Terms Of Time Delay Research Articles

Exponential Stability of a Kirchhoff Plate Equation with Structural Damping and Internal Time Delay

In this manuscript, we investigate the exponential stability of a Kirchhoff plate equation with free boundary conditions in a bounded domain of R2. First, we consider the case where the model is subjected only to structural damping and, using the energy method, we prove the exponential decay of the energy associated with this model. Second, we consider the case where structural damping with a linear internal time delay term is applied, and we use the same technique to derive the exponential stability of the new model. Finally, we examine the scenario where the model is governed by structural damping with an added fractional time delay term and, by constructing an appropriate Lyapunov function, we show that the energy associated with the system is exponentially stable. This work improves upon prior results concerning the Kirchhoff plate equation with frictional damping, where exponential stability could not be achieved.

Novel reachable set estimation results for delayed linear systems with bounded disturbance

Reachable set estimation is a prominent research topic in control theory and systems science. Reachable set estimation for time-delay systems has drawn a lot of interest. Until now, most approaches to the reachable set estimation problem of time-delay systems have involved building intricate Lyapunov functionals and utilizing LMI techniques. This has resulted in complicated LMI conditions and a proof procedure. The reachable set estimation issue for delayed linear systems with bounded disturbance will be reviewed in this paper. A novel reachable set estimation lemma with a time-delay term is proposed, and based on the acquired lemma, a sufficient condition is given to bound the reachable set estimation of the systems under discussion. In addition, an event-based sufficient criterion for reachable set estimation is also provided. The theoretical analysis in this paper is succinct when compared to previous findings, and the obtained conditions are simple to validate. Lastly, two examples are presented to confirm that the theoretical results hold true.

Energy-dependent intrinsic time delay of gamma-ray bursts on testing Lorentz invariance violation

High-energy photons of gamma-ray bursts (GRBs) might be emitted at different intrinsic times with energy dependence at the source. In this letter, we expand the model from previous works on testing the Lorentz Invariance Violation (LV) with the observed GRB data from the Fermi Gamma-ray Space Telescope. We reanalyze the previous data with the full Bayesian parameter estimation method and get consistent results by assuming that the time delays are due to an LV term and a constant intrinsic time delay term. Subsequently, we neglect the LV effect and only consider the intrinsic time delay effect. We assume a common intrinsic time delay term along with a source energy correlated time delay of high-energy photons. We find that the energy-dependent emission times can also explain the observed GRB data of high-energy photon events. Finally, we integrate these two physical mechanisms into a unified model to distinguish and evaluate their respective contributions using the observed GRB data.

PD distributed control and stability analysis for DC microgrids with multiple time delays

Distributed control is widely used for coordination of multiple distributed generations (DGs) in a microgrid (MG), but the information transmission in practice is inevitably suffered from time delays, which will deteriorate system performance and even cause system instability. To solve this problem, a proportional-differential (PD) distributed control method for DC MGs is proposed in this paper. Firstly, a small-signal system model considering multiple time delays including measurement delay and communication delay is established. The introduction of time-delayed differential terms results in the system being transformed into a neutral time-delayed system (NTDS). Then, the time delay margin (TDM) under different delayed scenarios is accurately determined by the frequency-domain stability analysis, and the relationship between the TDM and the differential gain is quantified. Compared with the conventional proportional (P-type) distributed control method, the TDM is enhanced effectively. In addition, an indicator is proposed to quantify the enhancement effect of introducing differential terms on TDM. Finally, the effectiveness of the proposed method and the accuracy of the stability analysis are verified by simulation and hardware-in-loop (HIL) tests.

Dynamics and stability analysis of enzymatic cooperative chemical reactions in biological systems with time-delayed effects

The mathematical modeling and dynamic analysis of time-delayed enzymatic chemical reactions in biological systems are presented in this research. The objective is to examine the function of time lags in these reactions and to get a complete knowledge of the behavior of biological systems in a reaction to modifications in the quantity present of reactants and products. The model, which is based on delay differential equations, includes a time delay term to account for the lag between changes in the concentration of reactants, reaction rate constants and product responses. The findings give insight into how enzymatic processes behave dynamically and how stability is impacted by time lags, oscillation and general efficiency of the system. These results have significant importance for our comprehension of how biological processes are regulated and for the creation of biological control structures.

