structural control: overview and fundamentals structural control: overview and fundamentals akira...

Structural Control: Structural Control: Overview and FundamentalsOverview and Fundamentals

Akira Nishitani Akira Nishitani

Vice President & ProfessorVice President & Professor 　　　　　　　　　　　　　　　　　　WASEDA University, Tokyo, JapanWASEDA University, Tokyo, Japan

anix@[email protected]

OutlineOutline 1.1. Introduction for Introduction for WASEDAWASEDA and Myself and Myself 2.2. Introduction for Structural ControlIntroduction for Structural Control 3.3. Some keywords for structural controlSome keywords for structural control

4.4. Brief view of active structural Brief view of active structural controlcontrol 5.5. Components of control systemComponents of control system 6.6. Semiactive structural control Semiactive structural control 7.7. Smart damping or smart dampers Smart damping or smart dampers ContinuedContinued

Outline Outline (Cont’d)(Cont’d) 8.8. Significance of nonlinearity or artificially-added Significance of nonlinearity or artificially-added

nonlinearity in structural controlnonlinearity in structural control 9.9. Semiactive variable slip-force level dampersSemiactive variable slip-force level dampers 10.10. Future directions Future directions

Appendix Appendix LQ control and LQG control LQ control and LQG control

■ ■ 1. Introduction for:1. Introduction for:

Waseda Univ. and myself

About About Waseda Univ.Waseda Univ.

Waseda UniversityWaseda University since 1882 since 1882　　　　

Waseda UniversityWaseda University since 1882 since 1882　　　　早稲田大学早稲田大学

Waseda University:Waseda University:

-- Second oldest private university in Japan, foundSecond oldest private university in Japan, founded in ed in 1882.1882.

- - 125125th Anniversary in th Anniversary in 20072007..

- the - the firstfirst private university in Japan that establis private university in Japan that established engineering school.hed engineering school.

- Waseda Department of Architecture is the secon- Waseda Department of Architecture is the second oldest in Japan.d oldest in Japan.

DataData of Waseda Universityof Waseda University::

-- Number of students: Number of students: 50,00050,000

- Number of students in School of - Number of students in School of Science and Engineering: Science and Engineering: 7,0007,000

- More than - More than 100,000100,000 application forms application forms submitted to the Admission Center every submitted to the Admission Center every yearyear

About myself.

MyselfMyself :

-- PhD at Columbia, PhD at Columbia, 19801980 - Vice-President, Waseda Univ. - Vice-President, Waseda Univ.

since 2006. since 2006.

- Professor of Structural Engineering - Professor of Structural Engineering in Dept. of Architecture, sincin Dept. of Architecture, since 1993.e 1993.

Myself Myself (Cont’d)(Cont’d) :

- Have been doing researches related to smarHave been doing researches related to smart structures technology including active/semit structures technology including active/semiactive structural control for nearly 20 years.active structural control for nearly 20 years.

- Have been involved to the activity of - Have been involved to the activity of IASCMIASCM [[ International Association forInternational Association for Structural Control and MoStructural Control and Monitoring ]nitoring ] since its establishment in 199 since its establishment in 1994. 4.

Myself Myself (Cont’d)(Cont’d) : - Have been the Chairperson of the Have been the Chairperson of the

JSPSJSPS [Japan Society[Japan Society for Promotion offor Promotion of Science]Science] 157th Committee157th Committee onon Structural Structural Response ControlResponse Control since April 2007. since April 2007.

- Currently, Vice-President, - Currently, Vice-President, JAEEJAEE [Japan [Japan

Association of Earthquake Engineering]Association of Earthquake Engineering]..

■ ■ 2. Introduction for:2. Introduction for:

Structural Control

Structural Control:Structural Control:

▲ Active control

▲ Passive control


▲ Active control

▲ Passive control

With or without Energy supply

With or without Control computer


▲ Active control

▲ Passive control

With Energy supply

With Control computer


▲ Active control

▲ Passive control

Without Energy supply

Without Control computer


▲ Active control - Full-active control

- Semi-active or Semiactive control

- Hybrid control

▲ Passive control - Base Isolation

- Passive damper-based 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:Seismic Response Control Principles:

1.1. Reduce the effect of seismic excitation.Reduce the effect of seismic excitation.

2. Prevent a structure from exhibiting the 2. Prevent a structure from exhibiting the resonance vibration.resonance vibration.

