Bifurcation analysis in a delay model of IVGTT glucose-insulin interaction

In this paper, a delayed differential model based on the intravenous glucose tolerance test is considered. The conditions to determine stability or instability of the model's steady state are obtained. We obtain the necessary conditions for the appearance of a bifurcation, and we investigate the direction and stability of the local bifurcation. For this purpose, the normal form theory is used. In addition, the numerical diagrams in the direction of theoretical results are drawn.

Adaptive fault tolerant control for time-varying delay system with actuator fault and mismatched disturbance

In this paper, the fault tolerant control (FTC) problem for a class of continuous Lipschitz nonlinear systems with actuator fault, mismatched disturbance, and time-varying delay is investigated. An adaptive integral sliding mode fault tolerant control (AISMFTC) technique is proposed. First, a composite observer is designed to estimate the states and disturbance simultaneously, by introducing a sliding mode observer, the actuator fault is reconstructed. Then, in accordance with the estimated information, an AISMFTC method is designed. In the AISMFTC scheme, two adaptive laws and compensators are contained to compensate the observer errors, deal with the effects of actuator fault and attenuate the disturbance. Furthermore, the H_∞performance is considered for the robustness of the system. Finally, the effectiveness of the proposed method is illustrated by two examples.

Optimized robust control for industrial unstable process via the mirror-mapping method

In this work, a novel optimized robust control algorithm, based on the mirror-mapping method, is proposed for a class of industrial unstable process with time delay. The optimizing criterion is to minimize the sensitivity function to enhance its robustness. The controllers are designed based on the Padé approximated mirror-mapping process with a stable form, other than the original unstable system. The developed algorithm could release the internal stability constraints to the unstable plant. By using the graphical stability criterion, a systematic methodology is derived to obtain the exact stabilizing region, where the sole design parameter is related to the stability degree of the closed-loop system. The proposed algorithm is with characteristics of concise and efficient design. Three experiments has been employed to illustrate that the control effects can achieve the satisfied performance in aspects of disturbance rejection and robustness.

Rapid estimation of PID minimum variance

PID controllers are the most common type of controllers used in industry. However, to find the best PID performance is a challenging task. Assessment of the best PID performance leads to the minimization of the deviation from set point as indicated by closed loop transfer function. This is a non-convex optimization problem and there is no direct solution for finding this benchmark. Solving this problem iteratively as proposed in literature requires long calculation times. Furthermore, iterative methods are not guaranteed to find the minimum value. Using as many as possible infinite impulse response coefficients, or increasing the number of finite impulse coefficients gradually, causes undesirably large calculation times. We propose a fast method to evaluate the minimum variance by a fixed number of finite impulse response coefficients. This finite impulse model is double the size of the stable system impulse response (it contains the transient response and the same duration of steady state). Thus it avoids undesired iteration, and consequently, the PID minimum variance is quickly evaluated. Time is a critical factor as the purpose to assess this index is for use in online monitoring. The proposed method is tested on benchmark simulation examples from literature.

Effects of a Lag Schedule with Progressive Time Delay on Sign Mand Variability in a Boy with Autism

For some children with autism, mand training can produce highly repetitive manding unless the environment is arranged in a manner that promotes mand variability. Prior research demonstrated that mand training using a lag schedule and progressive time delay increased variability in vocal manding in children with autism. Whether lag schedules have similar effects on sign mand topographies is unknown. The current study evaluated the effects of mand training with a Lag 1 schedule of reinforcement and progressive time delay (TD) on topographical variability and the development of a sign mand response class hierarchy in a boy with autism. The results suggest independent use of all sign mand topographies occurred, a mand response class hierarchy was developed, and topographically variant sign manding increased under the Lag 1 + TD schedule compared to a Lag 0 schedule of reinforcement. Implications for practitioners, limitations, and directions for future research are discussed.

