Small Time Delay Research Articles

Second-Order Integral Sliding Mode Control for Uncertain Systems With Control Input Time Delay Based on Singular Perturbation Approach

This note proposes a robust integral sliding mode (RISM) manifold and a corresponding design method for stabilization control for uncertain systems with control input time delay. Delay-independent sufficient condition for the existence of the RISM surface is given in terms of LMI. An improved sliding mode control (SMC), which is delay-dependent and suitable for small input time delay, keeps system stay on the neighborhood of the RISM surface in finite time. With uncertainties and disturbances, the reaching condition for the neighborhood of the RISM is satisfied. Furthermore, the control makes second-order sliding mode. Based on a numerical example, the proposed method is verified to be efficient and feasible.

Impact of Delays for Electric Vehicles With Direct Yaw Moment Control

This paper investigates the impact of time delay factors on the lateral motion of electric vehicles with direct yaw moment control (DYC). The existence of internal time delay factors is inescapable in electric vehicle (EV) systems, which might affect the effectiveness of DYC. Computer simulation shows that DYC works well at small time delays, while significant oscillation or even loss of stability occurs when the delays are large enough. A frequency-domain method is used to determine the stability limit of the time-delayed system.

Large-time dynamics of the asymptotic Lohe model with a small time-delay

We study the asymptotic behavior of an ensemble of identical Lohe oscillators on the unit sphere in the presence of small time delay interaction effects. When there is no time delay, the ensemble of identical Lohe oscillators collapses asymptotically to a one-cluster ensemble on the sphere; its asymptotic dynamics are governed by linear motion on the unit sphere with a constant natural velocity. We show that the presence of a small time delay can induce rich dynamical features such as asymptotic changes in the velocity and asymptotic low-dimensional dynamics in high-dimensional cases. For d = 1, the Lohe dynamics is equivalent to the Kuramoto dynamics via polar coordinates. In this case, the modified asymptotic frequency is uniquely determined by an implicit relation based on the natural frequency, coupling strength, and time delay. For d = 3, we show that the dynamics of identical Lohe oscillators converges to the Kuramoto dynamics for properly chosen initial configurations. We also provide several numerical simulations to confirm our analytical results.

Hysteresis model and adaptive vibration suppression for a smart beam with time delay

This paper mainly presents experimental verifications of vibration suppression for a cantilever beam bonded with a piezoelectric actuator by an adaptive controller. Using the Hamilton Principle and the Bouc–Wen Equation, a dynamical mathematical model is proposed to describe a hysteresis property with different time delay for the smart beam. It is concluded that the hysteresis characteristic of the smart beam is influenced not only by the amplitude and frequency of the input voltage but also by the time delay. Based on the nonlinear model, the adaptive controller with time delay is adopted to attenuate the free vibration of the smart beam. Through some simulations and experiments, the vibration suppression effect can be improved with a proper small time delay in the control system. Moreover, the vibration amplitude attenuation rates at the fundamental frequency with the simulations and the experiments are up to 85.938% and 84.505% respectively. Obviously the adaptive regulator with a proper small time delay is proved to have the capacity of improving the vibration suppression effect.

Ultrafast photoelectron spectroscopy of solutions: space-charge effect

The method of time-resolved XUV photoelectron spectroscopy is applied in a pump–probe experiment on a liquid micro-jet. We investigate how the XUV energy spectra of photoelectrons are influenced by the space charge created due to ionization of the liquid medium by the pump laser pulse. XUV light from high-order harmonic generation is used to probe the electron population of the valence shell of iron hexacyanide in water. By exposing the sample to a short UV pump pulse of 266 nm wavelength and ∼55 fs duration, we observe an energy shift of the spectral component associated with XUV ionization from the Fe 3d(t2g) orbital as well as a shift of the water spectrum. Depending on the sequence of the pump and probe pulses, the arising energy shift of photoelectrons acquires a positive or negative value. It exhibits a sharp positive peak at small time delays, which facilitates to determine the temporal overlap between pump and probe pulses. The negative spectral shift is due to positive charge accumulated in the liquid medium during ionization. Its dissipation is found to occur on a (sub)nanosecond time scale and has a biexponential character. A simple mean-field model is provided to interpret the observations. A comparison between the intensity dependencies of the spectral shift and the UV ionization yield shows that the space-charge effect can be significantly reduced when the pump intensity is attenuated below the saturation level of water ionization. For the given experimental conditions, the saturation intensity lies at W cm−2.

