Application for Structural Control

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

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

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

 

m 0 0 M

    

        

k k k

 

k K

   

x X

     

m M

  



   

u u

   

m 0 m M

    



       

k k 0 K

   

x a X

     

m M

  



   

u u

 

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

 

m 0 m M

    



       

k k 0 K

   

x a X

     

m M

  



   

u u

 

From

(



the first raw ,

  

)



kx a

 







(



  

(



    



)

 

kx a



   



)

 



kx a

Combining

M X

 

the above with

 





(





the second raw of (1),

   



) (1)

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

M X

 

 





( 



    



) (



)   

  (



) 







AMD x x a

x

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.

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

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

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

Car Body or Building Spring Damper

x g

Computer control of of suspension systems in 1980s.

Computer control of buildings in 1989.

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

x z g ( ω ) ( ω )

1 0

Low damping High damping

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

Skyhook damper

C

C z x

Skyhook damper

C

z C

C (z-x

) = C

z x

Skyhook damper

C

z

C

C (z-x

) = C

z

C = C

[z / (z-x

)]

x

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

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,

C max C min

4 2

C min C max

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

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

＝

α/

（

＋

）

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-

)/((1+

)

α=0.7

α=0.8

α=1.0

α=0.9

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

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

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 :



  2

ς ω

0 

0 2





u d dt

  

        0

0 2  1 2

ς ω

0      

       0 1   

This equation is rewritten as :

    0 1   





The state equation:





In the above,

: determinis tic, then

: determinis tic.

LQ control.

The state equation:





In the above,

: stationary Gaussian white with zero mean, then noise

: stationary Gaussian with zero mean,

: stationary Gaussian with zero mean.

LQG control



lim

 

and

 0

[



(

)

(

)



(

are probabilis tic, )]

dt J

is also probabilis tic.

[

u J

]



and

x E

   

lim

  1

 0

[



(

)

(

) are stationary .



(

)]

   

[

]

 1

lim

 

 0

(

[



(

)

(

)]



[

(

)])

and

are stationary .

[

]

 1

lim

 

 0

(

[



(

)

(

)]



[

(

)])

dt E

[

]



lim

 

[

]



lim

 

(

[



]



[

])

(

[



]



[

])

 0

T dt

and

are stationary .

[

]



lim

 

(

[



]



[

Control input is given by ])

(

)

 

(

) Feedback gain

is given by



 1



satisfying the following equation :







Pbr

 1





 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.