Transcript Application for Structural Control
Structural Control: Overview and Fundamentals
Akira Nishitani Vice President & Professor WASEDA University, Tokyo, Japan [email protected]
Outline
1. Introduction for WASEDA and Myself 2. Introduction for Structural Control 3. Some keywords for structural control 4. Brief view of active structural control 5. Components of control system 6. Semiactive structural control 7. Smart damping or smart dampers Continued
Outline
(Cont’d) 8.
Significance of nonlinearity or artificially-added nonlinearity in structural control
9.
Semiactive variable slip-force level dampers 10. Future directions Appendix LQ control and LQG control
■
1. Introduction for:
Waseda Univ. and myself
About
Waseda Univ.
Waseda University
since 1882
Waseda University
早稲田大学
since 1882
Waseda University:
-
-
Second oldest private university in Japan, founded in 1882.
125 th Anniversary in 2007 .
- the first private university in Japan that established engineering school.
- Waseda Department of Architecture is the second oldest in Japan.
Data
of Waseda University
:
-
Number of students: 50,000 - Number of students in School of Science and Engineering: 7,000 - More than 100,000 application forms submitted to the Admission Center every year
About myself.
Myself :
-
PhD at Columbia, 1980 - Vice-President, Waseda Univ. since 2006. - Professor of Structural Engineering in Dept. of Architecture, since 1993.
Myself
(Cont’d)
:
-
Have been doing researches related to smart structures technology including active/semiactive structural control for nearly 20 years.
- Have been involved to the activity of
IASCM [ International Association for Structural Control and Monitoring ]
since its establishment in 1994.
Myself
(Cont’d)
:
-
Have been the Chairperson of the JSPS
[Japan Society for Promotion of Science] 157th Committee on Structural Response Control
since April 2007. - Currently, Vice-President, JAEE
Association of Earthquake Engineering]
.
[Japan
■
2. Introduction for: Structural Control
Structural Control:
▲
Active control
▲
Passive control
Structural Control:
▲
Active control
▲
Passive control
With or without Energy supply With or without Control computer
Structural Control:
▲
Active control
▲
Passive control
With Energy supply With Control computer
Structural Control:
▲
Active control
▲
Passive control
Without Energy supply Without Control computer
Structural Control:
▲
Active control
-
Full-active control
-
Semi-active or Semiactive control
▲ -
Hybrid control Passive control
Base Isolation -
Passive damper-based control
Structural Control:
▲ The idea of seismic structural control: not a totally new idea.
▲ The basic principles for seismic response control: presented in Japan in 1960.
Seismic Response Control Principles:
1. Reduce the effect of seismic excitation.
2. Prevent a structure from exhibiting the resonance vibration.
3. Transfer the vibration energy of a main structure to the secondary oscillator.
4. Put additional damping effect to a structure.
5. Add a control force to a structure.
These ideas were proposed by Kobori and Minai in 1960.
Professor Takuji Kobori
They proposed the idea of: Seismic-Response-Controlled Structures or
制震構造
.
Seismic-response-controlled structure Building Nonlinear mechanism Nonlinear mechanism Nonlinear mechanism Nonlinear mechanism
Seismic Response Control Principles:
1. Reduce the effect of seismic excitation.
Base Isolation
2. Prevent a structure from exhibiting the resonance vibration.
Base Isolation
3. Transfer the vibration energy of a structure to the secondary oscillator.
TMD Control
4. Put additional damping effect to a structure.
Passive damper control
5. Add a control force to a plant.
AMD Control
Japan has been leading the world in terms of the practical applications of structural control schemes .
Practical Applications in Japan: # of Buildings: Base isolation: over 2,000 Passive dampers: over 300 Active control: over 40
■ Keywords for structural control.
- TMD - AMD - Smart damper - Semiactive damper - Controllable damper - LQ control - LQG control - Feedback control - Feed-forward control
- TMD: Tuned Mass Damper - AMD: Active Mass Damper - Smart damper - Semiactive damper - Controllable damper - LQ control - LQG control - Feedback control - Feed-forward control
- TMD: Tuned Mass Damper - AMD: Active Mass Damper Smart damper - Semiactive damper - Controllable damper - LQ control - LQG control - Feedback control - Feed-forward control
There are many kinds of ‘ smart ’ expressions such as
‘smart’ cars, ‘smart’ dampers, ‘smart’ structures, ‘smart’ medicine,
etc.
