Structural Dynamics & Vibration Control Lab. 1 Kang-Min Choi, Ph.D. Candidate, KAIST, Korea...

Structural Dynamics & Vibration Control Lab. 1

Kang-Min Choi, Ph.D. Candidate, KAIST, Korea

Jung-Hyun Hong, Graduate Student, KAIST, Korea

Ji-Seong Jo, Section Manager, POSCO E&C, Korea

In-Won Lee, Professor, KAIST, Korea

Active Control for Seismic Response

Reduction Using Modal-Fuzzy Approach

The 18th KKCNN Symposium (2005) Kaohsiung, TaiwanDec. 20-21, 2005

Structural Dynamics & Vibration Control Lab., KAIST, Korea 2

CONTENTS

Introduction

Proposed Method

Numerical Example

Conclusions


Introduction

Death : 14,491 Magnitude : 7.4

• Sumatra, Indonesia (2004)• Sumatra, Indonesia (2004)

Recent Earthquakes

Death : 5,400 Magnitude : 7.2• Kobe, Japan (1995)• Kobe, Japan (1995)

Death : 283,106 Magnitude : 9.0

• Gebze, Turkey (1999)• Gebze, Turkey (1999)

• Kashmir, Pakistan (2005)• Kashmir, Pakistan (2005) Death : 30,000 Magnitude : 7.6

To increase the safety and reliability, structural control is required.

Structural Dynamics & Vibration Control Lab., KAIST, Korea

4 4

• Passive control system

-Vibration control without external power

-Energy dissipation of structure

-No adaptability to various external load

-Large deformation of devices

-Examples: Lead rubber bearing, Viscous damper

• Active control system -Vibration control with external power

-Adaptability to various loading conditions

-Large external power

-Examples: Active mass damper, Hydraulic actuator


5 5

Control Algorithms

• Active control algorithms

- Linear optimal control algorithm

- Sliding mode control algorithm

- Adaptive control algorithm

- Fuzzy control algorithm

- Modal control algorithm


• Fuzzy control algorithm has been recently proposed for the active structural control of civil engineering systems.

• The uncertainties of input data from the external loads and structural responses are treated in a much easier way by the fuzzy controller than by classical control theory.

• It offers a simple and robust structure for the specification of nonlinear control laws.


• Modal control algorithm represents one control class in which the vibration is reshaped by merely controlling some selected vibration modes.

• Civil structures has hundred or even thousand DOFs. its vibration is usually dominated by first few modes, modal control algorithm is especially desirable for reducing vibration of civil structure.


Conventional fuzzy controller

One should determine state variables which are used as inputs of the fuzzy controller.

- It is very complicated and difficult for the designer to select state variables used as inputs among a lot of state variables.

One should construct the proper fuzzy rule.

- Control performance can be varied according to many kinds of fuzzy rules.


Objective

Development of active fuzzy control algorithm on modal coordinates


Proposed Method

Modal Algorithm- Equation of motion for MDOF system

(2)

- Using modal transformation

(3)

- Modal equation

(4)


(5)

(6)

- Displacement

- State space equation

Controlled displacement

Residual displacement


Modal algorithm is desirable for civil structure.

- Civil structure involves tens or hundreds of thousands DOFs.

- Vibration is dominated by the first few modes.


Active Modal-fuzzy Control System

Structure

Fuzzy Controller

Modal Structure


Modal-fuzzy control system

Input variables

Output variables

Fuzzification

Defuzzification

Fuzzy inference

• Fuzzy inference : membership functions, fuzzy rule

• Input variables : mode coordinates ),(

)( df• Output variable : desired control force


- Development of fuzzy controller on modal coordinates

- Easy to select fuzzy input variables

- Use of information of all DOFs

- Serviceability of modal approach

- Easy to treat the uncertainties of input data

- Robustness of fuzzy controller

Characteristics


Six-Story Building (Jansen and Dyke 2000)

Numerical Example

ControlComputer

gx

6ax

5ax

4ax

3ax

2ax

1axHA

HA

fd

fd

- System data• Mass of each floor

: 0.277 N/(cm/sec2)

• Stiffness

: 297 N/cm

• Damping ratio

: 0.5% for each mode


Frequency Response Analysis

0

4000

8000

12000

0 2 4 6 8 10

- Under the scaled El Centro earthquake

1st F

loo

r6th

Flo

or

Frequency, Hz Frequency, Hz Frequency, Hz

103

104102

105 107

106

12

8

4

0

200000

400000

600000

800000

1000000

0 2 4 6 8 10

0

20000000

40000000

60000000

80000000

0 2 4 6 8 10

0

200

400

600

800

0 2 4 6 8 10

0

10000

20000

30000

40000

50000

0 2 4 6 8 10

0

1000000

2000000

3000000

4000000

5000000

0 2 4 6 8 10

10

8

6

4

2

8

6

4

2

5

4

3

2

1

5

4

3

2

1

8

6

4

2

PS

DP

SD

PS

DP

SD

PS

DP

SD

PSD of Displacement PSD of Velocity PSD of Acceleration


• In frequency analysis, the first mode is dominant.

- The responses can be reduced by modal-fuzzy control using the lowest one mode.


