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Author: W. M. Wonham
Publisher: Springer Science & Business Media
ISBN: 3662226731
Category : Science
Languages : en
Pages : 357
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Book Description
In writing this monograph my objective is to present arecent, 'geometrie' approach to the structural synthesis of multivariable control systems that are linear, time-invariant, and of finite dynamic order. The book is addressed to graduate students specializing in control, to engineering scientists engaged in control systems research and development, and to mathematicians with some previous acquaintance with control problems. The label 'geometrie' is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometrie) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometrie properties of distinguished state subspaces. Indeed, the geometry was first brought in out of revulsion against the orgy of matrix manipulation which linear control theory mainly consisted of, not so long ago. But secondlyand of greater interest, the geometrie setting rather quickly suggested new methods of attacking synthesis which have proved to be intuitive and economical; they are also easily reduced to matrix arith metic as soonas you want to compute. The essence of the 'geometrie' approach is just this: instead of looking directly for a feedback laW (say u = Fx) which would solve your synthesis problem if a solution exists, first characterize solvability as a verifiable property of some constructible state subspace, say J. Then, if all is weIl, you may calculate F from J quite easily.
Author: W. M. Wonham
Publisher: Springer Science & Business Media
ISBN: 3662226731
Category : Science
Languages : en
Pages : 357
Get Book
Book Description
In writing this monograph my objective is to present arecent, 'geometrie' approach to the structural synthesis of multivariable control systems that are linear, time-invariant, and of finite dynamic order. The book is addressed to graduate students specializing in control, to engineering scientists engaged in control systems research and development, and to mathematicians with some previous acquaintance with control problems. The label 'geometrie' is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometrie) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometrie properties of distinguished state subspaces. Indeed, the geometry was first brought in out of revulsion against the orgy of matrix manipulation which linear control theory mainly consisted of, not so long ago. But secondlyand of greater interest, the geometrie setting rather quickly suggested new methods of attacking synthesis which have proved to be intuitive and economical; they are also easily reduced to matrix arith metic as soonas you want to compute. The essence of the 'geometrie' approach is just this: instead of looking directly for a feedback laW (say u = Fx) which would solve your synthesis problem if a solution exists, first characterize solvability as a verifiable property of some constructible state subspace, say J. Then, if all is weIl, you may calculate F from J quite easily.
Author: W. Murray Wonham
Publisher:
ISBN: 9783540960713
Category : Control theory
Languages : en
Pages : 334
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Book Description
Author: Walter Murray Wonham
Publisher:
ISBN: 9783662226759
Category : Mathematical optimization
Languages : en
Pages : 347
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Book Description
In writing this monograph my objective is to present arecent, 'geometrie' approach to the structural synthesis of multivariable control systems that are linear, time-invariant, and of finite dynamic order. The book is addressed to graduate students specializing in control, to engineering scientists engaged in control systems research and development, and to mathematicians with some previous acquaintance with control problems. The label 'geometrie' is applied for several reasons. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract (geometrie) style. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometrie properties of distinguished state subspaces. Indeed, the geometry was first brought in out of revulsion against the orgy of matrix manipulation which linear control theory mainly consisted of, not so long ago. But secondlyand of greater interest, the geometrie setting rather quickly suggested new methods of attacking synthesis which have proved to be intuitive and economical; they are also easily reduced to matrix arith metic as soonas you want to compute. The essence of the 'geometrie' approach is just this: instead of looking directly for a feedback laW (say u = Fx) which would solve your synthesis problem if a solution exists, first characterize solvability as a verifiable property of some constructible state subspace, say J. Then, if all is weIl, you may calculate F from J quite easily.
Author: Shankar P. Bhattacharyya
Publisher: Cambridge University Press
ISBN: 1108841686
Category : Mathematics
Languages : en
Pages : 697
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Book Description
A graduate text providing broad coverage of linear multivariable control systems, including several new results and recent approaches.
Author: S.G. Tzafestas
Publisher: Springer Science & Business Media
ISBN: 9400964781
Category : Technology & Engineering
Languages : en
Pages : 509
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Book Description
The foundation of linear systems theory goes back to Newton and has been followed over the years by many improvements such as linear operator theory, Laplace Transformation etc. After the World War II, feedback control theory has shown a rapid development, and standard elegant analysis and synthesis techniques have been discovered by control system workers, such as root-locus (Evans) and frequency response methods (Nyquist, Bode). These permitted a fast and efficient analysis of simple-loop control systems, but in their original "paper-and-pencil" form were not appropriate for multiple loop high-order systems. The advent of fast digital computers, together with the development of multivariable multi-loop system techniques, have eliminated these difficulties. Multivariable control theory has followed two main avenues; the optimal control approach, and the algebraic and frequency-domain control approach. An important key concept in the whole multivariable system theory is "ob servability and controllability" which revealed the exact relationships between transfer functions and the state variable representations. This has given new insight into the phenomenon of "hidden oscillations" and to the transfer function modelling of dynamic systems. The basic tool in optimal control theory is the celebrated matrix Riccati differential equation which provides the time-varying feedback gains in a linear-quadratic control system cell. Much theory presently exists for the characteristic properties and solution of this Riccati equation.