Outgrowing seizures in Childhood Absence Epilepsy: time delays and bistability

We formulate a conductance-based model for a 3-neuron motif associated with Childhood Absence Epilepsy (CAE). The motif consists of neurons from the thalamic relay (TC) and reticular nuclei (RT) and the cortex (CT). We focus on a genetic defect common to the mouse homolog of CAE which is associated with loss of GABA_A receptors on the TC neuron, and the fact that myelination of axons as children age can increase the conduction velocity between neurons. We show the combination of low GABA_A mediated inhibition of TC neurons and the long corticothalamic loop delay gives rise to a variety of complex dynamics in the motif, including bistability. This bistability disappears as the corticothalamic conduction delay shortens even though GABA_A activity remains impaired. Thus the combination of deficient GABA_A activity and changing axonal myelination in the corticothalamic loop may be sufficient to account for the clinical course of CAE.

Design of feedforward and feedback position control for passive bilateral teleoperation with delays

Bilateral teleoperation systems connected to computer networks such as the internet must be able to operate with varying time delays since such systems can easily become unstable. A passivity concept has been used as the framework to solve the stability problem in the bilateral control of teleoperation systems. Passivity and tracking performance are recovered using a control architecture that incorporates time varying gains into the transmission path, feedforward, and feedback position control. The proposed architecture has an inner component that can accommodate any configuration but still remain stable and passive even with varying time delay. The simulation results for a single degree of freedom master/slave system demonstrate the performance of the proposed control architecture.

A Comparison of Prompt Delays with Trial-and-Error Instruction in Conditional Discrimination Training

Many prompting procedures exist for teaching skills to individuals with autism spectrum disorder and intellectual disability; however, direct comparisons between variations of prompt delay are rarely made. Here, we compared three variations of prompt delay (2-s or 5-s constant delay and 5-s progressive delay) alongside trial-and-error instruction. Four learners were taught a conditional discrimination task using a match-to-sample arrangement. Performances were compared using effectiveness and efficiency measures in an adapted alternating treatments design. A procedural modification, in the form of differential reinforcement, was applied to the prompt delay procedure for two of the four participants. With or without this procedural modification, results suggest progressive prompt delay may be effective and the most efficient in reducing learner errors during instruction.

Effects of time delay and body temperature on measurements of central venous oxygen saturation, venous-arterial blood carbon dioxide partial pressures difference, venous-arterial blood carbon dioxide partial pressures difference/arterial-venous oxygen difference ratio and lactate

BACKGROUND

Central venous oxygen saturation (ScvO₂), venous-arterial blood carbon dioxide partial pressures difference (Pv-aCO₂), venous-arterial blood carbon dioxide partial pressures difference/arterial-venous oxygen difference ratio (Pv-aCO₂/Ca-vO₂) and lactate are important parameters employed during shock resuscitation. We designed this study to confirm the effects of time delay and body temperature on measurements of these four parameters.

METHODS

Arterial and central venous blood samples were simultaneously drawn by plastic syringes via indwelling intra-arterial and central venous catheters from critically ill patients. Blood gas analyses were performed on both samples and repeated after 10, 20, 30, 40, 50 and 60 min. Patients were divided into a control group and a high temperature group according to whether the body temperature was greater than 38 °C.

RESULTS

A total of 30 critically ill patients were enrolled. There was a trend of increasing values for ScvO₂, Pv-aCO₂, Pv-aCO₂/Ca-vO₂ and lactate over time (P < 0.001). The ScvO₂ differences were all lower in high temperature group after 10, 20, 30, 40, 50 and 60 min when compared to the corresponding differences in the control group (P < 0.05). The differences in lactate values were slightly higher in the high temperature group, relative to the control group after 20, 30, 40, 50 and 60 min (P < 0.05).

CONCLUSIONS

Measurements of ScvO₂, Pv-aCO₂, lactate and Pv-aCO₂/Ca-vO₂ were affected by time delay or body temperature. We recommend that arterial and central venous blood gas samples be analyzed quickly within 10 min, especially for patients with body temperature <38 °C.

