Using Delay for Control

Networked control of AC microgrid

Time-delays are frequently a source of instability, but for some systems, the presence of delay may have a stabilizing effect. A time-delay approach to sampled-data control, where the system is modeled as a continuous-time system with the delayed control input became popular in networked control systems, where the plant and the controller exchange data via communication network. In the present talk delay effects on stability, positivity and control will be discussed. A time-delay approach to sampled-data and network-based control of ODE and PDE systems will be presented, where variable sampling intervals, communication delays and scheduling protocols are taken into account. Differently from other approaches, this approach allows communication delays larger than the sampling intervals in the presence of scheduling protocols. As an application of PDE results, a network-based deployment of multi-agent systems via PDEs will be considered. Finally a very recent time-delay approach, this time to averaging, will be presented. Here the time-delay approach provides constructive upper bounds on the small parameter that preserve the stability.

This paper deals with time delays which exist in networked control systems due to presence of communication network. Time delay impact on networked control system stability is analyzed, and some relations for maximum allowable delay bound estimation are given as well. It is shown, on example of DC motor control, that the system behaves in desired manner and remains stable when appropriate values of regulator parameters are chosen to match estimated maximum time delay.

Delay-dependent stability criteria for a class of networked control systems with multi-input and multi-output☆

This paper is concerned with stability criteria of networked control systems (NCSs) with both the time-varying network-induced delay and data packet dropout taken into account. A continuous time model of NCSs with time-varying and uncertainties is proposed. Based on the dividing of the time-varying delay, a new Lyapunov functional is constructed, and a delay-dependent stability criterion is derived to guarantee the globally asymptotic stability of the networked control systems (NCSs). Expressed in terms of linear matrix inequalities (LMIs), the stability condition can be checked using the numerically efficient Matlab LMI Control Toolbox. Compared with some report methods, no slack matrix variable is introduced and the proposed methods gave a much less conservative maximum allowable delay bound (MADB). A numerical example is provided to demonstrate the effectiveness of the proposed method.

In this article, we characterize the joint effects of plant uncertainty, transmission delay, and fading channel on the stabilization problem of networked control systems (NCSs). We assume that the controller remotely controls the plant and the control packet is transmitted over a delayed and fading channel. We formulate the integrated system as an uncertain discrete-time stochastic system with both input delay and multiplicative noise. The innovative contributions of this article are described as follows. We propose a set of necessary and sufficient conditions for stabilizing an uncertain-free system. Moreover, for the general uncertain model, we derive the necessary and sufficient stabilization condition in terms of symmetric matrix homogeneous polynomials, which can be verified by linear matrix inequality (LMI) feasibility test. As an application, under the parallel transmission strategy, we derive an explicit formula for computing the maximum allowable delay bound, which is uniquely determined by system parameters and signal-to-noise ratio.

Time-delay is unavoidable, encountered in many practical systems such as networked control systems, communication networks, manufacturing, and biology. On the one hand, it often represents a source of instability and oscillation. On the other hand, the appearance of delay can have a stabilizing effect, and delayed feedback control can be used to stabilize some unstable systems. Considering its theoretical and practical importance, increasing attention has been focused on the analysis and synthesis of time-delay systems, and various new approaches have been proposed to reduce their conservatism. The aim of reducing the conservatism of delay-dependent stability criteria is to establish new stability criteria to provide a maximal allowable delay as large as possible. Among different techniques, the reduced conservatism is mainly obtained by constructing an improved Lyapunov functional and employing a tighter bound on some weighted cross products. A great number of effective methods have been provided such as delay-partitioning method, convex combination method, Wirtinger-based inequality, and Bessel–Legendre inequality.

This article addresses the problem of controller design for networked control systems over digital communication. The systems under consideration are stabilised via state feedback, where the effects of sampled signal, state quantisation, network-induced delay and packet dropout are considered. The proposed delay-dependent stability criteria are formulated in the form of a linear matrix inequality, which ensure asymptotic stability and a prescribed H ∞ performance level for networked control systems with admissible uncertainties. Maximum allowable delay bound of networked control systems is obtained by solving a convex optimisation problem. Furthermore, a numerical example is given to illustrate the effectiveness of the main result.

In this paper, an H∞ direct output feedback control algorithm is employed to design the control system in reducing structural seismic responses. Control forces are obtained from the multiplication of direct output measurements by a pre-calculated time-invariant feedback gain matrix. To achieve optimal control performance, the strategy to select both control parameters γ and α is developed. Analytical results show that the decrease of γ or the increase of α makes better control performance, but requires larger control forces. It is also found that lower and upper bounds of γ and α exist. The selection beyond these values will cause control system instability. In this paper, analytical expressions of the upper and lower bounds of γ and α are derived. Structural seismic responses can thus be reduced effectively with appropriate selection of γ and α. Moreover, control force execution time delay cannot be avoided. Relatively small delay time not only can render the control ineffective, but also may cause system instability. In this study, explicit formulas to calculate maximum allowable delay time and critical control parameters are derived for the design of a stable control system. Some solutions are also proposed to increase the maximum allowable delay time. The desired control performance can be guaranteed even with time delay.

