Closed-Loop Identification using Routine Operating Data: the Effect of Time Delay

Closed-loop identification with routine operating data: Effect of time delay and sampling time

In a neuronal system, propagation speed of neuronal information is mainly determined by the length, the diameter, and the kind of the axons between the neurons. Thus, some communications between neurons are not instantaneous, and others are instantaneous or with some negligible delay. In the past years, effects of time delay on neuronal dynamics, such as synchronization, stochastic resonance, firing regularity, etc., have been investigated. For stochastic resonance, it has been reported recently that stochastic multi-resonance in a neuronal system can be induced by time delay. However, in these studies, time delay has been introduced to every connection of the neuronal system. As mentioned in the beginning, in a real neuronal system, communication between some neurons can be instantaneous or with some negligible delays. Thus, considering the effect of partial time delay (time delay is called as partial time delay if only part of connections are delayed) on neuronal dynamics could be more meaningful.In this paper, we focus on discussing effect of partial time delay on response amplitude of a Watts-Strogatz neuronal network which is locally modeled by Rulkov map. With the numerically obtained results, we can see that partial time delay can induce a stochastic multi-resonance which is indicated by the multi-peak characteristics in the variation of response amplitude with partial time delay. Namely, partial time delay could also induce stochastic multi-resonance in a neuronal system. Moreover, we also find that optimal response amplitude can be reached in much wider range of the partial time delay value when delayed connections are less (i.e., the partial time delay probability is small). This is different from the case in which all connections are delayed, where response amplitude become optimal only when time delay is nearly the multiples of external signal's period. But the range of the partial time delay value becomes narrower and narrower with the increasing of the partial time delay probability and when the partial time delay probability is large enough, response amplitude becomes optimal only when time delay is nearly the multiples of external signal period. It is similar to the case where all connections are delayed. Furthermore, effects of random rewiring probability and total link number in the neuronal network on partial time delay induced stochastic multi-resonance are also studied. It is found that partial time delay induced stochastic multi-resonance is robust to random rewiring probability but not robust to total link number. Stochastic resonance is a very important nonlinear phenomenon in neuroscience, thus, our obtained results could have some implications in this field.

The effect of pre-analytical handling on the stability of fractalkine, monocyte chemoattractant protein 1 (MCP1), interleukin 6 and interleukin 8 in samples of human cerebrospinal fluid

This study establishes a novel time-delay fractional SEIHR infectious disease model to investigate the effects of saturated incidence rates and time delays on different populations, including susceptibles, infected individuals, recovered individuals, and latent infected individuals. First, the existence and boundedness of the model’s solutions are verified, confirming its well-posedness. Subsequently, the existence of equilibria is analyzed, and the impact of parameter variations on the system is explored by examining the equilibria ϵ0 and ϵ∗, as well as the basic reproduction number R0. Additionally, the global dynamics of the equilibria are further analyzed using the Lyapunov method, while Hopf bifurcation theory is applied to explore the conditions under which the system shifts from stability to oscillatory behavior. Numerical simulations further validate the theoretical analysis, showing that time-delay effects significantly influence the system’s responsiveness and the rate of disease transmission. Moreover, when the time delay τ crosses the critical threshold τ0, the system exhibits periodic oscillations. By predicting periodic fluctuations and incorporating memory effects and persistent influences, we can better control epidemics, emphasizing the importance of time-delay adjustments and enhancing the system’s biological realism.

Performance assessment of MIMO systems based on I/O delay information

Telementoring allows a less experienced surgeon to benefit from an expert surgical consultation, reducing cost, travel, and the learning curve associated with new procedures. However, there are several technical limitations that affect practical applications. One potentially serious problem is the time delay that occurs any time data are transferred across long distances. To date, the effect of time delay on surgical performance has not been studied. A two-phase trial was designed to examine the effect of time delay on surgical performance. In the first phase, a series of tasks was performed, and the numbers of robotic movements required for completion was counted. Programmed incremental time delays were made in audiovisual acquisition and robotic controls. The number of errors made while performing each task at various time delay intervals was noted. In the second phase, a remote surgeon in Baltimore performed the tasks 9000 miles away in Singapore. The number of errors made was recorded. As the time delay increased, the number of operator errors increased. The accuracy needed to perform remote robotic procedures was diminished as the time delay increased. A learning curve did exist for each task, but as the time delay interval increased, it took longer to complete the task. Time delay does affect surgical performance. There is an acceptable delay of <700 msec in which surgeons can compensate for this phenomenon. Clinical studies will be needed to evaluate the true impact of time delay.