3. Transfer the vibration energy of a main 3. Transfer the vibration energy of a main structure to the secondary oscillator.structure to the secondary oscillator.

4. Put additional damping effect to a 4. Put additional damping effect to a structure.structure.

5. Add a control force 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

Nonlinear Nonlinear mechanismechanismm

Building




Seismic Response Control Principles:Seismic Response Control Principles:

1.1. Reduce the effect of seismic excitation.Reduce the effect of seismic excitation. Base IsolationBase Isolation2. Prevent a structure from exhibiting the 2. Prevent a structure from exhibiting the

resonance vibration.resonance vibration. Base IsolationBase Isolation3. Transfer the vibration energy of a 3. Transfer the vibration energy of a

structure to the secondary structure to the secondary oscillator.oscillator.

TMD ControlTMD Control4. Put additional damping effect to a 4. Put additional damping effect to a

structure.structure. Passive damper controlPassive damper control5. Add a control force to a plant. 5. Add a control force to a plant. AMD AMD

ControlControl

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- TMD- AMD- AMD- Smart damper- Smart damper- Semiactive damper- Semiactive damper- Controllable damper- Controllable damper- LQ control- LQ control- LQG control- LQG control- Feedback control- Feedback control- Feed-forward control - Feed-forward control

- TMD: - TMD: Tuned MassTuned Mass DamperDamper

- AMD: - AMD: ActiveActive MassMass DamperDamper

- Smart damper- Smart damper- Semiactive damper- Semiactive damper- Controllable damper- Controllable damper- LQ control- LQ control- LQG control- LQG control- Feedback control- Feedback control- Feed-forward control - Feed-forward control

- TMD: - TMD: Tuned MassTuned Mass DamperDamper

- AMD: - AMD: ActiveActive MassMass DamperDamper

- - SmartSmart damper damper- Semiactive damper- Semiactive damper- Controllable damper- Controllable damper- LQ control- LQ control- LQG control- LQG control- Feedback control- Feedback control- Feed-forward 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 interpretationof ‘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 4. Overview of active structural active structural control: control:

- - In 1989,In 1989, a real building with active control technology a real building with active control technology

applied was completed in Tokyo, Japan.applied was completed in Tokyo, Japan.

- - This was the first This was the first full scalefull scale implementation of active or computer-based implementation of active or computer-based response controlresponse control in the world. in the world.

Professor Takuji Kobori

The name of the building:The name of the building:

Kyobashi Seiwa BuildingKyobashi Seiwa Building (Currently, (Currently,

Kyobashi Center BuildingKyobashi Center Building))

Kyobashi Center Building

- This building employed an - This building employed an AMDAMD system.system.

-- AMDAMD is one of the typical active is one of the typical active control devices or actuators for control devices or actuators for buildings.buildings.

AMDAMD

- - AMDAMD is a mass of weight is a mass of weight installed into the top floor or installed into the top floor or near top floor,near top floor,

which is manipulated by which is manipulated by a control computer a control computer based on the response data. based on the response data.

The inertial force The inertial force resulting from resulting from AMDAMD movement movement

responding toresponding to

StructureStructure

Seismic or wind excitationSeismic or wind excitation

Control forceControl force

AMD

AMD

Driving ForceDriving Force

Building

AMD

AMD

Driving Force

u

Building

Mass of AMD m

Mass of Building M

AMDxa

X

xg

x

k

Kbuilding or main structure

The equation of motion of a structural The equation of motion of a structural system with system with AMD AMD integrated is:integrated is:

u

ux

M

m

X

x

Kk

0k

X

x

M0

mm

u

ux

M

m

X

x

Kkk

kk

X

x

M0

0m

gaa

g

The equation of motion of a structural The equation of motion of a structural system with system with AMD AMD integrated:integrated:

