Constant Delay Research Articles

Dynamic behavior and stability of energy efficient electro-magnetic suspension of rotors involving time delay

Energy efficient contact less suspension of high-speed rotor shafts in application areas such as power-plants and Flywheel Energy Storage Systems (FESS), can be achieved through Active Magnetic Bearings (AMBs). Inevitably, there exists time delay in sensing the rotor displacement and actual application of control force by electromagnets, thus leading to system instability. This paper therefore analyses stability of AMBs, with constant time delay. FESS is modelled as a rigid rotor-AMB system. Performance of two different control laws, (i) PID and (ii) a recently introduced Four-Element (FE) law, are compared. The governing equations are transformed to frequency domain, to exploit Pade's approximation in modeling time delayed value of feedback signal and stability analysis is carried out by analyzing the system poles. This methodology has been verified using experimental results from the existing literature. Numerical simulation of delay differential equations is also used to validate analytical results. The FE control law shows promise in tolerating delay, as compared to conventional PID controller thus leading to AMB system with higher possible spin speed and relaxed sampling constraints on AMB system instrumentation. One of the prospective applications of this work is in design of flywheel energy storage systems for an electric vehicle.

Essential Enzyme Kinetics: A Textbook for Molecular Life Scientists

Energy efficient contact less suspension of high-speed rotor shafts in application areas such as power-plants and Flywheel Energy Storage Systems (FESS), can be achieved through Active Magnetic Bearings (AMBs). Inevitably, there exists time delay in sensing the rotor displacement and actual application of control force by electromagnets, thus leading to system instability. This paper therefore analyses stability of AMBs, with constant time delay. FESS is modelled as a rigid rotor-AMB system. Performance of two different control laws, (i) PID and (ii) a recently introduced Four-Element (FE) law, are compared. The governing equations are transformed to frequency domain, to exploit Pade's approximation in modeling time delayed value of feedback signal and stability analysis is carried out by analyzing the system poles. This methodology has been verified using experimental results from the existing literature. Numerical simulation of delay differential equations is also used to validate analytical results. The FE control law shows promise in tolerating delay, as compared to conventional PID controller thus leading to AMB system with higher possible spin speed and relaxed sampling constraints on AMB system instrumentation. One of the prospective applications of this work is in design of flywheel energy storage systems for an electric vehicle.

Novel criteria for global robust stability of dynamical neural networks with multiple time delays

This research article considers the problem regarding global robust asymptotic stability of the general type of dynamical neural networks involving multiple constant time delays. Some new sufficient criteria are proposed for the existence, uniqueness and global asymptotic stability of the equilibrium point of this neural network model whose network parameters possess uncertainties. This paper will first address the existence and uniqueness problem for equilibrium points by utilizing the Homomorphic transformation theory. Secondly, by exploiting a novel Lyapunov functional candidate, the sufficient conditions for asymptotic stability of equilibrium points of this class of delayed neural networks will be established. The derived robust stability conditions are expressed independently of the constant time delay parameters and define some novel relationships among network parameters of the considered neural network. Thus, the applicability and validity of the obtained robust stability conditions for delayed-type neural networks can be easily tested. The comprehensive comparisons among the results of the current article and some of previously derived corresponding results will also be made by giving an illustrative numerical example.

Oscillations in second order linear neutral impulsive differential equations with constant delays

Sufficient conditions are established for the oscillation of all solutions of a class of second order neutral differential equations with constant delay arguments and constant impulsive jumps for the cases where the coefficient p is a constant and when p is a variable. Examples are provided for clarity.

A Versatile 200-V Capacitor-Coupled Level Shifter for Fully Floating Multi-MHz Gate Drivers

This brief presents a novel level-shifter circuit for high-frequency high-voltage (HV) gate-drives. The proposed level shifter (LS) is designed based on a capacitive-coupler/current mirror/ latch structure which helps to extend operation voltage of a floating supply into the negative range, achieves sub-ns and constant delay, and consumes very low power from the floating supply. Additionally, common-mode noise cancellers based on a cross-current mirror and transmission gates are also presented to enhance the dV/dt immunity of the LS against slewing of the floating ground. Implemented in 0.18 μm HV BCD-on-SOI (bipolar-CMOS-DMOS on silicon-on-isolator) process, the post-layout simulation of the proposed design shows a delay of 680 ps, 200 V/ns of dV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SSF</sub> /dt slew rate immunity, It dissipates no static power and only 8.1 pJ/transition from the floating supply, improving FoM <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> and FoM <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of the proposed LS by 3 times and 11.7 times compared to respective state-of-the-art works.

