Time-delay Stability Research Articles

The stability and accuracy analysis of automatic steering system with time delay

The paper presents a systematic method of stability analysis for automatic steering system involving a time delay and some external disturbances. The analysis focuses on the stability of automatic steering system with increase of the time delay from zero to infinity. Firstly, the structure and dynamic model of automatic steering system are briefly introduced, and PD control algorithm is adopted to further analysis the time delay mechanism of control system of automatic steering system. Then the time delay dynamic models of automatic steering system with PD control algorithm are derived, the time delay stability interval and critical time delay of automatic steering system are calculated by using the generalized Sturm criterion method. Finally, the accuracy of critical time delay calculation by proposed method, and the stability and accuracy of automatic steering system with time delay and external disturbance are illustrated by numerical simulations.

Computation of Time Delay Stability Margin for the Automated Vehicular Platoon

Due to the limited band width and congestion of communication channels in the wireless vehicle-to-vehicle (V2V) communication, time delay inevitably arises and dramatically leads to the disturbances for the automated vehicular platoon. This paper focuses on computing the exact time delay stability margin. In this study, we treat this problem as a stability issue of a consensus system with time delay, where each vehicle in the platoon is recognized as a node, and the interconnected information flow is represented as a graph. Then, the distributed controller is designed by combining the states of the vehicle itself and its neighbouring vehicles. Furthermore, the stability of the entire platoon is analysed according to the characteristic equation of the closed-loop system, and a necessary and sufficient condition for the exact time delay stability margin is obtained. Especially, for the automated vehicular platoon with undirected topology, it is revealed that exact time delay stability margin is determined by the largest eigenvalue of the augmented Laplacian matrix. Furthermore, a rapid method for finding exact time delay stability margin is proposed. Finally, numerical simulations demonstrate that this work generates exact and satisfactory time delay stability margin for the automated vehicular platoon.

Comparison of Cross-Correlation and Joint-Recurrence Quantification Analysis Based Methods for Estimating Coupling Strength in Non-linear Systems

Time-delay stability (TDS) analysis is a method for quantifying interactions in multivariate systems by identifying stable temporal relationships in time series data (1). This method has been used to create network representations of complex systems. As originally presented, the TDS method relies on cross-correlation—a linear analysis that is restricted to estimating relationships between unidimensional time series, and which, by itself, often does not adequately characterize interactions between many nonlinear complex systems of theoretical and practical interest. Thus, modifying TDS so that it relies on joint recurrence quantification analysis (JRQA), an intrinsically nonlinear multidimensional framework, and then comparing the ability of the two approaches to detect interactions in nonlinear systems is an important task. In the present work, we first show how TDS can be extended using JRQA, a method which is capable of multidimensional assessment of relationships in nonlinear systems. In our application of JRQA, we introduce a modification in the form of a weighting factor that accounts for the truncation of time series that results from time-delayed JRQA. We also modify TDS by correcting for a bias in the method, and show how analogs of recurrence-based metrics can also be obtained for TDS. We evaluate how TDS results obtained with JRQA compare to those obtained with cross-correlation for known dynamics of coupled non-linear oscillators and from unknown dynamics of multivariate behavioral signals measured from dyads performing a joint problem-solving task. We conclude that TDS using cross-correlation provides results that are comparable to those obtained with JRQA at a much-reduced computational cost.

Time delay and non-Gaussian noise-enhanced stability of foraging colony system

In view of the role of external noise, the statistical characteristics of foraging colony system with non-Gaussian noise and time delay are investigated. By means of the small time delay approximation and the Markov approximation, the expressions of stationary probability distribution and mean first passage time (MFPT) of foraging colony system are derived. Using the stochastic second-order Runge–Kutta algorithm, the stationary probability distribution of system, MFPT from the metastable state to stable state, and the probability density function (PDF) of the first passage time from the metastable state to stable state are stimulated. The results show that: (i) the external noise intensity α and the parameter q of departure from Gaussian noise can induce transition phenomenon; (ii) the MFPT as a function of α shows a minimum, which is enhanced by internal noise; (iii) the external noise can enhance stability of system; (iv) time delay-enhanced stability of system occurs.

