semi-active smart-dampers and resetable actuators for multi

210 Pages·2008·1.68 MB·English

SEMI-ACTIVE SMART-DAMPERS AND RESETABLE ACTUATORS FOR MULTI-
LEVEL SEISMIC HAZARD MITIGATION OF STEEL MOMENT RESISTING
FRAMES
__________________________________________________________

A thesis

submitted in fulfilment

of the requirements of the Degree

of

Master of Mechanical Engineering

in the

University of Canterbury

by

S. J. Hunt

_______________

University of Canterbury
2002
ABSTRACT

This thesis explores the creation and assessment of semi-active control algorithms for both
squat shear buildings and tall flexible structures. If cost-effective, practicable, semi-active
structural control systems can be developed, the potential reduction in loss of both property
and lives due to seismic events is significant. Semi-active controllers offer many of the
benefits of active systems, but have power requirements orders of magnitude smaller, and do
not introduce energy to the structural system. Previous research into semi-active controllers
has shown their potential in linear simulations with single earthquake excitations. The
distinguishing feature of this investigation is the use of appropriate non-linear modelling
techniques and realistic suites of seismic excitations in the statistical assessment of the semi-
active control systems developed.

Finite element time-history analysis techniques are used in the performance assessment of the
control algorithms developed for three and nine story structural models. The models include
non-linear effects due to structural plasticity, yielding, hysteretic behaviour, and P-delta
effects. Realistic suites of earthquake records, representing seismic excitations with specific
return period probability, are utilised, with lognormal statistical analysis used to represent the
response distribution.

In addition to displacement focused control laws, acceleration and jerk regulation control
methods are developed, showing that potential damage reduction benefits can be obtained
from these new control approaches. A statistical assessment of control architecture is
developed and undertaken, examining the distribution of constant maximum actuator
authority for both squat shear buildings, and tall slender structures, highlighting the need to
consider non-linear structural response characteristics when implementing semi-active control
systems. Finally, statistical analysis of all results and normalised values shows the efficacy of
each control law and actuator type relative to different magnitude seismic events. As a result,
this research clearly presents, for the first time, explicit tradeoffs between control law,
architecture type, non-linear structural effects, and seismic input characteristics for the semi-
active control of civil structures.
ACKNOWLEDGMENTS

I would like to sincerely thank Dr Geoff Chase, my principal advisor, for his guidance and
patience during the development of this work. His constant enthusiasm and commitment
were an inspiration to me, and without his willingness to share his experience, knowledge,
and appreciation of good coffee, this research may never have flown. I also wish to thank my
external advisor, Assistant Professor Luciana Barroso, from Texas A&M University, whose
friendly support and willingness to help during the hard times were invaluable.

The steep learning curve required in this research was aided with guidance and
encouragement from Professor John Mander and Dr Bruce Deam from the University of
Canterbury Department of Civil Engineering, and Associate Professor Greg MacRae from the
University of Washington College of Engineering.

I would like to thank the University of Canterbury Research Office for the summer research
scholarship that helped kick this research into life. In addition, thanks are extended to Dr
Geoff Shaw and the Christchurch Hospital ICU Research Trust, who provided me with an
opportunity to broaden my research horizons, as well as pay the rent!

I would like to thank my fellow post-grads, Dean Kirk, Mark Carey, Manda Batchelor, Blair
Liddell, Chris Pretty, Bram Smith, and Zhu Hui Lam, whose encouragement and suggestions
have been invaluable. Particular thanks to Jonathan Harrington for the late night cups of tea
and company when everyone else was smart enough to be home in bed, and Dave Arnold for
taking an active interest in my research and being willing to wade through my drafts. Thanks
also to my two best mates, Nick (Nanna) Thompson and Andy Gibbs, whose close friendship
make living life more special.