Indeed, “ The Merriam-Webster Paperback Dictionary ” gives a modern interpretation of ‘smart.’
Containing a microprocessor of limited calculating capability.
With the names such as
‘smart structures,’ ‘intelligent structures,’ ‘dynamic intelligent buildings,’
etc., civil structures have been getting more and more human beings-like characteristics.
■
4. Overview of active structural control:
In 1989, a real building with active control technology applied was completed in Tokyo, Japan.
This was the first
full scale implementation of active or computer-based response control
in the world.
Professor Takuji Kobori
The name of the building:
Kyobashi Seiwa Building
(Currently,
Kyobashi Center Building
)
Kyobashi Center Building
- This building employed an AMD system.
-
AMD is one of the typical active control devices or actuators for buildings.
AMD AMD
AMD is a mass of weight installed into the top floor or near top floor, which is manipulated by a control computer based on the response data.
The inertial force resulting from AMD movement
Control force
Structure
responding to
Seismic or wind excitation
AMD Driving Force AMD Building
AMD Driving Force Mass of AMD m AMD u Building Mass of Building M
X x
K
AMD x a k building or main structure
x
g
The equation of motion of a structural system with AMD integrated is:
m 0 0 M
x
k k k
k K
x X
m M
x
g
u u
m 0 m M
x
a
k k 0 K
x a X
m M
x
g
u u
The equation of motion of a structural system with AMD integrated:
m 0 m M
x
a
k k 0 K
x a X
m M
x
g
u u
From
m
(
x
a
the first raw ,
)
kx a
m
x
g
u
m
(
x
a
m
(
x
a
x
g
)
kx a
u
x
g
)
u
kx a
Combining
M X
KX
the above with
M
x
g
m
(
x
a
the second raw of (1),
x
g
) (1)
The equation of motion of a structural system with AMD integrated:
M X
KX
M
x
g
m
(
x
a
x
g
) (
M
m
)
KX
(
M
m
)
x
g
m
x
a
AMD x x a
x
g
As a result, since the birth of the world’s first active-controlled building, now
more than 40
buildings in Japan have installed a variety of active control schemes.
Full-scale active control implementations:
Kyobashi Seiwa Bldg.,
1989
Bidg. #21, Kajima Technical Research Institute,
1990
Sendagaya INTES,
1992
Applause Tower,
1992
Osaka ORC 200,
1992
Kansai Airport Control Tower,
1992
Long Term Credit Bank,
1993
Ando Nishikicho Bldg.,
1993
Porte Kanazawa,
1994
Shinjuku Park Tower,
1994
RIHGA Royal Hotel,
1994
MHI Yokohama Bldg.,
1994
Hikarigaoka J City,
1994
Hamamatsu ACT City,
1994
Riverside Sumida,
1994
Hotel Ocean 45,
1994
Osaka WTC Bldg.,
1995
Full-scale active control implementations(cont.):
Dowa Kasai Phoenix Tower,
1995
Rinku Gate Tower,
1995
Hirobe Miyake Bldg,
1995
Plaza Ichihara,
1995
HERBIS Osaka,
1997
Nisseki Yokohama Bldg.,
1997
Itoyama Tower,
1997
Otis Elevator Test Tower,
1998
Bunka Gakuen,
1998
Oita Oasis Hiroba 21,
1998
Odakyu Southern Tower,
1998
Kajima Shizuoka Bldg.,
1998
Sotetsu Bldg.,
1998
Century Park Tower,
1999
Sosokan, Keio Univ.,
2000
Gifu Regional Office, Chubu Power Electric Company,
2001
However, most of these implementations were mainly aimed at the response control against small/moderate seismic strong wind excitation.
or
The ultimate goal of active control:
To enhance the structural safety against severe seismic events.
Need to establish such a control scheme as to achieve the final goal of active structural control.
Reference: A. Nishitani and Y. Inoue (2001).
“ Overview of the application of active/semiactive control in Japan,” Earthquake Engineering & Structural Dynamics , Vol. 30(11), pp.1565-1574.
