robust hybrid control of a seismically excited cable-stayed bridge

Robust Hybrid Control of

a Seismically Excited Cable-Stayed Bridge

JSSI 10th Anniversary Symposium on

Performance of Response Controlled Buildings

Kyu-Sik Park, Post-Doctoral Researcher, KAIST, Korea

Hyung-Jo Jung, Assistant Professor, Sejong Univ., Korea

Woon-Hak Kim, Professor, Hankyong National Univ., Korea

In-Won Lee, Professor, KAIST, Korea

Structural Dynamics & Vibration Control Lab., KAIST 2 2

Introduction

Robust hybrid control system

Numerical examples

Conclusions

Contents


Introduction

Hybrid control system (HCS)

A combination of passive and active/semiactive control devices

• Passive devices: insure the control system robustness

• Active/semiactive devices: improve the control performances

The overall system robustness may be negatively impacted

by active/semiactive device or active/semiactive controller

may

cause instability due to small margins.

A combination of passive and active/semiactive control devices

• Passive devices: insure the control system robustness

• Active/semiactive devices: improve the control performances

The overall system robustness may be negatively impacted

by active/semiactive device or active/semiactive controller

may

cause instability due to small margins.


Objective

Apply a hybrid control system for vibration control of

a seismically excited cable-stayed bridge

Apply a robust control algorithm to improve the controller robustness

Apply a hybrid control system for vibration control of

a seismically excited cable-stayed bridge

Apply a robust control algorithm to improve the controller robustness


Robust Hybrid Control System (RHCS)

Control devices

Passive control devices

• Lead rubber bearings (LRBs)

• Design procedure: Ali and Abdel-Ghaffar (1995)

• Bouc-Wen model

Passive control devices

• Lead rubber bearings (LRBs)

• Design procedure: Ali and Abdel-Ghaffar (1995)

• Bouc-Wen modelLRBF

rxyD

yF

ekpk

LRBF

rxyD

yF

ekpk

1

( , ) (1 )

1

LRB r r e r e y

n n

i r r ry

F x x k x k D y

y A x x y y x yD


Active control devices

• Hydraulic actuators (HAs)

• An actuator capacity has a capacity of 1000 kN.

• The actuator dynamics are neglected.

Active control devices

• Hydraulic actuators (HAs)

• An actuator capacity has a capacity of 1000 kN.

• The actuator dynamics are neglected.


Control algorithm: -synthesis method

where : structured singular value: transfer function of closed-loop system : perturbation

Cost function Cost function

(1)

Advantages Advantages

• Combine uncertainty in the design procedure

• Guarantee the stability and performance (robust performance)

• Combine uncertainty in the design procedure

• Guarantee the stability and performance (robust performance)

supd dy wJ j

N

d dy wN

Δ


Frequency dependent filters Frequency dependent filters

• Kanai-Tajimi filter • Kanai-Tajimi filter

(2)

10-2

100

102

104

106

10-10

10-8

10-6

10-4

10-2

100

102

Frequency (rad/sec)

Mag

init

ud

e

El Centro Mexico CityGebze K-T filter

2

0

2 2

2

2

g g g

g

g g g

S sW

s s

0 El Centro 0 ~ 10 rad/secMexico City Gebze

max mean ,

17 rad/sec,

0.3

g gx x

g

g

S S


• High-pass and low-pass filters

(3), (4)

10-2

100

102

104

106

10-1

100

Frequency (rad/sec)

Mag

nit

ud

e

Wz

Wu

10.2 1

601

1240

,u

s

Ws

11

601

130

z

s

Ws

10.2 1

601

1240

,u

s

Ws

11

601

130

z

s

Ws


• Additive uncertainty filter

(5)

10-1

100

101

102

103

104

100

101

102

103

Frequecy (rad/sec)

SV

, mag

nit

ud

e

Evaluation ModelDesign Model

10-1

100

101

102

103

104

10-4

10-3

10-2

10-1

100

101

102

Frequency (rad/sec)

SV

-dif

f, m

agn

itu

de

SV-diff-xg2yWxg2y

• Multiplicative uncertainty filter

(6)

2 2

1 2 2 2

2 2

1 1 1

2

2gx

c s sW

s s

y

1

1

42

1 2

10.32,

10,

1.71 10 ,

0.8

c

0.01W u u


LRB-installed

structure

Sensor-synthesis methodHA

Block diagram of robust hybrid control systemBlock diagram of robust hybrid control system

ey

my

syactiveu

activef

gx ey

my

syactiveu

activef

gx


Analysis model

Bridge model

• Bill Emerson Memorial Bridge

· Benchmark control problem

· Located in Cape Girardeau, MO, USA

· 16 shock transmission devices (STDs) are employed between the tower-deck connections.

Bridge model

• Bill Emerson Memorial Bridge

· Benchmark control problem

· Located in Cape Girardeau, MO, USA

· 16 shock transmission devices (STDs) are employed between the tower-deck connections.

