Constant Time Delay Research Articles

Analysis of Frequency Regulation Capability of Doubly Fed Induction Generator and Supercapacitor Energy Storage Based on Dynamic Power Flow

The grid-integrated doubly fed induction generator (DFIG) is required to participate in the frequency regulation of the power system. The supercapacitor energy storage (SES) is capable of enhancing the frequency regulation capability of the DFIG in a coupled manner. The SES is connected to the DC capacitor of the DFIG and provides active power response through the droop control. The dynamic power flow (DPF) model is established to quantify the frequency response of the power system when the DFIG-SES system participates in the frequency regulation. The integration of the SES affects the internal power flow distribution of the DFIG; thus, the detailed model of the DFIG is incorporated into the DPF analysis. Considering the different response speeds of the synchronous generator (SG), the SES, and the DFIG to the frequency regulation, the first-order inertia delay in the governor control of the SG is included in the DPF model. The impact of the delay time constant on the continued operation time of the SES is analyzed. With the same deloading percentage, the output power of the DFIG is adjusted based on a variable droop coefficient scheme to fully utilize its active power reserve. The feasibility and effectiveness of the DFIG-SES scheme to participate in the frequency regulation are analyzed based on the DPF and verified through numerical analysis.

Effects of Using Constant Time Delay in Small Group Instruction to Teach Number Identification Skills to Students with Intellectual Disability

This study aims to examine the effectiveness of constant time delay (CTD) in a small group teaching arrangement implemented in distance learning on teaching identifying the names of numbers with two digits. A multiple probe design across subjects was used to assess the effect of CTD. Participants of the study were four elementary school students with intellectual disabilities. Maintenance and acquisition of non-target skills through observational learning was assessed. Results showed that all students acquired and maintained the target skills. Data of observational learning showed that students acquired some of the non-target skills. Keywords: Intellectual Disability، Constant Time Delay، Number Identification، Small-Group instruction, Distance Learning, Multiple Probe Design.

Stability and [formula omitted]-gain of positive fractional-order coupled differential-difference systems with unbounded time-varying delays

This work aims to research the positivity, stability, and L∞-gain of incommensurate fractional-order coupled differential-difference systems (FOCDDSs) with unbounded time-varying delays. By virtual of the Banach’s fixed point theorem, the existence and uniqueness of the solution of FOCDDs is given. A necessary and sufficient criterion ensuring the positivity of delayed FOCDDSs is put forward. Then, by analyzing the monotonicity of system trajectories and constructing sample data systems, a necessary and sufficient criterion realizing the stability of positive FOCDDSs is obtained. Different from related works, there is no need to require the Lyapunov–Krasovskii function or the comparison between the counterpart with constant time delays by the proposed approach. To obtain the L∞-gain of FOCDDSs, two auxiliary systems are developed to calculate the limit of the state trajectory. Eventually, a numerical experiment is performed to verify the rationality of the results.

Intention-reflected predictive display for operability improvement of time-delayed teleoperation system

Robotic teleoperation is highly valued for its ability to remotely execute tasks that demand sophisticated human decision-making or that are intended to be carried out by human operators from a distance. However, when using the internet as a communication framework for teleoperation, high latency, and fluctuations make accurate positioning and time-dependent tasks difficult. To mitigate the negative effects of time delay, this paper proposes a teleoperation system that uses cross reality (XR) as a predictive display of the outcome of operators’ intended actions and develops a time-delay aware shared control to fulfill the intention. The system targets a liquid pouring task, wherein a white ring that indicates the intended height of the liquid surface is overlayed onto the beaker in a delayed camera image to close the visual feedback loop on the leader side. Simultaneously, the shared control automatically completes the pouring action to track the intended liquid height. The performance of the proposed system is validated based on liquid pouring experiments performed by human subjects. When compared with direct control, the absolute error rate decreased significantly for a constant round-trip time delay of 0.8 s and 1.2 s, similarly for a time-varying delay of 0.4 s and 0.8 s. Moreover, when the time-varying delay was 0.8 s, operators achieved significantly higher accuracy while maintaining comparable operation time. These results indicate that our proposed system improves operability even in the presence of time-varying delays in communication networks.

On the finite time force estimation for bilateral teleoperation of robot manipulators with time varying delays

One of the biggest challenges in the bilateral teleoperation of robot manipulators is to get transparency and telepresence between the local (master) and the remote (slave) manipulator. For these goals, it is advisable to transfer contact force measurements from one side to the other through the communication channel. However, there may be some reasons for which it is not necessarily desirable to employ force sensors. For instance, they are expensive, sensitive to noise, and they can be too big to be used in some small devices. Therefore, some estimation approaches may be advisable. This contribution shows the design of a position/force control scheme for bilateral teleoperators with time varying delays based on the estimation of velocities and forces by using only joint position measurements. Under some relaxed assumptions it is shown that position and force tracking errors become ultimately bounded with arbitrarily small ultimate bound in finite time. To the best of the authors’ knowledge there are no control schemes for bilateral systems with all the previous characteristics since the available ones assume constant time delays. The new proposal is tested by means of simulations and experiments showing a good performance both in free and constrained motion.