TRIAL REGISTRATION

ChiCTR, ChiCTR1800014484 . Registered 16 January 2018.

Heating-up control with delay-free output prediction for industrial jacketed reactors based on step response identification

To improve the heating-up control performance for industrial jacketed reactors typically involved with long input delay, a predictor-based two-degree-of-freedom (2DOF) control scheme is proposed for the heating-up process operation, based on model identification from a practical step response test. By performing a simple step test (i.e., turning on the electrical heater with certain power (e.g., 50% or 100% of the heating power) to observe the heating-up temperature response), a transfer function identification method is developed to establish an integrating type process model with time delay for describing fundamental dynamics of the heating-up response. Based on the identified model, a predictor-based 2DOF control structure is established, where the delay-free output prediction is obtained by constructing two filters. The 2DOF controllers are analytically derived by proposing the desired transfer functions for the set-point tracking and load disturbance rejection, respectively. There is a single adjustable parameter in each controller (or filter), which may be monotonically tuned to obtain the desired control (or prediction) performance. Illustrative examples from the existing references and a practical application to a 4-liter jacketed reactor for pharmaceutical crystallization are given to demonstrate the effectiveness and advantage of the proposed identification and control methods in comparison with the existing methods.

Measuring ethylene in postharvest biology research using the laser-based ETD-300 ethylene detector

BACKGROUND

Ability to measure ethylene is an important aspect of postharvest management, as knowledge of endogenous ethylene production is used in assessing physiological status, while response of crops to exogenous ethylene informs efforts needed to control unwanted ripening. An ethylene monitoring device with a laser-based photoacoustic detector, ETD-300, was recently developed by Sensor Sense B.V., Nijmegen, The Netherlands. In terms of performance, the ETD-300 is superior to all other current ethylene measurement devices, with a sensitivity of 0.3 nL L-1, a response time of 5 s, and an ability to monitor ethylene in real time. Although the ETD-300 is relatively easy to operate, the performance and correctness of the data obtained depends on the choice of settings, which depends on the application.

RESULTS

This article provides a description of different ways in which the ETD-300 can be used in postharvest research for monitoring ethylene production and ethylene presence in an environment. We provided guidelines on selecting the appropriate method (Continuous Flow, Stop and Flow, and Sample methods), and operational curves for deciding on suitable combination of free volume, flow rates, and period for the different measurement methods.

CONCLUSIONS

Using these guidelines and operational curves, ETD-300 users can considerably reduce the measurement effort by limiting trial and error in establishing appropriate methodologies for their application. The guidelines also comment on accurate use of the ETD-300, as using the inappropriate settings could lead to erroneous measurements. Although these methodologies were developed primarily for postharvest application, they can be applied in other plant science research.

Asymptotic stability of delayed consumer age-structured population models with an Allee effect

In this article we study a nonlinear age-structured consumer population model with density-dependent death and fertility rates, and time delays that model incubation/gestation period. Density dependence we consider combines both positive effects at low population numbers (i.e., the Allee effect) and negative effects at high population numbers due to intra-specific competition of consumers. The positive density-dependence is either due to an increase in the birth rate, or due to a decrease in the mortality rate at low population numbers. We prove that similarly to unstructured models, the Allee effect leads to model multi-stability where, besides the locally stable extinction equilibrium, there are up to two positive equilibria. Calculating derivatives of the basic reproduction number at the equilibria we prove that the upper of the two non-trivial equilibria (when it exists) is locally asymptotically stable independently of the time delay. The smaller of the two equilibria is always unstable. Using numerical simulations we analyze topologically nonequivalent phase portraits of the model.

Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period

In this paper, we analyze a delayed SEIR epidemic model in which the latent and infected states are infective. The model has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number R 0 , is less than or equal to unity. We investigate the effect of the time delay on the stability of endemic equilibrium when R 0 > 1 . We give criteria that ensure that endemic equilibrium is asymptotically stable for all time delays and a Hopf bifurcation occurs as time delay exceeds the critical value. We give formulae for the direction of Hopf bifurcations and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold reduction for functional differential equations. Numerical simulations are presented to illustrate the analytical results.

Ultrasonic guided wave focusing in waveguides with constant irregular cross-sections

As essential components of a high-speed railway system, switch rails can be easily damaged by sophisticated operating conditions. Therefore, precise online detection for switch rails is necessary. Methods based on ultrasonic guided waves are ideal candidates for structural integrity of the switch rails, which are natural waveguides with irregular cross-sections. However, energy decentralization in the wave propagation severely restricts detectability. Phased array systems have been developed and implemented to steer and focus acoustic energy in waveguides of ordinary cross-sections such as pipes and plates. This paper proposes a method for ultrasonic guided wave focusing in waveguides with constant irregular cross-sections. We analyzed the characteristics of the guided waves generated by partial loadings based on a semi-analytical finite element method (SAFEM). An algorithm was developed for calculating the amplitude weights and time delays required to modulate excitation signals. Two coefficients were defined to evaluate the wave focusing results, namely the half area coefficient (HAC) and half energy coefficient (HEC). Numerical simulations to verify the proposed method were carried out for a switch rail base with a constant irregular cross-section. The results demonstrate that the guided acoustic beam has been effectively steered to focus at the pre-determined locations with enhanced acoustic wave energy. Furthermore, the influence of various factors on guided wave focusing was studied. Excitation signals of low center frequencies with narrow bandwidths are recommended for ideal focusing results.

Barometric pressure change and heart rate response during sleeping at ~ 3000 m altitude

We investigated effects of change in barometric pressure (P _B) with climate change on heart rate (HR) during sleep at 3000 m altitude. Nineteen healthy adults (15 males and four females; mean age 32 years) participated in this study. We measured P _B (barometry) and HR (electrocardiography) every minute during their overnight stay in a mountain lodge at ~ 3000 m. We also measured resting arterial oxygen saturation (SpO₂) and evaluated symptoms of acute mountain sickness (AMS) by using the Lake Louise Questionnaire at 2305 and 3000 m, respectively. P _B gradually decreased during the night at the speed of approximately - 0.5 hPa/h. We found that HR during sleep decreased linearly as P _B decreased in all subjects, with significance (r = 0.492-0.893; all, P < 0.001). Moreover, cross correlation analysis revealed that HR started to decrease after ~ 15 min following the decrease in P _B, on average. SpO₂ was 93.8 ± 1.7% at 2305 m before climbing, then decreased significantly to 90.2 ± 2.2% at the lodge before going to bed, and further decreased to 87.5 ± 2.7% after waking (all, P < 0.05). Four of the 19 subjects showed a symptom of AMS after waking (21%). Further, the decrease in HR in response to a given decrease in P _B (ΔHR/ΔP_B) was negatively related with a decrease in SpO₂ from before going to bed to after waking at 3000 m (r = - 0.579, P = 0.009) and with total AMS scores after waking (r = 0.489, P = 0.033).

H∞ control for time-delay systems with randomly occurring nonlinearities subject to sensor saturations, missing measurements and channel fadings

The H_∞ control problem for a class of time-delay systems with randomly occurring nonlinearities (RONs) is addressed in this paper. Sensor saturations, missing measurements and channel fadings are governed by random variables obeying the Bernoulli distributions. The measurement output is subject to both data missing and randomly occurring sensor saturations (ROSSs) described by sector-nonlinearities as well as the channel fadings caused typically in wireless communication. The aim of the addressed problem is to design a full-order dynamic output-feedback controller such that the closed-loop system is exponentially mean-square stable and satisfies the prescribed H_∞ performance constraint. Sufficient conditions are presented by resorting to intensive stochastic analysis and matrix inequality techniques, which not only guarantee the existence of the desired controller for all possible time-delays, RONs, missing measurements and ROSSs but also lead to the explicit expressions of such controllers. Finally, a numerical example is given to demonstrate the applicability of the proposed control scheme.

