Exact Delay Research Articles

Computation of the exact time delay margin for vehicle platoon under generic communication topologies

Due to the limited bandwidth and transmission congestion of the vehicle platoon's communication, it is inevitable to induce time delay, which significantly degrades the control performance of the vehicle platoon, even resulting in instability. This paper focuses on analyzing the internal stability under generic communication topologies and presents a method of computing the exact time delay margin (ETDM). The proposed method can offer a necessary and sufficient internal stability condition with no conservatism. Firstly, to reduce the analytical complexity and computational burden elegantly, we decompose the closed-loop platoon dynamics into a set of individual subsystems via similarity transformation and matrix factorization. This decomposition approach is applicable for any general communication topology. Secondly, an explicit formula is deduced to compute the ETDM by surveying the characteristic roots' distribution of all these individual subsystems. It is further demonstrated that only the positive purely imaginary roots need to be considered to compute the ETDM. Finally, simulations are conducted to demonstrate the effectiveness of the theoretical claims.

Hotspots and photon rings in spherically symmetric space–times

ABSTRACT Future black hole (BH) imaging observations are expected to resolve finer features corresponding to higher order images of hotspots and of the horizon-scale accretion flow. In spherical space–times, the image order is determined by the number of half-loops executed by the photons that form it. Consecutive-order images arrive approximately after a delay time of ≈π times the BH shadow radius. The fractional diameters, widths, and flux-densities of consecutive-order images are exponentially demagnified by the lensing Lyapunov exponent, a characteristic of the space–time. The appearance of a simple point-sized hotspot when located at fixed spatial locations or in motion on circular orbits is investigated. The exact time delay between the appearance of its zeroth and first-order images agrees with our analytic estimate, which accounts for the observer inclination, with $\lesssim 20~{{\ \rm per\ cent}}$ error for hotspots located about ≲ 5M from a Schwarzschild BH of mass M. Since M87⋆ and Sgr A⋆ host geometrically thick accretion flows, we also explore the variation in the diameters and widths of their first-order images with disc scale-height. Using a simple ‘conical torus’ model, for realistic morphologies, we estimate the first-order image diameter to deviate from that of the shadow by $\lesssim 30~{{\ \rm per\ cent}}$ and its width to be ≲ 1.3M. Finally, the error in recovering the Schwarzschild lensing exponent (π), when using the diameters or the widths of the first and second-order images is estimated to be $\lesssim 20~{{\ \rm per\ cent}}$. It will soon become possible to robustly learn more about the space–time geometry of astrophysical BHs from such measurements.

Spatial Localization of a Transformer Robot Based on Ultrasonic Signal Wavelet Decomposition and PHAT-β-γ Generalized Cross Correlation.

Because large oil-immersed transformers are enclosed by a metal shell, the on-site localization means it is difficult to achieve the accurate location of the patrol micro-robot inside a given transformer. To address this issue, a spatial ultrasonic localization method based on wavelet decomposition and PHAT-β-γ generalized cross correlation is proposed in this paper. The method is carried out with a five-element stereo ultrasonic array for the location of a transformer patrol robot. Firstly, the localization signal is decomposed into wavelet coefficients of different scales, which would realize the adaptive decomposition of the frequency of the localization signal from low frequencies to high frequencies. Then, the wavelet coefficients are denoised and reconstructed by using the semi-soft threshold function. Second, a modified phase transform-beta-gamma (PHAT-β-γ) method is used to calculate the exact time delay between different sensors by increasing the weights of the PHAT weighting function and introducing a correlation function. Finally, by using the proposed method, the accurate localization of the transformer patrol micro-robot is achieved with a five-element stereo ultrasonic array. The simulation and test results show that inside a transformer experimental oil tank (120 cm × 100 cm × 100 cm, L × W × H), the relative error of transformer patrol micro-robot spatial localization is within 4.1%, and the maximum localization error is less than 3 cm, which meets the requirement of engineering localization.

Exact delay range for the stabilization of linear systems with input delays

This paper is concerned with the exact delay range making input‐delay systems unstabilizable. The exact range means that the systems are unstabilizable if and only if the delay is within this range. Contributions of this paper are to characterize the exact range and to present a computation method to derive this range. It is shown that the above range is related to unstable eigenvalues of the system matrix. In the discrete‐time case, if none of the eigenvalues of the system matrix is a unit root, then the above range is a finite set. If there exist some eigenvalues which are unit roots, this range may be a finite set or may be composed of several arithmetic progressions. When this range contains finite elements, the number of these elements is bounded by the geometric multiplicities of eigenvalues. When this range contains arithmetic progressions, the number of such progressions is bounded by the above multiplicities. On the other hand, our results can provide an upper bound for the well‐known delay margin, which is the maximal delay value achievable by a robust controller to stabilize systems.