Quantification of the Feedback Regulation by Digital Signal Analysis Methods: Application to Blood Pressure Control Efficacy

Six different metrics of mutual coupling of simultaneously registered signals representing blood pressure and pulse interval dynamics have been considered. Stress test responses represented by the reaction of the recorded signals to the external input by tilting the body into the upright position have been studied. Additionally, to the conventional metrics like the joint signal coherence Coher and the sensitivity of the pulse intervals response to the blood pressure changes baroreflex sensitivity (BRS), also alternative indicators like the synchronization coefficient Sync and the time delay stability estimate TDS representing the temporal fractions of the analyzed signal records exhibiting rather synchronous dynamics have been determined. In contrast to BRS, that characterizes the intensity of the pulse intervals response to the blood pressure changes during observed feedback responses, both Sync and TDS likely indicate how often such responses are being activated in the first place. The results indicate that in most cases BRS is typically reciprocal to both Sync and TDS suggesting that low intensity of the feedback responses characterized by low BRS is rather compensated by their more frequent activation indicated by higher Sync and TDS. The proposed additional indicators could be complementary for the differential diagnostics of blood pressure regulation efficacy and also lead to a deeper insight into the involved concomitant factors this way also aiming at the improvement of the mathematical models representing the underlying feedback control mechanisms.

Three-dimensional modeling and time-delay stability analysis for robotics docking simulation

Hardware-in-the-loop simulations of two interacting bodies are often accompanied by a time delay. The time delay, however small, may lead to instability in the hardware-in-the-loop system. The present work investigates the source of instability in a two spacecraft system model with a time-delayed contact force feedback. A generic compliance-device-based contact force model is proposed with elastic, viscous, and Coulomb friction effects in three dimensions. A 3D nonlinear system model with time delay is simulated, and the effect of variations in contact force model parameters is studied. The system is then linearized about a nominal state to determine the stability regions in terms of parameters of the spring-dashpot contact force model by the pole placement method. Furthermore, the stability analysis is validated for the nonlinear system by energy observation for both the stable and unstable cases.

Time delay and cross-correlated Gaussian noises-induced stochastic stability and regime shift between steady states for an insect outbreak system

In this paper, we focus on investigating the stochastic stability and the regime transition between the endangered state and the boom state for a time-delayed insect growth system driven by correlated external and internal noises. By use of the Fokker–Planck equation, the method of small time delay approximation and the fast descent method, we explore in detail the joint action of noise terms and time delay on the mean reproduction and depression time for the insect population. Our investigations indicate that the pseudo-resonance phenomenon of the mean first-passage time (MFPT) occurs because of the impact of different noises and time delay. Through the numerical calculation, it is discovered that multiplicative noise can speed up the shift of the insect population from the boom state to the endangered one, while the noise correlation and time delay can propel the insect system to evolve from the endangered state to the boom state and improve the biological stability. In addition, the impact of the additive noise on the stability of the biological system depends on the positive and negative situation of the noise correlation. On the other hand, during the process of suppressing the insect explosion, it is beneficial to the pest control to amplify the association noise strength and weaken the intensities of the multiplicative, additive noises and time delay. However, during the process of eliminating the pests, it can produce nice effect on the disinsection to increase time delay, the intensities of multiplicative and additive noises and weaken the strength of noise correlation.

Indicator of serious flight delays with the approach of time-delay stability

Passenger flight delays, causing much disorder of air traffics, economic losses of airlines, and downgrading the travel quality of millions of people, are ubiquitous phenomena in airports all over the world. Investigation based on real data from the view point of statistical physics is rarely seen. In the present work, big data of such delay records over 20 years accumulated by Bureau of Transportation Statistics in the United States are downloaded and purified by us. We account the departure and arrival records of such flights between certain pair of airports as time series, and rectify them by defining dimensionless velocity of the flights. Furthermore, we find the varying cross-correlations among such time series with the approach of time delay stability, and describe the correlations with temporal networks for correlation states. Deterministic correspondences between the average degrees of temporal networks and delay ratios of passenger flights are verified in different sampling groups of flights with the longest records. The mean degrees of correlation networks usually emerge a peak prior to that of high delay ratios, which serves an indicator for the precaution to serious flight delays.