Numerical Examples


Configuration of control devices (LRBs+HAs)

(3+2)

(3+2)

(3+4)

(3+4)

(3+4)

(3+4)

(3+2)

(3+2)

Bent 1 Pier 2 Pier 3 Pier 4

142.7 m 350.6 m 142.7 m


Bent 1

4 actuators2 actuators

Pier 2 Pier 3 Pier 4

bottom viewof bridge deck

edge girder

towerdeck

LRB

Placement of control devices


0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0T im e (se c )

-3

-2

-1

0

1

2

3

4

Acc

eler

atio

n (m

/s2 )

El C entro

PGA: 0.348gPGA: 0.348g

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0T im e (se c )

-2

-1

0

1

2

Acc

eler

atio

n (m

/s2 )

M exico C ity

PGA: 0.143gPGA: 0.143g

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0T im e (se c )

-2

-1

0

1

2

3

Acc

eler

atio

n (m

/s2 )

G ebze

PGA: 0.265gPGA: 0.265g

0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )

0

1

2

3

4

5

6

7

8

Pow

er S

pect

ral D

ensi

ty

0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )

0

1

2

3

4

5

6

Pow

er S

pect

ral D

ensi

ty

0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )

0

1

2

3

4

5

6

7

8

9

Pow

er S

pect

ral D

ensi

ty

Historical earthquake excitations Historical earthquake excitations


- Max. responses J1: Base shear J2: Shear at deck level J3: Base moment J4: Moment at deck level J5: Cable deviation J6: Deck dis.

- Normed responses J7: Base shear J8: Shear at deck level J9: Base moment J10: Moment at deck level J11: Cable deviation

Evaluation criteria Evaluation criteria


Analysis results

Control performances Control performances

Displacement under El Centro earthquake

(a) STDs (b) RHCS


Cable tension under El Centro earthquake

(a) STDs (b) RHCS


Base shear force under El Centro earthquake

(a) STDs (b) RHCS


Evaluation criteria Passive Active Semiactive Hybrid I Hybrid II

J1. Max. base shear 0.546 0.523 0.468 0.485 0.497

J2. Max. deck shear 1.462 1.146 1.283 0.921 1.170

J3. Max. base moment 0.619 0.416 0.485 0.443 0.454

J4. Max. deck moment 1.266 0.821 1.184 0.656 0.752

J5. Max. cable deviation 0.208 0.154 0.219 0.143 0.144

J6. Max. deck dis. 3.830 1.465 3.338 1.553 1.117

J7. Norm base shear 0.421 0.368 0.370 0.377 0.360

J8. Norm deck shear 1.550 1.005 1.351 0.899 0.976

J9. Norm base moment 0.482 0.316 0.404 0.338 0.307

J10. Norm deck moment 1.443 0.682 1.607 0.728 0.617

J11. Norm cable deviation 0.022 0.016 0.019 0.017 0.015

• Maximum evaluation criteria for all the three earthquakes • Maximum evaluation criteria for all the three earthquakes

Passive: LRB, Active: HA/, Semiactive: MRD/SMC,

Hybrid I: LRB+HA/LQG, Hybrid II: LRB+HA/

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 J11

Passive

Active

Semiactive

Hybrid I

Hybrid II


Controller robustness

• The dynamic characteristic of as-built bridge is not identical to the numerical model.

• There are large differences at high frequencies between evaluation and design models.

• There is a time delay of actuator introduced by the controller dynamics and A/D input and D/A output conversions.

Controller robustness

• The dynamic characteristic of as-built bridge is not identical to the numerical model.

• There are large differences at high frequencies between evaluation and design models.

• There is a time delay of actuator introduced by the controller dynamics and A/D input and D/A output conversions.

Robust analysis should be performed to verify the applicability of the control system.


where : nominal stiffness matrix: perturbed stiffness matrix: perturbation amount

• Stiffness matrix perturbation

• Mass matrix perturbation

· Additional snow loads (97.7 kg/m2, UBC) are added to the deck.

where : time delay: time delay amount: sampling time (0.02 sec)

• Time delay of actuator

(7)

(8)

pert (1 ) K K

pertKK

sT

sT

pert (1 ) K K

pertKK

sT

sT


0

10

20

30

40

50

60

70

80

90

±5% ±10% ±15% ±20%

Stiffness Perturbation (%)

Max

. Var

iati

on (

%)

w/o snow, El Centrow/o snow, Mexico Cityw/o snow, Gebzew/ snow, El Centrow/ snow, Mexico Cityw/ snow, Gebze

Max. variation of evaluation criteria vs. variation of stiffness perturbation


0

5

10

15

20

25

30

35

40

0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Time Delay (sec)

Max

. Var

iati

on (

%)

w/o snow, El Centrow/o snow, Mexico Cityw/o snow, Gebzew/ snow, El Centrow/ snow, Mexico Cityw/ snow, Gebze

Max. variation of evaluation criteria vs. variation of time delay


Max. variation of evaluation criteria vs. variation of stiffness perturbation and time delay (w/o snow)


Max. variation of evaluation criteria vs. variation of stiffness perturbation and time delay (w/ snow)


Robust hybrid control system

Control performances is superior to passive control system and slightly better than active and semiactive control systems. Has excellent robustness without loss of control performances

Control performances is superior to passive control system and slightly better than active and semiactive control systems. Has excellent robustness without loss of control performances

could be used for cable-stayed bridges containing

many uncertainties

Conclusions


Thank you for your attention!

This research is supported by the National Research Laboratory program from the Ministry of Science of Technology and the Grant for Pre-Doctoral Students from the Korea Research Foundation in Korea.

Acknowledgements

robust hybrid control of a seismically excited cable-stayed bridge

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