Active structural control:
-
The full-scale active control implementation to a civil structure has opened the door to ‘modern’
earthquake engineering
or ‘modern’
structural engineering
.
Structural engineering is now integrating more and more
modern, advanced and IT-related technologies
.
■
5. Components of Control System:
-
How is a control system composed?
From the point of view of system control engineering, …..
Control System:
Plant structure
whose -
-
responses are controlled
Sensors Control computer Control actuator (Controller)
Control System:
Control Input Seismic Input
Plant
Sensors Actuator Controller
Seismic Structural Control:
1. Reduce the effect of seismic excitation which a
plant
is subjected to.
2. Prevent a
plant
from exhibiting the resonance vibration.
3. Transfer the vibration energy of a
plant
to a
control-actuator
.
4. Put additional damping effect to a
plant
.
5. Add a control force to a
plant
through
an actuator or actuators.
Passive Control System:
Plant structure
whose
■ ■
responses are controlled
Sensors Control computer Control actuator
(Controller)
Base Isolation:
Plant structure
whose
■ ■
responses are controlled
Sensors Control computer Control actuator
(Controller)
Passive Damper Control:
1. Reduce the effect of seismic excitation.
2. Prevent a
plant
from exhibiting the resonance vibration.
3. Transfer the vibration energy of a
plant
to a
control-actuator .
4. Put additional damping effect to a
plant
.
5. Add a control force to a
plant
.
TMD Control:
1. Reduce the effect of seismic excitation.
2. Prevent a
plant
from exhibiting the resonance vibration.
3. Transfer the vibration energy of a
plant
to a
control-actuator.
4. Put additional damping effect to a 5. Add a control force to a
plant
.
plant
.
Base Isolation:
1. Reduce the effect of seismic excitation.
2. Prevent a
plant
from exhibiting the resonance vibration.
3. Transfer the vibration energy of a
plant
to a
control-actuator
.
4. Put additional damping effect to a
plant.
5. Add a control force to a
plant
.
Active Control System:
Plant structure
whose responses are controlled
Sensors Control computer Control actuator
(Controller)
AMD Control:
1. Reduce the effect of seismic excitation.
2. Prevent a
plant
from exhibiting the resonance vibration.
3. Transfer the vibration energy of a
plant
to a secondary vibration system.
4. Put additional damping effect to a
plant
.
5. Add a control force to a
plant.
Theoretically,
There are two kinds of active control schemes: ……..
Theoretically,
There are two kinds of active control schemes:
Feedback control
and
Feed-forward control.
External input such as seismic excitation
Plant
Sensors Control Input Output Actuator Controller
External input such as seismic excitation
Plant
Sensors Control Input Output Actuator Controller Feedback Control
External input such as seismic excitation Control Input
Plant
Sensors Controller+ Actuator Output Feedback Control
External input such as seismic excitation
Plant
Response Control Input Controller Feedback Control
External input excitation H(s) Response Control Input G(s) Feedback Control
External input excitation Plant transfer function Control Input H(s) Response Feedback gain G(s) Feedback Control
External input excitation Plant transfer function Control Input H(s) Response Feedback gain G(s) Feedback Control
Controller+ Actuator Sensors External input such as seismic excitation
Plant
Control Input Response
External input excitation G(s) Control Input
H(s)
Response
External input excitation G(s) Control Input
H(s)
Response Feed-forward Control
■
6. Semiactive Structural Control:
-
What is semiactive control?
- How is semiactive control conducted?
Semiactive control:
Combines the beneficial features of both of passive and active control systems.
Semiactive control:
Passive control:
No energy supply to a control actuator needed.
Active control:
Flexibility, Adaptability, Efficient performance.
Semiactive control:
Less energy - More efficiency - Better performance
Control System:
Plant structure
whose -
-
responses are controlled
Sensors Control computer Control actuator (Controller)
Control System:
Seismic Input
Plant
Actuator Controller Sensors
Semiactive control:
There are two major ways defining or characterizing semiactive control concept.
The most general definition:
Semiactive control is ……
The most general definition:
Semiactive control is conducted by changing or controlling a part of charactersitics of control actuator only at appropriate time instants.
The most general definition:
Semiactive control is conducted by changing or controlling a part of charactersitics of control actuator only at appropriate time instants.
