Time Delay Parameter Research Articles

H∞ cruise control for high-speed trains with process and data transmission time-varying delay

This paper investigates an H∞ cruise control strategy for uncertain high-speed trains (HSTs) with two time-varying delays. The multibody model of the cascading car is established, taking into account the influence of the flexible coupler and the basic resistance (rolling mechanical resistance + aerodynamic resistance) in the actual operation process. There are many uncertainties in the actual operation of the train, such as disturbances caused by gusts and track irregularities and time-varying delays caused by flexible couplers. Based on the above factors, this paper fully considers and supplements the multibody model. A cruise control strategy based on Lyapunov stability theory and linear matrix inequality (LMI) is proposed. The state feedback control rate with input short time delay is designed, and a cruise control method with double time-varying delays is proposed by sampling data. Constructed Lyapunov–Krasovskii function (LKF) with time-delay parameters for time-delay systems to fully introduce the information of time delays. In view of the disturbance effect, the sufficient condition to suppress the disturbance is given. The proposed H∞ cruise control method controls the fluctuating speed and displacement of the train to quickly converge to the steady state. The HST at equilibrium tracks the desired velocity and ensures a stable relative displacement. The specified H∞ interference attenuation level is achieved to ensure safe and comfortable operation. Two numerical simulations are carried out to illustrate the effect of state time-varying delay and disturbance on train stationarity, which proves the superiority of the proposed method.

Experimental research on vehicle active suspension based on time-delay control

To improve the ride comfort of the vehicle and the high-efficiency control requirements of the suspension, this paper proposes a time-delay control strategy and the idea of using a linear motor as the actuator. This paper analyses the damping characteristics of the time-delay control strategy in the time domain and frequency domains. A linear equivalent excitation method is proposed to optimise the optimal time-delay control parameters under complex excitations. The stability of the system is analysed. The damping effect of time-delay control active suspension is verified by numerical simulation. An experimental hardware platform of a linear motor and active suspension was built further to verify the effectiveness of the time-delay control strategy. The experimental results show that the relative errors of root mean square values of experimental and simulation results are within 16% under each working condition. The experimental results verify the effectiveness of the simulation results.

Optimal Choices of Reconstruction Parameters United Improved C-C Algorithm and Improved G-P Algorithm

For the phase space reconstruction of chaotic time series, the precise selection of delay and embedding dimension is indispensable. Therefore, this paper makes an in-depth study on the selection of reconstruction parameters, and puts forward some suggestions for improving the theoretical defects of the original C-C algorithm and G-P algorithm. The modified C-C algorithm optimizes the intermediate determination parameters of delay time and embedded window of the original algorithm, and makes the selection of delay time and embedded window more accurate. The improved G-P algorithm optimizes the range of neighborhood radius and the selection of scale-free interval, and improves the calculation accuracy of embedding dimension. On the theoretical basis, Lorenz sequence and Rossler sequence are used to verify, and the simulation results can be obtained. The improved algorithm can select parameters more accurately. Finally, the parameters obtained by the two improved algorithms are compared, and it is considered that the phase space reconstruction can be better by using the improved C-C algorithm to solve the delay and the improved G-P algorithm to solve the embedding dimension.

Dynamical analysis of a damped harmonic forced duffing oscillator with time delay