PurposeThe model for digitally controlled three-phase pulse width modulation (PWM) boost rectifiers is a sampled data model, which is different from the continuous time domain models presented in previous studies. The controller, which is tuned according to the model in continuous time domain and discretized by approximation methods, may exhibit some unpredictable performances and even result in unstable systems under some extreme situations. Consequently, a small-signal discrete-time model of digitally controlled three-phase PWM boost rectifier is required. The purpose of this paper is to provide a simple but accurate small-signal discrete-time model of digital controlled three-phase PWM boost rectifier, which explains the effect of the sampling period, modulator and time delays on system dynamic and improves the control performance.Design/methodology/approachBased on the Laplace domain analysis and the waveforms of up-down-count modulator, the small signal model of digital pulse width modulation (DPWM) in the Laplace domain is presented. With a combination of state-space average and a discrete-time modeling technique, a simplified large signal discrete time model is developed. With rotation transformation and feed-forward decoupling, the large-signal model is decoupled into a single input single output system with rotation transformation. Then, an integrated small signal model in the Laplace domain is constructed that included the time delay and modulation effect. Implementing the modified z-transform, a small-signal discrete-time model is derived from the integrated small signal model.FindingsIn a digital control system, besides the circuit parameters, the location of pole of open-loop transfer function is also related to system sampling time, affecting the system stability, and the time delay determines the location of the zero of open-loop transfer function, affecting the system dynamic. In addition to the circuit parameters discussed in previous literature, the right half plane (RHP) zero is also determined by the sampling period and the time delay. Furthermore, the corner frequency of the RHP zero is mainly determined by the sampling period.Originality/valueThe model developed in this paper, accounting for the effect of the sampling period, modulator and time delays on the system dynamic, give a sufficient insight into the behavior of the digitally controlled three-phase PWM rectifier. It can also explain the effect of sampling period and control delay time on system dynamic, accurately predict the system stability boundary and determine the oscillation frequency of the current loop in critical stable. The experimental results verify that the model is a simple and accurate control-oriented small-signal discrete-time model for the digitally controlled three-phase PWM boost rectifier.

Effects of time delay on transient behavior of a time-delayed metastable system subjected to cross-correlated noises

This study begins with a brief overview of the problem of harmonic distortion and its effect on the quality of electric power, how the active power filter mitigate this problems then investigate the effect of control circuit time delay on the performance of Active Power Filter (APF). Active filter is an electronic power system that absorbs harmonic currents in the network, generated by nonlinear loads. The nonlinear load seems the main source of harmonic distortion in the power system. A shunt active power filter with optimized PI discussed in this study. Delay times are inevitable in Digital Signal Processing (DSP) based controllers can significantly degrade the performance of active power filter. Active filter performance can be affected by the delay between the control and measurement of the output current of SAPF and load current harmonics. The proposed filter reduces harmonic distortion is within an acceptable range.

