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At least 19 records

Stability analysis for linear systems with time delays

Time delays in the mathematical description of a physical system occur whenever the system is affected not only by conditions at the present time, but also by conditions which have occurred in the past. The tau-decomposition method, as refined by Lee and Hsu, is a method for studying the effects of time delay on the stability of retarded dynamical systems. In this paper, the method is extended to examine the stability and relative stability of: (1) retarded systems with many time delays; and (2) a class of neutral systems with one delay. Applications are included which illustrate the power of the technique.

Barker, L. K.↗

Topology property analysis and application of stable time-delay regions for linear multiple time-delay systems

This study examines the relationship between the topology of stable time-delay regions and the stability analysis of an linear multiple time delay system. To analyze the topology of stable time-delay regions, we construct a function with a value equal to zero for the time-delay points on the boundaries of stable time-delay regions. The function is continuous and differentiable in the whole defining field with a global minimum of zero so that we can locate the boundaries by minimizing the value of the function. Based on the topology analysis, we proposed a performance validation approach for controllers that are designed to stabilize the system using feedback signals with time delays. The method based on the topology analysis is simple and reliable so that can deal with a linear time-invariant system with high order and multiple time delays (more than 3). The example case study shows that the above method is reliable and enables ultra-low latency coordination and control for the future power grid with ubiquitous power electronics.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Measurements of Pilot Time Delay as Influenced by Controller Characteristics and Vehicles Time Delays

A study to measure and compare pilot time delay when using a space shuttle rotational hand controller and a more conventional control stick was conducted at NASA Ames Research Center's Dryden Flight Research Facility. The space shuttle controller has a palm pivot in the pitch axis. The more conventional controller used was a general-purpose engineering simulator stick that has a pivot length between that of a typical aircraft center stick and a sidestick. Measurements of the pilot's effective time delay were obtained through a first-order, closed-loop, compensatory tracking task in pitch. The tasks were implemented through a space shuttle cockpit simulator and a critical task tester device. The study consisted of 450 data runs with four test pilots and one nonpilot, and used three control stick configurations and two system delays. Results showed that the heavier conventional stick had the lowest pilot effective time delays associated with it, whereas the shuttle and light conventional sticks each had similar higher pilot time delay characteristics. It was also determined that each control stick showed an increase in pilot time delay when the total system delay was increased.

Privoznik, C. M.↗

Controlling the breakdown delay time in pulsed gas discharge

Abstract In experiment and 2D3V PIC MCC simulations, the breakdown development in a pulsed discharge in helium is studied for U = 3.2 kV and 10 kV and P = 100 Torr. The breakdown process is found to have a stochastic nature, and the electron avalanche develops in different experimental and simulation runs with time delays ranging from 0.3 to 8 μ s. Nevertheless our experiments demonstrate that the breakdown delay time distribution can be controlled with a change of the pulse discharge frequency. The simulation results show that the breakdown process can be distinguished in three stages with (a) the ionization by seed electrons, (b) the ions drift to the cathode and (c) the enhanced ionization within the cathode sheath by the electrons emitted from the cathode. The effects of variation of seed electron concentrations, voltage rise times, voltage amplitudes and ion–electron emission coefficients on the breakdown development in the pulsed gas discharge are reported.

Schweigert, I. V. (ORCID:0000000223641228)↗

Solid state variable time delay

Variable time delay line does not require use of a magnetic field to control a time delay, and can both amplify and delay a signal. Device is inexpensive and space saving, it does not require mecanically moving components, eliminating detrimental vibrations in a sensitive environment.

Fitzgerald, T. M.↗

Effects of computing time delay on real-time control systems

The reliability of a real-time digital control system depends not only on the reliability of the hardware and software used, but also on the speed in executing control algorithms. The latter is due to the negative effects of computing time delay on control system performance. For a given sampling interval, the effects of computing time delay are classified into the delay problem and the loss problem. Analysis of these two problems is presented as a means of evaluating real-time control systems. As an example, both the self-tuning predicted (STP) control and Proportional-Integral-Derivative (PID) control are applied to the problem of tracking robot trajectories, and their respective effects of computing time delay on control performance are comparatively evaluated. For this example, the STP (PID) controller is shown to outperform the PID (STP) controller in coping with the delay (loss) problem.

Shin, Kang G.↗

Delay time for the onset of beam plasma discharge

The interaction of a nonrelativistic electron beam with a neutral gas in a large chamber is considered, and the time interval before ignition of beam plasma discharge (BPD) is studied. A new theoretical expression for the time delay before BPD ignition is found as a function of the critical current necessary for BPD to be established. There are two parameters in the theoretical expression, and both are derived from two different experiments. These parameters are used to write the time evolution equation for plasma density as a function of time.

