Structural Control: Overview and Fundamentals Akira Nishitani Vice President & Professor　　　　　　　　　WASEDA University, Tokyo, Japan anix@waseda.jp

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 since 1882　　早稲田大学

Waseda University: - 125th Anniversary in 2007. - Second oldest private university in Japan, founded in 1882. - 125th 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 : - Vice-President, Waseda Univ. since 2006. - 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 [Japan Association of Earthquake Engineering].

■ 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: 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: Reduce the effect of seismic excitation. Base Isolation 2. Prevent a structure from exhibiting the resonance vibration. 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

‘smart’ expressions such as ‘smart’ cars, 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

which is manipulated by a control computer based on the response data. - 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 u Mass of AMD m AMD Building Mass of Building M

x AMD xa k X building or main structure K xg

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

The equation of motion of a structural system with AMD integrated: (1)

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

AMD xa x xg

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 or 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 (Controller) - Control actuator

Control System: Plant Sensors Actuator Controller Seismic Input Control Input Plant Sensors Actuator Controller

Seismic Structural Control: Reduce the effect of seismic excitation which a plant is subjected to. Prevent a plant from exhibiting the resonance vibration. Transfer the vibration energy of a plant to a control-actuator. Put additional damping effect to a plant. Add a control force to a plant through an actuator or actuators.

Passive Control System: ✓ ■ Plant structure whose responses are controlled ■ Sensors ■ Control computer (Controller) ■ Control actuator ✓

Base Isolation: ✓ ■ Plant structure whose responses are controlled ■ Sensors ■ Control computer (Controller) ■ Control actuator ✓

Passive Damper Control: Reduce the effect of seismic excitation. Prevent a plant from exhibiting the resonance vibration. Transfer the vibration energy of a plant to a control-actuator. Put additional damping effect to a plant. Add a control force to a plant.

TMD Control: Reduce the effect of seismic excitation. Prevent a plant from exhibiting the resonance vibration. Transfer the vibration energy of a plant to a control-actuator. Put additional damping effect to a plant. Add a control force to a plant.

Base Isolation: Reduce the effect of seismic excitation. Prevent a plant from exhibiting the resonance vibration. Transfer the vibration energy of a plant to a control-actuator. Put additional damping effect to a plant. Add a control force to a plant.

Active Control System: ✓ ■ Plant structure whose responses are controlled ■ Sensors ■ Control computer (Controller) ■ Control actuator ✓ ✓ ✓

AMD Control: Reduce the effect of seismic excitation. Prevent a plant from exhibiting the resonance vibration. Transfer the vibration energy of a plant to a secondary vibration system. Put additional damping effect to a plant. Add a control force to a plant.

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

There are two kinds of active control schemes: Theoretically, There are two kinds of active control schemes: Feedback control and Feed-forward control.

Plant Sensors Actuator Controller Control Input Output External input such as seismic excitation Plant Sensors Control Input Output Actuator Controller

Plant Feedback Control Sensors Actuator Controller Control Input External input such as seismic excitation Plant Sensors Control Input Output Actuator Controller Feedback Control

Plant Feedback Control Sensors Controller+Actuator Control Input External input such as seismic excitation Plant Sensors Control Input Output Controller+Actuator Feedback Control

Plant Feedback Control Controller Response Control Input 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 H(s) Response Control Input Feedback gain G(s) Feedback Control

External input excitation Plant transfer function H(s) Response Control Input Feedback gain G(s) Feedback Control

Plant Controller+Actuator Sensors Response Control Input External input such as seismic excitation Plant Response

G(s) Control Input H(s) External input excitation Response

G(s) H(s) Feed-forward Control Response Control Input External input excitation 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.

No energy supply to a control actuator needed. Active control: 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 (Controller) - Control actuator

Control System: Seismic Input Plant Sensors Actuator Controller

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, the movement of AMD could make an entire structure vibrate even in case of no other external input excitation.

On the contrary, the 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

One of smart control schemes 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 xg Damper

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

z Car Body Spring xg Damper

- Ride Comfort  Absolute movement of car body = 0 - Driving Stability = Movement of ground

Trade-off between 　　　 ride comfort and driving stability Spring Damper Variable

Transfer function from xg to z

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 xg

Skyhook damper Csh z C xg

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

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

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: Plant Seismic Input Act. 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.　　　　　　

Autonomous-decentralized control system (AD control system) 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.

Damper Spring

Cmax Cmin K + Vel Disp By properly choosing the damping coefficient,

2 Cmax Cmin 1 3 Cmin Cmax Passive Damper Hysteresis 4

Cmax Cmax Cmax Cmax

② ① ① ③ ④ ② ②

③ ③ ④ 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.

- Basic concept - Control effect - Oil hydraulic dampers ■ 8. Significance of nonlinearity 　or artificially-added nonlinearity in structural control - Basic concept - Control effect - Oil hydraulic dampers

tan-1βK tan-1αK tan-1αK tan-1(α+β)K Linear structure Bi-linear subsystem tan-1βK tan-1αK tan-1αK tan-1(α+β)K

γ＝α/（α＋β）

tan-1 γK tan-1 K

W ΔW Damping Coefficient =　　 　ΔW/W/(4π)

tan-1γK tan-1 K 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 　 α= 0.3; β= 0.7　　　　 El Centro 1940 earthquake NS component with 2 m/sec2　　　　　　

Response Accelerations α=β= 0.5 0.5　① α=0.3, β= 0.7

Response Displacement α=β= 0.50.5 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

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.　　

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 　 α= 0.3; β= 0.7　　　　 El Centro 1940 earthquake NS component with 2 m/sec2　　　　　　

Response Accelerations α=β= 0.5 0.5　① α=0.3, β= 0.70.7

Response Displacement α=β= 0.50.5 α= 0.3, β= 0.7 0.7

Damper hystereses α= β= 0.5 0.5 α= 0.3, β= 0.70.7

Case 1: α=β= 0.5 Estimated damping coefficient = 0.087

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

(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.　

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 Constant slip-force level shear force (kN) Variable slip-force level shear force (kN) 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 strategies, or smart passive 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: Linear, Quadratic LQG: Linear, Quadratic and Gaussian -

■ LQ control & LQG control: Two schemes for optimal control: Response: whether probabilistic or deterministic? If the response is probabilistic, then the control input will be probabilistic.  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:

The state equation:

The state equation: LQG control

LQG control: LQG control statistically satisfies the samllest value of E[J].

Little people discuss other people. Average people discuss events. 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.