Discontinuous Galerkin Time Stepping for Semilinear Parabolic Problems with Time Constant Delay

Discontinuous Galerkin Time Stepping for Semilinear Parabolic Problems with Time Constant Delay

Justification of the method for determining the reliability of the operator of a mobile fire fighting installation

The object of research is the operator of a mobile fire installation; the subject of research is the operator’s characteristics, particularly his reliability. The method of determining the reliability of a mobile fire installation operator as a functional element of a dynamic system is substantiated. Operator failure is interpreted as the output of its frequency characteristics beyond permissible limits. Analytical dependences for variations of the operator’s frequency characteristics on variations of its parameters – transmission coefficient, delay time, and time constant are constructed. The amplitude and phase reliability of the operator of a mobile fire installation are determined using the Laplace functions, the arguments of which are the permissible values of variations in the frequency characteristics of the operator and variations of its parameters. Determination of variations of operator parameters is carried out by the instrumental method using the operator’s activity monitoring system. The test effect on the operator of a mobile fire installation is carried out in the form of a rectangular pulse that formalizes the change in the position of the combustion cell at a priori a given distance over a priori predetermined time. A signal characterizing the operator’s response to the test impact is determined using the Laplace integral transform. Measuring the parameters of this signal allows you to determine the variations in operator parameters that are used to determine its reliability. It is shown that for variations of operator parameters, the values of which are 10.0 % with RMS deviations of 3.3 %, with a probability of 0.8715 the amplitude-frequency and phase-frequency characteristics at the time of its control will not differ from their nominal values by more than 5.0 %. The requirements regarding the reliability of the operator’s activity control system are determined

Combined H∞ and anti‐disturbance control for semi‐Markovian jump systems via a nonlinear disturbance observer

AbstractThis paper investigates a combined and anti‐disturbance control problem for a class of semi‐Markovian jump nonlinear systems with constant time delay, and both modeled and unmodeled disturbances. In particular, the modeled disturbance is thought to be produced by a nonlinear exogenous system and is estimated by introducing a mode‐dependent nonlinear disturbance observer. The desired controller for the addressed system is then proposed, which consists of two components: (i) state feedback, which ensures the system's stochastic stability by attenuating the unmodeled disturbance; and (ii) disturbance estimate, which compensates for the modeled disturbance effect. Following that, a novel mode‐dependent asymmetric Lyapunov‐Krasovskii functional is used to derive the sufficient conditions for the existence of the proposed controller and disturbance observer. The developed theoretical results are supported by three numerical examples that demonstrate the utility of the proposed design method.

The Effectiveness of the Constant Time Delay Procedure in Teaching Reading and Writing with the Sound-Based Sentence Method

Introduction: The present study was planned since no practical study adapted for individuals with special needs (ISN) was found in teaching reading and writing with the sound-based sentence method (SBSM). There were few studies aimed at teaching reading and writing, and the skills targeted in these studies were limited. This study aimed to determine the effectiveness of the constant time delay procedure (CTDP) in teaching reading and writing with the sound-based sentence method to individuals with special needs. In addition to the said main purpose, the permanence of reading and writing skills and their generalizability across materials and persons were also examined. Moreover, the opinions of families and teachers of ISN were obtained to collect social validity data.Method: Three INS were included in this study. Of these, two were girls, and one was a boy, all aged seven. They attended the second grade as full-day co-teaching inclusive students and had not learned reading and writing. The study employed a multiple probe design across behaviors, one of the single-subject research designs. The study aimed to teach three behaviors and eighteen sub-behaviors, including six sub-behaviors in each behavior.Findings: The study showed that two participants acquired reading and writing skills in all the sub-behaviors (closed syllables, open syllables, three-letter monosyllables, three-letter two syllables, words, and sentences) of all three behaviors (syllables, words, and sentences consisting of e-l-a-k-i-n sounds, syllables, words, and sentences consisting of o-m-u-t-ü-y sounds, syllables, words, and sentences consisting of the combination of sounds in these two groups [e-l-a-k-i-n-o-m-u-t-ü-y]); that the skills they acquired were permanent; that they generalized these skills across persons and materials, while one participant acquired skills in the first three sub-behaviors (closed syllables, open syllables, three-letter monosyllables) only in the first behavior. Considering the social validity findings of the study, the participants’ families and primary school teachers expressed positive opinions about the study.Discussion: The findings obtained were discussed within the framework of the literature indicating the negative aspects of teaching reading and writing with the SBSM.