Numerical algorithm for fractional order population dynamics model with delay

For a fractional-diffusion equation with nonlinearity in the differentiation operator and with the effect of functional delay, an implicit numerical method is constructed based on the approximation of the fractional derivative and the use of interpolation and extrapolation of discrete history. The source of this problem is a generalized model from population theory. Using a fractional discrete analogue of Gronwall's lemma, the convergence of the method is proved under certain conditions. The resulting system of nonlinear equations using Newton's method is reduced to a sequence of linear systems with tridiagonal matrices. Numerical results are given for a test example with distributed delay and a model example from the theory of population with concentrated constant delay.

COViD-19 is a Game Changer for Digital Health Transformation in Belgium

In December 2019, health authorities in Wuhan, China, reported a cluster of patients with pneumonia of unknown cause. A new type of coronavirus has been identified as the cause. Since then, the epidemic has spread to many countries on all continents. The corona pandemic has put just about every vital social component in trouble, especially testing the limits of our health care systems. But there was also a major impact in many economic sectors that were obliged to cease their activities from the first lockdown. After more than 15 months of crisis with a long-term curtailment of personal freedoms, the psychosocial consequences are now also incalculable. The length of the lockdowns, the disappearance of social contact and the constant delay of perspective take their toll the longer, the more.

Sequential predictors for delay-compensating feedback stabilization of bilinear systems with uncertainties

We construct delay-compensating input-to-state stabilizing feedback controllers for a class of nonlinear control systems that include bilinear systems that have pointwise delays in their inputs. Our new approach for delay compensation does not require constructing or estimating distributed terms in the formulas for the stabilizing control laws. We allow arbitrarily long constant input delays. We illustrate our findings in a power system example.

Optimized dosage control of the ozonation process in drinking water treatment

Ozonation is an important process in drinking water treatment. Determination of optimal ozonation dose is of significant importance for enhancing the quality of treated water and reducing the energy cost. It is known that keeping the dissolved ozone residual constant is an effective and reliable dosage control scheme. However, some external disturbances, such as large changes in raw water quality and water flow rate, always exist in the ozonation process. Meanwhile, the ozonation is a nonlinear process with large time constant and long time delay. Thus, it has been always a challenge for dosage control to maintain the dissolved ozone residual constant. The traditional control strategies such as PID and MPC merely utilize feedback regulation to suppress disturbances. This will degrade the control performance when strong disturbances occur. In this work, an effective control method integrating MPC method with disturbance observer (DO) is put forward to improve disturbance suppression performance. DO is utilized to estimate the disturbances and uncertainties, and then the estimated values are employed to conduct feed-forward compensation. The test results indicate that significant disturbance suppression improvements can be accomplished under the proposed method in comparison with the conventional MPC method in the ozonation process.

Memory-Based Integral Sliding-Mode Control for T-S Fuzzy Systems With PMSM via Disturbance Observer.

In this article, the disturbance observer (DOB)-based memory integral sliding-mode control (ISMC) is designed for the permanent magnet synchronous motor (PMSM) model subject to mismatched disturbance through the Takagi-Sugeno (T-S) fuzzy approach. Different from the previous studies, a memory-based ISMC scheme that has a constant delay is taken for the first time to design the ISMC for the T-S fuzzy systems. The DOB is given to estimate the disturbances, which are incorporated in the controller design to counteract the disturbance. To fully abide by the model characteristics of the PMSM-based T-S fuzzy systems and DOB, an integral-type fuzzy switching surface function (IFSSF), which involves state-dependent input matrix and memory parameter simultaneously, is defined. From the IFSSF, the fuzzy ISMC is designed to ensure the reachability condition in finite time. Besides that, the designed fuzzy ISMC can effectively attenuate the mismatched disturbances based on the H∞ control theory. Also, a set of sufficient conditions is derived to ensure the global asymptotic stability for the sliding-mode dynamics by the proposed controller. Finally, the applicability of designed DOB-based memory fuzzy ISMC methodology is demonstrated by a controller design for the PMSM model.