This paper is concerned with a time-delayed controller of a damped nonlinear excited Duffing oscillator (DO). Since time-delayed techniques have recently been the focus of numerous studies, the topic of this investigation is quite contemporary. Therefore, time delays of position and velocity are utilized to reduce the nonlinear oscillation of the model under consideration. A much supplementary precise approximate solution is achieved using an advanced Homotopy perturbation method (HPM). The temporal variation of this solution is graphed for different amounts of the employed factors. The organization of the model is verified through a comparison between the plots of the estimated solution and the numerical one which is obtained utilizing the fourth order Runge–Kutta technique (RK4). The outcomes show that the improved HPM is appropriate for a variety of damped nonlinear oscillators since it minimizes the error of the solution while increasing the validation variety. Furthermore, it presents a potential model that deals with a diversity of nonlinear problems. The multiple scales homotopy technique is used to achieve an estimated formula for the suggested time-delayed structure. The controlling nonlinear algebraic equation for the amplitude oscillation at the steady state is gained. The effectiveness of the proposed controller, the time delays impact, controller gains, and feedback gains have been investigated. The realized outcomes show that the controller performance is influenced by the total of the product of the control and feedback gains, in addition to the time delays in the control loop. The analytical and numerical calculations reveal that for certain amounts of the control and feedback signal improvement, the suggested controller could completely reduce the system vibrations. The obtained outcomes are considered novel, in which the used methods are applied on the DO with time-delay. The increase of the time delay parameter leads to a stable case for the DO, which is in harmony with the influence of this parameter. This drawn curves show that the system reaches a stable fixed point which assert the presented discussion.

Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance.

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter P, which controls STDP, on the characteristic rewiring frequency parameter F, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing P (which enhances the weakening effect of STDP on synaptic weights) and decreasing F (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter τ_{c} has some appropriate values. (ii) Increasing the synaptic time delay τ_{c} induces multiple CR (MCR)-the occurrence of multiple peaks in the degree of coherence as τ_{c} changes-in small-world and random networks, with MCR becoming more pronounced at smaller values of P and F. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

High telepresence control for the relay communication based space teleoperation

This paper studies the high telepresence control for the relay communication based space teleoperation. High telepresence requires real-time, accurate force perception and good position tracking, but all of them are destroyed or affected by time delay. To eliminate the influence of time delay, direct recursive generalized predictive control (DR-GPC) is quoted into this paper to realize position tracking. As for the other two properties, the pseudo position-force (Pseudo-PF) feedback strategy (composed of parameter identification and force reconstruction) is a good way as it can provide real-time and precise force feedback when environment change slowly and time delay is relatively small. However, complex and changeable environment and serious and complex time delay in space teleoperation make the environment force parameter available to force reconstruction is outdated and cannot realize accurate force rebuilding. To solve this problem, we propose a dual regression Pseudo-PF feedback strategy. Compared with the traditional one, its biggest change is the introduction of dual regression that consists of time delay prediction and parameter regression. The former predicts time delay and provides it to the latter to determine the forward prediction steps, while the latter regresses the actual latest and precise environment force parameter according to the forward prediction steps. With the cooperation of time delay prediction and parameter regression, the influence of fast changing environment or serious and complex time delay on force reconstruction can be effectively overcome, so as to realize real-time and accurate force feedback. Finally, DR-GPC and dual regression Pseudo-PF feedback strategies cooperate to achieve high telepresence control, and simulation is given to show its effectiveness.

Price Dynamics of a Delay Differential Cobweb Model

The paper uses a new technique to find a unique solution to a delay differential cobweb model (formulated from a joint supply-demand function of price) with real model parameters via the Lambert W-function without considering any complex branches. The dynamics of the model are demonstrated with simulations and found to complement previous studies using literature values. However, the condition for instability δ / β > 1 in the previous studies was defied by our model due to the time delay associated with the supply function. The practical application and advantage of this model over the existing models are that the stability of this model is not limited to only the ratio of price elasticity of demand and supply but also the time-delay parameter (i.e., a missing link in the previous models). Our model, on the other hand, loses its stability when the time delay associated with the supply function is fixed at τ = 1.8 . Since most of the physical systems, including economical systems, are time-delay inherent and such stability conditionalities should not limit their performance, it is recommended that such systems be modelled using delay differential functions. The novelty of this research is that there has not been a definite general solution to the cobweb model with a time delay whose price dynamics mimic the behaviour of the existing cobweb models in the literature. An illustrative example in a delayed fractional-order differential equation also buttressed the importance of the time delay in the model, aside from the impact of the ratio of the price elasticity of supply and demand.

