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Title: Multiple-input Describing Functions and Nonlinear System Design
Author: Arthur Gelb and Wallace E. Vander Velde
Pages: 655
Year: 1968
Publisher: McGraw-Hill Book Company, New York
Description:
The theory of automatic control has been advanced in important ways during recent years, particularly with respect to stability and optimal contro1. These are significant contributions which appeal to many workers, including the writers, because they answer important questions and are both theoretically elegant and practically useful. These theories do not, however, Jay to rest all questions of importance to the control engineer. The designer of th attitude control system for a space vehicle booster which, for simplicity, utilizes a rate-switched engine gimbal drive, must know the characteristics of the limit cycle oscillation that the system will sustain and must have some idea of how the system will respond to attitude commands while continuing to limit-cycle. The designer of a chemical process control system must be able to predict the transient oscillations the process may experience during start-up due to the limited magnitudes of important variables in the system. The designer of a radar antenna pointing system with limited torque capability must be able to predict the rms pointing error due to random wind disturbances on the antenna, and must understand how these random disturbances will influence the behavior of the system in its response to command inputs. But more important than just being able to evaluate how a given system will behave in a postulated situation is the fact that these control engineers must design their systems to meet specifications on important characteristics. Thus a complicated exact analytical tool, if one existed, would be of less va1ue to the designer than an approximate tool which is simple enough in application to give insight into the trends in system behavior as a function of system parameter values or possible compensations, hence providing the basis for system design. As an analytical tool to answer questions such as these in a way which is useful to the system designer, the multiple-input describing function remains unexcelled.
This book is intended to provide a comprehensive documentation of describing function theory and application. It begins with a unified theory of quasi-linear approximation to nonlinear operators within which are embraced all the useful describing functions.. It continues with the application of these describing functions to the study of a wide variety of characteristics of nonlinear-system operation under different input conditions.. Emphasis is given to the design of these nonlinear systems to meet specified operating characteristics. The book concludes with a complete tabular and graphical presentation of the different describing functions discussed in the text, corresponding to a broad family of nonlinear functions. Dealing as it does with the sing1e subject of describing functions, the book would seem to be very specialized in scope. And so it is. Yet the range of practical and important questions regarding the operation of nonlinear systems which this family of describing functions is capable of answering is so broad that the writers have had to set deliberate limits on the lengths of chapters to keep the book within reasonable size. Thus the subject is specialized to a single analytical tool which has exceedingly broad applicability.
This presentation is intended both for graduate students in control theory and for practicing control engineers. Describing function theory is applicable to problems other than the analysis and design of feedback control systems, and this is illustrated by some of the examples and problems in the book. But the principal application has been to control systems, and this has been the major focus of the book. The presentation is too comprehensive, and the subject too specialized, for the book to serve as the textbook in most graduate control courses, but it can serve very well as one of several reference books for such courses. In a graduate control course in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology, the subject of this book is covered in a period of four or five weeks twelve to fifteen lecture hours. The presentation of this book is not abbreviated primarily by omitting whole sections; rather the principal ideas of almost every section are summarized briefly in class.. A selection of these concepts is further developed through the problems. Such a presentation does not bring the student to the point of mastery of the subject, but it can give him a good understanding of the principal ideas underlying describing function theory and application. With this, the student can recognize the areas of useful applicability and can readily use the book as a reference to help him address the problems that arise in his professional experIence.
The practicing control engineer should find tl1e book valuable as a complete reference work in the subject area. If his background in mathematics is not sufficient to enable him to foJlow the theoretical development of Chapter] comfortably, he can omit that chapter and will stilI find a complete presentation in every chapter except Chapters 7 and 8, based on the physically motivated concept of harmonIc analysis of the nonlinearity output. Chapter 7, whIch includes random processes at the nonlinearity input, requires a statistical approach.. But this too reduces to a rather simple matter in the very important class of problems involving static single-valued nonlinearities. Chapter 8 treats transient responses by related forms of quasi-linearization which are developed completely within that
chapter. Thus it is hoped that every control engineer will find the principal ideas presented in a manner which is meaningful and appealing to him.
