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![Page 1: Model-based Real-Time Hybrid Simulation for Large-Scale Experimental Evaluation Brian M. Phillips University of Illinois B. F. Spencer, Jr. University.](https://reader035.fdocuments.in/reader035/viewer/2022062619/55173949550346f5558b60a4/html5/thumbnails/1.jpg)
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
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INTRODUCTION
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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
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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
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SERVO-HYDRAULIC SYSTEM MODEL
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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
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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
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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
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MODEL-BASED ACTUATOR CONTROL
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Regulator Redesign
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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:
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Model-Based ControlFeedforward Feedback Links
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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
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LARGE-SCALEEXPERIMENTAL STUDY
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Prototype Structure
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Actuator 3
Actuator 1
Actuator 2
Experimental Substructure
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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
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Input 1 Input 2 Input 3
Output 1
Output 2
Output 3
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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
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5 Hz BLWN Tracking
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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 %
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15 Hz BLWN Tracking
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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
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Prototype Structure
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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
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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
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0 10 20 30 40 50-0.1
-0.050
0.050.1
Time (sec)
Acc
el (
g)
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Semi-Active RTHS Results0.12x Northridge
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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)
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CONCLUSIONS
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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
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Thank you for your attention
23
The authors would like to acknowledge the support of the National Science Foundation under award CMMI-1011534.