Adaptive command filter control for switched time‐delay systems with dead‐zone based on an exact disturbance observer

AbstractThe focus of this article lies in the adaptive command filter tracking control problems for a class of switched time‐delay systems with an asymmetric dead‐zone and external disturbance under arbitrary switching. First, the external disturbance is estimated via an exact disturbance observer. Then, an echo state network (ESN) was adopted to approximate unknown function in system without tuning the weights between a reservoir and an input layer. Second, the time‐varying input of the dead‐zone model is considered as uncertain physical quantity of the system based on the dead‐zone slope boundary information. Third, an adaptive command filtered controller is employed to conquer the matter of “explosion of complexity” encountered in the traditional backstepping method. The filtering errors present in a dynamic surface control (DSC) approach are effectively eliminated by means of error compensation signals. A prescribed performance control (PPC) is resorted to confine the system output to meet prescribed steady‐state and transient tracking performances. The time delay terms are compensated by a Lyapunov–Krasovskii functional. The semi‐globally ultimately uniformly boundedness of all states in the closed‐loop system is ensured by the Liapunov's stability criterion. Finally, the validity of the developed control scheme is further verified through a simulation example.

Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers.

In order to handle second order lead processes with time delay, this paper provides a unique dominant pole placement based filtered PID controller design approach. This method does not require any finite term approximation like Pade to obtain the quasi-polynomial characteristic polynomial, arising due to the presence of the time delay term. The continuous time second order plus time delay systems with zero (SOPTDZ) are discretized using a pole-zero matching method with specified sampling time, where the transcendental exponential delay terms are converted into a finite number of poles. The pole-zero matching discretization approach with a predetermined sampling period is also used to discretize the continuous time filtered PID controller. As a result, it is not necessary to use any approximate discretization technique, such as Euler or Tustin, to derive the corresponding discrete time PID controller from its continuous time counterpart. The analytical expressions for discrete time dominant pole placement based filtered PID controllers are obtained using the coefficient matching approach, while two distinct kinds of non-dominant poles, namely all real and all complex conjugate, have been taken into consideration. The stabilizable region in the controller and design parameter space for the chosen class of linear second order time delay systems with lead is numerically approximated using the particle swarm optimization (PSO) based random search technique. The efficacy of the proposed method has been validated on a class of SOPTDZ systems including stable, integrating, unstable processes with minimum as well as non-minimum phase zeros.

Existence of Mild Solutions to Delay Diffusion Equations with Hilfer Fractional Derivative

Because of the prevalent time-delay characteristics in real-world phenomena, this paper investigates the existence of mild solutions for diffusion equations with time delays and the Hilfer fractional derivative. This derivative extends the traditional Caputo and Riemann–Liouville fractional derivatives, offering broader practical applications. Initially, we constructed Banach spaces required to handle the time-delay terms. To address the challenge of the unbounded nature of the solution operator at the initial moment, we developed an equivalent continuous operator. Subsequently, within the contexts of both compact and non-compact analytic semigroups, we explored the existence and uniqueness of mild solutions, considering various growth conditions of nonlinear terms. Finally, we presented an example to illustrate our main conclusions.

Research and Application of Two-Dimensional Time-Delayed Tri-Stable Stochastic Resonance System for Bearing Fault Detection

The time-delayed feedback term can improve the output of a system, while the two-dimensional stochastic resonance (SR) system has a stronger signal amplification capability. To improve the output signal-to-noise ratio (SNR) of the system, this paper proposes a two-dimensional time-delayed tri-stable stochastic resonance system (TDTDTSR) based on the advantages of the above two systems. First, the steady-state probability density function (SPD), the mean first-pass time (MFPT), and the output SNR are derived under adiabatic approximation theory, and the effects of different system parameters on them are investigated. Next, TDTDTSR and the classical two-dimensional tri-stable stochastic resonance system (CTDTSR) system are simulated numerically. The results show that the mean signal-to-noise gain (MSNRG) of TDTDTSR system is higher than that of the CTDTSR system. Finally, the system parameters are optimized using a genetic algorithm, and the application of TDTDTSR to bearing fault detection is compared with CTDTSR and the novel piecewise symmetric two-dimensional tri-stable stochastic resonance (NPSTDTSR) systems. The experimental results demonstrate that TDTDTSR system has better performance, providing valuable theoretical support and practical engineering applications for the system in subsequent analyses.

Improved results for T-S fuzzy systems with two additive time-varying delays via an extended binary quadratic function negative-determination lemma

This paper is concerned with the stability and stabilization problems for T-S fuzzy systems with two additive time-varying delays. Firstly, a novel Lyapounov-Krasovskii functional (LKF) is constructed by delay-product-type functional method together with the state vector augmentation. In order to handle time-delay square terms introduced into the derivative of LKF, an extended binary quadratic function negative-determination lemma is proposed. A less conservative delay-dependent stability condition is developed since not only some new bounding technologies are employed to deal with integral terms, but also the proposed lemma is employed to dispose nonlinear time-delay terms in derivative of constructed function. Then, the corresponding controller design method for closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, four numerical examples are given to illustrate the superiority and effectiveness of the proposed criteria.