Adaptive characteristics .
This definition leads to: Large power not needed.
Required power not dependent of the magnitude of seismic excitation.
The second significant point:
Semiactive control operation
does not inject mechanical energy
into a plant structure or control device or actuator.
The second significant point:
Semiactive control operation
does not inject mechanical energy
into a plant structure or control device or actuator.
It has
much less potential
to destabilize the structure.
In typical semiactive control:
Actuator: Damper Controlled characteristics such as the
damping coefficient
, the magnitude of
relief load
, etc., of the damper are controlled.
This kind of dampers are ……..
Typical semiactive control:
Actuator: Damper Ccontrolled characteristics such as the
damping coefficient
, the magnitude of
relief load
, etc. of the damper are controlled.
This kind of dampers are called
‘controllable’ dampers
.
Then,
for example,
consider a type of
semiactive
control in which the damping coefficients of installed viscous dampers are controlled.
Then,
for example,
consider a type of
semiactive
control in which the damping coefficients of installed viscous dampers are controlled.
This change would not have any effect on the structure which is not subject to any other external input excitation.
On the contrary,
t he movement of AMD could make an entire structure vibrate
even in case of no other external input excitation
.
On the contrary,
t he movement of AMD would make an entire structure vibrate
even in case of no other external input excitation
.
This is very significant
difference
between full-active and semi-active control.
AMD Power AMD Building
Controlled dampers
Smart dampers One of smart control schemes
Control scheme based on “ smart ” or “ controlled ” dampers
■
7. Smart damping or Smart Dampers
Vibration Control
- Buildings - Motor vehicle suspensions
z
Car Body or Building Spring Damper
x g
-
Computer control of of suspension systems in 1980s.
-
Computer control of buildings in 1989.
z
Car Body Spring Damper
x g
- Ride Comfort
Absolute movement of car body = 0 - Driving Stability
Movement of car body = Movement of ground
Trade-off between ride comfort and driving stability Spring Damper
Variable
Transfer function from
x g
to
z
x z g ( ω ) ( ω )
1 0
Low damping High damping
2
For better ride comfort, smaller absolute accelerations.
High damping is not appropriate for the high-frequency region.
Constant damping is not appropriate.
Skyhook damper
z x
g
Skyhook damper
C
sh
C z x
g
Skyhook damper
C
sh
z C
.
.
C (z-x
g
) = C
sh
.
z x
g
Skyhook damper
C
sh
z
.
C
.
C (z-x
g
) = C
sh
.
z
C = C
sh
.
.
.
[z / (z-x
g
)]
x
g
Pioneering Implementations of Smart Damping:
• Kajima Shizuoka Building • Keio University Soso-kan Building • Chubu Electric Power (CEP) Gifu Regional Office Building
Kajima Shizuoka Building
-
Kajima Shizuoka Building
The World’s first
smart damping
or
semiactive variable damping
implementation to a building.
Variable damping system in
Kajima Shizuoka Bldg.
:
The damping coefficients of oil-dampers is controlled so that
LQG-based optimal control force
should be provided in terms of damping force.
Keio Univ. Soso-kan Building
-
Keio Univ. Soso-kan Building
The world’s first smart base isolated building or building with base isolation
integrating semiactively-controlled
variable damping system.
CEP Gifu Regional Office Building
-
CEP Gifu Regional Office Building :
The world’s first building employing an
autonomous-decentralized semiactive smart damping
system.
Autonomous-decentralized control system
A-D Control System:
Seismic Input Act.
Plant
Sensors Act.
Act.
Controller Controller Sensors Controller Sensors
Autonomous-Decentralized Control System:
-
Each of distributed control systems is autonomously controlled by its own local, decentralized controller , not by only one center controller.
- Height of a huge, high-rise building - Width of a huge building with very wide floors One central control computer does not seem appropriate .
Autonomous-decentralized
control system (AD control system)
A-D Semiactive Damper
Switching Oil Damper with Built-in Controller
“Switching oil damper with built-in controller” -The ‘damper’ is a Maxwell type of system consisting of a stiffness element (spring) and a
controllable oil damper element
.
