Critical Time Delay Research Articles

Periodic Response and Stability of a Maglev System with Delayed Feedback Control Under Aerodynamic Lift

In this research, the periodic response and stability of a nonlinear maglev system under the combined effects of steady and unsteady aerodynamic lifts is investigated, considering time delay in the feedback control loop. First, a nonlinear maglev system with a single levitation point that accounts for the nonlinearity of the electromagnetic force, time delay in the feedback control loop, and effect of aerodynamic lift is established. Then the periodic solutions of the maglev system with aerodynamic lift and time delays are obtained by an incremental harmonic balance analysis, in which the explicit time-delay action matrices used indicate that the effect of time delay on the response of the maglev system is periodic. The stability of the periodic solutions based on a finite difference continuous time approximation method and Floquet theory is studied, from which the critical time delay is obtained. Also, the relationship between the periodic vibration amplitude and the time delay is examined, along with the steady aerodynamic lift coefficient, and frequency of the unsteady aerodynamic lift, as well as the variation of critical delay with respect to the position feedback and velocity feedback with the control gain parameters. In addition, the stability boundary for the simultaneous time-delayed position and velocity feedback is obtained.

Approximate and exact stability analysis of 1-DOF and 2-DOF single-actuator real-time hybrid substructuring

This paper presents approximate and exact stability analysis to determine the critical time delays of one and two degree of freedom (DOF) single-actuator real-time hybrid substructuring (RTHS). The approximate stability analysis is based on applying the Routh-Hurwitz stability criterion using a first-order Taylor expansion of the actuator dynamics represented by a constant gain and pure time delay. The exact stability analysis involves solving the critical frequencies first by canceling the exponential delay term of the closed-loop characteristic equation through multiplication by its complex conjugate. The exact critical time delays are then found using the phase of the closed-loop characteristic equation evaluated at the critical frequencies. These stability analysis techniques are applied to several 1-DOF and 2-DOF mass-spring configurations of single-actuator RTHS. Results show that the critical time delays are highly dependent on the mass, stiffness, and damping partitioning of the physical and numerical substructures as well as the actuator gain. This information provides useful insight into the stability behavior of a particular substructure partitioning configuration to evaluate the feasibility of conducting RTHS tests of these systems.

Essential Workflow and Performance Measures for Optimizing Acute Ischemic Stroke Treatment in India.

Essential Workflow and Performance Measures for Optimizing Acute Ischemic Stroke Treatment in India.

CYAD-101: An innovative non-gene edited allogeneic CAR-T for solid tumor cancer therapy.

3032 Background: In contrast to autologous CAR-T cell therapies, allogeneic donor-derived CAR-T cells can be banked and used in a timely fashion overcoming the critical time delay of just in time autologous cell manufacture. CYAD-101 is an allogeneic CAR-T that uses a non-gene edited peptide-based technology (TIM) to control graft versus host disease (GvHD) combined with a NKG2D-based CAR. Pre-clinical studies confirmed that CYAD-101 maintained CAR-directed anti-tumor activity in the absence of the induction of GvHD. Clinical grade CYAD-101 cells were produced for the phase 1 alloSHRINK trial (NCT03692429). Methods: A bank of clinical grade CYAD-101 cells was generated through two production runs using a single donor apheresis. Together, the bank generated > 53 billion CYAD-101 cells suitable for the entire dose escalation segment and short expansion phase of the trial (15 patients in total). Both runs showed high consistency with the CYAD-101 product generated composed mainly of CD4+ T cells (>85%) with a transduction level of > 92%, low relative expression of CD69/CD25 and largely absent expression levels of PD-1/LAG-3. The CYAD-101 cells were predominantly (>80%) CD45RA−/ CD62L−/ CD27− suggestive of an effector memory T cell population. Results: Upon co-culture with target K562 cells, CYAD-101 readily produced IFN-γ that was blocked by a NKG2D blocking antibody confirming specificity of the CAR. CYAD-101 cells showed in vitro cytotoxicity against tumor cells and produced an array of Th1 (IFN-γ, IL-2 and TGF-β) and Th2 (IL-4, IL-5) cytokines. Importantly, minimal IFN-γ was produced upon TCR stimulation while stimulation with a non-TCR mitogen (PMA + ionomycin) lead to high levels of IFN-γ. Together, these data show that clinical grade CYAD-101 cells were able to functionally respond through the CAR but showed minimal TCR-driven activation. Fifteen refractory metastatic CRC patients who had previously failed at least one line of oxaliplatin—containing therapy were treated with three doses of CYAD-101 cells given on Day 3 of three successive FOLFOX chemotherapy cycles. Updated clinical results continue to demonstrate an encouraging clinical activity (2 patients with partial response and 9 with stable disease) and the absence of GvHD in the context of CYAD-101 cell engraftment. Conclusions: These early clinical results demonstrate the safety and tolerability of a non-gene edited predominantly CD4+ CAR-T therapeutic approach. The initial observations of clinical activity in metastatic CRC patients warrants the continued development of this therapy. Clinical trial information: NCT03692429 .