Traveling wave solutions in a two-group SIR epidemic model with constant recruitment

Host heterogeneity can be modeled by using multi-group structures in the population. In this paper we investigate the existence and nonexistence of traveling waves of a two-group SIR epidemic model with time delay and constant recruitment and show that the existence of traveling waves is determined by the basic reproduction number [Formula: see text] More specifically, we prove that (i) when the basic reproduction number [Formula: see text] there exists a minimal wave speed [Formula: see text] such that for each [Formula: see text] the system admits a nontrivial traveling wave solution with wave speed c and for [Formula: see text] there exists no nontrivial traveling wave satisfying the system; (ii) when [Formula: see text] the system admits no nontrivial traveling waves. Finally, we present some numerical simulations to show the existence of traveling waves of the system.

A simple tuning method of fractional order PIλ-PDμ controllers for time delay systems

In this paper, a practical tuning technique is presented to obtain all stabilizing fractional order PI^λ-PD^μ controller parameters ensuring stability for processes with time delay using the stability boundary locus and the weighted geometrical center (WGC) methods. The method is based on obtaining of stability regions plotted by using the stability boundary locus in the (k_d,k_f)-plane and (k_p,k_i)-plane, and then computing the weighted geometrical centers of these regions. After obtaining PD^μ controller parameters using the WGC method from the stability region, desired PI^λ controller parameters are computed by the same procedure. This paper provides a simple and efficient tuning method to obtain stabilizing parameters of PI^λ-PD^μ controller for time delay systems. The important advantages of the method are both calculating of controller parameters without using any complex solution methods and ensuring the stability of closed loop system. Illustrative examples are given to demonstrate the benefits and the simplicity of the proposed method.

A generalized smith predictor for unstable time-delay SISO systems

In this work, a generalization of the Smith Predictor (SP) is proposed to control linear time-invariant (LTI) time-delay single-input single-output (SISO) systems. Similarly to the SP, the combination of any stabilizing output-feedback controller for the delay-free system with the proposed predictor leads to a stabilizing controller for the delayed system. Furthermore, the tracking performance and the steady-state disturbance rejection capabilities of the equivalent delay-free loop are preserved. In order to place this contribution in context, some modifications of the SP are revisited and recast under the same structure. The features of the proposed scheme are illustrated through simulations, showing a comparison with respect to the corresponding delay-free loop, which is here considered to be the ideal scenario. In order to emphasize the feasibility of this approach, a successful experimental implementation in a laboratory platform is also reported.

Pulse vaccination of an epidemic model with two parallel infectious stages and time delays

An epidemic model with two parallel infectious stages and time delays and pulse vaccination is proposed. We introduce four thresholds and further obtain the conditions that the disease will be extinct or not. Corollaries show that under condition that θ > max { θ ∗ 1 , θ ∗ 2 } the disease will fade out, and if θ < min { θ 1 ∗ , θ 2 ∗ } , the disease will be endemic. Our results indicate that a larger pulse vaccination rate will lead to the eradication of a disease. Furthermore, two thresholds ℜ ∗ 1 and ℜ ∗ 2 show that the diversity of the contagiousness affects the basic properties of these models. In addition, numerical results indicate that the probability for an infected individual to enter different infective compartments greatly affects two infective compartments.

Control for delayed bilateral teleoperation of a quadrotor

This paper proposes a cascade control scheme for delayed bilateral teleoperation of a quadcopter. The strategy transforms a 6D real quadcopter to an easy-to-teleoperate 3D virtual quadcopter. The scheme is formed by a P+d plus PID controller for each dof. The analysis based on Lyapunov theory gets as result the way to set the control parameters depending on the magnitude of the asymmetric time delays (forward and backward delays). This technic aims to reach stability, simplicity and good performance in practice. Besides, experimental tests about delayed bilateral teleoperation of a quadcopter including the proposed control scheme are shown in order to evaluate the system performance.