Spring Damper
C max C min Vel + K Disp
By properly choosing the damping coefficient,
1
C max C min
4 2
C min C max
3
Passive Damper Hysteresis
C max C max C max C max
① ② ① ④ ③ ② ②
④ ③ ③ ④
- Each damper autonomously controlled by its own decentralized controller
Autonomous-decentralized control system
-Several newly constructed buildings in Japan have installed this type of
semiactive damper systems
.
-“Switching oil damper with built-in controller”
The Shi’odome District
The Shi’odome Kajima Tower
The Shi’odome Kajima Tower
Roppongi Tower
Autonomous-decentralized control system
Control operation could be conducted based upon the response information only in the neighborhood of each control devise.
Autonomous-decentralized control + Artificial Nonlinearity concept seems appropriate or fitted to structural control against
severe seismic excitations
.
■ 8. Significance of nonlinearity or artificially-added nonlinearity in structural control - Basic concept - Control effect - Oil hydraulic dampers
Bi-linear subsystem
tan -1 βK
Linear structure
tan -1 αK tan -1 αK tan -1 ( α +β)K
γ
=
α/
(
α
+
β
)
tan -1 K tan -1 γ K
Δ W W Damping Coefficient = ΔW/W/( 4π )
tan -1 γK tan -1 K Equivalent viscous damping ratio = (1-
γ
)/((1+
γ
)
π
)
α=0.7
α=0.8
α=1.0
α=0.9
β
What would happen to a SDOF structure subjected to seismic excitation with this algorithm?
Case 1: α=β=0.5
Case 2: α<β α= 0.3; β= 0.7
El Centro 1940 earthquake NS component with 2 m/sec
2
Response Accelerations α=β= 0.5
0.5
①
α=0.3, β= 0.7
Response Displacement α=β= 0.5
0.5
α= 0.3, β= 0.7
0.7
Damper hystereses α= β= 0.5
0.5
α=0.3
, β= 0.7
As an AD semiactive control system integrating artificial nonlinearity philosophy,
Variable slip-force level dampers
■
9.
Semiactive
Variable Slip-force Level Dampers
- Basic concept - Control effect - Oil hydraulic dampers
- Basic concept:
- Semiactive control - Utilizing artificial nonlinearity - Autonomous-decentralized system
Force slip-force-level fSlip-levelforce スリ ップレベル displacem ent 層間 変 位
A damper is controlled
so that it begins to slip at the occurrence of peak velocity.
- No need for modeling.
- Only local response information needed.
Damper ductility factor = 2
The effectiveness of this scheme:
is analytically measured in terms of equivalent viscous damping ratio.
Damper+Structure
tan
-1
αK tan
-1
(α+β)K
What would happen to a SDOF structure subjected to seismic excitation with this algorithm?
Case 1: α=β=0.5
Case 2: α<β α= 0.3; β= 0.7
El Centro 1940 earthquake NS component with 2 m/sec
2
Response Accelerations
α=β= 0.5
0.5
① α=0.3, β= 0.7
0.7
Response Displacement
α=β= 0.5
0.5
α= 0.3, β= 0.7
0.7
Damper hystereses
α= β= 0.5
0.5
α= 0.3
, β= 0.7
0.7
Case 1: α=β= 0.5 Estimated damping coefficient = 0.087
Case 2: α= 0.3; β= 0.7
Estimated damping coefficient = 0.162
Acceleration Response Spectrum
Simulation for a 20-storie high rise building:
-
Steel structural model accounting for shear and bending deformations.
Natural Period of original structural model:
-
1st Mode: 1.78 sec
-
2nd Mode: 0.577 sec
-
3rd Mode: 0.310 sec
-
Dampers are installed on every floor.
-
Each damper is controlled only based upon the interstory drift response velocity.
Autonomous decentralized control .
-
Damper is effective only on shear deformation.
Autonomous-Decentralized Control System:
-
Each of distributed control systems is autonomously controlled by its own local, decentralized controller , not by only one center controller.
Building 1: α=β= 0.7
Building 2: α=β= 1.0
20 18 16 14 12 10 8 6 4 2 0 1 α= β =1.0 α= β =0.7 uncontrolled 1.5
2 2.5
acceleration[m/s 2 ] 3 20 18 16 14 12 10 8 6 4 2 0 0 α= β =1.0 α= β =0.7 uncontrolled 0.05
0.1
displacement[m] 0.15
0.2
(a) Accelerations (b) displacements Maximum resoponses
The presented concept can be put into practice utilizing an oil hydraulic damper-based device.