The mission of producing this thesis has been made easier through the support and constant
encouragement of my family. Mum and Dad, I appreciate your guidance and wisdom, and
the faith you have given me that I can succeed, with God’s help, at whatever I put my heart
into. Maree, your friendship is something I cherish, and I thank you for your down-to-earth
words of reassurance that always remind me that life is bigger than school. Matt, the chats
about our coming adventures have helped me see the light at the end of the tunnel, and even
though you are on the other side of the world, I am always aware that my big brother is
looking out for me.

Finally, I would like to dedicate this thesis to my fiancé Kate, who throughout my University
career has had a level of dedication and patience greater than I’d have thought humanly
possible. Kate, you have constantly lightened the burden with your unconditional love and
support, and I hope that in our life together I can in some way give you back a little of what
you have given me. Let the good times roll! J
CONTENTS

ABSTRACT............................................................................................................................................................I
ACKNOWLEDGMENTS...................................................................................................................................II
LIST OF FIGURES..........................................................................................................................................VII
LIST OF TABLES..............................................................................................................................................IX
1. INTRODUCTION........................................................................................................................................1
1.1 MOTIVATION..........................................................................................................................................1
1.2 OBJECTIVES AND SCOPE.........................................................................................................................4
1.3 LITERATURE SURVEY ON SEMI-ACTIVE STRUCTURAL CONTROL...........................................................5
1.4 OVERVIEW...........................................................................................................................................10
1.5 CHAPTER SUMMARY............................................................................................................................11
2. BUILDINGS AND EARTHQUAKE SUITES.........................................................................................13
2.1 SAC3 STRUCTURAL SYSTEM...............................................................................................................13
2.2 SAC9 STRUCTURAL SYSTEM...............................................................................................................14
2.3 EARTHQUAKE SUITES...........................................................................................................................16
2.4 CHAPTER SUMMARY............................................................................................................................19
3. MODELS AND CONTROL SIMULATION...........................................................................................21
3.1 STRUCTURAL MODELS.........................................................................................................................21
3.1.1 Finite Element Formulation............................................................................................................21
3.1.2 Non-linear Modelling Techniques...................................................................................................24
3.1.3 Assembled Non-linear Structural Model.........................................................................................31
3.2 SIMULATION IMPLEMENTATION...........................................................................................................32
3.3 CHAPTER SUMMARY............................................................................................................................34
4. ACTUATOR ARCHITECTURE & CONTROL DESIGN....................................................................35
4.1 INTRODUCTION.....................................................................................................................................35
4.2 ACTUATOR ARCHITECTURE..................................................................................................................36
4.2.1 SAC3 Actuator Architecture............................................................................................................37
4.2.2 SAC9 Actuator Architecture............................................................................................................38
4.3 MR DAMPER CLIPPED QUASI-BANG-BANG CONTROLLER....................................................................41
4.3.1 Introduction.....................................................................................................................................41
4.3.2 Moving-Zero Definition...................................................................................................................42
4.3.3 Dead-band Definition......................................................................................................................44
4.3.4 Control Law Description.................................................................................................................45
4.4 LQR CLIPPED OPTIMAL CONTROLLER.................................................................................................48
4.5 LQRY CLIPPED OPTIMAL CONTROLLER...............................................................................................51
4.6 RESETABLE ACTUATOR CONTROLLER.................................................................................................52
4.6.1 Introduction.....................................................................................................................................52
4.6.2 Control Law Description.................................................................................................................54
4.7 JQR CLIPPED OPTIMAL CONTROLLER..................................................................................................56
4.8 BASE ISOLATION HYBRID CONTROLLER..............................................................................................59
4.9 CHAPTER SUMMARY............................................................................................................................61
5. SAC3 SIMULATION RESULTS..............................................................................................................67
5.1 INTRODUCTION.....................................................................................................................................67
5.2 STATISTICAL TOOLS.............................................................................................................................68
5.3 SAC3 UNCONTROLLED RESPONSE.......................................................................................................72
5.4 SINGLE FLOOR ACTUATOR ARCHITECTURE – SAC3-A1......................................................................74
5.4.1 Clipped Quasi-bang-bang Control..................................................................................................75
5.4.2 LQR Clipped Optimal Control........................................................................................................77
5.4.3 LQRy Clipped Optimal Control......................................................................................................80
5.4.4 Clipped Resetable Control..............................................................................................................82
5.4.5 JQR Clipped Optimal Control.........................................................................................................84
5.5 MULTI-FLOOR ACTUATOR ARCHITECTURES – SAC3-A2 & SAC3-A3...............................................86
5.5.1 Initial Actuator Architecture Assessment........................................................................................88
5.5.2 SAC3-A2-1 (7:3:0) Architecture......................................................................................................91
5.5.3 SAC3-A3-1 (6:3:1) Architecture......................................................................................................95
5.6 HYBRID CONTROL..............................................................................................................................101
5.7 CHAPTER SUMMARY..........................................................................................................................103
6. SAC9 SIMULATION RESULTS............................................................................................................107
6.1 INTRODUCTION...................................................................................................................................107
6.2 SAC9 UNCONTROLLED RESPONSE.....................................................................................................108
6.3 PRELIMINARY INVESTIGATION...........................................................................................................109
6.3.1 Actuator-Actuator Interaction.......................................................................................................110
6.3.2 Actuator Placement.......................................................................................................................114
6.4 SAC9-A3 ACTUATOR ARCHITECTURE...............................................................................................115
6.4.1 LQR Clipped Optimal Control......................................................................................................116
6.4.2 LQRy Clipped Optimal Control....................................................................................................118
6.4.3 Clipped Resetable Control............................................................................................................121
6.5 SAC9-A8 ACTUATOR ARCHITECTURE...............................................................................................123
6.5.1 LQR Clipped Optimal Control......................................................................................................124
6.5.2 LQRy Clipped Optimal Control....................................................................................................126
6.5.3 Clipped Resetable Control............................................................................................................128
6.6 CHAPTER SUMMARY..........................................................................................................................129
6.7 SAC9 RESULT TABLES......................................................................................................................133
6.7.1 SAC9 Uncontrolled Result Tables.................................................................................................133
6.7.2 SAC9-A3 Result Tables.................................................................................................................135
6.7.3 SAC9-A8 Result Tables.................................................................................................................140
7. PERFORMANCE NORMALISATION & COMPARISON................................................................145
7.1 INTRODUCTION...................................................................................................................................145
7.2 NORMALISED RESULTS & COMPARISONS..........................................................................................148
7.2.1 Hysteretic Energy Performance Normalisation: SAC3 & SAC9...................................................148
7.2.2 Control Energy Performance Normalisation: SAC9.....................................................................160
7.3 PASSIVE CONTROL COMPARISON.......................................................................................................164
7.4 EXTREME EARTHQUAKE CONTRIBUTION...........................................................................................169
7.5 IMPACT OF TRACKING PERMANENT DEFLECTIONS.............................................................................170
7.6 JERK DISTRIBUTION GRAPHICAL PERFORMANCE ASSESSMENT..........................................................175
7.7 CHAPTER SUMMARY..........................................................................................................................177
8. SUMMARY & CONCLUSIONS............................................................................................................183
9. FUTURE WORK.....................................................................................................................................191
10. REFERENCES.....................................................................................................................................193
LIST OF FIGURES