Anaerobic digestion of municipal and animal wastes provides a potentially important means of producing energy sustainably. The reliable production of methane from anaerobic digestion requires that bacteria metabolise municipal and agricultural wastes to produce mainly carbon dioxide and methane. Our model uses Monod based kinetics and is complex since the biomass concentration growth is inhibited with the increase in substrate. The production of methane depends on the number of methanogenic bacteria; there is evidence from previous chemostats experiments that there is a time delay in population number of these cells to respond to changes in substrate concentrations. In this article we focus on determining the dynamical response of the methane production rate under different dynamics of feed conditions and temperatures. Since there is a delay in the methane bacteria mass response, we include the effects of the delay on the dynamics of the system based on modification of kinetics in a simple fermentation anaerobic model. We compare the dynamics of the system with and without delay to show the contribution of delay to the overall stability of the system. References O. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi, J. P. Steyer. Dynamical model development and parameter identification for an anaerobic wastewater treament process. Biotechnol. Bioeng. 75:424–438, 2001. doi:10.1002/bit.10036 T. F. Thingstad and T. I. Langeland. Dynamics of chemostat culture: The effect of a delay in cell response. J. Theor. Biol. , 48:149–159, 1974. doi:10.1016/0022-5193(74)90186-6 J. R. Beddington and R. M. May. Time delays are not nessarily destabilizing. Math. Biosci. 27:109–119, 1975. doi:10.1016/0025-5564(75)90028-0 K. Y. San and G. Stephanopoulos. The effect of growth rate delays in substrate-inhibited kinetics on the optimal profile of fed-batch reactors. J. Theor. Biol. 28:356–361, 1986. doi:10.1002/bit.260280308 G. Stephanopoulos and K. Y. San. Studies on-line bioreactor identification. I. Theory. Biotechnol. Bioeng. 26:1176–1188, 1984. doi:10.1002/bit.260261006 A. A. Khan, A. J. Stacey and J. J. Shepherd. Optimization of methane output for an anaerobic waste digester. ANZIAM J. 54:C523–C539, 2013. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6322 J. F. Andrews. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnol. Bioeng. 10:707–723, 1968. doi:10.1002/bit.260100602 D. J. Batstone, J. Keller, I. Angelidaki, S. V. Kalyuzzhni, S. G. Pavlostathis, A. Rozzi, W. T. M. Sanders, H. Siegrist, and V. A. Vavilin. Anaerobic digestion model No. 1 (ADM1). Water Sci. Technol. 45(10):65–73, 2002 http://wst.iwaponline.com/content/45/10/65 K. J. Beers. Numerical methods for chemical engineering: Applications in Matlab . Cambridge, New York, USA, 2007. http://www.cambridge.org/us/academic/subjects/engineering/chemical-engineering/numerical-methods-chemical-engineering-applications-matlab J. F. Andrews. The development of a dynamic model and control strategies for the anaerobic digestion process. In Mathematical Models in Water Pollution Control , A. James (ed). Wiley, 1978. A. W. Bush and A. E. Cook. The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater J. Theor. Biol. 63:385–395, 1976. doi:10.1016/0022-5193(76)90041-2 L. F. Shampine, I. Gladwell and S. Thompson. Solving ODEs with Matlab . Cambridge, New York, USA, 2003. http://www.cambridge.org/us/academic/subjects/mathematics/numerical-analysis/solving-odes-matlab?format=PB

The effect of time delay on binary signal detection via a bistable system in the presence of white or colored Gaussian noise is investigated. By defining the bit error rate based on the solution of the approximated Fokker—Planck equation, the detector performance is investigated theoretically and is verified by Monte Carlo simulation. It is shown that, when the system parameter or noise intensity is optimally chosen, the increasing time delay generally improves the system performance. It is also shown that it is more difficult to accurately predict the system performance with a larger time delay and correlation time. This may inspire more thorough investigations in cooperative effects of a nonlinear system and time delay on signal processing.