Time-Delay Stability Analysis for Hybrid Energy Storage System With Hierarchical Control in DC Microgrids

Hybrid energy storage system (HESS) plays an important role in the operation of dc microgrids which have attracted significant research attention recently. The hierarchical control is widely adopted for the coordination of multiple energy storages in a HESS. As the hierarchical control comprises the centralized and the decentralized control levels, the time delays during signal transfer processes between two control levels may significantly affect HESS operation and may lead to instability. In this paper, considering the multiple delays in the hierarchical control processes, the maximum delayed time (MDT) is defined to assess the stability margin for a HESS. An accurate and effective method based on small signal stability model is then proposed to determine the MDT of a HESS to maintain its stability. The effectiveness and correctness of the proposed method are verified using a lab-scale dc microgrid.

Time delay and non-Gaussian noise-induced stochastic stability and stochastic resonance for a metapopulation system subjected to a multiplicative periodic signal

In this paper, the stable state transformation and the effect of the stochastic resonance (SR) for a metapopulation system are investigated, which is disturbed by time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal. By use of the fast descent method, the approximation of the unified colored noise and the SR theory, the dynamical behaviors for the steady-state probability function and the SNR are analyzed. It is found that non-Gaussian noise, the colored Gaussian noise and time delay can all reduce the stability of the biological system, and even lead to the population extinction. Inversely, the self-correlation times of two noises can both increase the stability of the population system and be in favor of the population reproduction. As regards the SNR for the metapopulation system induced by the noise terms and time delay, it is discovered that time delay and the correlation time of the multiplicative noise can effectively enhance the SR effect, while the multiplicative noise and the correlation time of the additive noise would all the time suppress the SR phenomena. In addition, the additive noise can effectively motivate the SR effect, but not alter the peak value of the SNR. It is worth noting that the departure parameter from the Gaussian noise plays the diametrical roles in stimulating the SR effect in different cases.

Multiple Time-delay Stability Analysis for the DC-Microgrid Cluster with Distributed Control

With the increasing availability of DC microgrids (MGs), the DC-MG cluster will develop quickly as the connection of different DC MGs. To alleviate the burden of the central control, the distributed control strategy is attracting more and more interests among researchers. Besides, the communication cost is obviously reduced with only one receiver of the global system information. However, the bidirectional neighboring communication will make the communication network more complex, which makes DC-MG cluster as a time-delay system. Moreover, the different time-delay values among neighboring MGs further deteriorate the whole system to a multiple time-delay issue. To maintain the stable operation of DC-MG cluster, the cluster treatment of characteristic roots (CTCR) is proposed in the work for the stability analysis considering the multiple time delays.

Time-delay stability switching boundary determination for DC microgrid clusters with the distributed control framework

In a DC microgrid cluster, distributed DC microgrids are integrated to manage diverse and distributed energy resources. Without the reliance on a management center, the distributed control framework is capable of the cluster deployment by only adjacent collaborations. However, the communication among microgrids and the formation of dispatch signals inevitably lead to time delays, which might cause the system disorder and multiple-delay couplings. Considering these unstable effects, the lack of time-delay study challenges the cluster stability and burdens the energy application. The key contributions of this paper are the definition and detection of the time-delay stability switching boundary for the DC microgrid cluster with the distributed control framework, which reveals time delays switching the system stability and proves the delay-induced oscillation. Through the established time-delay model and the proposed method based on the cluster treatment of characteristic roots, the explicit time-delay stability switching boundary is detected in the delay space, which forms a determination flow of five stages: (1) system initialization: according to the cluster parameter values, the established time-delay model is initialized; (2) space transformation: applying the space mapping and the rationalization, the Sylvester resultant is constructed in the spectral delay space; (3) spectral boundary sketch: in uniformly divided blocks, spectral boundaries are found from the resultant; (4) crossing root calculation: with the spectral boundaries, crossing roots are calculated solving the characteristic equation; (5) boundary determination: back-mapping the spectral boundaries with the crossing roots, the overall boundary is presented. Comprehensive case studies are performed to study the time-delay stability switching boundary and to validate the proposed approach. The boundary existence and feature demonstrate the time-delay effect. Furthermore, the classified stable areas are revealed as well as the relevant strategies for the stability enhancement.