)(

(1), of rawsecondthewithabovetheCombining

)(

)(

)(

,rawfirsttheFrom

gag

aga

aga

gaa

gaa

xXxmxMKXXM

kxuxXxm

ukxxXxm

uxmkxXxm

u

ux

M

m

X

x

Kk

0k

X

x

M0

mm

(1)

The equation of motion of a structural The equation of motion of a structural system with system with AMD AMD integrated:integrated:

ag

gag

xmxmMKXXmM

xXxmxMKXXM

)()(

)(

AMD xa

x

xg

As a result,As a result,

since the birth of the world’s first since the birth of the world’s first active-controlled building, active-controlled building, now now more than 40more than 40 buildings buildings in Japan have installed in Japan have installed a variety of active control schemes. a variety of active control schemes.

Full-scale active control implementations: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, 1992Kansai 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, 1995Rinku Gate Tower, 1995Hirobe Miyake Bldg, 1995Plaza Ichihara, 1995HERBIS Osaka, 1997Nisseki Yokohama Bldg., 1997Itoyama Tower, 1997 Otis Elevator Test Tower, 1998 Bunka Gakuen, 1998Oita Oasis Hiroba 21, 1998Odakyu Southern Tower, 1998Kajima Shizuoka Bldg., 1998Sotetsu Bldg., 1998Century Park Tower, 1999Sosokan, Keio Univ., 2000Gifu Regional Office, Chubu Power Electric Company, 2001

However,However,

most of these implementations were most of these implementations were mainly aimed at the response control mainly aimed at the response control against against small/moderate seismicsmall/moderate seismic oror strong wind excitation.strong wind excitation.

The ultimate goal of active control:The ultimate goal of active control:

To enhance the structural safety To enhance the structural safety against severe seismic events.against severe seismic events.

Need to establish such a Need to establish such a control scheme as to achieve the control scheme as to achieve the final goal of active structural final goal of active structural control.control.

Reference:Reference:

A. Nishitani and Y. Inoue (2001).A. Nishitani and Y. Inoue (2001).

　　““ Overview of the application of active/semiactive control in Overview of the application of active/semiactive control in Japan,”Japan,”

　　 Earthquake Engineering & Structural DynamicsEarthquake Engineering & Structural Dynamics, Vol. 30(11), pp.15, Vol. 30(11), pp.1565-1574.65-1574.

Active structural control:Active structural control:

-- The full-scale active control implementation The full-scale active control implementation to a civil structure has opened the door to a civil structure has opened the door to to ‘modern’‘modern’ earthquake engineeringearthquake engineering or or ‘modern’‘modern’ structural engineeringstructural engineering..

- - Structural engineering is now integrating Structural engineering is now integrating more and more more and more modern, advanced and modern, advanced and IT-related technologiesIT-related technologies..

■ ■ 5. Components of 5. Components of Control System: Control System:

- How is a control system composed?

From the point of view of From the point of view of system control engineering, …..system control engineering, …..

Control System:Control System:

- Plant structurePlant structure whose whose responses are controlledresponses are controlled - SensorsSensors- Control computerControl computer (Controller)(Controller)- - Control actuatorControl actuator


Plant

Sensors

Controller

Actuator

Control Input

Seismic Input

Seismic Structural Control:Seismic Structural Control:

1.1. Reduce the effect of seismic excitation Reduce the effect of seismic excitation whichwhich a a plantplant is subjected to. is subjected to.

2.2. Prevent a Prevent a plantplant from exhibiting from exhibiting the resonance vibration. the resonance vibration.

3.3. Transfer the vibration energy of a Transfer the vibration energy of a plantplant to a to a control-actuatorcontrol-actuator..

4.4. Put additional damping effect to a Put additional damping effect to a plantplant..

5.5. Add a control force to a Add a control force to a plant plant throughthrough an actuator or actuators. an actuator or actuators.

