Semi-Discretization for Time-Delay Systems PDF Download
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Author: Tamás Insperger
Publisher: Springer Science & Business Media
ISBN: 1461403359
Category : Mathematics
Languages : en
Pages : 181
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Book Description
This book presents the recently introduced and already widely referred semi-discretization method for the stability analysis of delayed dynamical systems. Delay differential equations often come up in different fields of engineering, like feedback control systems, machine tool vibrations, balancing/stabilization with reflex delay. The behavior of such systems is often counter-intuitive and closed form analytical formulas can rarely be given even for the linear stability conditions. If parametric excitation is coupled with the delay effect, then the governing equation is a delay differential equation with time periodic coefficients, and the stability properties are even more intriguing. The semi-discretization method is a simple but efficient method that is based on the discretization with respect to the delayed term and the periodic coefficients only. The method can effectively be used to construct stability diagrams in the space of system parameters.
Author: Tamás Insperger
Publisher: Springer Science & Business Media
ISBN: 1461403359
Category : Mathematics
Languages : en
Pages : 181
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Book Description
This book presents the recently introduced and already widely referred semi-discretization method for the stability analysis of delayed dynamical systems. Delay differential equations often come up in different fields of engineering, like feedback control systems, machine tool vibrations, balancing/stabilization with reflex delay. The behavior of such systems is often counter-intuitive and closed form analytical formulas can rarely be given even for the linear stability conditions. If parametric excitation is coupled with the delay effect, then the governing equation is a delay differential equation with time periodic coefficients, and the stability properties are even more intriguing. The semi-discretization method is a simple but efficient method that is based on the discretization with respect to the delayed term and the periodic coefficients only. The method can effectively be used to construct stability diagrams in the space of system parameters.
Author: Tam?'s Insperger
Publisher:
ISBN: 9781461403364
Category :
Languages : en
Pages : 186
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Book Description
Author: Jian-qiao Sun
Publisher: World Scientific
ISBN: 9814525510
Category : Technology & Engineering
Languages : en
Pages : 355
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Book Description
Analysis and control of time-delayed systems have been applied in a wide range of applications, ranging from mechanical, control, economic, to biological systems. Over the years, there has been a steady stream of interest in time-delayed dynamic systems, this book takes a snap shot of recent research from the world leading experts in analysis and control of dynamic systems with time delay to provide a bird's eye view of its development. The topics covered in this book include solution methods, stability analysis and control of periodic dynamic systems with time delay, bifurcations, stochastic dynamics and control, delayed Hamiltonian systems, uncertain dynamic systems with time delay, and experimental investigations of delayed structural control.
Author: Qingbin Gao
Publisher: Butterworth-Heinemann
ISBN: 0128149299
Category : Technology & Engineering
Languages : en
Pages : 490
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Book Description
Stability, Control and Application of Time-Delay Systems gives a systematic description of these systems. It includes adequate designs of integrated modeling and control and frequency characterizations. Common themes revolve around creating certain synergies of modeling, analysis, control, computing and applications of time delay systems that achieve robust stability while retaining desired performance quality. The book provides innovative insights into the state-of-the-art of time-delay systems in both theory and practical aspects. It has been edited with an emphasis on presenting constructive theoretical and practical methodological approaches and techniques. - Unifies existing and emerging concepts concerning time delay dynamical systems - Provides a series of the latest results in large-delay analysis and multi-agent and thermal systems with delays - Gives in each chapter numerical and simulation results in order to reflect the engineering practice
Author: Bin Zhou
Publisher: Springer
ISBN: 3642542069
Category : Technology & Engineering
Languages : en
Pages : 494
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Book Description
This book provides a systematic approach to the design of predictor based controllers for (time-varying) linear systems with either (time-varying) input or state delays. Differently from those traditional predictor based controllers, which are infinite-dimensional static feedback laws and may cause difficulties in their practical implementation, this book develops a truncated predictor feedback (TPF) which involves only finite dimensional static state feedback. Features and topics: A novel approach referred to as truncated predictor feedback for the stabilization of (time-varying) time-delay systems in both the continuous-time setting and the discrete-time setting is built systematically Semi-global and global stabilization problems of linear time-delay systems subject to either magnitude saturation or energy constraints are solved in a systematic manner Both stabilization of a single system and consensus of a group of systems (multi-agent systems) are treated in a unified manner by applying the truncated predictor feedback and predictor feedback The properties of the solutions to a class of parametric (differential and difference) Lyapunov matrix equations are presented in detail Detailed numerical examples and applications to the spacecraft rendezvous and formation flying problems are provided to demonstrate the usefulness of the presented theoretical results This book can be a useful resource for the researchers, engineers, and graduate students in the fields of control, applied mathematics, mechanical engineering, electrical engineering, and aerospace engineering.