Stochastic dynamical characteristics for a time-delayed insect outbreak model driven by correlated multiplicative and additive noises

In this paper, we numerically investigate the stability and transient properties of an insect outbreak model driven by correlated multiplicative, additive Gaussian noises and time delay. By using the Fokker–Planck equation, the small time delay method and the fast descent method, we analyze the mean reproduction and decline time of the insect growth system. Numerical results show that the resonant phenomenon of maximization of the mean first-passage time (MFPT) appears due to the joint action of all kinds of noises and time delay. It can hold down the insect population transfer from the stable state of a small number to the large one, enhance effectively the stability of the system and further inhibit the expansion of the insect population to increase noises intensities and time delay. In the process of restraining the expansion of the insect population, the increase of the association noise strength caused by the intrinsic noise and the extrinsic noise, and time delay make a beneficial contribution to restraining the outbreak of the insect population. Analogously, the appropriate multiplicative and additive noise intensities can play a positive role in the inhibition of pests. On the contrary, during the process of destroying a large number of insects, the increase of all noises and time delay can produce positive effects on controlling a plague of insects.

Enhancement of mobility in an interacting colloidal system under feedback control.

Feedback control schemes are a promising way to manipulate transport properties of driven colloidal suspensions. In the present article, we suggest a feedback scheme to enhance the collective transport of colloidal particles with repulsive interactions through a one-dimensional tilted washboard potential. The control is modeled by a harmonic confining potential, mimicking an optical "trap," with the center of this trap moving with the (instantaneous) mean particle position. Our theoretical analysis is based on the Smoluchowski equation combined with dynamical density functional theory for systems with hard-core or ultrasoft (Gaussian) interactions. For either type of interaction, we find that the feedback control can lead to an enhancement of the mobility by several orders of magnitude relative to the uncontrolled case. The largest effects occur for intermediate stiffness of the trap and large particle numbers. Moreover, in some regions of the parameter space the feedback control induces oscillations of the mean velocity. Finally, we show that the enhancement of mobility is robust against a small time delay in implementing the feedback control.

Substorm evolution of auroral structures

AbstractAuroral arcs are often associated with magnetically quiet time and substorm growth phases. We have studied the evolution of auroral structures during global and local magnetic activity to investigate the occurrence rate of auroral arcs during different levels of magnetic activity. The ground‐magnetic and auroral conditions are described by the magnetometer and auroral camera data from five Magnetometers — Ionospheric radars — All‐sky cameras Large Experiment stations in Finnish and Swedish Lapland. We identified substorm growth, expansion, and recovery phases from the local electrojet index (IL) in 1996–2007 and analyzed the auroral structures during the different phases. Auroral structures were also analyzed during different global magnetic activity levels, as described by the planetary Kp index. The distribution of auroral structures for all substorm phases and Kp levels is of similar shape. About one third of all detected structures are auroral arcs. This suggests that auroral arcs occur in all conditions as the main element of the aurora. The most arc‐dominated substorm phases occur in the premidnight sector, while the least arc‐dominated substorm phases take place in the dawn sector. Arc event lifetimes and expectation times calculated for different substorm phases show that the longest arc‐dominated periods are found during growth phases, while the longest arc waiting times occur during expansion phases. Most of the arc events end when arcs evolve to more complex structures. This is true for all substorm phases. Based on the number of images of auroral arcs and the durations of substorm phases, we conclude that a randomly selected auroral arc most likely belongs to a substorm expansion phase. A small time delay, of the order of a minute, is observed between the magnetic signature of the substorm onset (i.e., the beginning of the negative bay) and the auroral breakup (i.e., the growth phase arc changing into a dynamic display). The magnetic onset was observed to precede the structural change in the auroral display. A longer delay of a few minutes was found between the beginning of the growth phase and the first detected auroral structure.

Designing and Implementing a Portable Near-Infrared Imaging System for Monitoring of Human's Brain Functional Activity1

Designing and Implementing a Portable Near-Infrared Imaging System for Monitoring of Human's Brain Functional Activity1

Particle formation and its control in dual frequency plasma etching reactors

The behavior of a particle cloud in plasma etching reactors at the moment when radio frequency (RF) power changes, that is, turning off and transition steps, was observed using the laser-light-scattering method. Two types of reactors, dual-frequency capacitively coupled plasma (CCP) and the hybrid CCP/inductively coupled plasma (ICP), were set up for experiments. In the hybrid CCP/ICP reactor (hereafter ICP reactor), the position and shape of the cloud were strongly dependent on the RF frequency. The particle cloud becomes larger and approaches the electrode as the RF frequency increases. By turning the lower frequency power off later with a small delay time, the particle cloud is made to move away from the electrode. Maintaining lower frequency RF power only was also helpful to reduce the particle cloud size during this transition step. In the ICP reactor, a sufficient bias power is necessary to make a particle trap appear. A similar particle cloud to that in the CCP reactor was observed around the sheath region of the lower electrode. The authors can also use the low-frequency effect to move the particle cloud away from the substrate holder if two or more bias powers are applied to the substrate holder. The dependence of the particle behavior on the RF frequencies suggests that choosing the proper frequency at the right moment during RF power changes can reduce particle contamination effectively.