Stability Analysis of the Vehicular Platoon with Sensing Delay and Communication Delay: CTCR Paradigm via Dixon Resultant

For the vehicular platoon consisting of connected automotive vehicles, time delays degrade both the internal stability and string stability. In this study, the internal stability and string stability of the vehicular platoon suffering from sensing delay and communication delay are investigated. In the internal stability analysis, the necessary and sufficient internal stability condition is obtained and the exact time delay margins (ETDMs) are derived via the cluster treatment of characteristic root (CTCR) paradigm. A Dixon resultant matrix–based method is proposed to determine the kernel and offspring hypersurfaces of the CTCR paradigm, and then the computational burden of deriving the ETDMs is reduced significantly. In the string stability analysis, we first propose the string stability conditions for the situation no matter how large the frequency of the leader vehicle’s maneuver is. Furthermore, the more practical string stability conditions are studied by considering only the region of low frequency, where most of the energy of the spacing errors exists. Then, a lower bound of the time headway is deduced to enhance road capacity, so the potential of the vehicular platoon is fully motivated. Numerical simulations are provided to illustrate the effectiveness of the theoretical claims.

Flow-shop scheduling with exact delays to minimize makespan

The flow-shop scheduling problem with exact delays is generalization of no-wait flow-shop scheduling in which an exact delay exists between the consecutive tasks of each job. The problem with distinct delays to minimize the makespan is strongly NP-hard even for the two-machine case with unit execution time tasks. Providing polynomial-time solutions for special cases of the problem, we show that the two-machine permutation flow-shop case is solvable in O(nlogn) time, while the case with more than two machines is strongly NP-hard. We also show that the multi-machine case with delays following the ordered structure possesses the pyramidal-shaped property and propose an O(n2)-time dynamic program to solve it. We further improve the time complexity of the solution algorithm to O(nlogn) under certain conditions.

Time to Smile: How Onset Asynchronies Between Reciprocal Facial Expressions Influence the Experience of Responsiveness of a Virtual Agent

Human social interactions are highly coordinated in time and involve the reciprocal exchange of facial emotional expressions. While timing has been identified as an important factor in social communication via gaze or speech, so far there has been no systematic investigation on how the temporal delays in the exchange of facial emotional expressions between interactive partners influence the experience of responsiveness. In the present study, 40 participants were cued to direct a facial emotional expression (angry or happy) towards a virtual agent in front of them and the virtual agent would then react with a congruent facial expression. The temporal delay between the cue and the reaction was manipulated as an independent variable. Exact delays between facial expressions were determined based on the onset latencies of participants’ facial expressions measured via facial EMG (M. Zygomaticus and M. Corrugator). Ratings of experienced responsiveness of the virtual agent were collected as a dependent measure. Using a linear mixed effect model in a growth curve analysis revealed that experienced responsiveness peaked at delays around 700 ms. Moreover, experienced responsiveness at shorter temporal delays was higher when happy versus angry facial expressions were exchanged, while the reversed pattern was found at longer delays. Our results demonstrate a crucial role of timing in non-verbal communication, suggesting that temporal relations between facial expressions are processed as social information. Furthermore, our results can inform the implementation of virtual social interactions.

Approximation algorithms for coupled task scheduling minimizing the sum of completion times

In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several variants of this problem that are known to be mathcal{N}mathcal{P}-hard, while also proving mathcal{N}mathcal{P}-hardness for two variants whose complexity was unknown before. Using these results, together with constant-factor approximations for the makespan objective from the literature, we also introduce the first results on bi-objective approximation in the coupled task setting.

Delay-Dependent Stability Region for the Distributed Coordination of Delayed Fractional-Order Multi-Agent Systems

Delay and especially delay in the transmission of agents’ information, is one of the most important causes of disruption to achieving consensus in a multi-agent system. This paper deals with achieving consensus in delayed fractional-order multi-agent systems (FOMAS). The aim in the present note is to find the exact maximum allowable delay in a FOMAS with non-uniform delay, i.e., the case in which the interactions between agents are subject to non-identical communication time-delays. By proving a stability theorem, the results available for non-delayed networked fractional-order systems are extended for the case in which interaction links have nonequal communication time-delays. In this extension by considering a time-delay coordination algorithm, necessary and sufficient conditions on the time delays and interaction graph are presented to guarantee the coordination. In addition, the delay-dependent stability region is also obtained. Finally, the dependency of the maximum allowable delay on two parameters, the agent fractional-order and the largest eigenvalue of the graph Laplacian matrix, is exactly determined. Numerical simulation results are given to confirm the proposed methodologies.

