Control of structures

421 Pages·1986·9.635 MB·English

by  H. H. E. Leipholz, M. Abdel-Rohman (auth.)

Control of structures
MECHANICS OF ELASTIC STABILITY
Editors: H.H.E. Leipholz and G.lE. Oravas
H.H.E. Leipholz, Theory of elasticity. 1974.
ISBN 90-286-0193-7
L. Librescu, Elastostatics and kinetics of anisotropic and heterogeneou:
shell-type structures. 1975.
ISBN 90-286-0035-3
C.L. Dym, Stability theory and its application to structural mechanics
1974.
ISBN 90-286-0094-9
K. Huseyin, Nonlinear theory of elastic stability. 1975.
ISBN 90-286-0344-1
H.H.E. Leipholz, Direct variational methods and eigenvalue problems if
engineering. 1977.
ISBN 90-286-0106-6
K. Huseyin, Vibrations and stability of multiple parameter systems. 1978
ISBN 90-286-0136-8
H.H.E. Leipholz, Stability of elastic systems. 1980.
ISBN 90-286-0050-7
V.V. Bolotin, Random vibrations of elastic systems. 1984.
ISBN 90-247-2981-5
D. Bushnell, Computerized buckling analysis of shells. 1985.
ISBN 90-247-3099-6
L.M. Kachanov, Introduction to continuum damage mechanics. 1986.
ISBN 90-247-3319-7
H.H.E. Leipholz and M. Abdel-Rohman, Control of structures. 1986.
ISBN 90-247-3321-9
Control of structures
by
H.H.E. Leipholz
University of Waterloo
Ontario, Canada
M. Abdel-Rohman
University of Kuwait
Kuwait
1986 MARTINUS NIJHOFF PUBLISHERS ....
a member of the KLUWER ACADEMIC PUBLISHERS GROUP ...
DORDRECHT / BOSTON / LANCASTER ,~~
Distributors
for the United States and Canada: Kluwer Academic Publishers, 190 Old Derby
Street, Hingham, MA 02043, USA
for the UK and Ireland: Kluwer Academic Publishers, MTP Press Limited,
Falcon House, Queen Square, Lancaster LAI lRN, UK
for all other countries: Kluwer Academic Publishers Group, Distribution Center,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands
Library of Congress Cataloging in Publication Data
Leipholz, H. H. E. (Horst H. E.), 1919-
Control of structures.
(Mechanics of elastic stability; 11)
Includes bibliographies and index.
1. Structural dynamics. 2. Control theory.
I. Abel-Rohman, M. II. Title. III. Series.
TA654.L44 1986 624.1'71 86-5365
ISBN ·13978·94·010·8458·1 e· ISBN ·13978·94·009·4402·2
DOl: 10.1007/978·94·009·4402·2
ISBN 90-247-3321-9 (this volume)
ISBN 90-247-2743-X (series)
Copyright
© 1986 by Martinus Nijhoff Publishers, Dordrecht.
Reprint of the original edition 1986
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted in any form or by any means, mechanical,
photocopying, recording, or otherwise, without the prior written permission of
the publishers,
Martinus Nijhoff Publishers, P.O. Box 163, 3300 AD Dordrecht,
The Netherlands.
v
Preface
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.
H.B.E. Leipholz
Waterloo, Ontario, Canada
M. Abdel-Rohman
Kuwait
Spring, 1985
VII
Table of Contents
PREFACE v
CHAPTER 1 - INTRODUCTION TO STRUCTURAL CONTROL
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
1.2 Structural Control ............................. 3
1.3 Classification of Structural Control........... 4
1.4 Elaboration of Vibration Control ....•.......... 10
1.4.1 Response to a Constant Force
with Finite Rise Time ....•.............. 11
1. 4.2 Effect of Damping .....................•. 13
1.5 Active Control of ODOF Systems ................. 16
1. 5.1 Control Using an Auxiliary Mass ......... 17
1.5.2 Control Using Auxiliary
Tendons (Springs) ............ ,.......... 19
1.5.3 Control Using an Auxiliary Damper ....... 20
1.6 The Control Devices............................ 21
1.6.1 Electro-Hydraulic Servomechanism ........ 22
1.6.2 Proportional Gain Controller ............ 24
1.6.3 Automatic Gain Controller ............... 25
1.7 References. . . . . . . . • . • • . . . . . . . . . . . . . . . . . . . . . . . . . 25
APPENDIX A - CLASSICAL CONTROL THEORy ...................... 26
A.l Introduction· . . . • . • . . . . . . . . • . . . . . . . . . • . . . . . . . . . 26
A.2 Feedback Control Systems ......•.•.............. 27
A.3 Design of a Control System ....••............... 28
A.3.l .stability· . . . . . . . . . . . . . . . .. . .. . . . . . . . . 29
A.3.1.l Routh's Criterion ..................... 30
A. 3.1. 2 Root Locus ............................ 31
A.3.1.3 Bode Plots.· •• ·•....•......•.......... 31
A.3.l.4 Polar Plots and Nyquist's
Stabi Iit y Criterion .............•..... 32
A. 3.1.5 Nichols' Charts .....•................. 32
A.3.2 Steady-State Accuracy ................. 32
A.3.3 Satisfactory Transient Response ....... 33
A.3.4 Satisfactory Frequency Response .•..... 35
A.4 References. . . . . . . . . . . . . . . . . . . . . . . . . • . • . . . . . . . . . 35