A 2-Dof LQR based PID controller for integrating processes considering robustness/performance tradeoff

This paper focuses on the analytical design of a Proportional Integral and Derivative (PID) controller together with a unique set point filter that makes the overall Two-Degree of-Freedom (2-Dof) control system for integrating processes with time delay. The PID controller tuning is based on the Linear Quadratic Regulator (LQR) using dominant pole placement approach to obtain good regulatory response. The set point filter is designed with the calculated PID parameters and using a single filter time constant (λ) to precisely control the servo response. The effectiveness of the proposed methodology is demonstrated through a series of illustrative examples using real industrial integrated process models. The whole range of PID parameters is obtained for each case in a tradeoff between the robustness of the closed loop system measured in terms of Maximum Sensitivity (M_s) and the load disturbance measured in terms of Integral of Absolute Errors (IAE). Results show improved closed loop response in terms of regulatory and servo responses with less control efforts when compared with the latest PID tuning methods of integrating systems.

Dynamics of vaccination in a time-delayed epidemic model with awareness

This paper investigates the effects of vaccination on the dynamics of infectious disease, which is spreading in a population concurrently with awareness. The model considers contributions to the overall awareness from a global information campaign, direct contacts between unaware and aware individuals, and reported cases of infection. It is assumed that there is some time delay between individuals becoming aware and modifying their behaviour. Vaccination is administered to newborns, as well as to aware individuals, and it is further assumed that vaccine-induced immunity may wane with time. Feasibility and stability of the disease-free and endemic equilibria are studied analytically, and conditions for the Hopf bifurcation of the endemic steady state are found in terms of system parameters and the time delay. Analytical results are supported by numerical continuation of the Hopf bifurcation and numerical simulations of the model to illustrate different types of dynamical behaviour.

Passivity-based control framework for task-space bilateral teleoperation with parametric uncertainty over unreliable networks

Bilateral teleoperation systems developed in joint-space or in task-space without taking into account parameter uncertainties and unreliable communication have limited practical applications. In order to ensure stability, improve tracking performance, and enhance applicability, a novel task-space control framework for bilateral teleoperation with kinematic/dynamic uncertainties and time delays/packet losses is studied. In this paper, we have demonstrated that with the proposed control algorithms, the teleoperation system is stable and position tracking is guaranteed when the system is subjected to parametric uncertainties and communication delays. With the transformation of scattering variables, a packet modulation, called Passivity-Based Packet Modulation (PBPM), is proposed to cope with data losses, incurred in transmission of data over unreliable network. Moreover, numerical simulations and experiments are also presented to validate the efficiency of the developed control framework for task-space bilateral teleoperation.

Global hopf bifurcation of a delayed equation describing the lag effect of media impact on the spread of infectious disease

We proposed a delay differential model, associated with the response time for individuals to the current infection, to examine the media impact on the transmission dynamics of infectious diseases. We investigated the global bifurcation by considering the delay as a bifurcation parameter and examined the onset and termination of Hopf bifurcations from a positive equilibrium. Numerical studies to identify ranges of parameters for coexisting multiple periodic solutions are guided by the bifurcation analysis and the Matlab package DDE-BIFTOOL developed by Engelborghs et al. Further, we parameterized the proposed model on the basis of the 2009 A/H1N1 pandemic influenza data in Shaanxi province, China, and estimated the basic reproduction number to be 1.79 [95% CI (1.77-1.80)] and the time delay to be 2.94 days [95% CI (2.56-3.24)]. Our main results indicated that media impact with time delay significantly influenced the transmission dynamics of infectious diseases.