Optimized auto-focusing method for 3D ultrasound imaging in NDT

In this work, we propose an optimized auto-focusing algorithm to be used with ultrasound matrix arrays for three-dimensional imaging in the presence of interfaces. Its main application is for non-destructive-testing (NDT), where usually two mediums with different propagation velocities are present. The refraction at the interface between those mediums complicates the calculation and the application of the focusing delays, which requires iterative processes that are usually the main bottleneck for high-speed inspections.We tackle this problem by generalizing the virtual array concept previously proposed for linear arrays and plane images to the case of matrix-arrays and three-dimensional (3D) beamforming. Furthermore, we propose a two-dimensional iterative algorithm for exact time-of-flight calculation to the two foci per scan line required by the virtual array. The mathematical formulation for the 3D case is obtained and the time-delay errors are analyzed by simulation. Finally, image quality with the proposed method is compared with that obtained with conventional Total Focusing Method (TFM) and exact delay calculation. The principal conclusion is that the virtual array approach generates images with equivalent quality to those obtained by exact calculation, while it reduces more than two orders of magnitude the computation load.

Consensusability of First-Order Multiagent Systems Under Distributed PID Controller With Time Delay.

This article analyzes the consensus of first-order multiagent systems under the network topology with a directed spanning tree. A distributed PID controller with time delay is designed. D-parameterization approach is used and the crossing set consisting of frequencies such that at least one characteristic root is on the imaginary axis is identified. It is proven that the rightward crossings of the characteristic roots are always guaranteed. The exact delay margin is then determined. Numerical simulation is proposed to demonstrate the theoretical analysis.

Networked control system stability analysis of pipeline system with networked-induced delay

This paper presents the design of Networked Control Systems (NCS) for pipeline systems. NCS plays an important role in controlling and monitoring large-scale systems such as pipeline systems. To implement the NCS, one must derive the pipe model and consider the network communication constraints. Here, the pipeline model is divided into two sections for simplicity. For example, in a long pipeline system, one can use a higher number of sections in order to give a better result for the analysis. Then let’s consider a networked-induced delay as the network communication constraint. The discretize pipe dynamics model is derived to support the NCS scheme in the pipeline system. The stability analysis of the proposed NCS is derived by taking into account the small and the large networked-induced delay. Then the optimal LQR control is designed for both stabilizing and tracking. The stability region of the pipeline system in the NCS scheme with networked-induced delay is derived and depicted to provide stability information. The design of the proposed controller under network constraint (networked-induced delay) must consider the stability plot that is divided into the stable region and unstable region. In this research, let’s assume that it is possible to measure the exact time delay and then consider the allowable sampling time for the controller. The proposed controller is designed by considering the NCS scheme with time delay both for regulator and tracking problems. By using the proposed controller, the pipeline system can be controlled in the presence of network-induced delay, which commonly occurs in a distributed system. The simulation verifies the stability analysis of the proposed optimal control for the pipeline systems with the NCS scheme under networked induced delay

Special issue on PID control in the information age: Theoretical advances and applications

Special issue on PID control in the information age: Theoretical advances and applications

Phase space approximations for dispersive propagation

Sounds propagating in shallow water can undergo frequency-dependent changes, specifically damping and dispersion. Phase space analysis and approximations have yielded a clear physical picture of these frequency-dependent effects. In particular, in position-wavenumber phase space, each mode propagates, approximately, at constant velocity given by its group velocity. In time-frequency phase space, each mode undergoes a frequency-dependent time shift given, approximately, by its group slowness. The effects of damping (i.e., a complex dispersion relation) are also clearly manifest. We review and extend various phase space approximations for dispersive propagation, and explore their accuracy. We show that one can recover the exact spectral magnitude and group delay of the propagating pulse from the phase space approximations. One reason the approximations are generally very good is that one does not have to assume that the initial spectrum is slowly varying, as is done, for example, in the stationary phase approximation.

Generalization of Harmonic State-Space Framework to Delayed Periodic Systems for Stability Analysis of the Modular Multilevel Converter

Stability analysis of the modular multilevel converter (MMC) requires accurate models over wide frequency ranges, accounting for both the time-periodic nature of internal dynamics and non-passive behavior resulting from time delays. Frequency-lifting techniques such as harmonic state-space (HSS) can be used to tackle the time-periodicity and obtain linear time-invariant models on which classical stability analysis techniques can be applied. However, exact time delays are generally approximated by rational polynomial functions to study the eigenvalues of ordinary differential equations (ODEs), which leads to inaccuracies at higher frequencies. Such approximations can be avoided by preserving delays in their exact form and studying eigenvalues of delay differential equations (DDEs). To that end, this article presents the generalization of the original ODE-based HSS framework to DDEs, accounting for both time-delay and time-periodic behaviors of the MMC. The generalized HSS framework benefits from the insights of eigenvalues and participation factors analysis while at the same time guaranteeing the derivation of accurate frequency-response models. Using the developed HSS-DDE framework, AC and DC-side admittances of the MMC are obtained and validated against frequency scans. Lastly, the stability of a test system is studied in both time and frequency domains to show the advantages of the developed framework.