Figure 1.1: Devastating effects of 2002 Afyon Earthquake (M=6.2) on a residential concrete
building...............................................................................................................................3
Figure 1.2: 20-ton MR damper developed by the Lord Corporation.........................................8
Figure 2.1: SAC3 structural system showing centreline dimensions and member sections....14
Figure 2.2: SAC9 structural system showing centreline dimensions and beam sections.........15
Figure 2.3: Spectral acceleration plots for full and odd half earthquake suite (1 DOF system
with 2% critical damping) [Breneman 2000]...................................................................18
Figure 3.1: Lumped plasticity model for beam-column elements............................................23
Figure 3.2: Stiffness definitions for hysteretic torsional spring-damper model.......................27
Figure 3.3: Schematic of Bouc-Wen hysteretic relation..........................................................28
Figure 3.4: Schematic of the Bouc-Wen hysteresis loop.........................................................29
Figure 3.5: P-delta effects on a cantilever column...................................................................30
Figure 4.1: SAC3 actuator architectures: (a) SAC3-A1 (b) SAC3-A2 (c) SAC3-A3..............37
Figure 4.2: SAC9 actuator architectures: (a) SAC9-A3 (b) SAC9-A8....................................40
Figure 4.3: Schematic showing possible combinations of structural displacement and velocity
used for MR damper quasi-bang-bang controller.............................................................42
Figure 4.4: Example of time-varying equilibrium tracking for the SAC3 LQRy controlled
floor 1 drift – Elysian Park earthquake.............................................................................44
Figure 4.5: Schematic of MR damper quasi-bang-bang control law for a single actuator.......46
Figure 4.6: Schematic of a resetable actuator attached to a 1 DOF system.............................53
Figure 4.7: Schematic of base isolation and structural system.................................................61
Figure 5.1: Maximum drift distribution for SAC3 floor 1 - uncontrolled and resetable
controller...........................................................................................................................70
Figure 5.2: SAC3 actuator architectures: (a) SAC3-A2 (b) SAC3-A3....................................87
Figure 6.1: SAC9 uncontrolled yielded response. (a) Permanent drifts. (b) Permanently
deformed shape...............................................................................................................111
Figure 6.2: First four modes for SAC9 uncontrolled response..............................................112
Figure 6.3: Schematic of actuator-actuator interaction for resetable controller.....................114
Figure 6.4: Schematic of SAC9-A3 actuator architecture......................................................116
Figure 6.5: Schematic of SAC9-A8 actuator architecture......................................................124
Figure 7.1: SAC3-A1 average drifts across earthquake suites: (a) Peak drifts, (b) Permanent
drifts................................................................................................................................150
Figure 7.2: SAC3-A1 tracking comparison. (a) Uncontrolled floor 1 drift. (b) LQRy
controlled floor 1 drift with and without tracking..........................................................172
Figure 7.3: Floor 1 total structural jerk distribution for SAC3 linear model – Kobe Earthquake
(high suite)......................................................................................................................176
Figure 7.4: Effect of actuator force clipping on total structural jerk, during strong motion..177
LIST OF TABLES