Distributed immune time-delay SEIR-S model for new power system information network virus propagation

The new power system information network has the security problem of computer virus attack, and the study of its transmission mechanism is helpful to discover the law and influence of virus transmission. In this paper, the research method of epidemic theory is introduced, and a new Susceptible-Exposed-Infectious-Recovered-Susceptible(SEIR-S) virus model is proposed. The immune time-delay parameter is introduced to simulate the evolution and mutation of the virus so that nodes immune to the virus can still be re-infected after a certain time interval. At the same time, the immune time of different nodes is different, and the distributed immune time delay is used to enhance the authenticity of the simulated virus transmission; and considering the influence of the scale-free characteristics of the information network, this paper establishes a continuous Markov chain based on time. The transmission process of the virus, and then deduce the theoretical analysis results of the virus infection rate threshold. Based on theoretical analysis, the propagation process of the SEIR-S virus model with distributed immune time delay was simulated by using the Monte Carlo method, and the accuracy of the threshold formula of virus infection rate was verified. The influence rule of the hysteresis parameter, that is, increasing the average immune time of nodes to viruses can reduce the infection density of the network in a steady, and at the same time, making the immune time of network nodes obey a normal distribution can effectively reduce the oscillation effect of viruses on the network.

Fluidelastic instability of a rod bundle subjected to jet cross-flow

Jet flow emanating from loss of coolant accident (LOCA) holes in the baffle plates of some pressurized water reactors (PWRs) was found responsible for flow-induced vibration in nuclear fuel bundles. This could cause fretting wear of the fuel rods at the spacer grid location. Experimental tests on prototypical rod bundles subjected to jet cross-flow showed a strong vibration response akin to fluidelastic instability of tube arrays in uniform cross-flow. Vibrations similar to flow-periodicity resonance response have also been reported.Fluidelastic instability (FEI) is the most critical flow-induced vibration mechanism. For fuel rods subject to jet-cross flow, it is important to identify the specific mechanism underlying the rod vibrations and in particular, confirm possible fluidelastic instability. In previous work, a few stability boundary correlations based on the Connors equation were developed for the baffle jetting (i.e. 2D jet) problem in PWRs. With the exception of these correlations, no theoretical model accounting for fluid–structure interaction under jet cross-flow has been reported.To investigate possible fluidelastic instability, the quasi-steady model, initially developed for tube arrays in uniform cross-flow, is extended to the problem of a rod bundle subjected to a jet cross-flow. In the extended quasi-steady model, a new formulation of the fluidelastic forces as functions of the projected rod area derivative is proposed to account for the variation of the projected area through the LOCA hole (i.e. circular jet).A significant limitation of the ‘classical’ quasi-steady model is the poor representation of the time delay effect, known to be critical for correct fluidelastic instability prediction. This shortcoming is addressed in the present work. Furthermore, unsteady flow effects are partly taken into account experimentally measuring the time delay parameter for this jet-cross-flow configuration.For the present highly compact rod array, a new test apparatus is designed and built to directly measure the time delay parameter. The new results show that the time delay to be non-constant, strongly dependent on Reynolds number while relative independent of reduced velocity for Low Re. For High Re, the time delay depends on both Re and reduced flow velocity. Based on the new measurements, a formulation for the time delay parameter, dependent on Reynolds number and reduced velocity is proposed for the highly packed fuel rod bundle.The new extended quasi-steady model conclusively confirms that the vibration phenomenon observed in experimental tests is clear fluidelastic instability induced by the jet cross-flow. Moreover, the model predicts the critical jet velocity for fluidelastic instability with an error of 9% when the new Reynolds number dependent time delay formulation is employed.