Non-fragile PD control of linear time-delay positive discrete-time systems

This paper addresses the issue of proportional-derivative (PD) controllers design for positive linear systems in the discrete-time domain, which still remains a challenging problem in positive systems theory. The specific aim is to design a PD controller for a system with constant time delay, which simultaneously ensures closed-loop system stability and preserves positivity. Moreover, additive gain variation of the controller is considered in the synthesis process. Systematic formulation and tractable algorithms are developed to find the PD controller gains for positive stabilization. The performance of such methods is validated by numerical examples.

Delay Effects in the Dynamics of Human Controlled Towing of Vehicles

Abstract A simplified mechanical model of vehicle towing is constructed. The towing procedure is modeled by means of two blocks connected with a linear spring that represents the elastic drawbar. The driver in the towing car controls the velocity of towing, while the driver of the towed vehicle tries to maintain a constant tension in the drawbar. Both control forces are subjected to a constant time delay that represents the reaction time of the operators. Utilizing the translational symmetry of the system, Routh reduction is carried out to make the governing equations as compact as possible. Stability charts are constructed in the space of the control parameters and the fastest decay of signals is identified. As time delay increases, the stable domain disappears and reappears periodically. Guidelines are provided for the design of the elasticity of the drawbar, which takes into account the masses of the vehicles and the average reaction time of the drivers.

Optimized adaptive filtering for fault estimation of the dynamics of high-speed train based on robust extended Kalman filter

In this paper, an optimized adaptive robust extended Kalman filter is proposed based on random weighting factors and an improved whale optimization algorithm for fault estimation of the dynamics of high-speed trains with constant time delays, drastically changing noise and stochastic uncertainties. Robust upper bounds are proposed to improve the performance of the extended Kalman filter by decreasing the influence of the linearization error on filtering for the dynamics of high-speed trains with constant time delays, and its robustness is proven to guarantee the feasibility of the proposed upper bounds. Furthermore, considering drastically changing noise with unknown statistics, a random weighting adaptive algorithm is proposed to implement unbiased noise estimation so that the robust extended Kalman filter can still be implemented well. In addition, a differential evolution algorithm and adaptive parameter are introduced to improve the performance of the whale optimization algorithm so that the stochastic uncertainties are optimized, and the influence of the stochastic uncertainties on filtering is further decreased. The simulation results in the three conditions show that, compared with the variational Bayes adaptive iterated extended Kalman filter, using the proposed method, the position, speed and fault estimation errors are decreased by 31.8%, 33.2% and 28.3%, respectively, on average, which depends on more accurate noise estimation.

Practical consensus for heterogeneous multi-agent systems with gain fluctuations via resilient sampled-data control

This study proposes a sampled-data-based practical consensus control method for heterogeneous multi-agent systems with gain fluctuations. First, the heterogeneous multi-agent system is formulated together with randomly occurring nonlinear dynamics. Second, unlike the existing studies, a more general retarded sampled-data control approach is designed, which involves the gain fluctuations along with the actual sampling pattern and constant time delay, to achieve the practical consensus of the considered system. By utilizing the aperiodic sampling information, and looped functional approach, a Wirtinger’s inequality-based discontinuous Lyapunov-Krasovskii functional is constructed to derive the delay-dependent stability condition of the closed-loop system in the form of linear matrix inequality. Finally, numerical simulation is presented to illustrate the derived theoretical results.

A Novel Computation of Delay Margin Based on Grey Wolf Optimisation for a Load Frequency Control of Two-Area-Network Power Systems

In classical power systems, frequency measurements are transferred via a specialised communication channel, resulting in time delay. The time delay plays a major role in a power system, which can reduce the dynamic performance of the load–frequency control (LFC) system and can destabilise the system. The research to date has tended to focus on developing a new algorithm to determine the delay margin (DM) rather than looking into a hybrid algorithm which includes a nature-inspired metaheuristic optimisation technique. This paper introduces a novel method for computing the DM based on grey wolf optimisation (GWO), specifically for the constant time delay. In the proposed method, GWO is employed to optimise the minimum error of the spectral radius and to determine the best design variable of the crossing frequency. With the help of the proposed method, the sweeping range is no longer required, which improves the accuracy of the result. To evaluate the proposed method, a two-area network power system is considered as a case study. Furthermore, the effect of the PI controller gains on the DM is taken into account. The proposed method efficacy is demonstrated by comparing it with the most recently published methods. The results demonstrate that the proposed method is remarkably better than the existing methods found in the literature, where the smallest percentage inaccuracy using the simulation-based DM based on GWO is found to be 0.000%.

