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Author: Ashraf M. Abou-Rayan
Publisher:
ISBN:
Category : Nonlinear oscillators
Languages : en
Pages : 382
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Book Description
Author: Ashraf M. Abou-Rayan
Publisher:
ISBN:
Category : Nonlinear oscillators
Languages : en
Pages : 382
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Book Description
Author: Ashraf Mohamed Abou-Rayan
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 191
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Book Description
Author: Elbert Hendricks
Publisher: Springer Science & Business Media
ISBN: 3540784861
Category : Technology & Engineering
Languages : en
Pages : 555
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Book Description
Modern control theory and in particular state space or state variable methods can be adapted to the description of many different systems because it depends strongly on physical modeling and physical intuition. The laws of physics are in the form of differential equations and for this reason, this book concentrates on system descriptions in this form. This means coupled systems of linear or nonlinear differential equations. The physical approach is emphasized in this book because it is most natural for complex systems. It also makes what would ordinarily be a difficult mathematical subject into one which can straightforwardly be understood intuitively and which deals with concepts which engineering and science students are already familiar. In this way it is easy to immediately apply the theory to the understanding and control of ordinary systems. Application engineers, working in industry, will also find this book interesting and useful for this reason. In line with the approach set forth above, the book first deals with the modeling of systems in state space form. Both transfer function and differential equation modeling methods are treated with many examples. Linearization is treated and explained first for very simple nonlinear systems and then more complex systems. Because computer control is so fundamental to modern applications, discrete time modeling of systems as difference equations is introduced immediately after the more intuitive differential equation models. The conversion of differential equation models to difference equations is also discussed at length, including transfer function formulations. A vital problem in modern control is how to treat noise in control systems. Nevertheless this question is rarely treated in many control system textbooks because it is considered to be too mathematical and too difficult in a second course on controls. In this textbook a simple physical approach is made to the description of noise and stochastic disturbances which is easy to understand and apply to common systems. This requires only a few fundamental statistical concepts which are given in a simple introduction which lead naturally to the fundamental noise propagation equation for dynamic systems, the Lyapunov equation. This equation is given and exemplified both in its continuous and discrete time versions. With the Lyapunov equation available to describe state noise propagation, it is a very small step to add the effect of measurements and measurement noise. This gives immediately the Riccati equation for optimal state estimators or Kalman filters. These important observers are derived and illustrated using simulations in terms which make them easy to understand and easy to apply to real systems. The use of LQR regulators with Kalman filters give LQG (Linear Quadratic Gaussian) regulators which are introduced at the end of the book. Another important subject which is introduced is the use of Kalman filters as parameter estimations for unknown parameters. The textbook is divided into 7 chapters, 5 appendices, a table of contents, a table of examples, extensive index and extensive list of references. Each chapter is provided with a summary of the main points covered and a set of problems relevant to the material in that chapter. Moreover each of the more advanced chapters (3 - 7) are provided with notes describing the history of the mathematical and technical problems which lead to the control theory presented in that chapter. Continuous time methods are the main focus in the book because these provide the most direct connection to physics. This physical foundation allows a logical presentation and gives a good intuitive feel for control system construction. Nevertheless strong attention is also given to discrete time systems. Very few proofs are included in the book but most of the important results are derived. This method of presentation makes the text very readable and gives a good foundation for reading more rigorous texts. A complete set of solutions is available for all of the problems in the text. In addition a set of longer exercises is available for use as Matlab/Simulink ‘laboratory exercises’ in connection with lectures. There is material of this kind for 12 such exercises and each exercise requires about 3 hours for its solution. Full written solutions of all these exercises are available.
Author: Ho-Seong Mha
Publisher:
ISBN:
Category : Piecewise linear topology
Languages : en
Pages : 360
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Book Description
The (nonlinear) response behavior of a piecewise-linear system is investigated under both deterministic and stochastic excitations in this study. A semi-analytical procedure is developed to predict the system behavior by evaluating the joint probability density functions of the Fokker-Planck equations of the stochastic piecewise-linear system under random excitations via a path-integral solution procedure. From an analysis of the deterministic system, nonlinear system behavior is derived for further analysis of the corresponding stochastic system. The influence of variations in other parameters on the response behavior are also examined. In the stochastic system analysis, which represents a more realistic approach to understanding the system behavior, a Markov process approach is used. By introducing random perturbations in the harmonic excitation, the stochastic responses are examined and compared to those of the corresponding deterministic system. Stability of the various responses including regular and chaotic motions, is investigated by varying the noise intensity. Routes to chaos in period-doubling processes with and without external random perturbations are studied and compared. Stationarity and ergodicity of the chaotic responses of the system are examined via time domain and probability domain simulations. Potential coexisting responses of the piecewise-linear system are examined via the path-integral solutions. It is found that the path-integral solutions can provide global information of the system behavior in the probability domain, and can also verify the potential coexisting responses and discern the relative strength of the coexisting response attractors.