Stabilization of Delayed Boolean Networks Using Constrained State Pinning Control

Pinning control is applied to ensure the stabilization of Boolean networks (BNs) with time delay parameter. The time delay parameter in this article follows an independent identical distribution. Using semi-tensor product of matrices, the considered BN with time delay is converted to a high dimensional switching BN and the switching signal is the time delay signal. Different from general switching BN, the structure matrices of all subsystems are independent with each other, structure matrices of all subsystems for the high dimensional switching BN depend on the original BN structure matrix. Pinning control is designed to guarantee the global stochastic stability of the considered system. Furthermore, the global stochastic stability of BN with time delay parameter is proved to be equivalent to the stability of BN without time delay parameter, which greatly reduces the computational complexity and simplifies the control design. For the considered BN with finite cycles, constrained pinning control is applied with limitation that only one state of each undesired cycle is under control. With this constraint, the minimal number of pinning control nodes is further investigated. Some algorithms are presented to obtain the new structure matrix, with which, pinning control can be solved by the obtained methods. Both numerical examples and biological example illustrate the effectiveness of the results.

Research on Coordinated Control of Braking Mode Switching for Enhancing Switching Quality Considering Communication Delay and Time-Varying Model Parameters

In the process of braking mode switching of electro-hydraulic brake (EHB) system, there exist time delay and time-varying model parameters in the actual control process, result in the delay of state transfer and controller effectiveness degradation. In response to the above concerns, a torque coordinated control strategy is provided. Firstly, the motor compensation control algorithm is provided to reduce the fluctuation of the actual braking torque as well as considering the braking feeling and energy recover. On top of which, an optimization model incorporating braking feeling and braking energy recover is developed; Secondly, the improved non-dominated sorting genetic algorithm (NSGA-II) is applied to optimize the distribution coefficient to achieve the higher recover energy and stable braking feeling; Furthermore, given the communication delay exists in the compensation control process, which is liable to cause decreasing the quality of braking mode switching, a coordinated delay compensation control strategy consisting of improved compensation module of RBF-Smith, braking mode coefficient solver module, braking force distribution module, and motor compensation control module is introduced. The proposed control algorithm is examined under various time delays and the results indicate that the algorithm effectively tackles communication delay and time-varying model parameters in mode switching stabilization.

A general framework for robust stability analysis of neural networks with discrete time delays

Robust stability of different types of dynamical neural network models including time delay parameters have been extensively studied, and many different sets of sufficient conditions ensuring robust stability of these types of dynamical neural network models have been presented in past decades. In conducting stability analysis of dynamical neural systems, some basic properties of the employed activation functions and the forms of delay terms included in the mathematical representations of dynamical neural networks are of crucial importance in obtaining global stability criteria for dynamical neural systems. Therefore, this research article will examine a class of neural networks expressed by a mathematical model that involves the discrete time delay terms, the Lipschitz activation functions and possesses the intervalized parameter uncertainties. This paper will first present a new and alternative upper bound value of the second norm of the class of interval matrices, which will have an important impact on obtaining the desired results for establishing robust stability of these neural network models. Then, by exploiting wellknown Homeomorphism mapping theory and basic Lyapunov stability theory, we will state a new general framework for determining some novel robust stability conditions for dynamical neural networks possessing discrete time delay terms. This paper will also make a comprehensive review of some previously published robust stability results and show that the existing robust stability results can be easily derived from the results given in this paper.

Investigation of wind turbine blade ultrasonic pulse-echo signal decomposition based on the matching pursuit algorithm

The ultrasonic testing method is commonly used to detect the internal defects of wind turbine blades, but difficulty is found in judging the echo position due to the waveform superposition caused by the thin web. In this paper, an improved matching tracking algorithm is proposed to decompose the ultrasonic detection echo of wind turbine blades. This method extracts the time-delay parameter of the echo to estimate the time-of-flight (TOF), which provides the necessary information for further judgement of hidden defects in the wind turbine blades. The effectiveness of the proposed method is verified via simulation experiments and real tests.