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

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

Stability Analysis Of Delayed Fractional Integro-Differential Equations With Applications Of RLC Circuits

This article presents the stability analysis of delay integro-differentialequations with fractional order derivative via some approximation techniques forthe derived nonlinear terms of characteristic exponents. Based on these techniques,the existence of some analytical solutions at the neighborhood of their equilibriumpoints is proved. Stability charts are constructed and so both of the critical timedelay and critical frequency formulae are obtained. The impact of this work into thegeneral RLC circuit applications exposing the delay and fractional order derivativesis discussed.

Time-delayed control of a nonlinear asymmetrical rotor near the major critical speed with flexible supports

In this study the nonlinear dynamics of an asymmetrical rotating shaft is investigated. The high-static-low dynamic stiffness are used. Also, the active time-delayed proportional derivative controller is employed to. The control signals include time delays. The effects of the proportional and derivative gains, flexible supports and added damping on the nonlinear behaviors of the system are examined. Also, the influences of the proportional and derivative gains on the critical time delays are investigated. As a result, it can be seen that a proportional derivative controller can decrease the unstable regions, and flexible supports improve the stability conditions of the system.

Alternate stability switches induced by time delay in nonlinear fractional oscillators

The van der Pol–Duffing oscillator equipped with fractional time delay feedback is investigated, with emphasis on in-depth stability analysis of equilibrium. An analytical stability criterion is deduced, based on which the parameter space of the feedback gain coefficient and the fractional order is split into time-delay-dependent and -independent regions. In the time-delay-dependent region, it appears that the equilibrium may experience stability losing or gaining repeatedly, named as a stability switch. Moreover, the critical time delay for stability switch happening is determined semi-analytically. An interesting finding consists in a series of alternate stability switches as the fractional order is fixed in a certain range. It implies the fractional time delay feedback would be potentially applicable to design flexible and efficient controllers to suppress or actuate certain motions of nonlinear dynamical systems.

Fall-back time for photo-ionized Cs atoms attached to superfluid 4He nanodroplets

We have studied the dynamic evolution of a Cs atom photo-excited from 6s to 6p and 7s states on a helium droplet using time-dependent 4He-DFT simulations. Depending on the excited electronic state, the Cs impurity remains on the droplet surface or it is ejected. Upon subsequent photo-ionization of the excited Cs atom the resulting Cs+ cation may either be ejected or come back to the droplet, depending on the time delay between photo-excitation and photo-ionization. We have calculated the critical time delay separating these two different behaviors, as well as final ion velocities. These observables will be used for future comparison with planned pump-probe experiments.

Stability analysis of real-time hybrid simulation in consideration of time delays of actuator and shake table using delay differential equations

Real-time hybrid simulation evaluates the response of a structure in real time. In this study, a building with multi-story structure is divided into numerical and experimental substructures, and the vibration behavior of the experimental story is studied among the real-time simulation of the other stories. For applying the effect of static and inertial forces produced by the other stories to the experimental story, an electrohydraulic actuator and a shake table are used, respectively. The dynamics of the electrohydraulic actuator and the shake table can be estimated entirely by time delays, and these delays in the loop of simulation can reduce accuracy and cause system instability. Therefore, a delayed differential equation is used to determine the critical time delays depending on the system parameters. Results of simulation show the effect of non-dimensional parameters and time delays on the stability margin of hybrid simulation.