VIII Contents
page
CHAPTER 2 - MORPHOLOGY OF STRUCTURAL CONTROL ............... 37
2.1 Preliminary Remarks ............................ 37
2.2 On the Basics and the Actual Nature of
Structural Control Problems .................... 39
2.3 Examples. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48
2.4 The Modal Approach ............................. 60
2.5 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
CHAPTER 3 - AUTOMATIC ACTIVE CONTROL OF SIMPLE
SPAN BRIDGES ................................... 67
3.1 Mathematical Models of Simple Span Bridges ..... 67
3.2 Active Control Mechanisms in Bridges ........... 69
3.2.1 Control through Auxiliary Masses· ...... 69
3.2.2 Control through Auxiliary Tendons ...... 70
3.2.3 Control through Auxiliary Dampers ...... 71
3.2.4 Control using Aerodynamic Appendages ... 71
3.3 Active Control by Classical Control Methods ..... 72
3.3.1 Equation of Motion of the System ...... . 72
3.3.2 Control of the Fundamental Mode
of Vibration ......................... . 76
3.3.2.1 Stabi Ii ty Requirement ......... · .. ······ 79
3.3.2.2 Damping Requirement .................. . 79
3.3.2.3 Steady State Error Requirement ........ . 82
3.3.2.4 Sensitivity Requirement ............... . 83
3.3.2.5 Controlled System's Response .......... . 84
3.3.2.6 Summary and Conclusion················· 87
3.3.3 Control of Three Modes of Vibration···· 88
3.3.3.1 Controlled Systems' Response .......... . 91
3.3.3.2 Design of the Control System
using a Servomechanism ............... . 93
3.3.3.3 Design of the Control System
using a Proportional Controller··· .... . 95
3.3.3.4 Summary and Conclusions ............... . 97
3.4 Active Structural Control by Pole
Assignment Method .............................. 98
3.4.1 The Pole Assignment Method······· ..... . 99
3.4.l.l Controllabili ty ....................... . 100
3.4.1.2 Observability························· . 100
3.4.1.3 Design Procedure······················· 101
3.4.1.4 Design of State Feedback··············· 102
3.4.1.5 Design of Output Feedback ............. . 104
3.4.1.6 Design of the Observer················· 105
Contents IX
page
3.4.2 Application of the Pole Assignement
Method ................................. 108
3.4.2.1 Example 1 .............................• 109
3.4.2.2 Example 2 ...........•.................. 115
3.4.2.3 Example 3 ..............•............... 117
3.4.3 Summary' and Conclusion ......•.......... 122
3.5 Active Structural Control by Optimal
Control Methods ................................. 124
3.5.1 TIle Optimal Control Problem .....•.....• 124
3.5.2 Solution of the Optimal
Control Problem ........................ 128
3.5.3 Numerical Applications ..............•.. 130
3.5.3.1 Application of the Regulator Problem .... 132
3.5.3.2 Application of the Tracking Problem ... ·. 135
3.5.4 Summary and Conclusions ................ 143
3.6 Study of Secondary Effects ...................... 144
3.6.1 Inertia Effect of the Moving Load······· 145
3.6.1.1 Uncontrolled Response··················· 148
3.6.1.2 Controlled Response using a
Regulator Control System .............. . 150
3.6.1.3 Controlled Response using a
Tracking Control System ...........•.... 155
3.6.2 Normal Force Effect····················· 160
3.6.2.1 Passive Control Response················ 162
3.6.2.2 Active Control Response using a
Regulator Control System .............. . 162
3.6.2.3 Act). ve Control Response using a
Tracking Control System ............... . 167
3.6.3 Effect of Uneveness of the
Bridge Deck ........................... . 167
3.6.3.1 Uncontrolled Response ................. . 171
3.6.3.2 Active Control Response using a
Regulator Control System· ............. . 174
3.6.3.3 Active Control Response using a
Tracking Control System ............... . 179
3.6.4 Stochastic Control Against Uneveness···· 183
3.6.4.1 Stochastic Control Problem ............ . 183
3.6.4.2 Numerical Application ................. . 188
3.6.4.3 Summary and Conclusions· ....... ,~ ...... . 194
3.6.5 Effect of Various Moving Loads·········· 195
3.6.5.1 Pulsating Force Moving with
Constant Speed ........................ . 195
3.6.5.2 Uniform Load Moving with
Constant Speed ........................ . 196
3.6.5.3 Concentrated Load Moving with
Decelerated Speed ..................... . 200
3.6.5.4 Concentrated Load Moving with
Accelerated Speed ..................... . 203
3.6.6 Summary and Conclusions······ .......... . 207
x Contents
page
3.7 Optimal Control and Sensors Locations ............ 208