Finite rate of innovation sampling of Gaussian pulse streams with variable shape

The existing Finite Rate of Innovation (FRI) sampling theory can realize the efficient measurement of Gaussian pulse streams with fixed modal functions. However, it is hard to sample that signal with variable pulse width factors by a sub-Nyquist rate. To get around this challenge, we propose an extended FRI sampling method based on Taylor series expansion in this paper, where the signal is first filtered by the exponential reproducing kernel, then each pulse can be reconstructed sequentially. For a single pulse, we first prove that the pulse width factor does not interfere with the estimation process of the time delay parameter, and we also present its Cramer-Rao lower Bound (CRB). The signal Fourier coefficient can then be reformulated by the Taylor series expansion of order N−1 to realize the decoupling of the pulse width factor before the final estimation. We derive the order limit of expansion from the perspective of numerical stability, and we also give the upper bound on the estimation error of the pulse width factor for N=2. Simulation results show that, compared with the classical methods, the proposed state-of-the-art algorithm can achieve a higher precision reconstruction of the Gaussian pulse stream signal.

Performance enhancement of duobinary modulation-based DWDM system using particle swarm optimization

Abstract The next-generation light wave communication DWDM networks can accommodate large number of channels to efficiently utilize the bandwidth (BW). However, in the deployment of DWDM system mixing of two or more waves limits the performance due to four wave mixing (FWM) nonlinearity in fiber. This article, presents improved performance analysis of DWDM using a proposed improved duobinary modulation (IDBM), modified duobinary modulation (MDBM) and duobinary modulation (DBM) model for mitigation of FWM nonlinearities has been estimated experimentally through interference of noise on optical signal, FWM efficiency, FWM power etc. In IDBM, a unit delay in addition to time delay parameter is also utilized for generation of electrical duobinary pulses. The parameters of both delay blocks are tuned through particle swarm optimization (PSO) technique to improve the performance. The overall proposed IDBM effectively decreases the FWM. The results obtained for IDBM in terms of Q-factor 8.9, OSNR 18 dB, FWM power −87 dBm and FWM efficiency −70 dB shows substantial improvement with the recommended IDBM technique in comparison to DBM and MDBM schemes.

Study of A Delayed SIVA Within-Host Model of Dengue Virus Transmission

During the process of immune response to the infection caused by dengue virus, antibodies are generated by plasma cells which are produced by B-cells. In some cases, it is observed that there is a delay in the production of plasma cells from B-cells which causes a delay in the immune response. We propose a SIVA within-host model of the virus transmission with delayed immune response to articulate the dynamics of the cell and virus population. The stability analysis of different equilibrium states is also studied. The basic reproduction number (BRN) of the model is computed using next generation matrix (NGM) method. The local stability analysis is discussed using the method of linearisation. The stability conditions of the equilibrium states are validated using the Li´enard - Chipart criterion. Hopf bifurcation analysis is carried out as the system has time lag in the immune response. Three equilibrium states, namely, virus free equilibrium state, endemic equilibrium state with and without immune response, have been observed. It has been found that the virus free equilibrium state is locally asymptotically stable if BRN is less than or equal to 1. Additionally, the conditions for the stability of the endemic equilibrium points are derived and elaborated. Numerical simulations for different values of time delay parameter τ are presented and illustrated using graphs. A Hopf bifurcation is observed if the delay parameter τ crosses a threshold value and then the system becomes unstable with periodic solution. To determine the relative importance of the model parameters to the virus transmission and prevalence, sensitivity analysis of the parameters is illustrated using graphs. Due to the time lag in the immune response, an increase in the virus growth is observed in large quantity. As a result, the infection spreads more quickly within the host.

Research on high performance control strategy of slab thickness based on T-S fuzzy control

To address the difficulty of controlling the dynamic stability of the system after time-varying delay of the plate thickness detection at the final stand of the hot strip finishing mill. Firstly, a T-S fuzzy model based on rolling force and thickness state is established for the final stand of the hot strip finishing mill, and the maximum time delay for plate thickness detection is divided into several time delay intervals to establish a linear constant state space model of the time delay subintervals. Secondly, a distributed state feedback controller satisfying sufficient conditions for stability is solved by using the parallel distribution compensation (PDC) principle combined with Lyapunov stability theory and linear matrix inequality (LMI) methods. Simulation comparisons with current M-AGC and Smith prediction M-AGC system (Smith-AGC) show that our method can effectively reduce overshoot and oscillations in the dynamic response of the exit plate thickness when the operating conditions change and the system time delay parameters are mismatched, so that the system has better stability and dynamic performance.