Passive Control System:Passive Control System:

■ Plant structurePlant structure whose whose responses are controlledresponses are controlled ■ ■ SensorsSensors■ Control computerControl computer (Controller)(Controller)■ ■ Control actuatorControl actuator

✓✓

Base Isolation:Base Isolation:


✓✓

Passive Damper Control:Passive Damper Control:

1.1. Reduce the effect of seismic excitation.Reduce the effect of seismic excitation.2.2. Prevent a Prevent a plantplant from exhibiting from exhibiting

the resonance vibration. the resonance vibration.3.3. Transfer the vibration energy of a Transfer the vibration energy of a

plantplant to a to a control-actuatorcontrol-actuator..4.4. Put additional damping effect to aPut additional damping effect to a

plantplant..5.5. Add a control force to a Add a control force to a plantplant..

TMD Control:TMD Control:

1.1. Reduce the effect of seismic excitation.Reduce the effect of seismic excitation.2.2. Prevent a Prevent a plantplant from exhibiting from exhibiting

the resonance vibration. the resonance vibration.3.3. Transfer the vibration energy of aTransfer the vibration energy of a

plant plant to ato a control-actuator.control-actuator.4.4. Put additional damping effect to aPut additional damping effect to a

plantplant..5.5. Add a control force to a Add a control force to a plantplant..

Base Isolation:Base Isolation:

1.1. Reduce the effect of seismic excitation.Reduce the effect of seismic excitation.2.2. Prevent aPrevent a plantplant from exhibitingfrom exhibiting

the resonance vibration.the resonance vibration.3.3. Transfer the vibration energy of a Transfer the vibration energy of a

plant plant to a to a control-actuatorcontrol-actuator..4.4. Put additional damping effect to a Put additional damping effect to a

plant.plant.5.5. Add a control force to a Add a control force to a plantplant..

Active Control System:Active Control System:


✓✓✓✓

AMD Control:AMD Control:

1.1. Reduce the effect of seismic excitation.Reduce the effect of seismic excitation.2.2. Prevent a Prevent a plant plant from exhibiting from exhibiting

the resonance vibration. the resonance vibration.3.3. Transfer the vibration energy of aTransfer the vibration energy of a

plantplant to a secondary vibration to a secondary vibration system.system.

4.4. Put additional damping effect to aPut additional damping effect to a plantplant..

5.5. Add a control force to aAdd a control force to a plant.plant.

Theoretically,Theoretically,

There are two kinds of active There are two kinds of active control schemes: ……..control schemes: ……..

Theoretically,Theoretically,

There are two kinds of active There are two kinds of active control schemes:control schemes: FeedbackFeedback control control andand Feed-forwardFeed-forward control. control.

Plant

Sensors

Controller

Actuator

Control Input

External input such as seismic excitation

Output

Plant

Sensors

Controller

Actuator

Control Input


Output

Feedback Control

Plant

Sensors

Controller+Actuator

Control Input


Output

Feedback Control

Plant

Response

Controller

Control Input


Feedback Control

H(s)

G(s)

Control Input

External input excitation

Feedback Control

Response

H(s)

G(s)

Control Input

External input excitation

Feedback Control

Response

Feedback gain

Plant transfer function

Plant

Sensors

Controller+Actuator

Control InputExternal

input such as seismic excitation Respons

e

H(s)

G(s)Control InputExternal

input excitation Respons

e

H(s)

G(s)Control InputExternal

input excitation Respons

e

Feed-forward Control

■ ■ 6. Semiactive Structural 6. Semiactive Structural Control: 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


- Plant structurePlant structure whose whose responses are controlledresponses are controlled - SensorsSensors- Control computerControl computer (Controller)(Controller)- - Control actuatorControl actuator


Plant

Sensors

Controller

Actuator

Seismic Input

Semiactive control:Semiactive control:

There are two major ways defThere are two major ways defining or characterizing ining or characterizing semiacsemiactive controltive control concept. concept.