FORECASTING THE TIME DELAY IN DELIVERY OF PHARMACEUTICAL PRODUCTS

Supply chain management system is a centralized system which controls and plans the activities involved from production to delivery of a product. Disruption in treatment and loss of life occurs due to delay in delivery of pharmaceutical products. The objective is to do a model using Machine learning algorithms to determine: Classification to predict which product will be delayed and Regression shows how much time it will be delayed exactly. This study will use publicly available supply chain data which helps to identify primary aspect of predicting whether HIV drugs are delivered in time or not. It will then use these factors to predict how long delays are likely to be, thus allowing HIV/Supply Chain program managers to know details of the products which are going to be delayed and quantify the exact delay. and how much it will be delayed. so that they can take mitigating action to save lives and avoid additional supply chain costs. We will use Machine learning prediction model to predict which product will be delayed and regression model shows how much time it will be delayed exactly.

Norwegian tunnel excavation: Increasing digitalisation in all operations

AbstractIn the past decades, Norwegian tunnelling has undertaken a major digital development in all operations from planning to the excavation phase. The breakthrough is driven by digital contract requirements from forward‐leaning clients and innovative industrial stakeholders, aiming for ever more efficient, quality‐oriented and risk‐reducing operations. A formal milestone documenting this development was the publication of Digitalisation in Norwegian Tunnelling in 2019. From 2019, most contracts of new infrastructure tunnels must deliver a level 3 Building Information Modeling (BIM) model. Control systems for drilling jumbos are fully digitalised. All drilling must be monitored and documented with Measurement While Drilling techniques. Via cloud servers, the drilling information is interpreted and delivered live to face engineers for decision support. Sensors are used to monitor rock grouting flow and pressure in each drill hole. Digital electronic detonators with exact delay time are used for blasting. Geotechnical mapping is carried out on field tablets. High‐resolution scans with RGB imaging must be carried out on the exposed rock surface and after rock support/linings. The next step is to utilise all the collected data to a higher degree by advanced analysis with machine learning (ML) and similar techniques for automation and optimisation. This study reviews and exemplifies the digital focus and achievements in core operations in Norwegian tunnel excavation.

Membranotronics: Bioinspired Nonlinear Ion Transport with Negative Differential Resistance Based on Elastomeric Membrane System

AbstractBiological neural networks enable rapid communication between cells, which has inspired the development of artificial smart neuro‐mimetic systems. In this work, freestanding elastomeric membranes are fabricated with 3D structured holes to induce nonlinear ion‐based transport. These 3D microholes are embedded in a soft polymeric membrane via a grayscale lithographical process and demonstrate ionic rectification, negative differential ionic resistance, ionic conductivity gating, and spiking under an applied electric field bias. The ion transport behavior of these membranes is affected by the shape, size, number, and chemical functionalization of the embedded microholes. The microholes are functionalized with responsive poly(N‐isopropylacrylamide) polymer brush layers allowing to alter the electric gating behavior by external stimuli that includes temperature and chemical composition of the surrounding environment. The electrically biased membranes with a linear array of eight equidistantly spaced microholes exhibit synchronous gating of ionic transport through each one. These individual microholes are equipped with circumjacent blocking stretchable electrodes to simultaneously measure the exact onset time delay of the spikes during the synchronous gating. The operation of the freestanding elastomeric membranes with embedded microholes mimics the behavior of neural membranes. Membranotronics will pave the way toward bioinspired soft artificial neuro‐mimetic systems mechanically and electrochemically comparable to their biological counterpart.

Exact Delay Bounds of Second-Order Multi-Agent Systems With Input and Communication Delays: From Algebra and Geometric Perspective

This brief studies the delay bounds problem of second-order multi-agent systems with input and communication delays under the directed graph. Firstly, the systems with input delay only are studied and the delay margin of input delay is given. Then the critical value of communication delay is considered for the fixed input delay within the proposed scope. Then, the input delay and communication delay are analyzed simultaneously from geometric perspective. The explicit geometric description of the consensus crossing curves is obtained. Then the consensus regions can be completely determined.

A generalized sequential subpredictor for input delayed systems under time-varying delay mismatches

For input delayed systems, the sequential subpredictor (SSP) control scheme has the advantage that arbitrarily large delays can be tolerated in the control loop by introducing more and more subpredictors. However, an exact delay compensation is not possible in the presence of time-varying delay mismatches, and larger delays cannot therefore be obtained by increasing the number of subpredictors. To alleviate this limitation and enhance robustness against time-varying delay uncertainties, a generalized sequential subpredictor (SSP) control scheme is proposed by introducing new observer parameters that can be designed via Linear Matrix Inequalities (LMI) and Cone-Complementarity Linearization (CCL) algorithm. Finally, the effectiveness of the proposed method is illustrated by a simulation example.