Control Of Structures

This book is an outgrowth of several years of teaching and research of the two authors in the field of structural dynamics and control. The content of the book is based on structural dynamics, classical and modern control theory and involves also recent developments that took place with respect to the control of systems with distri buted masses. It is hoped that the book will serve the researcher and the practicing engineer in the areas of ci vi 1, mechanical and aeronautical engineering. It may also be of interest to applied mathematicians and to physicists. There is no question that the book can be used as a reference book for advanced courses in the above mentioned areas. The numerous examples will provide students with the necessary material for exercising themselves and for self studying. Thanks are due to Mrs. Cynthia Jones for preparing patiently and competently the typescript of the book. The services of Mrs. Linda Strouth, Solid Mechanics Division, University of Waterloo, rendered in producing the camera-ready copy of the book with great skill and devotion, are gratefully acknowledged. Special thanks go to Mr. Ir. Ad. C. Plaizier, at Martinus Nijhoff/Dr. W. Junk, who with much understanding and enthusiasm supervised the production of the book as Publisher. May the readers of it enjoy it, and may they have the fee ling of having gained something in turning to it and using it.

This book addresses problems in structural dynamics and control encountered in applications such as robotics, aerospace structures, earthquake-damage prevention, and active noise suppression. The rapid developments of new technologies and computational power have made it possible to formulate and solve engineering problems that seemed unapproachable only a few years ago. This presentation combines concepts from control engineering (such as system norms and controllability) and structural engineering (such as modal properties and models), thereby revealing new structural properties as well as giving new insight into well-known laws. This book will assist engineers in designing control systems and dealing with the complexities of structural dynamics.

Science is for those who learn; poetry for those who know. —Joseph Roux This book is a continuation of my previous book, Dynamics and Control of Structures [44]. The expanded book includes three additional chapters and an additional appendix: Chapter 3, “Special Models”; Chapter 8, “Modal Actuators and Sensors”; and Chapter 9, “System Identification. ” Other chapters have been significantly revised and supplemented with new topics, including discrete-time models of structures, limited-time and -frequency grammians and reduction, almo- balanced modal models, simultaneous placement of sensors and actuators, and structural damage detection. The appendices have also been updated and expanded. Appendix A consists of thirteen new Matlab programs. Appendix B is a new addition and includes eleven Matlab programs that solve examples from each chapter. In Appendix C model data are given. Several books on structural dynamics and control have been published. Meirovitch’s textbook [108] covers methods of structural dynamics (virtual work, d’Alambert’s principle, Hamilton’s principle, Lagrange’s and Hamilton’s equations, and modal analysis of structures) and control (pole placement methods, LQG design, and modal control). Ewins’s book [33] presents methods of modal testing of structures. Natke’s book [111] on structural identification also contains excellent material on structural dynamics. Fuller, Elliot, and Nelson [40] cover problems of structural active control and structural acoustic control.

A text/reference on analysis of structures that deform in use. Presents a new, integrated approach to analytical dynamics, structural dynamics and control theory and goes beyond classical dynamics of rigid bodies to incorporate analysis of flexibility of structures. Includes real-world examples of applications such as robotics, precision machinery and aircraft structures.

This book presents a comprehensive introduction to the field of structural vibration reduction control, but may also be used as a reference source for more advanced topics. The content is divided into four main parts: the basic principles of structural vibration reduction control, structural vibration reduction devices, structural vibration reduction design methods, and structural vibration reduction engineering practices. As the book strikes a balance between theoretical and practical aspects, it will appeal to researchers and practicing engineers alike, as well as graduate students.

This book, intended for people in engineering and fundamental sciences, presents an integrated mathematical methodology for advanced dynamics and control of structures and machines, ranging from the derivation of models up to the control synthesis problem. This point of view is particularly useful as the physical insight and the associated structural properties, related e.g. to the Lagrangian or Hamiltonian framework, can be advantageously utilized. To this end, up to date results in disciplines like continuum mechanics, analytical mechanics, thermodynamics and electrodynamics are presented exploiting the differential geometric properties, with the basic notions of this coordinate-free approach revisited in an own chapter. In order to illustrate the proposed methodologies, several industrial applications, e.g., the derivation of exact solutions for the deformation compensation by shaped actuation in elastic bodies, or the coordination of rigid and flexible joint robots, are discussed.

My objective in writing this book was to cross the bridge between the structural dynamics and control communities, while providing an overview of the potential of SMART materials for sensing and actuating purposes in active vibration c- trol. I wanted to keep it relatively simple and focused on systems which worked. This resulted in the following: (i) I restricted the text to fundamental concepts and left aside most advanced ones (i.e. robust control) whose usefulness had not yet clearly been established for the application at hand. (ii) I promoted the use of collocated actuator/sensor pairs whose potential, I thought, was strongly underestimated by the control community. (iii) I emphasized control laws with guaranteed stability for active damping (the wide-ranging applications of the IFF are particularly impressive). (iv) I tried to explain why an accurate pred- tion of the transmission zeros (usually called anti-resonances by the structural dynamicists) is so important in evaluating the performance of a control system. (v) I emphasized the fact that the open-loop zeros are more difficult to predict than the poles, and that they could be strongly influenced by the model trun- tion (high frequency dynamics) or by local effects (such as membrane strains in piezoelectric shells), especially for nearly collocated distributed actuator/sensor pairs; this effect alone explains many disappointments in active control systems.