A diffusive predator–prey system with additional food and intra-specific competition among predators

In this paper, a diffusive predator–prey system with additional food and intra-specific competition among predators subject to Neumann boundary condition is investigated. For non-delay system, global stability, Turing instability and Hopf bifurcation are studied. For delay system, instability and Hopf bifurcation induced by time delay and global stability of boundary equilibrium are discussed. By the theory of normal form and center manifold method, the conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived.

DC Microgrid Stability Analysis Considering Time Delay in the Distributed Control

Bus voltage maintenance is the major concern for the stable operation of DC microgrids. Instead of a central controller based on global information, the distributed control strategy in DC microgrid can eliminate the bus voltage deviation with neighboring communication. However, the time delay among neighboring distributed generators (DGs) is inevitable. Besides, the bidirectional interactions in the distributed control process may make the time-delay stability more complicated. In order to consider the stability issues, this paper builds the time-delay dynamic model of DC microgrids with distributed control strategy, which can be considered as a neutral time-delay system model. A neutral linear matrix inequality (LMI) stability criterion is then provided to perform the time-delay stability analysis. Two indices namely maximum delay (MD) and time cost (TC) are defined to simultaneously consider the conservativeness and the speed of the method. Effectiveness and correctness of the proposed method are validated by a DC microgrid testbed finally.

Age and gender dependency of physiological networks in sleep

Recently, time delay stability analysis of biosignals has been successfully applied as a multivariate time series analysis method to assess the human physiological network in young adults. The degree of connectivity between different network nodes is described by the so-called link strength. Based on polysomnographic recordings (PSGs), it could be shown that the network changes with the sleep stage. Here, we apply the method to a large set of healthy controls spanning six decades of age. As it is well known, that the overall sleep architecture is dependent both on age and on gender, we particularly address the question, if these changes are also found in the network dynamics. We find moderate dependencies of the network on gender. Significantly higher link strengths up to 13% are found in women for some links in different frequency bands of central and occipital regions in REM and light sleep (N2). Higher link strengths are found in men consistently in cardio-cerebral links in N2, but not significant. Age dependency is more pronounced. In particular a significant overall weakening of the network with age is found for wakefulness and non-REM sleep stages. The largest overall decrease is observed in N2 with 0.017 per decade. For individual links decrease rates up to 0.08 per decade are found, in particular for intra-brain links in non-REM sleep. Many of them show a significant decrease with age. Non-linear regression employing an artificial neural network can predict the age with a mean absolute error (MAE) of about five years, suggesting that an age-resolution of about a decade would be appropriate in normative data for physiological networks.

Effective method to determine time‐delay stability margin and its application to power systems

In an interconnected bulk power system, wide-area measurement system (WAMS) can provide abundant remote measurement for the coordinated control system. However, WAMS data have obvious time delays, which affect the performance of the control system and should be properly considered. Time-delay stability margin (TDSM) is an index to reflect the maximum delay that a time-delay system can sustain without losing its stability. To construct a coordinated control system based on WAMS data, it is crucial to accurately and rapidly determine the TDSM value. In this paper, a novel Jordan-Taylor-Schur (JTS) approach to determine the TDSM value of power system is proposed. It consists of three, Jordan standardization, Taylor separation and Schur simplification. With the three procedures of this method, the model dimension of time-delay system can be reduced, and the stability criterion derivation can be rebuilt to omit some unnecessary variables so that both the computational efficiency and accuracy can be boosted. Further, it is worth highlighting that the proposed method can be applied to various Lyapunov-based stability criteria to improve their efficiency with small errors. Finally, three power systems with time delays have been used to demonstrate the effectiveness of the proposed method.

