Servo-Hydraulic System Model

Report
Model-based Real-Time Hybrid
Simulation for Large-Scale
Experimental Evaluation
Brian M. Phillips
University of Illinois
B. F. Spencer, Jr.
University of Illinois
Yunbyeong Chae
Tony A. Friedman
Karim Kazemibidokhti
James M. Ricles
Purdue University
Lehigh University
Shirley J. Dyke
Purdue University
Quake Summit 2012
Boston, Massachusetts
June, 2012
Lehigh University
Lehigh University
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
x g
Numerical
Substructure
fmeas



u
x
Loading
System
Experimental
Substructure
f
Sensors
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
SERVO-HYDRAULIC SYSTEM
MODEL
5
MIMO System Model
 u1

u  u 2
u
 3
 f1

f   f2
 f
 3

Servo-Hydraulic System Gxu(s)



+
 +
G s s 
−





G a s 
 x1

x   x2
x
 3
G xf  s 
−
Actuator
Servo-Controller
and Servo-Valve
Specimen
As
Natural Velocity Feedback
ks

Gs s   0

 0
0
ks
0
0 

0

k s 


s


G a s   




ka
 pa
0
0

0
ka
s 
0




0


ka

 s  p a  
0
pa

A

A 0

 0
0
A
0
0

0

A 
6





Multi-Actuator Setup
Actuator 3
x3
f3
Servo-Controller 3
Actuator 2
x2
f2
Servo-Controller 2
Computer Interface
Actuator 1
x1
f1
Servo-Controller 1
Equations of motion:
 m 11

 m 21
m
 31
m 12
m 22
m 32
m 13   x1

m 23   x 2
m 33   x3





 c 11

 c 21
c
 31
c 12
c 22
c 32
c 13   x 1

c 23   x 2
c 33   x 3





 k 11

 k 21
k
 31
k 12
k 22
k 32
k 13   x 1

k 23   x 2
k 33   x 3
  f1
 
   f2
  f
  3





7
MIMO System Model
Component models:
G xf
 m 11 s 2  c 11 s  k 11

 s    m 21 s 2  c 21 s  k 21
m s2  c s  k
31
31
 31
ks

Gs s   0

 0
0
ks
0
m 12 s  c 12 s  k 12
2
m 22 s  c 22 s  k 22
2
m 32 s  c 32 s  k 32
2
0 

0

k s 
2
m 13 s  c 13 s  k 13 

2
m 23 s  c 23 s  k 23 
2
m 33 s  c 33 s  k 33 
A

A 0

 0
0
A
0
1


s


G a s   




0

0

A 
ka
 pa

0
0
0
ka
s 
0




0


ka

 s  p a  
0
pa

Servo-Hydraulicsystem
System Gmodel:
xu(s)
Servo-hydraulic
u
+
−
G s s 
+
G a s 
f
G xf  s 
x
−
G s  s  G a  s  G xf  s 
Actuator
Servo-Controller
Specimen
G xu  s  
I   G s  s   As  G a  s  G xf  s 
and Servo-Valve
As
Natural Velocity Feedback
8
MODEL-BASED ACTUATOR
CONTROL
9
Regulator Redesign
Servo-hydraulic system transfer function in state space:
z  A z  B u
Tracking error:
x  Cz
erx
Ideal system with perfect tracking:
z  A z  B u
x  Cz  r
Deviation system:
~
z  zz
u~  u  u
~
x  xx
~z  A ~z  B u~
~
x  C ~z   e
10
Model-Based Control
Feedforward Feedback Links
Total control law is a combination of feedforward and feedback:
u  u  u~  u FF  u FB
GFF(s)
uFF
Feedforward Controller
r
+
e
LQG
uFB
Feedback Controller
+
+
u
Gxu(s)
x
Servo-Hydraulic
Dynamics
11
LARGE-SCALE
EXPERIMENTAL STUDY
12
Prototype Structure
Actuator 3
Actuator 2
Actuator 1
Experimental Substructure
13
MIMO Transfer Function
Magnitude
Input 1
Input 2
Input 3
1.5
1
Output 1
0.5
0
0
10
20
0.04
0.04
0.02
0.02
0
0
10
20
0
TF Data
Model
0
10
20
0
10
20
0
10
20
Output 2
Magnitude
1.5
0.04
0.02
0
0.04
1
0.02
0.5
0
10
20
0
0
10
20
0
1.5
Output 3
0.04
0.04
0.02
0.02
0
0
10
20
0
1
0.5
0
10
20
Frequency (Hz)
0
14
MIMO Transfer Function
Phase
Input 1
0
Input 2
Input 3
200
200
TF Data
Model
-50
0
Output 1
-100
-150
0
10
20
Phase ()
200
Output 2
0
-200
0
10
20
100
-200
0
10
20
0
10
20
0
10
20
200
0
0
0
-100
-200
0
10
20
200
-200
0
10
20
200
-200
0
-50
Output 3
0
0
-100
-200
0
10
20
-200
0
10
20
Frequency (Hz)
-150
15
5 Hz BLWN Tracking
desired
RMS Error Norm
Disp 1 (mm)
No Comp
FF + FB w / Coupling
2
No Comp: 44.8%
FF + FB: 3.75 %
0
-2
Disp 2 (mm)
0
Disp 3 (mm)
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2
No Comp: 47.8%
FF + FB: 4.43 %
0
-2
0
Current (A)
0.2
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2
No Comp: 50.8%
FF + FB: 4.39 %
0
-2
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1
1.2
Time (sec)
1.4
1.6
1.8
2
3
2
1
0
16
15 Hz BLWN Tracking
Disp 1 (mm)
desired
1
FF + FB w / Coupling
0
-1
Disp 2 (mm)
0
Disp 3 (mm)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
No Comp: 97.8%
FF + FB: 10.7 %
1
1
No Comp: 96.6%
FF + FB: 13.5 %
0
-1
0
Current (A)
RMS Error Norm
No Comp
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1
No Comp: 98.1%
FF + FB: 11.5 %
0
-1
0
0.1
0.2
0.3
0.4
0
0.2
0.4
0.6
0.8
0.5
0.6
0.7
0.8
0.9
1
1
1.2
Time (sec)
1.4
1.6
1.8
2
3
2
1
0
17
Prototype Structure
Actuator 3
Actuator 2
Actuator 1
Mode
fn (Hz)
x
1
1.27
3.00%
2
4.04
6.00%
3
8.28
6.00%
Total Structure
Experimental Substructure
18
RTHS Parameters
 Ground acceleration

Numerical integration


Actuator control


CDM at 1024 Hz
FF + FB control w/ coupling
Structural control

Clipped-optimal
control algorithm
(Dyke et al., 1996)
Accel (g)

0.12x NS component
1994 Northridge earthquake
0.1
0.05
0
-0.05
-0.1
0
10
20
30
Time (sec)
40
50
19
Sim
20
FF + FB w / Coupling
0
-20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
Time (sec)
14
16
18
20
10
0
-10
5
0
-5
Grnd Acc (g)
3
2
1
0
-0.1
Force (kN)
Current (A) Disp 1 (mm)
Disp 2 (mm) Disp 3 (mm)
Semi-Active RTHS Results
0.12x Northridge
100
50
0
-50
-100
0.1
0
-5
0
Displacement (mm)
5
50
0
-50
-100
-50
0
Velocity (mm/s)
50
20
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
The authors would like to acknowledge the support of the National
Science Foundation under award CMMI-1011534.
Thank you for your attention
23

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