An iterative method to solve the time delay optimal control problem with bounded control variable

This paper presents an iterative approach for solving the optimal control problem (OCP) with time-delayed terms and bounded control variables. The projection function is used to construct the iterative method to approximate the control law. Employing the approximation of control law the approximation of state and the co-state variables are obtained. To the best of our knowledge, this paper is the first attempt to solve bounded and delayed OCPs with a projection function. The convergence theorem for the proposed method is also proven. Several numerical examples are added, showing the developed method's effectiveness to solve the time-delayed OCPs with bounded control variables.

Analysis of the free boundary problem of vascular tumor growth with periodic nutrient supply and time delay terms

Analysis of the free boundary problem of vascular tumor growth with periodic nutrient supply and time delay terms

Adaptive command filtered control for a class of nonlinear time delay systems with extreme learning machine

AbstractIn this paper, an extreme learning machine (ELM)‐based adaptive command filtered control method is investigated for a class of strict feedback nonlinear systems with unknown external disturbances and time delay. To begin with, the original system state equation is transformed into a new form on account of coordinate transformation. Subsequently, an ELM is adopted to approximate unknown functions which exist in the whole system states, without any prior knowledges of the ideal weight vectors and approximation errors. Secondly, a command filter is developed for the system under consideration, which can avoid the probem of “explosion of complexity” caused by repeated derivation of virtual control signals in traditional backstepping control. Meanwhile, error compensation signals are designed to conquer the shortcoming of a dynamic surface control (DSC) method. The combination of ELM and command filter technique has been used to construct corresponding controllers and adaptive laws. Effective handling of the impact of time delay terms is ensured through designing a novel Lyapunov–Krasovskii functional. The proposed strategy guarantees boundedness of all signals in the closed‐loop system and the tracking error asymptotically converges to a compact set around the origin. In the end, two continuous stirred tank reactors (CSTRs) are taken as example to further verify the efficiency of the put forward control method.

Stochastic analysis and vibration suppression of a time-delayed system with nonlinear energy sink

Nonlinear energy sink (NES) is of great significance in attenuating structural vibration. Time-delay phenomenon in a mechanical system is inevitable. Different from existing works, the influences of time-delayed factors in a nonlinear oscillator attached with NES are considered in this paper under Gaussian white noise (GWN). Firstly, the time-delayed term is transformed into a linear combination of stiffness and damping terms, and an equivalent system without the time-delayed term is obtained. Stationary probability density function (SPDF) is deduced by leveraging stochastic averaging method. Secondly, good agreement is observed between analytical and numerical results, which verifies the effectiveness of the method. Furthermore, bifurcation conditions for the amplitude of SPDF of the primary system are obtained, indicating that delayed time, feedback gain and damping coefficients can cause stochastic P-bifurcation of the primary system. Finally, the vibration suppression performance of NES is analyzed via energy variation and the time–history diagram of displacement.

A novel dynamic grey multivariate prediction model for multiple cumulative time-delay shock effects and its application in energy emission forecasting

Energy emission systems are often influenced by external information and policy shock. However, conventional grey models ignore the existence of the impact of multiple shock events and cumulative time-delay effects, which are crucial for achieving accurate forecasts. From a dynamic perspective, we aim to establish a multivariable grey prediction model considering the impact of multiple shock events, namely MSGTDM(1,N) model. Specifically, to accurately describe the impact of different types of external shocks on the system, three kinds of nonlinear dynamic shock functions are designed, including growth dynamic shock function, decline dynamic shock function, and slope dynamic shock function. Based on this, multi-dimensional instantaneous shock utility terms and cumulative time-delay utility terms are constructed to accurately measure shock effects. And Whale Optimization Algorithm is employed to determine the optimal parameters of the shock functions through comprehensive comparative analysis. The findings affirm the MSGTDM(1,N) model's higher predictive accuracy and validity. Consequently, the forecast results of China's carbon emissions from coal and natural gas consumption in 2022–2025 provide a reliable basis for adjusting the energy structure and implementing the “dual-carbon” policy effectively.

Low-order modeling of collective dynamics of four ring-coupled turbulent thermoacoustic oscillators

We investigate the low-order modeling of collective dynamics in a can-annular combustor consisting of four ring-coupled turbulent lean-premixed combustors. Each combustor is treated as an individual thermoacoustic oscillator, and the entire combustion system is modeled using four Van der Pol oscillators ring-coupled with dissipative, time-delay, and reactive coupling terms. We show that this model, despite its simplicity, can reproduce many collective dynamics observed in experiments under various combinations of equivalence ratios and combustor lengths, such as 2-can anti-phase synchronization, alternating anti-phase synchronization, pairwise anti-phase synchronization, spinning azimuthal mode, and 4 steady thermoacoustic oscillators. The phase relationship in the majority of cases can be quantitatively modeled. Moreover, by incorporating a reactive coupling term, the model is able to reproduce the frequency shift observed experimentally. This study demonstrates the feasibility of using a simple low-order model to reproduce collective dynamics in complex turbulent combustion systems. This suggests that this model could be used (i) to facilitate the interpretation of experimental data within the synchronization framework, (ii) to identify potential parameter regimes leading to amplitude death, and (iii) to serve as a basis for modeling the collective dynamics observed in more complicated multi-combustors.