The most general definition:The most general definition:

Semiactive control is …… Semiactive control is ……


Semiactive control is Semiactive control is conducted bconducted byy changing or controlling a part changing or controlling a part ofof charactersiticscharactersitics of of control actuatorcontrol actuator only at appropriate time insonly at appropriate time instants.tants.


Semiactive control is Semiactive control is conducted byconducted by changing or controlling a part ofchanging or controlling a part of chcharactersiticsaractersitics of of control actuatorcontrol actuator only at appropriate time instants.only at appropriate time instants.

Adaptive characteristicsAdaptive characteristics..

This definition leads to:This definition leads to:

- - Large power not needed.Large power not needed.

- - Required power not Required power not dependent dependent

of the magnitude of of the magnitude of

seismic excitation.seismic excitation.

The second significant point:The second significant point:

Semiactive control operation Semiactive control operation doedoes not inject mechanical energys not inject mechanical energy into a into a plant structure or control device or plant structure or control device or actuator. actuator.

The second significant point:The second significant point:

Semiactive control operation Semiactive control operation does ndoes not inject mechanical energyot inject mechanical energy into a plant s into a plant structure or control device or actuator. tructure or control device or actuator.

It has It has much less potentialmuch less potential to to destabilize the structure. destabilize the structure.

In typical semiactive control:In typical semiactive control:

Actuator: Actuator: DamperDamper

Controlled characteristics such as Controlled characteristics such as

the the dampingdamping coefficientcoefficient, ,

the magnitude of the magnitude of relief loadrelief load, etc., , etc.,

of the of the damperdamper are controlled. are controlled.

This kind of dampers are …….. This kind of dampers are ……..

Typical semiactive control:Typical semiactive control: Actuator: Actuator: DamperDamper

Ccontrolled characteristics such as Ccontrolled characteristics such as

the the dampingdamping coefficientcoefficient, ,

the magnitude of the magnitude of relief loadrelief load, etc. , etc.

of the of the damperdamper are controlled. are controlled.

This kind of dampers areThis kind of dampers are

called called ‘controllable’ ‘controllable’ dampersdampers..

Then, Then, for example,for example,

consider a type of consider a type of semiactivesemiactive control control in which the in which the damping coefficientsdamping coefficients o of installed viscous dampers are contrf installed viscous dampers are controlled. olled.

Then, Then, for example,for example,

consider a type of consider a type of semiactivesemiactive control control in which the damping coefficients in which the damping coefficients of installed viscous dampers are contof installed viscous dampers are controlled. rolled.

This change would not have any effect This change would not have any effect on the structure which is not subject to on the structure which is not subject to

any other external input excitation.any other external input excitation.

On the contrary,On the contrary,

tthe movement of AMD he movement of AMD couldcould make an entire structure vibrate make an entire structure vibrate even in case of no other external even in case of no other external input excitationinput excitation. .

On the contrary,On the contrary,

tthe movement of he movement of AMDAMD would make an would make an entire structure vibrate entire structure vibrate even in case of even in case of no other external input excitationno other external input excitation..

This is very This is very significantsignificant differencedifference between between full-activefull-active and and semi-activesemi-active control. control.

AMD

AMD

Power

Building

Controlled dampersControlled dampers

Smart dampersSmart dampers

One of smart control schemesOne of smart control schemes

Control scheme based on “Control scheme based on “smartsmart” or ” or ““controlledcontrolled” dampers ” dampers

■ ■ 7. Smart damping 7. Smart damping or Smart Dampers or Smart Dampers

Vibration Control

- Buildings

- Motor vehicle suspensions

Car Body or

Building 　Spring

Damper

z

xg

- Computer control of of suspension systems in 1980s.- Computer control of buildings in 1989.

Car Body

Spring

Damper

z

xg

- 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

DamperVariable

Transfer function from xg to z

)()(

ωxωz

g

1

2

High damping

Low damping

0

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

xg

Skyhook damper

z

xg

Csh

C

Skyhook damper

z

xg

Csh

C

C (z-xg) = Csh z...

Skyhook damper

zxg

Csh

CC (z-xg) = Csh z

...