The Tracking of Derivative Discontinuities for Delay Fractional Equations Based on Fitted L1 Method

Abstract In this paper, the analytic solution of the delay fractional model is derived by the method of steps. The theoretical result implies that the regularity of the solution at s + {s^{+}} is better than that at 0 + {0^{+}} , where s is a constant time delay. The behavior of derivative discontinuity is also discussed. Then, improved regularity solution is obtained by the decomposition technique and a fitted L ⁢ 1 {L1} numerical scheme is designed for it. For the case of initial singularity, the optimal convergence order is reached on uniform meshes when α ∈ [ 2 3 , 1 ) {\alpha\in[\frac{2}{3},1)} , α is the order of fractional derivative. Furthermore, an improved fitted L ⁢ 1 {L1} method is proposed and the region of optimal convergence order is larger. For the case t > s {t>s} , stability and min ⁡ { 2 ⁢ α , 1 } {\min\{2\alpha,1\}} order convergence of the fitted L ⁢ 1 {L1} scheme are deduced. At last, the numerical tests are carried out and confirm the theoretical result.

A Comparison of Video Performance Feedback and Self-Monitoring Strategies to Improve Pre-Service Teachers’ Implementation of Systematic Instruction

Teacher preparation programs play an important role in preparing future special education teachers in the implementation of evidence-based interventions for students with disabilities. The purpose of this study was to examine the social validity and effects of two training strategies––video performance feedback and self-monitoring—on systematic instruction implementation of 51 pre-service special education teachers enrolled in a cross-categorical program. Systematic instruction implementation focused on two common response prompting systems––constant time delay and system of least prompts––across discrete and chained skills. Our findings indicate that, overall, both training strategies were effective in improving pre-service teachers’ systematic instruction implementation. Across both training strategies and response prompting systems, there were significant gains in implementation when used to teach chained skills. Additionally, pre-service teachers found both training strategies effective and feasible. We present implications for teacher preparation and future research directions.

Stability and Bifurcation Analysis of the Caputo Fractional-Order Asymptomatic COVID-19 Model with Multiple Time-Delays

Throughout the last few decades, fractional-order models have been used in many fields of science and engineering, applied mathematics, and biotechnology. Fractional-order differential equations are beneficial for incorporating memory and hereditary properties into systems. Our paper proposes an asymptomatic COVID-19 model with three delay terms [Formula: see text] and fractional-order [Formula: see text]. Multiple constant time delays are included in the model to account for the latency of infection in a vector. We study the necessary and sufficient criteria for stability of steady states and Hopf bifurcations based on the three constant time-delays, [Formula: see text], [Formula: see text], and [Formula: see text]. Hopf bifurcation occurs in the addressed model at the estimated bifurcation points [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. The numerical simulations fit to real observations proving the effectiveness of the theoretical results. Fractional-order and time-delays successfully enhance the dynamics and strengthen the stability condition of the asymptomatic COVID-19 model.

The effect of the simultaneous Prompting–Constant time delay instructional sequence on the teaching of early academic skills to students with intellectual disabilities

This study investigated the effectiveness of combining simultaneous prompting (SP) and constant time delay (CTD) (hereafter SP–CTD instructional sequence) in teaching early academic skills to five students with intellectual disabilities (ID). A multiple-probe design was used to examine the functional relationship between the SP and CTD instructional sequence and the acquisition of letter–sound correspondences and number recognition. The results showed the effectiveness of the procedure, as all students acquired their target skills in 7–12 sessions, with an average error rate of 8%. Maintenance effects were assessed at 2, 6, and 10 weeks after the intervention to measure participants’ retention of these acquired skills. Three students preserved their skills with 100% accuracy, while two students did so with more than 90% accuracy. The data indicate that instruction consisting of probe trials, 0-s trials, and 5-s trials leads to improvements in early academic skills among students with ID.

A stochastic delayed SIS epidemic model with Holling type II incidence rate

In this article, a stochastic SIS epidemic model with constant time delay and Holling type II incidence rate is investigated. We firstly show the existence, uniqueness, and moment boundedness of the global positive solution. Then we extend the initial value space to a complete nonnegative continuous function space and obtain the existence of invariant measures for this system. Furthermore, the analysis of the asymptotic behavior around the disease-free equilibrium is given. To demonstrate, some numerical examples are provided to illustrate our results.

Mittag-Leffler Stability of Impulsive Nonlinear Fractional-Order Systems with Time Delays.

Stability analysis of impulsive nonlinear fractional-order system (FOS) is discussed. First, the existence and uniqueness of solutions for FOS is discussed with help of fixed point theory. The nonlinear system is considered with a constant time delay and impulsive effects. Then, novel sufficient conditions to prove the Mittag-Leffler stability (MLS) of FOS are established by using well known mathematical techniques. Also, the results are extended to present finite-time MLS conditions for considered nonlinear FOSs. Finally, examples are given to show the validity of the derived results.