Table 1.1: General structural performance level definitions and indicative drifts for steel
moment frames [BSSC 1997].............................................................................................9
Table 2.1: Spliced column sections for SAC9 structure (refer to Figure 2.2 for column
names)...............................................................................................................................15
Table 2.2: Names of earthquakes scaled within suites.............................................................17
Table 3.1: Distribution of SAC3 structural weight..................................................................21
Table 3.2: Distribution of SAC9 structural weight..................................................................22
Table 3.3: Modal properties of SAC3 and SAC9 structural models........................................24
Table 3.4: Modal Contribution for linear and non-linear SAC9 structural uncontrolled
responses...........................................................................................................................25
Table 4.1: SAC3 distributions of maximum actuator forces....................................................38
Table 4.2: SAC9 distributions of maximum actuator forces....................................................40
Table 5.1: SAC3 uncontrolled results for high suite................................................................73
Table 5.2: SAC3 uncontrolled results for medium suite..........................................................73
Table 5.3: SAC3 uncontrolled results for low suite.................................................................74
Table 5.4: SAC3-A1-1 results for high suite with quasi-bang-bang controller.......................76
Table 5.5: SAC3-A1-1 results for medium suite with quasi-bang-bang controller.................76
Table 5.6: SAC3-A1-1 Results for low suite with quasi-bang-bang controller.......................77
Table 5.7: SAC 3-A1-1 results for high suite with LQR controller.........................................78
Table 5.8: SAC3-A1-1 results for med suite with LQR controller..........................................79
Table 5.9: SAC3-A1-1 results for low suite with LQR controller...........................................80
Table 5.10: SAC3-A1-1 results for high suite with LQRy controller......................................81
Table 5.11: SAC3-A1-1 Results for medium suite with LQRy controller...............................81