In this paper, an H∞ direct output feedback control algorithm through minimizing the entropy, a performance index measuring the tradeoff between H∞ optimality and H2 optimality, is employed to design the control system in reducing structural responses due to dynamic loads such as earthquakes. The control forces are obtained from the multiplication of direct output measurements by a pre-calculated time-invariant feedback gain matrix. To achieve optimal control performance, the strategy to select both control parameters γ and α is extensively investigated. The decrease of γ or increase of α results in better control effectiveness, but larger control force requirement. For a single degree-of-freedom (SDOF) damped structure, exact solutions of output feedback gains and control parameters are derived. It can be proved analytically that the LQR control is a special case of the proposed H∞ control. Direct velocity feedback control is effective in reducing structural responses with very small number of sensors and controllers compared with the DOFs of the structure. In active control of a real structure, control force execution time delay cannot be avoided. Relatively small delay time not only can render the control ineffective, but also may cause system instability. In this study, explicit formulas to calculate maximum allowable delay time and critical control parameters are derived for the design of a stable control system. Some solutions are also proposed to increase the maximum allowable delay time.

The power gating technique is useful in reducing standby leakage current, but it increases the gate delay. For a functional unit, its maximum allowable delay (for a target clock period) limits the smallest standby leakage current its power gating can achieve. In this paper, we point out: in the high-level synthesis of a non-zero clock skew circuit, the resource binding (including functional units and registers) has a large impact on the maximum allowable delays of functional units; as a result, different resource binding solutions have different standby leakage currents. Based on that observation, we present the first work to draw up the timing driven power gating in high-level synthesis. Given a target clock period and design constraints, our goal is to derive the minimum-standby-leakage-current resource binding solution. Benchmark data show: compared with the existing design flow, our approach can greatly reduce the standby leakage current without any overhead.

Network Control.- Delay-Based Non-linear Observers for Congestion Control in Communication Networks.- On the Use of State Predictors in Networked Control Systems.- Networked Control Systems: Algorithms and Experiments.- Modeling and Closed Loop Control for Resource-Constrained Load Balancing with Time Delays in Parallel Computations.- Stability of Load Balancing Control.- Teleoperation.- Robust H ? Control of Bilateral Teleoperation Systems Under Communication Time-Delay.- Web Remote Control of Mechanical Systems: Delay Problems and Experimental Measurements of Round Trip Time.- PDE Approach for Time Delays in Robotized Teleoperation.- Emerging Methodologies.- From Time Delay to Distributed Parameter Systems in Communications.- Computing Maximum Delay Deviation Allowed to Retain Stability in Systems with Two Delays.- On Exact Controllability of Linear Time Delay Systems of Neutral Type.- New Computational Methods.- Applied Interval Computation: A New Approach for Time-Delays Systems Analysis.- Mathematical and Computational Tools for the Stability Analysis of Time-Varying Delay Systems and Applications in Mechanical Engineering.- Diffusive Representation for Operators Involving Delays.- OreModules: A Symbolic Package for the Study of Multidimensional Linear Systems.- Predictors, Inversion and Filtering.- Inversion and Tracking Problems for Time Delay Linear Systems.- Finite Impulse Response Systems for Almost Perfect Decoupling in Nonminimum-Phase Plants.- Linearization of the Power Amplifier in Mobile Telecommunications.- Merging Saturations and Input Delays.- Robust Sampled-Data Control: An Input Delay Approach.- Stabilization and Finite-Gain Stabilizability of Delay Linear Systems Subject to Input Saturation.- Global Asymptotic Stabilization of a PVTOL Aircraft Model with Delay in the Input.

On the delay bound for coordination of multiple generic linear agents under arbitrary topology with time delay

SummaryThis paper is concerned with the analysis of the mean square exponential stability and the almost sure exponential stability of linear stochastic neutral delay systems. A general stability result on the mean square and almost sure exponential stability of such systems is established. Based on this stability result, the delay partitioning technique is adopted to obtain a delay‐dependent stability condition in terms of linear matrix inequalities (LMIs). In obtaining these LMIs, some basic rules of the Ito calculus are also utilized to introduce slack matrices so as to further reduce conservatism. Some numerical examples borrowed from the literature are used to show that, as the number of the partitioning intervals increases, the allowable delay determined by the proposed LMI condition approaches hmax, the maximal allowable delay for the stability of the considered system, indicating the effectiveness of the proposed stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we present an improved delay-dependent absolute stability criterion for Lur’e systems with time delays. The guarantee of absolute stability is provided by Lyapunov-Krasovskii theorem with the Lyapunov functional containing the integral of sector-bounded nonlinearities. The Lyapunov functional terms involving delay are partitioned to be associated with each equidistant fragment on the length of time delay. Employing the Jensen inequality and S-procedure, the sufficient condition is derived from time derivative of the Lyapunov functional. Then, the absolute stability criterion expressed in terms of linear matrix inequalities (LMIs) can be efficiently solved using available LMI solvers. The bisection method is used to determine the maximum allowable time delays to ensure the stability of Lur’e systems in the presence of uncertain time-invariant delays. In addition, the stability criterion is extended to Lur’e systems subject to norm-bounded uncertainties by using the matrix eliminating lemma. Numerical results from two benchmark problems show that the proposed criteria give significant improvement on the maximum allowable time delays.