Computational Aspects of Linear Control

Computational Aspects of Linear Control PDF

Author: Claude Brezinski

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 296

ISBN-13: 1461302617

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Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed. The problem is to regulate the input in order to control the output, that is for obtaining a desired output. Such a mechanism, where the input is modified according to the output measured, is called feedback. The study and design of such automatic processes is called control theory. As we will see, the term system embraces any device and control theory has a wide variety of applications in the real world. Control theory is an interdisci plinary domain at the junction of differential and difference equations, system theory and statistics. Moreover, the solution of a control problem involves many topics of numerical analysis and leads to many interesting computational problems: linear algebra (QR, SVD, projections, Schur complement, structured matrices, localization of eigenvalues, computation of the rank, Jordan normal form, Sylvester and other equations, systems of linear equations, regulariza tion, etc), root localization for polynomials, inversion of the Laplace transform, computation of the matrix exponential, approximation theory (orthogonal poly nomials, Pad6 approximation, continued fractions and linear fractional transfor mations), optimization, least squares, dynamic programming, etc. So, control theory is also a. good excuse for presenting various (sometimes unrelated) issues of numerical analysis and the procedures for their solution. This book is not a book on control.

Stabilization Problems with Constraints

Stabilization Problems with Constraints PDF

Author: Vladimir A Bushenkov

Publisher: CRC Press

Published: 2021-12-17

Total Pages: 302

ISBN-13: 1000657469

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Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.

Stabilization Problems with Constraints

Stabilization Problems with Constraints PDF

Author: Vladimir A Bushenkov

Publisher: CRC Press

Published: 1998-04-29

Total Pages: 306

ISBN-13: 9789056991418

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Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.

Computational Aspects of Structural Acoustics and Vibration

Computational Aspects of Structural Acoustics and Vibration PDF

Author: Göran Sandberg

Publisher: Springer Science & Business Media

Published: 2009-06-18

Total Pages: 276

ISBN-13: 3211896511

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Computational methods within structural acoustics, vibration and fluid-structure interaction are powerful tools for investigating acoustic and structural-acoustic problems in many sectors of industry; in the building industry regarding room acoustics, in the car industry and aeronautical industry for optimizing structural components with regard to vibrations characteristics etc. It is on the verge of becoming a common tool for noise characterization and design for optimizing structural properties and geometries in order to accomplish a desired acoustic environment. The book covers the field of computational mechanics, and then moved into the field of formulations of multiphysics and multiscale. The book is addressed to graduate level, PhD students and young researchers interested in structural dynamics, vibrations and acoustics. It is also suitable for industrial researchers in mechanical, aeronautical and civil engineering with a professional interest in structural dynamics, vibrations and acoustics or involved in questions regarding noise characterization and reduction in building, car, plane, space, train, industries by means of computer simulations.

Mathematical and Computational Aspects

Mathematical and Computational Aspects PDF

Author: Carlos A. Brebbia

Publisher: Springer Science & Business Media

Published: 2013-11-21

Total Pages: 601

ISBN-13: 3662219085

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This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conference also discussed the engineering applications of the method and concentrated on a link between BEM practitioners, industrial users and researchers working on the latest development of the method. The editors would like to express their appreciation and thanks to Ms. Liz Newman and Mr. H. Schmitz for their unstinting work in the preparation of the Conference.

Explicit Nonlinear Model Predictive Control

Explicit Nonlinear Model Predictive Control PDF

Author: Alexandra Grancharova

Publisher: Springer

Published: 2012-03-22

Total Pages: 241

ISBN-13: 3642287808

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Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: ؠ Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; - Nonlinear systems with continuous control inputs and nonlinear systems with quantized control inputs; - Nonlinear systems without uncertainty and nonlinear systems with uncertainties (polyhedral description of uncertainty and stochastic description of uncertainty); - Nonlinear systems, consisting of interconnected nonlinear sub-systems. The proposed mp-NLP approaches are illustrated with applications to several case studies, which are taken from diverse areas such as automotive mechatronics, compressor control, combustion plant control, reactor control, pH maintaining system control, cart and spring system control, and diving computers.

Computational Aspects of Electric Polarizability Calculations

Computational Aspects of Electric Polarizability Calculations PDF

Author: George Maroulis

Publisher: IOS Press

Published: 2006

Total Pages: 542

ISBN-13: 9781586036430

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Covers such subjects as: Ab initio and Density functional theory calculations of electric polarizability and hyperpolarizability, intermolecular forces, aromaticity, electric properties of solvated molecules, NLO materials, Raman intensities, polarizability of metal and semiconductor clusters, relativistic effects on electric properties, and more.

Assessment and Future Directions of Nonlinear Model Predictive Control

Assessment and Future Directions of Nonlinear Model Predictive Control PDF

Author: Rolf Findeisen

Publisher: Springer

Published: 2007-09-08

Total Pages: 644

ISBN-13: 3540726993

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Thepastthree decadeshaveseenrapiddevelopmentin the areaofmodelpred- tive control with respect to both theoretical and application aspects. Over these 30 years, model predictive control for linear systems has been widely applied, especially in the area of process control. However, today’s applications often require driving the process over a wide region and close to the boundaries of - erability, while satisfying constraints and achieving near-optimal performance. Consequently, the application of linear control methods does not always lead to satisfactory performance, and here nonlinear methods must be employed. This is one of the reasons why nonlinear model predictive control (NMPC) has - joyed signi?cant attention over the past years,with a number of recent advances on both the theoretical and application frontier. Additionally, the widespread availability and steadily increasing power of today’s computers, as well as the development of specially tailored numerical solution methods for NMPC, bring thepracticalapplicabilityofNMPCwithinreachevenforveryfastsystems.This has led to a series of new, exciting developments, along with new challenges in the area of NMPC.

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