Model-based Real-Time Hybrid Simulation for Large-Scale Experimental Evaluation

Brian M. PhillipsUniversity of Illinois

B. F. Spencer, Jr.University of Illinois

Yunbyeong ChaeLehigh University

Karim KazemibidokhtiLehigh University

Shirley J. DykePurdue University

Tony A. FriedmanPurdue University

James M. RiclesLehigh University

Quake Summit 2012Boston, Massachusetts

June, 2012

INTRODUCTION

2

Large-Scale RTHS Project Performance-based design and real-time, large-scale

testing to enable implementation of advanced damping systems

Joint project between Illinois, Purdue, Lehigh, UConn, and CCNY

3

Hybrid Simulation Loop

Servo-hydraulic system introduces dynamics into the hybrid simulation loop

Actuator dynamics are coupled to the specimen through natural velocity feedback

When multiple actuators are connected to the same specimen, the actuator dynamics become coupled 4

NumericalSubstructure

u ExperimentalSubstructure

Sensorsffmeas

xLoadingSystem

Servo-Hydraulic System

gx

SERVO-HYDRAULIC SYSTEM MODEL

5

MIMO System Model

6

+

− −

Servo-Hydraulic System Gxu(s)

Natural Velocity Feedback

Actuator Specimen

sGa sGxf

As

sGs

Servo-Controllerand Servo-Valve

+

3

2

1

u

u

u

u

3

2

1

x

x

x

x

3

2

1

f

f

f

f

s

s

s

s

00

00

00

k

k

k

sG

A

A

A

A

00

00

00

a

a

a

a

a

a

a

00

00

00

ps

kps

kps

k

sG

Multi-Actuator Setup

3

2

1

3

2

1

333231

232221

131211

3

2

1

333231

232221

131211

3

2

1

333231

232221

131211

f

f

f

x

x

x

kkk

kkk

kkk

x

x

x

ccc

ccc

ccc

x

x

x

mmm

mmm

mmm

Equations of motion:

7

1x

2x

3xActuator 3

Actuator 1

Actuator 2

3f

2f

1fServo-Controller 1

Servo-Controller 2

Servo-Controller 3

Computer Interface

MIMO System Model

A

A

A

A

00

00

00

a

a

a

a

a

a

a

00

00

00

ps

kps

kps

k

sG

s

s

s

s

00

00

00

k

k

k

sG

1

33332

3332322

3231312

31

23232

2322222

2221212

21

13132

1312122

1211112

11

kscsmkscsmkscsm

kscsmkscsmkscsm

kscsmkscsmkscsm

sG xf

Component models:

Servo-hydraulic system model:

sGsGAssG

sGsGsGsG

xfas

xfas

xu

I

+

− −

Servo-Hydraulic System Gxu(s)

Natural Velocity Feedback

Actuator Specimen

sGa sGxf

As

u f x sGs

Servo-Controllerand Servo-Valve

+

8

MODEL-BASED ACTUATOR CONTROL

9

Regulator Redesign

10

uzz BA zx C

xre

uzz BA

rzx C

Servo-hydraulic system transfer function in state space:

Tracking error:

Ideal system with perfect tracking:

zzz ~

uuu ~

xxx ~

uzz ~~~ BA

ezx ~~ C

Deviation system:

Model-Based ControlFeedforward Feedback Links

11

FBFF~ uuuuu

Total control law is a combination of feedforward and feedback:

GFF(s)

LQG Gxu(s)e uFB

uFF

u

Feedforward Controller

Feedback Controller Servo-Hydraulic Dynamics

+

- +

+r x

LARGE-SCALEEXPERIMENTAL STUDY

12

Prototype Structure

13

Actuator 3

Actuator 1

Actuator 2

Experimental Substructure

0 10 200

0.5

1

1.5

0 10 200

0.02

0.04

0 10 200

0.02

0.04

TF Data

Model

0 10 200

0.02

0.04

Ma

gn

itud

e

0 10 200

0.5

1

1.5

0 10 200

0.02

0.04

0 10 200

0.02

0.04

0 10 200

0.02

0.04

Frequency (Hz)0 10 20

0

0.5

1

1.5

MIMO Transfer FunctionMagnitude

14

Input 1 Input 2 Input 3

Output 1

Output 2

Output 3

0 10 20-150

-100

-50

0

0 10 20-200

0

200

0 10 20-200

0

200

TF Data

Model

0 10 20-200

0

200

Ph

ase

()

0 10 20-200

-100

0

100

0 10 20-200

0

200

0 10 20-200

0

200

0 10 20-200

0

200

Frequency (Hz)0 10 20

-150

-100

-50

0

MIMO Transfer FunctionPhase

15

Input 1 Input 2 Input 3

Output 1

Output 2

Output 3

5 Hz BLWN Tracking

16

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-2

0

2

Dis

p 1

(m

m)

desired

No Comp

FF + FB w / Coupling

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-2

0

2

Dis

p 2

(m

m)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-2

0

2

Dis

p 3

(m

m)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

1

2

3

Cu

rre

nt

(A)

Time (sec)

RMS Error Norm

No Comp: 44.8%FF + FB: 3.75 %

No Comp: 47.8%FF + FB: 4.43 %

No Comp: 50.8%FF + FB: 4.39 %

15 Hz BLWN Tracking

17

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1

0

1

Dis

p 1

(m

m)

desired

No Comp

FF + FB w / Coupling

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1

0

1

Dis

p 2

(m

m)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1

0

1

Dis

p 3

(m

m)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

1

2

3

Cu

rre

nt

(A)

Time (sec)

No Comp: 97.8%FF + FB: 10.7 %

No Comp: 96.6%FF + FB: 13.5 %

No Comp: 98.1%FF + FB: 11.5 %

RMS Error Norm

Prototype Structure

18

Actuator 3

Actuator 1

Actuator 2

Mode fn (Hz) x

1 1.27 3.00%

2 4.04 6.00%

3 8.28 6.00%

Total Structure Experimental Substructure

Ground acceleration 0.12x NS component

1994 Northridge earthquake

Numerical integration CDM at 1024 Hz

Actuator control FF + FB control w/ coupling

Structural control Clipped-optimal

control algorithm (Dyke et al., 1996)

RTHS Parameters

19

0 10 20 30 40 50-0.1

-0.050

0.050.1

Time (sec)

Acc

el (

g)

Semi-Active RTHS Results0.12x Northridge

20

0 2 4 6 8 10 12 14 16 18 20

-5

0

5

Dis

p 1

(m

m) 0 2 4 6 8 10 12 14 16 18 20

-10

0

10

Dis

p 2

(m

m) 0 2 4 6 8 10 12 14 16 18 20

-20

0

20

Dis

p 3

(m

m)

Sim

FF + FB w / Coupling

0 2 4 6 8 10 12 14 16 18 200123

Cu

rre

nt

(A)

0 2 4 6 8 10 12 14 16 18 20-0.1

0

0.1

Grn

d A

cc (

g)

Time (sec)

-5 0 5-100-50

050

100

Displacement (mm)

Fo

rce

(kN

)

-50 0 50-100-50

050

Velocity (mm/s)

CONCLUSIONS

21

Conclusions

The source of actuator dynamics including actuator coupling has been demonstrated and modeled

A framework for model-based actuator control has been developed addressing Actuator dynamics Control-structure interaction

Model-based control has proven successful for RTHS Robust to changes in specimen conditions Robust to nonlinearities Naturally can be used for MIMO systems

22

Thank you for your attention

23

The authors would like to acknowledge the support of the National Science Foundation under award CMMI-1011534.