C = Csh [z / (z-xg)] . ..

Pioneering Implementations Pioneering Implementations of Smart Damping:of Smart Damping:

• Kajima Shizuoka Building

• Keio University Soso-kan Building• Chubu Electric Power (CEP) 　　　

Gifu Regional Office Building

Kajima Shizuoka Building

- - Kajima Shizuoka BuildingKajima Shizuoka Building

The World’s first The World’s first smart damping oror semiactive variable dampingsemiactive variable damping implementation to a building.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 BuildingKeio Univ. Soso-kan Building

The world’s first The world’s first smart base-smart base- isolatedisolated building or building or building with building with base isolationbase isolation integratingintegrating semiactively-controlled semiactively-controlled variable dampingvariable damping system.system.

CEP Gifu CEP Gifu Regional Office Regional Office BuildingBuilding

- - CEP Gifu Regional Office BuildingCEP 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:A-D Control System:

Plant

Sensors

Controller

Act.

Seismic Input

Sensors

Controller

Act.

Act.

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

+ DispKCmin

Cmax

Vel

By properly choosing the damping coefficient,

Cmin

Cmin

Cmax

Passive Damper Hysteresis

Cmax

1

2

3

4

Cmax

Cmax

Cmax

Cmax

① ①

②

②

②

③④

③ ③

④ ④

- Each damper autonomously controlled by its own decentralized controller


-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

Roppongi Tower

- Control operation could be conducted based upon the response information only in the neighborhood of each control devise.


+ Artificial Nonlinearity concept

seems appropriate or fitted to structural control against severe seismic excitations.

Autonomous-decentralized control

■ ■ 8. Significance of nonlinearity 8. Significance of nonlinearity 　　or artificially-added nonlinearity or artificially-added nonlinearity in structural control in structural control

　 - Basic concept

- Control effect

- Oil hydraulic dampers 　　　　　　　　　　　　　　　　　　　　　　　　　　　　

tan-1βK

tan-1(α+β)K

tan-1αK

tan-1αK

Linear structure

Bi-linear subsystem

γ ＝ α/ （ α ＋ β ）

　　　　　　　　

tan-1 K

tan-1 γK

Damping Coefficient = 　　　 ΔW/W/(4π)

ΔW W

tan-1 K

tan-1γK

Equivalent viscous damping ratio = (1-γ)/((1+γ)π)

α=0.7

α=0.8

α=0.9

α=1.0

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/sec2 　　　　　　

α=β= 0.5 0.5 　①

α=0.3, β= 0.7

Response Accelerations

Response Displacement

α= 0.3, β= 0.7 0.7

α=β= 0.50.5

Damper hystereses

α=0.3, β= 0.7

α= β= 0.5 0.5

As an AD semiactive control system integrating artificial nonlinearity philosophy,

Variable slip-force level dampers

■ ■ 9. 9. SemiactiveSemiactive Variable Variable Slip-force Level Dampers Slip-force Level Dampers

　 - Basic concept

- Control effect

- Oil hydraulic dampers 　　　　　　　　　　　　　　　　　　　　　　　　　　　　

- Basic concept:- Basic concept:

- Semiactive control

- Utilizing artificial nonlinearity

- Autonomous-decentralized system 　　　　　　　　　　　　　　　　　　　　　　　　　　　　

displacement

D 層間変位

Force

slip-force-level

fSlip-levelforce スリ

ップレベル

図 7 　完全弾塑性型

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. 　　

tan-1(α+β)K

tan-1 αK

Damper+Structure

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/sec2 　　　　　　

α=β= 0.5 0.5 　①

α=0.3, β= 0.70.7

Response Accelerations

Response Displacement

α= 0.3, β= 0.7 0.7

α=β= 0.50.5

Damper hystereses

α= 0.3, β= 0.70.7

α= β= 0.5 0.5

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 d

eformation. 　　　　　　

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:Building 1: α=β= 0.7

Building 2:Building 2: α=β= 1.0　　　　　　

　 Maximum resoponses (a) Accelerations (b) displacements

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. 　