Characteristics of the Energetic Igniters Through Integrating B/Ti Nano-Multilayers on TaN Film Bridge.

The energetic igniters through integrating B/Ti nano-multilayers on tantalum nitride (TaN) ignition bridge are designed and fabricated. The X-ray diffraction (XRD) and temperature coefficient of resistance (TCR) results show that nitrogen content has a great influence on the crystalline structure and TCR. TaN films under nitrogen ratio of 0.99 % exhibit a near-zero TCR value of approximately 10 ppm/°C. The scanning electron microscopy demonstrates that the layered structure of the B/Ti multilayer films is clearly visible with sharp and smooth interfaces. The electrical explosion characteristics employing a capacitor discharge firing set at the optimized charging voltage of 45 V reveal an excellent explosion performance by (B/Ti)n/TaN integration film bridge with small ignition delay time, high explosion temperature, much more bright flash of light, and much large quantities of the ejected product particles than TaN film bridge.

Delayed feedback induced multirhythmicity in the oscillatory electrodissolution of copper.

Occurrence of bi- and trirhythmicities (coexistence of two or three stable limit cycles, respectively, with distinctly different periods) has been studied experimentally by applying delayed feedback control to the copper-phosphoric acid electrochemical system oscillating close to a Hopf bifurcation point under potentiostatic condition. The oscillating electrode potential is delayed by τ and the difference between the present and delayed values is fed back to the circuit potential with a feedback gain K. The experiments were performed by determining the period of current oscillations T as a function of (both increasing and decreasing) τ at several fixed values of K. With small delay times, the period exhibits a sinusoidal type dependence on τ. However, with relatively large delays (typically τ ≫ T) for each feedback gain K, there exists a critical delay τcrit above which birhythmicity emerges. The experiments show that for weak feedback, Kτcrit is approximately constant. At very large delays, the dynamics becomes even more complex, and trirhythmicity could be observed. Results of numerical simulations based on a general kinetic model for metal electrodissolution were consistent with the experimental observations. The experimental and numerical results are also interpreted by using a phase model; the model parameters can be obtained from experimental data measured at small delay times. Analytical solutions to the phase model quantitatively predict the parameter regions for the appearance of birhythmicity in the experiments, and explain the almost constant value of Kτcrit for weak feedback.

Bifurcation analysis of a mathematical model for genetic regulatory network with time delays

In this paper, we aim to investigate the dynamics of a gene regulatory network which is a time-delayed version of the model proposed by Elowitz and Leibler [Nature 403 (2000) 335–338]. Based on the normal form theory and center-manifold reduction, Hopf bifurcations including the bifurcation direction and stability of the bifurcated periodic orbits are investigated. We also discuss effects of transcriptional rate and time delay on the amplitude and period of the oscillation of the network. It shows that variations of time delay or transcriptional rate can change the period and amplitude of the oscillation. More precisely, (i) the amplitude increases with small time delay, while the change of amplitude is not sensitive to relatively large time delay. However, the robustness of amplitudes is not true any more for the case of using the transcriptional rate as parameter, where amplitude always increases quickly and linearly with the transcriptional rate; (ii) the period of oscillation increases as the time delay increases, but it grows up initially as the transcriptional rate increases and then keeps unchanged to certain constant value, which implies that the robustness of period to the transcriptional rate variations occurs. Our numerical simulations also support the theoretical conclusions, namely both suggest that time delay and transcriptional rate can be used as control parameters in genetic regulatory networks.

Time delay control of hysteretic composite plate

Due to boosting usage of flexible and damping materials, it is of great significance for both science and engineering to explore active control methods for vibration within time-delayed hysteretic structures. This paper conducts theoretical and experimental research on a time-delayed controller for a flexible plate with a single-layer rubber glued on its back. First of all, the dynamic equation for a composite plate is given on the base of the Kirchhoff–Love assumption, where damping-restoring force is described by the Bouc–Wen hysteresis model. Then, the influence of time delay is taken into account and the state equation of the plate with time delay is obtained. Next, a standard state equation, with implicit time delay, is derived using one specific form of integral transformation and vector augmentation. Finally, an instantaneous optimal control method is used to design an active controller. This controller does not only involve state feedback of the current step, but also a linear addition of former state feedbacks within several steps. In order to verify this method, experimental work is conducted. Problems encountered like differential computation and lifting of displacement signal are also handled. According to a comparison between simulations and experiments, the control method given in this paper is feasible and valid, and it is available for both small and large time delay.