3.7.1 The Optimal Observer .................... 209
3.7.2 The Design Method ....................... 211
3.7.3 Numerical Examples ...................... 215
3.7.3.1 Example 1 .............................. 215
3.7.3.2 Example 2 .............................. 219
3.7.4 Conclusions ............................ 222
3.8 References ...................................... 223
CHAPTER 4 - AUTOMATIC ACTIVE CONTROL OF TALL BUILDINGS ....... 227
4.1 Introduction ..................................... 227
4.2 Building Response due to Wind Forces ............. 227
4.2.1 Wind Forces .......................... · .. 227
4.2.2 Stochastic Response ............ · .. ······ 232
4.2.3 Deterministic Analysis in the
Time Domain ............................. 238
4.2.4 Stochastic Analysis ..................... 240
4.3 Active Control of Tall Buildings ................ . 241
4.3.1 Movable Appendages.·· .................. . 242
4.3.2 Tuned Mass Dampers······················ 243
4.3.3 Acti ve Tendons ......................... . 245
4.3.4 Practical Control Mechanisms ........... . 246
4.4 Control Using Active Tendons ..................... 247
4.4.1 Design of the Control Force ............. 247
4.4.2 Response Analysis ....................... 251
4.5 Control Using Tuned Mass Dampers ................. 256
4.5.1 Design of the Active Control Law ...... ·. 256
4.5.2 Controlled Response ..................... 259
4.5.3 Effectiveness of Active TMD ............. 268
4.5.4 Concluding Remarks ...................... 273
4.5.5 Design of an Active TMD ................. 274
4.5.5.1 Stochastic Analysis ..................... 275
4.5.5.2 The Design Process for an
Acti ve TMD .. . . . . . . . . . . . . . . . . • . . . . . . . . . .. 277
4.5.5.3 Numerical Investigation ................. 278
4.5.5.4 Conclusions ............................. 287
4.6 Active Control By Means of Appendages ........... . 287
4.6.1 Design of Optimal Appendage
Movement·········· ..................... . 289
4.6.2 Contributions· ......................... . 293
4.6.3 Example 1 .............................. . 295
4.6.3.1 Klein's Method ......................... . 296
4.6.3.2 Soong's Method·························· 296
4.6.3.3 The Authors' Method .........•........... 296
Contents XI
page
4.6.4 Extension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 298
4.6.5 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 299
4.7 Stochastic Control of Tall Buildings ............. 306
4.7.1 Introduction· .......................... . 306
4.7.2 Equations of Motion· ................... . 307
4.7.3 Spectrum of Wind Forces ................ . 308
4.7.4 Design of Filters ...................... . 310
4.7.5 Design of a Stochastic Control Law······ 310
4.7.6 Numerical Investig"ations for
Tendon Control ......................... . 312
4.7.7 Numerical Investigation of Tuned
Mass Damper Control Application ........ . 318
4.7.8 Control by Appendages ....•.............. 323
4.7.9 Conclusions ............................ . 323
4.8 Control of Tall Buildings Taking Time
Delay into Account ............................... 323
4.8.1 Equations of Motion ..................... 324
4.8.2 Design of Control Laws .................. 325
4.8.3 Numerical Applications to
Tendon Control •......................... 326
4.8.4 Numerical Application to TMD Control .... 332
4.9 Feasibility of Active Control of Tall Buildings .. 337
4.9.1 Introduction ............................ 337
4.9.2 Feasibility of Active Tendon Control .... 337
4.9.3 Feasibility of Active Tuned Mass
Damper Control .......................... 345
4.9.4 Feasibility of Active Control
by Appendages ........................... 347
4.10 Finding a Practical Control Mechanism for
Tall Bui ldings ................................... 355
4.10.1 Introduction ............................ 355
4.10.2 The Uncontrolled Building Response ...... 356
4.10.3 Combined Passive Tendon and PTMD ........ 357
4.10.4 Combined Active Tendon and Passiv
Passi ve TMD ............................. 360
4.10.5 Combined Passive Tendon and
Active TMD ...................... " ....... 361
4.10.6 Combined Active Tendon and
Acti ve TMD .............................. 362
4.10.7 Combined Appendages, Passive
Tendon and PTMD ...........•.•........... 365
4.10.8 Combined Appendage, Active Tendon
and PTMD ................................ 365
4.10.9 Combined Appendage, Active Tendon
and ATMD ................................ 368
4.10.10 Conclusions ............................. 368
4.11 References ....................................... 369