Layer-wise multi-defect detection for laser powder bed fusion using deep learning algorithm with visual explanation

In Laser Powder Bed Fusion (LPBF), it is a major challenge to obtain detailed spatial information on different powder bed defects in real-time and simultaneously. Deep Learning (DL) algorithms under the field of Machine Learning (ML) have promoted the intelligent development of the powder bed defect detection method. However, they still need to be further evaluated in terms of detection accuracy and time delay, training data overhead, and model robustness under complex environments. Also, the DL model usually treated as a black-box demands further explanation. Herein, three advanced DL models are constructed using bounding boxes to locate multi-defects quickly and accurately for the powder spreading of LPBF. High detection accuracy is achieved with limited training samples through both data augmentation aiming at expanding image samples and model-based Transfer Learning (TL) used for transferring from the source domain to the target domain by reusing trained models. Further, the data augmentation method is employed to generate low-resolution images with interference to test the robustness of the detection model in harsh environments. Besides, visual feature maps and saliency maps were generated with the Detector Randomized Input Sampling for Explanation (D-RISE) method to help understand the validity of the defect detection process of the DL model. Overall, this work shows that the proposed multi-defect detection algorithms can provide comprehensive information on powder bed defects accurately and quickly.

Структура и элементная база приёмо-передающего модуля для организации подводной оптической беспроводной системы передачи данных

In the paper, the results of theoretical study of a wireless optical data transmission channel, as well as experimental study of its characteristics, taking into account different configurations of the optical component base of receiving and transmitting modules, were presented. The model of the wireless underwater optical communication channel with pulse-position modulation (4 bits per symbol) of digital data traffic with 100 Mbps is proposed. The model showed that to organize a communication channel on a 10 m path, the use of an array of light-emitting diodes (LEDs) is requires (the amount is up to 20 LEDs). For this case, a sufficiently large route budget will be provided, even with additional factor that reduce the efficiency of light propagation in seawater. The LEDs were chosen to organize the data transmission channel, since they have a wide radiation pattern and allow the implementation of a relatively simple driver circuit. The required optical radiation power is realized with the use of an array of LEDs. Schematic diagrams of the LEDs driver and power supply for the receiving and transmitting modules have been designed. A measuring layout with optical transmitter and receiver blocks has been implemented. The test signal is a regular sequence of pulses with a duty cycle of 2, and a frequency of 1 MHz. In the receiving module, the signal from the output of the pin photodiode is amplified using a wideband operational amplifier. Sets of 3 pin photodiodes and 10 LEDs were selected and tests were carried out to determine options for optical components that provide the best time characteristics of the output electrical signal in terms of delay time, rising and falling edges of pulses in a wireless optical airborne communication channel. Also, measurements were done on an air path with a length of 0.25-3 m using one or two LEDs as part of the transmitting module. It has been experimentally confirmed that the organization of a communication channel with a length of up to 10 m requires about 15-20 light-emitting diodes. Further study involves the designing and testing of a driver for the LEDs array and a prototype transceiver module.

Algebraic tools in autotuning design

Autotuners represent a combination of a relay feedback identification test and some control design method. In this contribution, models with up to three parameters are estimated by means of a single asymmetrical relay experiment. Then a stable low order transfer function with a time delay term is identified by a relay experiment. Autotuning principles then combine asymmetrical relay feedback tests with a control synthesis. Two algebraic control syntheses then are presented in this paper. The first one is based on the ring of proper and stable rational functions RPS. The second one utilizes a special ring RMS, a set of RQ-meromorphic functions. In both cases, controller parameters are derived through a general solution of a linear Diophantine equation in the appropriate ring. A final controller can be tuned by a scalar real parameter m>0. The presented philosophy covers a generalization of PID controllers and the Smith-like control structure. This contribution deals with the implementation of proposed autotuners and presents some illustrative examples.

Tracking control for a class of fractional order uncertain systems with time-delay based on composite nonlinear feedback control

<abstract><p>In this paper, we dealt with the tracking control problem of a class of fractional-order uncertain systems with time delays. In order to handle the effects brought by the uncertainties, external disturbances, time-delay terms, and to overcome the obstacles caused by inputs saturation, the tracking controller, which consisted of linear control law, nonlinear law, and robust control law proposed in this paper, was designed by combining the composite nonlinear feedback control method and the properties of fractional order operators. Furthermore, the validation of this tracking controller was proved.</p></abstract>