Author: William S. Levine
Publisher: CRC Press
ISBN: 1420073656
Category : Technology & Engineering
Languages : en
Pages : 1798
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Book Description
At publication, The Control Handbook immediately became the definitive resource that engineers working with modern control systems required. Among its many accolades, that first edition was cited by the AAP as the Best Engineering Handbook of 1996. Now, 15 years later, William Levine has once again compiled the most comprehensive and authoritative resource on control engineering. He has fully reorganized the text to reflect the technical advances achieved since the last edition and has expanded its contents to include the multidisciplinary perspective that is making control engineering a critical component in so many fields. Now expanded from one to three volumes, The Control Handbook, Second Edition organizes cutting-edge contributions from more than 200 leading experts. The third volume, Control System Advanced Methods, includes design and analysis methods for MIMO linear and LTI systems, Kalman filters and observers, hybrid systems, and nonlinear systems. It also covers advanced considerations regarding — Stability Adaptive controls System identification Stochastic control Control of distributed parameter systems Networks and networked controls As with the first edition, the new edition not only stands as a record of accomplishment in control engineering but provides researchers with the means to make further advances. Progressively organized, the first two volumes in the set include: Control System Fundamentals Control System Applications
Author: Velimir Jurdjevic
Publisher: American Mathematical Soc.
ISBN: 9780821807958
Category : Mathematics
Languages : en
Pages : 256
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Book Description
Control theory, a synthesis of geometric theory of differential equations enriched with variational principles and the associated symplectic geometry, emerges as a new mathematical subject of interest to engineers, mathematicians, and physicists. This collection of articles focuses on several distinctive research directions having origins in mechanics and differential geometry, but driven by modern control theory. The first of these directions deals with the singularities of small balls for problems of sub-Riemannian geomtery and provides a generic classification of singularities for two-dimensional distributions of contact type in a three-dimensional ambient space. The second direction deals with invariant optimal problems on Lie groups exemplified through the problem of Dublins extended to symmetric spaces, the elastic problem of Kirchhoff and its relation to the heavy top. The results described in the book are explicit and demonstrate convincingly the power of geometric formalism. The remaining directions deal with the geometric nature of feedback analysed through the language of fiber bundles, and the connections of geometric control to non-holonomic problems in mechanics, as exemplified through the motions of a sphere on surfaces of revolution. This book provides quick access to new research directions in geometric control theory. It also demonstrates the effectiveness of new insights and methods that control theory brings to mechanics and geometry.
Author: Pedro Albertos
Publisher: Springer Science & Business Media
ISBN: 1852338431
Category : Technology & Engineering
Languages : en
Pages : 357
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Book Description
This book focuses on control design with continual references to the practical aspects of implementation. While the concepts of multivariable control are justified, the book emphasizes the need to maintain student interest and motivation over exhaustively rigorous mathematical proof.
Author: Sarah C. Hamilton
Publisher: Springer
ISBN: 3642288049
Category : Technology & Engineering
Languages : en
Pages : 160
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Book Description
This monograph is aiming at researchers of systems control, especially those interested in multiagent systems, distributed and decentralized control, and structured systems. The book assumes no prior background in geometric control theory; however, a first year graduate course in linear control systems is desirable. Since not all control researchers today are exposed to geometric control theory, the book also adopts a tutorial style by way of examples that illustrate the geometric and abstract algebra concepts used in linear geometric control. In addition, the matrix calculations required for the studied control synthesis problems of linear multivariable control are illustrated via a set of running design examples. As such, some of the design examples are of higher dimension than one may typically see in a text; this is so that all the geometric features of the design problem are illuminated.
Author: Olivier Sename
Publisher: Springer
ISBN: 3642361102
Category : Technology & Engineering
Languages : en
Pages : 402
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Book Description
Vehicles are complex systems (non-linear, multi-variable) where the abundance of embedded controllers should ensure better security. This book aims at emphasizing the interest and potential of Linear Parameter Varying methods within the framework of vehicle dynamics, e.g. proposed control-oriented model, complex enough to handle some system non linearities but still simple for control or observer design, take into account the adaptability of the vehicle's response to driving situations, to the driver request and/or to the road sollicitations, manage interactions between various actuators to optimize the dynamic behavior of vehicles. This book results from the 32th International Summer School in Automatic that held in Grenoble, France, in September 2011, where recent methods (based on robust control and LPV technics), then applied to the control of vehicle dynamics, have been presented. After some theoretical background and a view on some recent works on LPV approaches (for modelling, analysis, control, observation and diagnosis), the main emphasis is put on road vehicles but some illustrations are concerned with railway, aerospace and underwater vehicles. The main objective of the book is to demonstrate the value of this approach for controlling the dynamic behavior of vehicles. It presents, in a rm way, background and new results on LPV methods and their application to vehicle dynamics.