Upper Limb Cortical-Muscular Coupling Analysis Based on Time-Delayed Back Maximum Information Coefficient Model.

In musculoskeletal systems, describing accurately the coupling direction and intensity between physiological electrical signals is crucial. The maximum information coefficient (MIC) can effectively quantify the coupling strength, especially for short time series. However, it cannot identify the direction of information transmission. This paper proposes an effective time-delayed back maximum information coefficient (TDBackMIC) analysis method by introducing a time delay parameter to measure the causal coupling. Firstly, the effectiveness of TDBackMIC is verified on simulations, and then it is applied to the analysis of functional cortical-muscular coupling and intermuscular coupling networks to explore the difference of coupling characteristics under different grip force intensities. Experimental results show that functional cortical-muscular coupling and intermuscular coupling are bidirectional. The average coupling strength of EEG → EMG and EMG → EEG in beta band is 0.86 ± 0.04 and 0.81 ± 0.05 at 10% maximum voluntary contraction (MVC) condition, 0.83 ± 0.05 and 0.76 ± 0.04 at 20% MVC, and 0.76 ± 0.03 and 0.73 ± 0.04 at 30% MVC. With the increase of grip strength, the strength of functional cortical-muscular coupling in beta frequency band decreases, the intermuscular coupling network exhibits enhanced connectivity, and the information exchange is closer. The results demonstrate that TDBackMIC can accurately judge the causal coupling relationship, and functional cortical-muscular coupling and intermuscular coupling network under different grip forces are different, which provides a certain theoretical basis for sports rehabilitation.

Dynamics of a predator-prey model with fear effects and gestation delays

<abstract><p>Recent studies have shown that, in addition to direct predation, fear of predators alters the physiological behavior of prey. Based on this fact, this paper investigates a three-species food chain based on ratio-dependent and Beddington-DeAngelis type functional responses, which incorporates fear effects and two gestation delays. The positivity, boundedness and existence of equilibrium points of the system are investigated, and the local stability behavior of the equilibrium points and the occurrence of Hopf-bifurcation when the time lag parameters exceed the critical values are studied by analyzing the corresponding characteristic equations. The main results show that Hopf-bifurcation occurs when the time delay parameters attain the thresholds. Finally, numerical simulations are performed to verify our main results.</p></abstract>

Stability and dynamics of spike-type solutions to delayed Gierer-Meinhardt equations

<p style='text-indent:20px;'>For a specific set of parameters, we analyze the stability of a one-spike equilibrium solution to the one-dimensional Gierer-Meinhardt reaction-diffusion model with delay in the components of the reaction-kinetics terms. Assuming slow activator diffusivity, we consider instabilities due to Hopf bifurcation in both the spike position and the spike profile for increasing values of the time-delay parameter <inline-formula><tex-math id="M1">\begin{document}$ T $\end{document}</tex-math></inline-formula>. Using method of matched asymptotic expansions it is shown that the model can be reduced to a system of ordinary differential equations representing the position of the slowly evolving spike solution. The reduced evolution equations for the one-spike solution undergoes a Hopf bifurcation in the spike position in two cases: when the negative feedback of the activator equation is delayed, and when delay is in both the negative feedback of the activator equation and the non-linear production term of the inhibitor equation. Instabilities in the spike profile are also considered, and it is shown that the spike solution is unstable as <inline-formula><tex-math id="M2">\begin{document}$ T $\end{document}</tex-math></inline-formula> is increased beyond a critical Hopf bifurcation value <inline-formula><tex-math id="M3">\begin{document}$ T_H $\end{document}</tex-math></inline-formula>, and this occurs for the same cases as in the spike position analysis. In all cases, the instability in the profile is triggered before the positional instability. If however the degradation of activator is delayed, we find stable positional oscillations can occur in this system.</p>