prove the existence of the time-dependent representation of time delay and its equality with the time-independent Eisenbud-Wigner representation. Finally, we use this identity to give a time-dependent interpretation of the Eisenbud-Wigner expression, which is commonly used for time delay in the literature.

Linear Rising Trajectories in the Time-Delay Analysis of the Scattering Amplitude

It is explicitly shown that the integration parameter in the background Regge integral can be understood as a time-delay variable, its average value being the time delay and distortion caused on a wave packet by a scatterer, as seen in the Breit system of coordinates. By means of the usual exponential Fourier transform, another time-delay variable is defined with a similar meaning for the scattering process as seen in the laboratory system of coordinates. The average over the energy of the scattering amplitude is related to a cutoff in the time-delay variables in both cases. A smooth energy variation of the scattering amplitudes corresponds to a small range of variation of the time-delay variable in the transformed amplitude. A Fourier analysis of the Veneziano-model amplitude results in a simple periodic structure in the time-delay variable. A parametrization of the scattering amplitudes in the time-delay representation is proposed, valid at high and intermediate energies. It is pointed out that the non-spin-flip pion-nucleon scattering amplitudes are consistent with such a parametrization. An interpretation of models with linearly rising trajectories in terms of multiscattering processes seems natural in the time-delay representation.