電磁リリーフ弁オリフィスピストン

ゴムブッシュ rubber bush

pistonorifice electromagnetic relief valve

図 13 　オイルダンパ

Experimental model of semiactive variable slip-force level damper

Relationship between damper velocity and electric voltage given to the valve

Experimental results responding to sinusoidal excitation with increasing amplitudes

shea

r for

ce (k

N)

shea

r for

ce (k

N)

Displacement (mm)

Constantslip-force level

Variableslip-forcelevel

Reference:Reference:

A. Nishitani, Y. Nitta and Y. Ikeda (2003). A. Nishitani, Y. Nitta and Y. Ikeda (2003).

“ “Semiactive structural-control based on variable slip-force lSemiactive structural-control based on variable slip-force level dampersevel dampers,” ,”

J. of Structural Engineering, ASCEJ. of Structural Engineering, ASCE,, Vol. 129(7), pp.933-940. Vol. 129(7), pp.933-940.

■■

-- SemiactiveSemiactive and and smartsmart concept based sche concept based schemes mes havehave been presented for structural c been presented for structural control of buildings as well as the ontrol of buildings as well as the full scale implementations of some of sucfull scale implementations of some of such schemes in Japan.h schemes in Japan.

- -

■■

-- The concept of semiactive variable slip-fThe concept of semiactive variable slip-force level dampers has been presented.orce level dampers has been presented.

■■ 10.10. Future directionsFuture directions:

-- SemiactiveSemiactive and and smartsmart strategies, or strategies, or smart smart passivepassive strategies, are expected to play m strategies, are expected to play more and more significant role in the futurore and more significant role in the future stage of structural engineering, integrae stage of structural engineering, integrating the ting the autonomous-decentralizedautonomous-decentralized concept. concept.

--

■■ Optimal control:Optimal control: LQ control & LQG controlLQ control & LQG control:

LQ:

Linear, Quadratic

LQG:

Linear, Quadratic and Gaussian

--

■■ LQ control & LQG controlLQ control & LQG control:

Two schemes for optimal control:

Response:Response: whetherwhether probabilistic probabilistic

or deterministic?or deterministic?

If the response isIf the response is probabilistic, probabilistic, thenthen the control input the control input will be will be probabilistic. probabilistic.

LQG controlLQG control..

--

■■ LQ control & LQG controlLQ control & LQG control:

In the case where

the response and control input are stationary, Gaussian random processes,

LQG controlLQG control..

--

The equation of motion of a structural The equation of motion of a structural system with system with control inputcontrol input::

cfbuAxx

fux

x

ωςωx

x

dt

d

ufxωxωςx

:as rewritten is equation This

1

0

1

0

2

10

2

020

200

The state equation:The state equation:

control. LQ

tic.determinis

then tic,determinis

then tic,determinis

above, the In

:

:

:

u

x

f

cfbuAxx

The state equation:The state equation:

mean.-zero withGaussian stationary

mean,-zero withGaussian stationary

then mean,-zero with

noise- whiteGaussian stationary

above, the In

:

:

:

u

x

f

cfbuAxx

LQG control

T

T

T

T

T

T

dttruEtQxtxET

JE

xu

dttrutQxtxT

EJE

J

xu

dttrutQxtxT

J

0

2

0

2

0

2

1

1

1

)])([)]()([(lim][

)]()()([lim][

)]()()([lim

.stationary are and

tic.probabilis also is

tic,probabilis are and If

])[][(lim][

])[][(lim][

)])([)]()([(lim][

2

0

2

0

2

1

1

ruEQxxEJE

dtT

ruEQxxEJE

dttruEtQxtxET

JE

xu

T

T

T

T

T

.stationary are and

Equation. Riccati

:equation following the satisfying

by given is gain Feedback

by given isinput Control

.stationary are and

01

1

2

QPbPbrPAPA

PbrG

G

tGxtPu

ruEQxxEJE

xu

T

)()(

])[][(lim][

LQG control: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.

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