Time‐delay stability control strategy considering the jump characteristic of power system

In view of the jump characteristic of power system, a time-delay stability control strategy that avoids the effect of jump progress is proposed in this study. First, the Newton–Leibniz formula based on the free weighting matrix and the time-delay system model considering Markov jump are introduced to the differential equation of Lyapunov–Krasovskii functional, and a non-linear minimising time-delay controller considering the jump characteristic of power system is designed. Then, the Schur complement is used to decouple the non-linear items in the control algorithm, so that the matrix inequalities containing the non-linear items are transformed to standard linear matrix inequalities. Thus, low solving efficiency due to iteration could be avoided. Time-domain simulation tests on the IEEE 16-machine 68-bus system verify that the proposed controller could effectively damp the inter-area oscillations before and after the system jump, and the system after jump will not go unstable due to the time-delay control measures before the jump. Compared with traditional time-delay control methods, the proposed method is suitable for power system with jump characteristic and has better computational efficiency.

Time-delay Stability Analysis of Stochastic Power System with Wind Power Connection

A method to analyze the time-delay stability of stochastic power system with wind power connection is proposed in this paper. First, the reduced-order electromagnetic model of double fed induction generator (DFIG) suitable for time-delay stability analysis is established. Meanwhile, the mechanical power of DFIG is selected as the stochastic excitation, and the mechanical system model of the stochastic wind power is established according to the Wiener process. Second, the state equations of the power system are derived based on the stochastic differential equation (SDE). Then, the Lyapunov–Krasovskii functional considering the stochastic characteristic of wind power is constructed, and the weak infinitesimal generating operators of the functional are calculated according to the differential formula. On this basis, the time-delay stability criterion for the power system under stochastic excitations is formulated. Finally, the variation of system time-delay stability upper bound with the stochastic excitation intensity of wind power, excitation magnification, and damping coefficient is analyzed using generalized eigenvalue problem (GEVP). Simulation results of IEEE 16-machine 68-bus system demonstrate that the time-delay stability upper bound of the power system decreases when the excitation magnification coefficient of synchronous generator increases, and it increases when the damping coefficient of synchronous generator increases. However, the effect of stochastic excitation intensity of wind power on the time-delay upper bound is more complex, and there is a distinct concave area in the change trend.

Research on Time Delay Stability of Power System using Fault Chains and Markov Process

A new method based on fault chains and the Markov process for analyzing time-delay power system stability is proposed in this article. First, reasonable fault chains are formed using the fault chain generation method based on network power flow. Second, by combining the fault chains and Markov processes, a class of Lyapunov–Krasovskii functionals considering the Markov jump is established. Free weighting items constructed with the Markov process transfer rate matrix and Newton–Leibniz formula, respectively, are then introduced to the weak infinitesimal operators in the Lyapunov–Krasovskii functional. Meanwhile, to lower the conservativeness of the method, the whole time-varying time-delay interval has been divided into two subintervals. Finally, the time-delay upper bound that the power system can bear in the case of cascading faults is calculated by means of the generalized eigenvalue problem. The efficiency and feasibility of the proposed method in solving the maximum time delay in the case of cascading faults have been validated by the dynamic time-domain simulation results. Comparative results with other methods show the proposed method has low conservativeness.

Asymptotic stabilization of stochastic high-order upper-triangular nonlinear systems with input time-varying delay

Based on the homogeneous domination approach and stochastic nonlinear time-delay system stability criterion, this paper investigates the global state-feedback stabilization problem for a class of stochastic high-order upper-triangular nonlinear systems with input time-varying delay. By skilfully choosing an appropriate Lyapunov–Krasoviskii functional and successfully solving several troublesome obstacles in the design and analysis procedure, a delay-independent state-feedback controller is designed to render the closed-loop system globally asymptotically stable in probability. The simulation example is given to verify the effectiveness of the proposed design scheme.