UWB dual-notched planar antenna by utilizing compact open meander slitted EBG structure

In this paper, an ultra-wideband (UWB) dual-notch planar antenna is presented. The antenna, in its structure, utilizes a compact electromagnetic bandgap (EBG) structure with new open meander slits to notch two frequency bands at around 3.5 and 5.5 GHz. The main idea is to place the new slitted mushroom-type EBG structure at the vicinity of the feedline to achieve filtering ability for the antenna. The presented EBG structure has many benefits, like notched bands with sharp roll off, independent control over the notched bands, little effects on antenna performance, easy switching configuration and reduction of the required number of EBG cells. The fabricated antenna shows −10 dB bandwidth of 2.63 up to 13 GHz with dual-notched in the frequency bands of 3.11–4.01 GHz and 5.15–5.98 GHz. Simulation and experimental results exhibit a close agreement with each other. The proposed UWB antenna with a flat transfer function and a constant group delay at the notched bands is a suitable choice for compact UWB communication systems.

Global exponential periodicity and stability of neural network models with generalized piecewise constant delay

Abstract In this paper, the global exponential stability and periodicity are investigated for delayed neural network models with continuous coefficients and piecewise constant delay of generalized type. The sufficient condition for the existence and uniqueness of periodic solutions of the model is established by applying Banach’s fixed point theorem and the successive approximations method. By constructing suitable differential inequalities with generalized piecewise constant delay, some sufficient conditions for the global exponential stability of the model are obtained. Typical numerical examples with simulations are utilized to illustrate the validity and improvement in less conservatism of the theoretical results. This paper ends with a brief conclusion.

A Greedy Flee in the Direction Routing Algorithm for Data Quality Control System of 3D Seismic Sensors Array

A rectangular array of seismic nodes is called a 3D seismic sensors array which is suitable for geographic routing. However, when certain seismic nodes have no location information, using detours or other methods to detect the path will increase latency and power consumption of geographic routing. It is challenging to maintain the high performance of geographic routing in practical 3D exploration networks. This letter proposes a greedy flee in the direction routing algorithm (GFDR). According to the feature that the intersection of the connection set of nodes is not empty, GFDR can drive the packet continuously forward in a specified direction without location information when the packet records the node ID of the path. Simulation results show that as the size of the area without location information (AWLI) increases, GFDR can keep the delivery ratio above 98%, while maintaining an approximately constant packet delay without increasing the number of packet-forwarding hops. A real seismic system experiment running GFDR algorithm confirms the simulation results and demonstrates the effectiveness of GFDR.

Existence and global exponential stability of equilibrium for impulsive neural network models with generalized piecewise constant delay

In this paper, we investigate the models of the impulsive cellular neural network with generalized constant piecewise delay (IDEGPCD). To guarantee the existence, uniqueness and global exponential stability of the equilibrium state, several new adequate conditions are obtained, which extend the results of the previous literature. The method is based on utilizing Banach’s fixed point theorem and a new IDEGPCD’s Gronwall inequality. The criteria given are easy to check and when the impulsive effects do not affect, the results can be extracted from those of the non-impulsive systems. Typical numerical simulation examples are used to show the validity and effectiveness of the proposed results. We end the paper with a brief conclusion.

Feedback stabilization of parabolic systems with input delay

&lt;p style='text-indent:20px;'&gt;This work is devoted to the stabilization of parabolic systems with a finite-dimensional control subjected to a constant delay. Our main result shows that the Fattorini-Hautus criterion yields the existence of such a feedback control, as in the case of stabilization without delay. The proof consists in splitting the system into a finite dimensional unstable part and a stable infinite-dimensional part and to apply the Artstein transformation on the finite-dimensional system to remove the delay in the control. Using our abstract result, we can prove new results for the stabilization of parabolic systems with constant delay: the &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ N $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-dimensional linear reaction-convection-diffusion equation with &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ N\geq 1 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; and the Oseen system. We end the article by showing that this theory can be used to stabilize nonlinear parabolic systems with input delay by proving the local feedback distributed stabilization of the Navier-Stokes system around a stationary state.&lt;/p&gt;

One scheme of stabilization and sample-data control for T-S fuzzy time-delay systems

In this article, a refined Lyapunov functional is proposed to study the stabilization problem for Takagi-Sugeno (T-S) fuzzy systems with time delays. Considering both the time-varying delays of the system and the constant delays of the part of sample-data control loop, the refined Lyapunov function in this paper makes it more practical in actual sampling control pattern compared with some existing research. Some techniques of dealing the linear matrix inequalities (LMIs) are used to derive the less conservative criteria and an example is presented in the end to prove the availability of the work.