Parish, J. L.↗

Extended quantitative rescattering model for simulating high-order harmonic streaking spectra by synchronization of an intense IR laser and a time-delayed attosecond XUV pulse

In this work, we theoretically investigate the modulated high-harmonic generation (HHG) driven by an intense few-cycle infrared (IR) laser field and a weak extreme-ultraviolet (XUV) pulse at a delayed time. We establish an extended quantitative rescattering (EQRS) model to simulate the HHG streaking spectra, with the ideas of correcting the IR ionization and the transition from the ground to continuum states in the strong-field approximation. The EQRS model has an accuracy comparable to that from “exactly” solving the time-dependent Schrödinger equation (TDSE). We reveal that the fringes in the streaking spectra are caused by the interference between the attosecond XUV pulse and harmonics resulting from different recombination pathways under the intense IR laser. We then demonstrate that the XUV pulse can be accurately retrieved by treating the single-atom TDSE results or macroscopic propagation results as the “input” data. This work provides with a tool for efficiently simulating and thoroughly analyzing the XUV-assisted HHG, which could also enhance its capability for tracing the electron dynamics involved in the strong-field phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A comparison of control modes for time-delayed remote manipulation

Transmission time delay in the communication channel of a manual control system is investigated. A time delay can exist in remote manipulation systems, caused by long communication distances or bandwidth limitations. Ferrell 1 conducted the first research in time-delayed manipulation using a two degree-of-freedom manipulator. His subjects, working at time delays of 1.0, 2.1, and 3.2 s, could accomplish tasks even requiring great accuracy. The subjects spontaneously adopted a pattern of moving cautiously, then waiting to see the results of their actions. In experiments with a six degree-of-freedom master-slave manipulator system and time delays of 1.0 to 6 s, Black 2 saw that subjects tried to use the move-and-wait strategy; but there were often difficulties. The subjects seemed to have a problem in holding the master arm stationary while waiting for feedback. Any undesired drifting of the master arm introduced a discrepancy between the positions of the master and slave. This discrepancy was not perceived because of the time delay. The subject would then begin his next move with an inherent error. The difficulty of effectively using the move-and-wait strategy with a master-slave manipulator suggested that rate control might be a more effective control mode with time delay.

Starr, G. P.↗

Correcting for Selection Biases in the Determination of the Hubble Constant from Time-Delay Cosmography

The time delay between multiple images of strongly lensed quasars has been used to infer the Hubble constant. The primary systematic uncertainty for time-delay cosmography is the mass-sheet transform (MST), which preserves the lensing observables while altering the inferred ⁠H 0 . The TDCOSMO collaboration used velocity dispersion measurements of lensed quasars and lensed galaxies to infer that mass sheets are present, which decrease the inferred H 0 by 8 per cent. Here, we test the assumption that the density profiles of galaxy–galaxy and galaxy–quasar lenses are the same. We use a composite star-plus-dark-matter mass profile for the parent deflector population and model the selection function for galaxy–galaxy and galaxy–quasar lenses. We find that a power-law density profile with an MST is a good approximation to a two-component mass profile around the Einstein radius, but we find that galaxy–galaxy lenses have systematically higher mass-sheet components than galaxy–quasar lenses. For individual systems, λ int correlates with the ratio of the half-light radius and Einstein radius of the lens. By propagating these results through the TDCOSMO hierarchical inference code, we find that H 0 is lowered by a further 3 per cent. Using a more recent measurement of velocity dispersions and our fiducial model for selection biases, we infer H 0 = 66 ± 4 (stat) ± 1 (model sys) ± 2 (measurement sys) km s -1 Mpc -1 for the TDCOSMO plus SLACS data set. The first residual systematic error is due to plausible alternative choices in modelling the selection function, and the second is an estimate of the remaining systematic error in the measurement of velocity dispersions for SLACS lenses. Accurate time-delay cosmography requires precise velocity dispersion measurements and accurate calibration of selection biases.

79 ASTRONOMY AND ASTROPHYSICS↗

Describing-function analysis of a ripple regulator with slew-rate limits and time delays

The effects of time delays and slew-rate limits on the steady-state operating points and performance of a free-running ripple regulator are evaluated using describing-function analysis. The describing function of an ideal comparator (no time delays or slew rate limits) has no phase shift and is independent of frequency. It is found that turn-on delay and turn-off delay have different effects on gain and phase and cannot be combined. Comparator hysteresis affects both gain and phase; likewise, time delays generally affect both gain and phase. It is found that the effective time delay around the feedback loop is one half the sum of turn-on and turn-off delays, regardless of whether the delays are caused by storage time or slew rate limits. Expressions are formulated for the switching frequency, switch duty ratio, dc output, and output ripple. For the case of no hysteresis, a simple, graphical solution for the switching frequency is possible, and the resulting switching frequency is independent of first-order variations of input or load.

Wester, Gene W.↗

Reversible electron spirals by chirped attopulses at zero time delay

A class of linear, spiral phenomena is discovered in the photoelectron momentum distribution when studying photoionization of S -state atoms by a pair of linearly chirped, oppositely circularly polarized attosecond pulses eventually delayed in time by $\tau$. This controllable effect, dubbed. reversible electron spirals because of its energy-dependent sense of rotation, is identified and can be isolated in the absence of time delay for the case of opposite chirp rates. Further, the astrophysical concept of spiral arm pitch angle is borrowed to gain a better insight into the energy dependence of the reversible spiral rotation, to determine the attochirp as well as the binding energy characteristic of an atomic target. Our results indicate potential applications in attochirpmetry and polarimetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Best-fit estimate of relativistic effects in time-delay experiments.

Time-delay experiments are analyzed within the frame of a curved space-time. Residuals from Newtonian best fits of relativistic data are used as a measure of the 'relativistic effects.' Radial transponder trajectories are considered. If the motion is towards the sun, the relativistic residuals are of the order of 100 m. If the motion is away from the sun, they are at the 10-km level and the fraction due to the second-order curvature of the metric is at the 1-km level. Those effects are significantly smaller than those calculated from the divergence of the Newtonian and relativistic predictions after exact fit of the initial measurements.

Richard, J.-P.↗