Author: Siyuan Xing
Publisher: Springer Nature
ISBN: 3031796691
Category : Technology & Engineering
Languages : en
Pages : 73
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Book Description
In this book, the global sequential scenario of bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is presented for a better understanding of global behaviors and motion transitions for one periodic motion to another one. A 1-dimensional (1-D), time-delayed, nonlinear dynamical system is considered as an example to show how to determine the global sequential scenarios of the bifurcation trees of periodic motions to chaos. All stable and unstable periodic motions on the bifurcation trees can be determined. Especially, the unstable periodic motions on the bifurcation trees cannot be achieved from the traditional analytical methods, and such unstable periodic motions and chaos can be obtained through a specific control strategy. The sequential periodic motions in such a 1-D time-delayed system are achieved semi-analytically, and the corresponding stability and bifurcations are determined by eigenvalue analysis. Each bifurcation tree of a specific periodic motion to chaos are presented in detail. The bifurcation tree appearance and vanishing are determined by the saddle-node bifurcation, and the cascaded period-doubled periodic solutions are determined by the period-doubling bifurcation. From finite Fourier series, harmonic amplitude and harmonic phases for periodic motions on the global bifurcation tree are obtained for frequency analysis. Numerical illustrations of periodic motions are given for complex periodic motions in global bifurcation trees. The rich dynamics of the 1-D, delayed, nonlinear dynamical system is presented. Such global sequential periodic motions to chaos exist in nonlinear dynamical systems. The frequency-amplitude analysis can be used for re-construction of analytical expression of periodic motions, which can be used for motion control in dynamical systems.
Author: Jean Jacques Loiseau
Publisher: Springer Science & Business Media
ISBN: 3642028969
Category : Mathematics
Languages : en
Pages : 407
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Book Description
Time delays are present in many physical processes due to the period of time it takes for the events to occur. Delays are particularly more pronounced in networks of interconnected systems, such as supply chains and systems controlled over c- munication networks. In these control problems, taking the delays into account is particularly important for performance evaluation and control system’s design. It has been shown, indeed, that delays in a controlled system (for instance, a c- munication delay for data acquisition) may have an “ambiguous” nature: they may stabilize the system, or, in the contrary,they may lead to deteriorationof the clos- loop performance or even instability, depending on the delay value and the system parameters. It is a fact that delays have stabilizing effects, but this is clearly con i- ing for human intuition. Therefore,speci c analysis techniquesand design methods are to be developed to satisfactorily take into account the presence of delays at the design stage of the control system. The research on time delay systems stretches back to 1960s and it has been very active during the last twenty years. During this period, the results have been presented at the main control conferences(CDC, ACC, IFAC), in specialized wo- shops (IFAC TDS series), and published in the leading journals of control engine- ing, systems and control theory, applied and numerical mathematics.
Author: Albert C. J. Luo
Publisher: Springer
ISBN: 3319427784
Category : Technology & Engineering
Languages : en
Pages : 307
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Book Description
This book examines discrete dynamical systems with memory—nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.
Author: Mohammad-Hassan Khooban
Publisher: Academic Press
ISBN: 032385804X
Category : Technology & Engineering
Languages : en
Pages : 308
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Book Description
Since delays are present in 99% of industrial processes, Control Strategy for Time-delay Systems covers all the important features of real-world practical applications which will be valuable to practicing engineers and specialists The book presents the views of the editors on promising research directions and future industrial applications in this area. Although the fundamentals of time-delay systems are discussed, the book focuses on the advanced modelling and control of such systems and will provide the analysis and test (or simulation) results of nearly every technique described in the book For this purpose, highly complex models are introduced to ?describe the mentioned new applications which are characterized by ?time-varying delays with intermittent and stochastic nature, several types of nonlinearities, and the presence ?of different time-scales. Researchers, practitioners and PhD students will gain insights into the prevailing trends in design and operation of real-time control systems, reviewing the shortcomings and future developments concerning the practical system issues such as standardization, protection and design.
Author: Wim Michiels
Publisher: SIAM
ISBN: 0898716322
Category : Mathematics
Languages : en
Pages : 383
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Book Description
An overall solution to the (robust) stability analysis and stabilisation problem of linear time-delay systems.