Active Optimal Controller Design (LQR)• Cost function

0

1lim dtRffQyyEJ cc

(7)

22IRwhere

Q : placing a weighting 9000(cm-2) on the relative displacements of all floors


Active Modal-fuzzy Controller Design

• Input variables : first mode coordinates• Output variable : desired control force

),( 11

• Fuzzy inference

)( df

• Membership function

- A type : triangular shapes (inputs: 5MFs, output: 5MFs)

- B type : triangular shapes (inputs: 5MFs, output: 7MFs)

A type : for displacement reductionB type : for acceleration reduction


- Membership functions- Membership functions

NL NS ZE PS PL

-x x0

Input membership function

Output membership function

NL NS ZE PS PM

-y y0

NM PL

: Negative Large

: Negative Small

: Zero

: Positive Small

: Positive Large

NL

NS

ZE

PS

PL

: Negative Large

: Negative Medium

: Negative Small

: Zero

: Positive Small

: Positive Medium

: Positive Large

NL

NM

NS

ZE

PS

PM

PL


• Fuzzy rule

- A type

NL NS ZE PS PL

NL PL PL PM PS ZE

NS PL PM PS ZE NS

ZE PM PS ZE NS NM

PS PS ZE NS NM NL

PL ZE NS NM NL NL

- B type

1

1

NL NS ZE PS PL

NL PL PL PS PS ZE

NS PL PS PS ZE NS

ZE PS PS ZE NS NS

PS PS ZE NS NS NL

PL ZE NS NL NL NL


Acc

el.

(m

/sec

2)

El Centro(PGA: 0.348g)

0 4 8 12 16 20

-8

-4

0

4

8

- 8

- 4

0

4

8

Input Earthquakes

• Medium amplitude (100% El Centro earthquake)• Medium amplitude (100% El Centro earthquake)

• High amplitude (120% El Centro earthquake)• High amplitude (120% El Centro earthquake)

• Low amplitude (80% El Centro earthquake)• Low amplitude (80% El Centro earthquake)


max,1

)(max

x

txJ i

it

max,2

/)(max

n

ii

it d

htdJ

max,3

)(max

ai

ai

it x

txJ

W

tfJ i

it

)(max

,4

Normalized maximum floor displacement

Normalized maximum inter-story drift

Normalized peak floor acceleration

Maximum control force normalized by the weight of the structure

- Evaluation criteria are used in the second generation linear control problem for buildings (Spencer et al. 1997)

Evaluation Criteria


0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5

Peak interstory drift (cm)

Flo

or

of

stru

ctur

e

Uncontrolled

LQR

Modal-fuzzy A

Modal-fuzzy B

Control Results

Fig. 1 Peak responses of each floor of structure to scaled El Centro earthquake

Peak interstory drift (cm)

Flo

or

of

stru

ctu

re

0

1

2

3

4

5

6

0 100 200 300Peak absolute acceleration (cm/sec 2̂)

Flo

or

of

stru

ctur

e

Uncontrolled

LQR

Modal-fuzzy A

Modal-fuzzy B

Peak absolute acceleration (cm/s2)

Flo

or

of

stru

ctu

re


- Though the proposed Type A performs significantly better than other systems restricted within the interstory drift, but the performance of peak acceleration is not good.

- A well designed proposed Type B balances the benefits of the different objectives within the requirements of the specific design scenario.

• Observations


Control strategy J1 J2 J3 J4

Optimal LQR

Active Modal-fuzzy control (A type)

Active Modal-fuzzy control (B type)

0.479

0.343

0.548

0.626

0.562

0.635

0.685

1.186

0.601

0.0178

0.0178

0.0134

• Medium amplitude• Medium amplitude


28 28

0

0.3

0.6

0.9

1.2

1.5

J1 J2 J3

LQRA typeB type

- Performance of proposed Type B is comparable to optimal control.

- Control force is relatively small compared to those of other controllers.

• Observations

J1 J2 J3

Evaluation criteria

Re

du

ctio

n f

ac

tor

J4×10



Optimal LQR



0.479

0.374

0.607

0.610

0.594

0.623

0.912

1.545

0.701

0.0178

0.0178

0.0134

• High amplitude• High amplitude

0

0.4

0.8

1.2

1.6

2

J1 J2 J3

LQR

A typeB type

J1 J2 J3

Evaluation criteria

Re

du

ctio

n f

ac

tor

J4×10


• Low amplitude• Low amplitude


Optimal LQR



0.474

0.289

0.504

0.657

0.573

0.624

0.586

1.386

0.773

0.0178

0.0178

0.0134

0

0.4

0.8

1.2

1.6

J1 J2 J3

LQR

A type

B type

J1 J2 J3

Evaluation criteria

Re

du

ctio

n f

ac

tor

J4×10


31 31

- Proposed method Type B gives comparable performance to optimal controller.

- Moreover, it is much easier to design control system than optimal controller.

• Observations

- Control force is relatively small compared to those of other controllers.


32 32

- Phase plane trajectory (Battaini et al. 1998)

Technique to reflect graphically the dynamic properties of control system in phase plane.

- Phase plane trajectory (Battaini et al. 1998)

Technique to reflect graphically the dynamic properties of control system in phase plane.

- Stability test for worst case of floor displacement

• Stability of proposed control system

Dis

pla

cem

ent

(cm

)

Time (sec)

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

0 20 40 60 80 100


33 33

- Stability test for worst case of floor acceleration

- Stability test for worst case of control force

Proposed control system is stable.

Acc

eler

atio

n (

g)

Time (sec)

Co

ntr

ol

forc

e (N

)

Time (sec)

-1.5

-1

-0.5

0

0.5

1

1.5

0 20 40 60 80 100

-40

-20

0

20

40

0 20 40 60 80 100


Conclusions

• A new active modal-fuzzy control strategy for seismic response reduction is proposed.

• Verification of the proposed method has been investigated according to various amplitude earthquakes.


• The performance of proposed method is comparable to optimal controller.

• The proposed method is convenient, simple and easy to apply to real civil structures.


Thank you

for your attention!

Structural Dynamics & Vibration Control Lab. 1 Kang-Min Choi, Ph.D. Candidate, KAIST, Korea...

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Transcript of Structural Dynamics & Vibration Control Lab. 1 Kang-Min Choi, Ph.D. Candidate, KAIST, Korea...