Code
http://ifile.it/m7365w9/mit-gelb.rar
http://rapidshare.com/files/192141562/mit-gelb.rar
Author: Arthur Gelb and Wallace E. Vander Velde
Pages: 655
Year: 1968
Publisher: McGraw-Hill Book Company, New York
Description:
The theory of automatic control has been advanced in important ways during recent years, particularly with respect to stability and optimal contro1. These are significant contributions which appeal to many workers, including the writers, because they answer important questions and are both theoretically elegant and practically useful. These theories do not, however, Jay to rest all questions of importance to the control engineer. The designer of th attitude control system for a space vehicle booster which, for simplicity, utilizes a rate-switched engine gimbal drive, must know the characteristics of the limit cycle oscillation that the system will sustain and must have some idea of how the system will respond to attitude commands while continuing to limit-cycle. The designer of a chemical process control system must be able to predict the transient oscillations the process may experience during start-up due to the limited magnitudes of important variables in the system. The designer of a radar antenna pointing system with limited torque capability must be able to predict the rms pointing error due to random wind disturbances on the antenna, and must understand how these random disturbances will influence the behavior of the system in its response to command inputs. But more important than just being able to evaluate how a given system will behave in a postulated situation is the fact that these control engineers must design their systems to meet specifications on important characteristics. Thus a complicated exact analytical tool, if one existed, would be of less va1ue to the designer than an approximate tool which is simple enough in application to give insight into the trends in system behavior as a function of system parameter values or possible compensations, hence providing the basis for system design. As an analytical tool to answer questions such as these in a way which is useful to the system designer, the multiple-input describing function remains unexcelled.
This book is intended to provide a comprehensive documentation of describing function theory and application. It begins with a unified theory of quasi-linear approximation to nonlinear operators within which are embraced all the useful describing functions.. It continues with the application of these describing functions to the study of a wide variety of characteristics of nonlinear-system operation under different input conditions.. Emphasis is given to the design of these nonlinear systems to meet specified operating characteristics. The book concludes with a complete tabular and graphical presentation of the different describing functions discussed in the text, corresponding to a broad family of nonlinear functions. Dealing as it does with the sing1e subject of describing functions, the book would seem to be very specialized in scope. And so it is. Yet the range of practical and important questions regarding the operation of nonlinear systems which this family of describing functions is capable of answering is so broad that the writers have had to set deliberate limits on the lengths of chapters to keep the book within reasonable size. Thus the subject is specialized to a single analytical tool which has exceedingly broad applicability.
This presentation is intended both for graduate students in control theory and for practicing control engineers. Describing function theory is applicable to problems other than the analysis and design of feedback control systems, and this is illustrated by some of the examples and problems in the book. But the principal application has been to control systems, and this has been the major focus of the book. The presentation is too comprehensive, and the subject too specialized, for the book to serve as the textbook in most graduate control courses, but it can serve very well as one of several reference books for such courses. In a graduate control course in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology, the subject of this book is covered in a period of four or five weeks twelve to fifteen lecture hours. The presentation of this book is not abbreviated primarily by omitting whole sections; rather the principal ideas of almost every section are summarized briefly in class.. A selection of these concepts is further developed through the problems. Such a presentation does not bring the student to the point of mastery of the subject, but it can give him a good understanding of the principal ideas underlying describing function theory and application. With this, the student can recognize the areas of useful applicability and can readily use the book as a reference to help him address the problems that arise in his professional experIence.
The practicing control engineer should find tl1e book valuable as a complete reference work in the subject area. If his background in mathematics is not sufficient to enable him to foJlow the theoretical development of Chapter] comfortably, he can omit that chapter and will stilI find a complete presentation in every chapter except Chapters 7 and 8, based on the physically motivated concept of harmonIc analysis of the nonlinearity output. Chapter 7, whIch includes random processes at the nonlinearity input, requires a statistical approach.. But this too reduces to a rather simple matter in the very important class of problems involving static single-valued nonlinearities. Chapter 8 treats transient responses by related forms of quasi-linearization which are developed completely within that
chapter. Thus it is hoped that every control engineer will find the principal ideas presented in a manner which is meaningful and appealing to him.
Code
http://ifile.it/m7365w9/mit-gelb.rar
http://rapidshare.com/files/192141562/mit-gelb.rar