-
A damper containing an electromagnetic relief valve is utilized.
The presented concept can be put into practice utilizing an oil hydraulic damper-based device.
-
A damper containing an electromagnetic relief valve is utilized.
This is a kind of variable-orifice damper.
ゴムブッシュ 図 13 オイルダンパ rubber bush
Experimental model of semiactive variable slip-force level damper
10 8 6 4 2 0 0 proposed model 5 10 Velocity[cm/s] Relationship between damper velocity and electric voltage given to the valve 8V 15 6V 4V 2V 0V
Experimental results responding to sinusoidal excitation with increasing amplitudes Constant slip-force level Variable slip-force level Displacement (mm)
Reference:
A. Nishitani, Y. Nitta and Y. Ikeda (2003). “ Semiactive structural-control based on variable slip-force level dampers ,” J. of Structural Engineering, ASCE , Vol. 129(7), pp.933-940.
■ -
-
Semiactive and smart concept based schemes have been presented for structural control of buildings as well as the full scale implementations of some of such schemes in Japan.
■
-
The concept of semiactive variable slip force level dampers has been presented.
■
10. Future directions:
-
-
Semiactive and smart smart passive strategies, or strategies, are expected to play more and more significant role in the future stage of structural engineering, integrating the autonomous decentralized concept.
■ Optimal control: LQ control & LQG control: LQ: L inear, Q uadratic LQG: L inear, Q uadratic
and
G aussian
■ LQ control & LQG control: Two schemes for optimal control: Response: whether probabilistic or deterministic?
If the response is probabilistic, then the control input probabilistic. will be
LQG control .
■ LQ control & LQG control: In the case where the response and control input are stationary, Gaussian random processes,
LQG control .
The equation of motion of a structural system with control input :
x
2
ς ω
0
ω
0 2
x
f
u d dt
x
0
ω
0 2 1 2
ς ω
0
x
0 1
u
This equation is rewritten as :
0 1
f
Ax
bu
cf
The state equation:
Ax
bu
cf
In the above,
f
: determinis tic, then
x
: determinis tic, then
u
: determinis tic.
LQ control.
The state equation:
Ax
bu
cf
In the above,
f
: stationary Gaussian white with zero mean, then noise
x
: stationary Gaussian with zero mean,
u
: stationary Gaussian with zero mean.
LQG control
J
If
u
1
T
lim
T
and
x
0
T
[
x
(
t
)
Qx
(
t
)
ru
2
(
t
are probabilis tic, )]
dt J
is also probabilis tic.
E
[
u J
]
and
x E
T
lim
1
T
0
T
[
x
(
t
)
Qx
(
t
) are stationary .
ru
2
(
t
)]
dt
E
[
J
]
1
T
lim
T
0
T
(
E
[
x
(
t
)
Qx
(
t
)]
E
[
ru
2
(
t
)])
dt
u
and
x
are stationary .
E
[
J
]
1
T
lim
T
0
T
(
E
[
x
(
t
)
Qx
(
t
)]
E
[
ru
2
(
t
)])
dt E
[
J
]
T
lim
E
[
J
]
T
lim
(
E
[
x
Qx
]
E
[
ru
2
])
1
T
(
E
[
x
Qx
]
E
[
ru
2
])
0
T dt
u
and
x
are stationary .
E
[
J
]
T
lim
(
E
[
x
Qx
]
E
[
ru
2
Control input is given by ])
Pu
(
t
)
Gx
(
t
) Feedback gain
G
is given by
G
r
1
b
P
satisfying the following equation :
PA
A
P
Pbr
1
b
P
Q
0
Riccati Equation.
LQG control: LQG control statistically satisfies the samllest value of E[J].
Epigram:
Little people discuss other people.
Average people discuss events.
Big people discuss ideas.
(M.S. Grewal, A.P. Andrews.
Kalman Filtering: Theory and Practice Using MATLAB
[Second Edition], John Wiley, 2001)
Thanks for your attention.