Advances in Modelling, Analysis, and Design of Delayed Systems

Mathematical Problems in Engineering, 2017

The subject of time-delay systems is a rather old research topic dating back to the works of Euler-Bernoulli in the XVIII century. Effective results in this area were initiated in the late fifties of the twentieth century since the works of Krasovskii and Razumikhin on the Lyapunov functions. However the significant progression in this area has been made during the last decade where numerous books, research, and survey papers and special issues have been devoted. Delay is not just a mathematical exercise but more importantly is rooted in many natural and man-made systems such as biology, processes industries, and mechatronic motions. In engineering applications, time-delays generally describe propagation phenomena, material or energy transfer in intercommoned systems, and data transmission in communication systems. They have been the main sources inducing oscillations, instability, and poor control performances. Stability analysis and robust control of such systems are then of theoretical and practical importance. Much effort in the analysis and synthesis of these systems has been dedicated to delay-dependent and delay-independent issues based both/either on Lyapunov methods and/or frequency domain techniques. However, it should be noted that there are still numerous challenging issues pending in many classes of time-delay systems.

Mokslas – Lietuvos ateitis, 2015

The paper is devoted to investigation of the robust stability of system with delay. The influence of process parameters on the stability of the whole system is tested and impact to the system parameters using the Smith predictor for robust systems is defined.

Computers & Structures, 1998

This paper investigates the time delay effects on the stability and performance of active feed back control systems for engineering structures. A computer algorithm is developed for stability analy sis of a SDOF system with unequal delay time pair in the velocity and displacement feedback loops. It is found that there may exist multiple stable regions in the plane of the time delay pair, which contain time delays greater than the maximum allowable values obtained by previous studies. The size, shape and location of these stable and unstable regions depend on the system parameters and the feedback control gains. For systems with multiple stable regions, the boundaries between the stable and unstable regions in the plane of the time delay pair are explicitly obtained. The delay time pairs that forms these boundaries are called the critical delay time pairs at which the steady-state response becomes unbounded. The conclusions are valid for both large and small delay times. For any system with mul tiple stable regions, preliminary guidelines obtained from an explicit formula are given to find the desir able delay time pair(s). When used, these desirable delay time pair(s) not only stabilize an unstable system with inherent time delays, but also significantly reduce the system response and control force. For any system with multiple stable regions, these desirable delay time pair(s) are above the maximum allowable delay times obtained by previous studies. Numerical results, for both steady-state and transi ent analysis, are given to investigate the performance of delayed feedback control systems subjected to both harmonic and real earthquake ground motion excitations.

Journal of Dynamic Systems, Measurement, and Control, 2003

This paper gives a broad overview of the stability and control of time-delay systems. Emphasis is on the more recent progress and engineering applications. Examples of practical problems, mathematical descriptions, stability and performance analysis, and feedback control are discussed.

ISRN Applied Mathematics, 2012

This paper reviews some subtleties in time-delay systems of neutral type that are believed to be of particular relevance in practice. Both traditional formulation and the coupled differential-difference equation formulation are used. The discontinuity of the spectrum as a function of delays is discussed. Conditions to guarantee stability under small parameter variations are given. A number of subjects that have been discussed in the literature, often using different methods, are reviewed to illustrate some fundamental concepts. These include systems with small delays, the sensitivity of Smith predictor to small delay mismatch, and the discrete implementation of distributed-delay feedback control. The framework prsented in this paper makes it possible to provide simpler formulation and strengthen, generalize, or provide alternative interpretation of the existing results.

2009

Time delays are usually unavoidable in many mechanical and electrical systems. The presence of delay typically imposes strict limitations on achievable feedback performance in both continuous and discrete systems. The presence of the delay complicates the design process as it makes continuous systems to be infinite dimensional and it significantly increases the dimensions in discrete systems. Most of classical methods used controller design cannot be used with delayed systems. In this study, the delay will be modeled using different approaches such as Pad'e approximation and Smith Predictor in continuous system and modified z-transform in discreet systems. In this study, the delays are assumed to be constant and known. The delays in the system are lumped in the plant model. This study will show the design of stable and optimal controller for time-delay systems using algebraic Riccati equation solutions and PID control. This study will also present comparison between these controllers.

Given that a time-delay system is stable for some delay h 0 > 0, a procedure is given to find the stability interval

Journal of Process Control, 2012

This paper focuses on the robust stability analysis of the filtered Smith predictor (FSP) dead-time compensator for uncertain processes with time-varying delays. For this purpose, a delay-dependent LMI-based condition is used to compute a maximum delay interval and tolerance to model uncertainties such that the closed-loop system remains stable. Some simulation results illustrate that the proposed controller gives larger delays intervals or better performance than similar approaches proposed in literature applied both to stable and unstable processes. (J.E. Normey-Rico).

The article provides sufficient conditions for both practical and finite time stability of linear continuous time delay systems described as

This paper overviews the research investigations pertaining to stability and stabilization of control systems with time-delays. The prime focus is the fundamental results and recent progress in theory and applications. The overview sheds light on the contemporary development on the linear matrix inequality (LMI) techniques in deriving both delay-independent and delay-dependent stability results for time-delay systems. Particular emphases will be placed on issues concerned with the conservatism and the computational complexity of the results. Key technical bounding lemmas and slack variable introduction approaches will be presented. The results will be compared and connections of certain delay-dependent stability results are also discussed.