Constant-Delay Enumeration for Nondeterministic Document Spanners

We consider the information extraction framework known as document spanners and study the problem of efficiently computing the results of the extraction from an input document, where the extraction task is described as a sequential variable-set automaton (VA). We pose this problem in the setting of enumeration algorithms, where we can first run a preprocessing phase and must then produce the results with a small delay between any two consecutive results. Our goal is to have an algorithm that is tractable in combined complexity, i.e., in the sizes of the input document and the VA, while ensuring the best possible data complexity bounds in the input document size, i.e., constant delay in the document size. Several recent works at PODS’18 proposed such algorithms but with linear delay in the document size or with an exponential dependency in size of the (generally nondeterministic) input VA. In particular, Florenzano et al. suggest that our desired runtime guarantees cannot be met for general sequential VAs. We refute this and show that, given a nondeterministic sequential VA and an input document, we can enumerate the mappings of the VA on the document with the following bounds: the preprocessing is linear in the document size and polynomial in the size of the VA, and the delay is independent of the document and polynomial in the size of the VA. The resulting algorithm thus achieves tractability in combined complexity and the best possible data complexity bounds. Moreover, it is rather easy to describe, particularly for the restricted case of so-called extended VAs. Finally, we evaluate our algorithm empirically using a prototype implementation.

Robust Cooperative Output Regulation of Heterogeneous Uncertain Linear Multiagent Systems With Unbounded Distributed Transmission Delays

This article studies the robust cooperative output regulation problem of heterogeneous uncertain linear multiagent systems under unbounded distributed transmission delays. A novel distributed observer is first proposed to estimate the state of an exosystem in the presence of unbounded distributed transmission delays. Then, two novel distributed controllers, one based on state feedback and the other based on output feedback, are further developed without any prior knowledge of the unbounded transmission delays. It is shown that the resulting closed-loop multiagent systems can achieve robust cooperative output regulation. It is also shown that the better transient performance is achieved with our proposed controllers in contrast to many existing low-gain controllers, which are proposed to deal with both bounded and unbounded transmission delays. Our results can be directly applied to solve cooperative output regulation problems of multiagent systems with bounded distributed or constant transmission delays. Furthermore, our results can also be directly applied to solve leader–following consensus problems of multiagent systems with unbounded distributed, bounded distributed, or constant transmission delays. Finally, a simulation example is provided to illustrate the effectiveness of the proposed controllers.

Prediction-Based Control for Mitigation of Axial–Torsional Vibrations in a Distributed Drill-String System

This article proposes a control strategy to stabilize the axial–torsional dynamics of a distributed drill-string system. An infinite-dimensional model for the vibrational dynamics of the drill string is used as a basis for controller design. In this article, both the cutting process and frictional contact effects are considered in the bit–rock interaction model. Moreover, models for the top-side boundary conditions regarding axial and torsional actuation are considered. The resulting model is formulated in terms of neutral-type delay differential equations that involve constant state delays, state-dependent state delays, and constant input delays arising from the distributed nature of the drill-string dynamics and the cutting process at the bit. Using a spectral approach, the stability and stabilizability of the associated linearized dynamics are analyzed to support controller design. An optimization-based continuous pole-placement technique has been employed to design a stabilizing controller. Since the designed state-feedback control law needs state prediction, a predictor with observer structure is proposed. Both the controller and the predictor only employ top-side measurements. The effectiveness of the control strategy, in the presence of measurement noise, is shown in a representative case study. It is also shown that the controller is robust to parametric uncertainty in the bit–rock interaction.

A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay

&lt;p style='text-indent:20px;'&gt;In present work, a step-by-step Legendre collocation method is employed to solve a class of nonlinear fractional stochastic delay differential equations (FSDDEs). The step-by-step method converts the nonlinear FSDDE into a non-delay nonlinear fractional stochastic differential equation (FSDE). Then, a Legendre collocation approach is considered to obtain the numerical solution in each step. By using a collocation scheme, the non-delay nonlinear FSDE is reduced to a nonlinear system. Moreover, the error analysis of this numerical approach is investigated and convergence rate is examined. The accuracy and reliability of this method is shown on three test examples and the effect of different noise measures is investigated. Finally, as an useful application, the proposed scheme is applied to obtain the numerical solution of a stochastic SIRS model.&lt;/p&gt;