Author: El-Kebir Boukas
Publisher: Springer Science & Business Media
ISBN: 1461200776
Category : Mathematics
Languages : en
Pages : 429
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Book Description
Most practical processes such as chemical reactor, industrial furnace, heat exchanger, etc., are nonlinear stochastic systems, which makes their con trol in general a hard problem. Currently, there is no successful design method for this class of systems in the literature. One common alterna tive consists of linearizing the nonlinear dynamical stochastic system in the neighborhood of an operating point and then using the techniques for linear systems to design the controller. The resulting model is in general an approximation of the real behavior of a dynamical system. The inclusion of the uncertainties in the model is therefore necessary and will certainly improve the performance of the dynamical system we want to control. The control of uncertain systems has attracted a lot of researchers from the control community. This topic has in fact dominated the research effort of the control community during the last two decades, and many contributions have been reported in the literature. Some practical dynamical systems have time delay in their dynamics, which makes their control a complicated task even in the deterministic case. Recently, the class ofuncertain dynamical deterministic systems with time delay has attracted some researchers, and some interesting results have been reported in both deterministic and stochastic cases. But wecan't claim that the control problem ofthis class ofsystems is completely solved; more work must be done for this class of systems.
Author: Abdellatif Ben Makhlouf
Publisher: Springer Nature
ISBN: 3031379705
Category : Technology & Engineering
Languages : en
Pages : 439
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Book Description
This book presents the separation principle which is also known as the principle of separation of estimation and control and states that, under certain assumptions, the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the system's state, which feeds into an optimal deterministic controller for the system. Thus, the problem may be divided into two halves, which simplifies its design. In the context of deterministic linear systems, the first instance of this principle is that if a stable observer and stable state feedback are built for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback are stable. The separation principle does not true for nonlinear systems in general. Another instance of the separation principle occurs in the context of linear stochastic systems, namely that an optimum state feedback controller intended to minimize a quadratic cost is optimal for the stochastic control problem with output measurements. The ideal solution consists of a Kalman filter and a linear-quadratic regulator when both process and observation noise are Gaussian. The term for this is linear-quadratic-Gaussian control. More generally, given acceptable conditions and when the noise is a martingale (with potential leaps), a separation principle, also known as the separation principle in stochastic control, applies when the noise is a martingale (with possible jumps).
Author: Péter Érdi
Publisher: Manchester University Press
ISBN: 9780719022081
Category : Chemical reactions
Languages : en
Pages : 296
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Book Description
Author: L. Arnold
Publisher: Springer Science & Business Media
ISBN: 3642680380
Category : Science
Languages : en
Pages : 239
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Book Description
This book contains the invited papers of the interdisciplinary workshop on "Stochastic Nonlinear Systems in Physics, Chemistry and Biology" held at the Center for Interdisciplinary Research (ZIF), University of Bielefeld, West Germany, October 5-11, 1980. The workshop brought some 25 physicists, chemists, and biologists - who deal with stochastic phenomena - and about an equal number of mathematicians - who are experts in the theory of stochastic processes - together. The Scientific Commitee consisted of L. Arnold (Bremen), A. Dress (Bielefeld), W. Horsthemke (Brussels), T. Kurtz (Madison), R. Lefever (Brussels), G. Nicolis (Brussels), and V. Wihstutz (Bremen). The main topics of the workshop were the transition from deterministic to stoch astic behavior, external noise and noise induced transitions, internal fluctuations, phase transitions, and irreversible thermodynamics, and on the mathematical side, approximation of stochastic processes, qualitative theory of stochastic systems, and space-time processes. The workshop was sponsored by ZIF, Bielefeld, and by the Universities of Bremen and Brussels. We would like to thank the staff of ZIF and H. Crauel and M. Ehrhardt (Bremen) for the perfect organization and their assistance. In addition, our thanks go to Professor H. Haken for having these Proceedings included in the Se ries in Synergetics. Bremen and Brussels L. Arnold and R. Lefever December 1980 v Contents Part I. Introduction: From Deterministic to Stochastic Behavior On the Foundations of Kinetic Theory By B. Misr~ and I. Prigogine (With 1 Figure) ............................. .
Author: Harold James Payne
Publisher:
ISBN:
Category : Electronic dissertations
Languages : en
Pages : 326
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Book Description
Author: Jian-Qiao Sun
Publisher: Elsevier
ISBN: 0080463983
Category : Mathematics
Languages : en
Pages : 427
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Book Description
This book is a result of many years of author’s research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress processes are also presented. Classical feedback control, active damping, covariance control, optimal control, sliding control of stochastic systems, feedback control of stochastic time-delayed systems, and probability density tracking control are studied. Many control results are new in the literature and included in this book for the first time. The book serves as a reference to the engineers who design and maintain structures subject to harsh random excitations including earthquakes, sea waves, wind gusts, and aerodynamic forces, and would like to reduce the damages of structural systems due to random excitations. · Comprehensive review of probability theory, and stochastic processes· Random vibrations· Structural reliability and fatigue, Non-Gaussian fatigue· Monte Carlo methods· Stochastic calculus and engineering applications· Stochastic feedback controls and optimal controls· Stochastic sliding mode controls· Feedback control of stochastic time-delayed systems· Probability density tracking control