Impedance-type kinesthetic haptic displays aim to render arbitrary desired dynamics to a human operator using force feedback. To render realistic virtual environments, the difference between desired and rendered dynamics must be small. In this paper, we analyze the closed-loop dynamics of haptic displays for three common virtual environments: a spring, a damper, and a spring-damper, including the effects of time delay and low-pass filtering. Using a linear model, we identify important parameters for the rendered dynamics in terms of effective impedances, a conceptual tool that decomposes the displays closed-loop impedance into components with physical analogs. Our results establish bandwidth limits for rendering effective stiffness and damping. The effective stiffness bandwidth is limited by the virtual stiffness and device mass, and the effective damping bandwidth is limited by the cut-off frequency of the low-pass filter which filters the device velocity estimate. We show that a general system impedance can be characterized by a mass, damper, and spring optimally by the solution to a convex optimization problem, and we present a quantitative metric, the Average Distortion Error (ADE), to describe the fidelity of this model. Time delay has no significant effect on characterized stiffness, and reduces characterized damping by the product of virtual stiffness and total time delay. Reducing the low-pass filter cut-off frequency reduces the characterized damping. Experimental data gathered with a Phantom Premium 1.5 validates the theoretical analysis. We also conducted human user experiments to investigate the effects of time delay and low-pass filtering on perceived stiffness and damping. Similar to the characterized dynamics results, we observed no significant effect of time delay on perceived stiffness, and increasing time delay resulted in reduced perceived damping. Lower filter cut-off frequencies resulted in lower perceived damping. This work informs haptic display design by presenting how closed-loop behavior changes with key parameters.

Purpose– The purpose of this research is to explore the effect of time delay on the perception of environmental risks beyond time discounting, and thus provide a reference for effective communication related to environment and environmental risks.Design/methodology/approach– Ten risk scenarios across four time delay conditions were designed. Computer program randomly presented different risk scenarios to student subjects. Risk perception was measured through equivalent certain loss elicited by bi-section method. In all, 50 students from Harbin Institute of Technology Shenzhen Graduate School participated in the experiment.Findings– Time delay makes the subjects optimistic toward environmental risk with the exclusion of time discounting. The more distant in time the occurrence of an environmental risk, the less in intensity subjects will perceive it as a severe threat. Also, there is a noticeable difference in environmental risk perception between males and females.Research limitations/implications– This tentative research focusses on exploring the existence of time delay effect on environmental risk perception. Only student subjects are recruited for this research. Future studies are needed to extend the population to people of different backgrounds in order to generalize the finding.Practical implications– Current ethical appeal of zero social discount rate is unlikely to be effective. Time delay effect in people's environmental risk perception should be acknowledged. Such an acknowledgement is the basis of trust in risk communication. Communication effort needs to address this time delay effect to make people alert to long-term environmental risks, and eventually change their environmental behaviors.Originality/value– The explorative research represents the first attempt to investigate the effect of time delay on environmental risk perception when time discounting is excluded. It suggests a new direction to understand public optimism toward delayed environmental risks, and reluctance to take proactive actions, and thus offers a new insight into related communication efforts.

Synchronization and firing patterns of neurons play a significant role in neural signal encoding and transduction of information processing of nervous systems. For real neurons, the signal transmission delay is inherent due to finite propagation speed of action potentials through axons, as well as both dendritic and synaptic processing. Time delay is universal and inevitable, and results in complex dynamical behavior, such as multistability and bifurcations leading to chaos. In this chapter, the authors provide a survey of some recent developments on the effects of time delay on synchronization and firing patterns in coupled neuronal systems. Basic concepts of firing patterns of neurons and complete and phase synchronization of oscillators are introduced. Synchronization and firing patterns in electrically coupled neurons as well as inhibitory and excitatory delayed synapses with time delay are presented. Delay effects on spatiotemporal dynamics of coupled neuronal activities are discussed. Some well-known neuron models are also included for benefit of the readers.

A 30-year history of research on dealing with the effects of time delay in the control loop on human teleoperation in space is reviewed. Experiments on the effects of delay on human performance are discussed, along with demonstrations of predictive displays to help the human overcome the delay. Supervisory control is shown to offer a variety of options, from switching to local impedance control upon contact with the environment to higher-level local automation. Wave transformation techniques to ameliorate the effects of delay are also described. Space teleoperations have tended to deal with the problem of time delay by avoiding it and not attempting to teleoperate from the ground. It is suggested that the US space effort might have gotten further ahead and at a lower cost with a greater is commitment to space teleoperation from the ground through the delay. Predictive display works well for free positioning. Local impedance control is recommended for control in contact with the environment, possibly accompanied by wave transformation techniques. Higher level supervisory control is always an option for sufficiently predictable tasks and will continue to improve with better sensors and task models.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>