Dynamics of coral reef models in the presence of parrotfish

AbstractThe decline of coral reefs characterized by macroalgae increase has been a global threat. We consider a slightly modified version of an ordinary differential equation (ODE) model proposed in Blackwood, Hastings, and Mumby [Theor. Ecol. 5 (2012), pp. 105–114] that explicitly considers the role of parrotfish grazing on coral reef dynamics. We perform complete stability, bifurcation, and persistence analysis for this model. If the fishing effort (f) is in between two critical values and , then the system has a unique interior equilibrium, which is stable if and unstable if . If is less (more) than these critical values, then the system has up to two (zero) interior equilibria. Also, we develop a more realistic delay differential equation (DDE) model to incorporate the time delay and treating it as the bifurcation parameter, and we prove that Hopf bifurcation about the interior equilibria could occur at critical time delays, which illustrate the potential importance of the inherent time delay in a coral reef ecosystem.Recommendations for Resource Managers One serious threat to coral reefs is overfishing of grazing species, including high level of algal abundance. Fishing alters the entire dynamics of a reef (Hughes, Baird, & Bellwood, 2003), for which the coral cover was predicted to decline rapidly (Mumby, 2006). One major issue is to reverse and develop appropriate management to increase or maintain coral resilience. We have provided a detailed local and global analysis of model (Blackwood, Hastings, & Mumby, 2012) and obtained an ecologically meaningful attracting region, for which there is a chance of stable coexistence of coral–algal–fish state. The healthy reefs switch to unhealthy state, and the macroalgae–parrotfish state becomes stable as the fishing effort increases through some critical values. Also, for some critical time delays, a switch between healthy and unhealthy reef states occurs through a Hopf bifurcation, which can only appear in the delay differential equation (DDE) model. Eventually, for large enough time delay, oscillations appear and an unhealthy state occurs.

Dynamics of Rodent Population With Two Predators

Modeling rodent populations has been always a challenge for population ecologists. These populations have oscillations that are dynamically complex. In this paper, we consider the population dynamics of rodents under the effect of the “specialist” and “generalist” predators with Beddington–DeAngelis and sigmoidal functional responses. We discover that the ODE system has one axial state and two boundary states. If the rate of predation by the generalist predator is more than the critical value \((c_2>c_2^*)\), then the system has a unique internal equilibrium which is stable if the predator’s intrinsic growth rate of population is more than the critical value \(s^*\). We show that the predation rates of the both predators (\(c_1, c_2\)) play an important role on rodent population dynamic. Then, we have considered a delay differential equation (DDE) model to account for the time delays in the transient dynamics. By treating time delays as the bifurcation parameter, we show that a Hopf bifurcation about the equilibria could happen for critical time delays. Finally, we gave an biological interpretation of our analytical results.

Bifurcations and Dynamics of a Predator–Prey Model with Double Allee Effects and Time Delays

In this paper, a predator–prey system with double Allee effects and time delay is considered. On the one hand, by using time delay as bifurcation parameter, the stability of the interior equilibrium point is studied. It is shown that under certain assumptions the equilibrium point of the delay model is locally asymptotically stable for all delay values, otherwise, there is a critical value, such that the equilibrium point is locally stable when time delay is less than the critical value, and Hopf bifurcation occurs when the delay crosses the critical value. Numerical simulations are carried out to validate the analytical results. On the other hand, we investigate the following four submodels respectively: the time-delayed system without Allee effect, the time-delayed system with Allee effect on predator, the time-delayed system with Allee effect on prey and the time-delayed system with double Allee effects. Compared with the situation without Allee effects, Allee effect on predator causes a decline of the equilibrium state of the predator, the equilibrium state of the prey and critical time delay are almost unaltered; Allee effect on prey and Allee effect on prey and predator all lead to the descent of the equilibrium state of the predator and prey, inversely, and critical time delay has an obvious rise. A comparison of the four cases indicates that Allee effect can alter the magnitudes of predator density and prey density at future time, the time that predator and prey cost to keeping steady state is also changed.

Hopf bifurcation and pattern formation in a delayed diffusive logistic model with spatial heterogeneity

In this paper, we study the Hopf bifurcation and spatiotemporal pattern formation of a delayed diffusive logistic model under Neumann boundary condition with spatial heterogeneity. It is shown that for large diffusion coefficient, a supercritical Hopf bifurcation occurs near the non-homogeneous positive steady state at a critical time delay value, and the dependence of corresponding spatiotemporal patterns on the heterogeneous resource function is demonstrated via numerical simulations. Moreover, it is proved that the heterogeneous resource supply contributes to the increase of the temporal average of total biomass of the population even though the total biomass oscillates periodically in time.