Time-delay effects on mixed-mode oscillations of modified chua’s system

Time-delay effects on the complex dynamics MMOs of modified chua’s system are investigated in the present paper. As the time delay varies, the change of the structure of the slow manifold is figured out firstly by using the method of stability switch. And then, on basis of the geometric singular perturbation theory, the time-delay effects on MMOs are stated. It is shown small time delay can only influence the patterns of small-amplitude oscillations; however, large time delay can eliminate the MMOs by destroying the canard explosion phenomenon and the special global return mechanism. In particular, the mechanism of time-delay-induced transitions from MMOs to complex oscillations and to bursting oscillations is stated.

Stability and mean extinction time for a metapopulation system subjected to two kinds of time delays and associated multiplicative and additive noises

In this paper, the stability and the mean extinction time for a double time-delayed metapopulation system driven by associated multiplicative and additive noises are investigated. By using the Fokker–Planck equation, the fast descent method and the method of small time delay, we obtain the expressions of stationary probability distribution and the mean extinction time. The numerical results demonstrate that the multiplicative, additive noises and time delay θ can destroy the stability of the system. Whereas, the associated noise and time delay τ can consolidate the population system. Meanwhile, the resonant phenomenon of the mean first-passage time (MFPT) occurs in the metapopulation system due to the joint action of different types of noises and time delays. The increase of the strength of associated noise and time delay τ can effectively prolong the extinction time of the metapopulation. Inversely, the additive noise plays a negative role in restraining the collapse of the population. On the other hand, the appropriate multiplicative noise intensity can also extend the life of the metapopulation system. However, the varying of time delay θ cannot change the maximum of the mean extinction time, but it could produce different effects on the MFPT under the conditions of different parameters.

Two degree of freedom control scheme for unstable processes with small time delay

In this work, a recently reported two degree of freedom control structure namely the Parallel Control Structure (PCS) is modified to achieve improved control performance for unstable processes. New tuning rules are proposed using a direct synthesis approach for unstable first order plus time delay (UFOPTD), unstable second order plus time delay (USOPTD) and integrating and unstable plus time delay (IUPTD) process models. The proposed method has two tuning parameters whose suitable values are recommended after studying their effect on the system performance and robustness. This is an advantage of the present work over the other reported control schemes where the authors provide suitable ranges of the tuning parameters values. Simulation examples show that the present scheme results in improved nominal and perturbed responses as compared to the recently reported methods. Also it is observed that satisfactory performance is achieved when the proposed tuning rules are applied on an isothermal chemical reactor which exhibits multiple steady state solutions.

Theoretical analysis of semiconductor ring lasers with short and long time-delayed optoelectronic and incoherent feedback

We report results on the asymptotic, bifurcation and numerical analysis of semiconductor ring lasers with negative optoelectronic feedback or incoherent optical feedback. We find that the dynamical behavior of both systems can be adequately described by two differential equations and one map with time delay on time-scales longer than the relaxation oscillations. On these timescales, the dynamics for both types of feedback is identical. We study the stationary solutions of this model and are able to obtain the analytical expressions of all local bifurcations. As we vary the feedback strength for small delay times comparable to the period of relaxation oscillations, the devices under consideration in the paper display both continuous wave operation and a period-doubling route to chaos. The intensities of two counter propagating modes of both systems exhibit in-phase chaotic behavior similar to single mode semiconductor lasers. However, for long delay times, the counter propagating modes show anti-phase chaotic oscillations. This anti-phase chaotic regime does not involve carrier dynamics and is a result of the bistable character of the semiconductor ring laser.

Robust Fractional Order Proportional Integral Control for Large Time-Delay System

In this paper, a new control method for large time delay system is proposed. Firstly, the decreasing time delay controller is used to remodel large delay time plant into small delay time plant. Then, a fractional robust proportional-integral controller (FOPI) is designed, using the phase margin and cut-off frequency at a specified point in the Bode plot of flat robust conditions, to guarantee the desired control performance and the robustness of the high order system to the gain order system. For comparison between the fractional order proportional integral controller and the traditional integer order PID (IOPID) controller, the IOPID controller is also designed following the same proposed tuning specifications. The simulation results indicates that the both designed controllers work efficiently. Furthermore, the FOPI controller makes the large time-delay system get better control effect, the system has high robustness, adaptive ability and anti-jamming ability.

Synchronization by small time delays

Synchronization is a phenomenon observed in all of the living and in much of the non-living world, for example in the heart beat, Huygens’ clocks, the flashing of fireflies and the clapping of audiences. Depending on the number of degrees of freedom involved, different mathematical approaches have been used to describe it, most prominently integrate-and-fire oscillators and the Kuramoto model of coupled oscillators. In the present work, we study a very simple and general system of smoothly evolving oscillators, which continue to interact even in the synchronized state. We find that under very general circumstances, synchronization generically occurs in the presence of a (small) time delay. Strikingly, the synchronization time is inversely proportional to the time delay.