Stability Diagram, Hysteresis, and Critical Time Delay and Frequency for the Kuramoto Model with Heterogeneous Interaction Delays

We investigate the dynamics of large, globally-coupled systems of Kuramoto oscillators with heterogeneous interaction delays. For the case of exponentially distributed time delays we derive the full stability diagram that describes the bifurcations in the system. Of particular interest is the onset of hysteresis where both the incoherent and partially synchronized states are stable for a range of coupling strengths — this occurs at a codimension-two point at the intersection between a Hopf bifurcation and saddle node bifurcation of cycles. By studying this codimension-two point we find the full set of characteristic time delays and natural frequencies where bistability exists and identify the critical time delay and critical natural frequency below which bistability does not exist. Finally, we examine the dynamics of the more general system where time delays are drawn from a Gamma distribution, finding that more homogeneous time delay distributions tend to both promote the onset of synchronization and inhibit the presence of hysteresis.

Partial pole assignment with time delays for asymmetric systems

Considering both single and multiple time delays, partial pole assignment for stabilising asymmetric systems is exemplified by friction-induced vibration and aerodynamic flutter. The control strategy is a single-input state feedback including constant time delays in the feedback loop. An unobservability condition is considered to assign some poles while keeping others unchanged. The receptance method is applied to avoid modelling errors from evaluating mass, damping and stiffness matrices by the finite element method. The solution is formulated in linear equations which allow determination of control gains. The stability of the closed-loop system is analysed by evaluating the first few dominant poles and determining a critical time delay. The numerical study shows that the proposed method is capable of making partial pole assignment with time delays. Since many structures and systems with non-conservative forces can be represented by asymmetric systems, this approach is widely applicable for vibration control of engineering structures.

Human balancing on rolling balance board in the frontal plane

Human balancing on rolling balance board in the frontal plane is analyzed using a two DoF mechanical model, where the human body is modeled by a four-bar linkage mechanism and the geometry of the balance board can be adjusted. Human nervous system is assumed to employ a proportional-derivative controller with constant feedback delay identical to the human reaction time. It is shown that a critical feedback delay exists for each geometry of the balance board. If the reaction delay is larger than the critical one, then there are no stabilizing control gains. A numerical algorithm was developed in order to find the critical time delay based on the mechanical model. The numerical results are compared with real balancing trials, and the corresponding feedback delays in the model are compared to the results of actual reaction time tests.

Dynamics of scroll waves with time-delay propagation in excitable media

Information transmission delay can be widely observed in various systems. Here, we study the dynamics of scroll waves with time-delay propagation among slices in excitable media. Weak time delay induces scroll waves to meander. Through increasing the time delay, we find a series of dynamical transitions. Firstly, the straight filament of a scroll wave becomes twisted. Then, the scroll wave breaks and forms interesting patterns. With long time delay, loosed scroll waves are maintained while their period are greatly decreased. Also, cylinder waves appears. The influences of diffusively coupling strength on the time-delay-induced scroll waves are studied. It is found that the critical time delay characterizing those transitions decreases as the coupling strength is increased. A phase diagram in the diffusive coupling-time delay plane is presented.

Time-Delay Effects on Controlled Seismically Excited Linear and Nonlinear Structures

The main purpose of this paper is to examine the influence of time delay associated with a semi-active variable viscous (SAVV) damper on the response of seismically excited linear and nonlinear structures. The maximum time delay is estimated on the basis of stability criteria, which consist of analyses of structural modal properties. Numerical computation of the critical time delay is performed by using dichotomic approach, which is based on multiple solving of the eigenvalue problem. Simulation results indicate that variable dampers can be effective in reducing the seismic response of structures, and that time-delay effects are important factors in control design of seismically excited structures. Furthermore, simulation results show degradation of performance whenever the actual delay exceeds the calculated critical time delay, which shows the accuracy and reliability of the proposed approach.

Chaotification of quasi-zero-stiffness system with time delay control

Since the control energy for chaotification of Duffing-type dynamics system depends on the linear stiffness of the system, a quasi-zero-stiffness (QZS) isolated system with time delay control is introduced for line spectrum reconstruction of acoustic noise of machinery vibration of underwater vehicles. To investigate the critical condition for chaotification, the stability analysis of the dynamic system with time delay is conducted by the generalized Sturm criterion, and the analytical expression for critical control parameters is obtained. By converting the time-delayed differential equations of the critical condition into discrete mappings through a finite difference scheme, the Lyapunov criterion for chaotification of the QZS system is acquired, which yields the same critical time delay control as the results obtained by the generalized Sturm criterion. Effective chaotification by setting control parameters in the unstable region is demonstrated by numerical examples, which proves the accurate guidance of the stability analysis on chaotification design.