real-time hybrid simulation with model-based multi-metric feedback
DESCRIPTION
Real-Time Hybrid Simulation with Model-Based Multi-Metric Feedback. B. F. Spencer, Jr. University of Illinois Brian M. Phillips University of Maryland. Introduction and Motivation. m 2. x 2 ( t ). c 2. k 2. m 1. x 1 ( t ). k 2. c 1. k 1. k 1. x. x i. x i+ 1. t i. t i+ 1. t. - PowerPoint PPT PresentationTRANSCRIPT
Real-Time Hybrid Simulation with Model-Based
Multi-Metric Feedback
B. F. Spencer, Jr.University of Illinois
Brian M. PhillipsUniversity of Maryland
INTRODUCTION AND MOTIVATION
Hybrid Simulation (pseudodynamic testing)
xi+1
Schematic procedure:
gx
R2
R1 Ri+1
Displacements imposed at slow rates
Time scale extension factor = 100 - 1000
Physical substructure
Numerical substructure
1
2
00m
m
M
1 2 2
2 2
c c cc c
C
gx
x2(t)
x1(t)m1
m2
c2
c1
k2
k1
Experimental component
k2
k1
1111 iiii FRxCxM x
tti ti+1
xi xi+1
Numerical integration
Numerical component
Real-Time Hybrid Simulation
1:1 time scaling Accurately test rate dependent structural components
(i.e. dampers, friction devices, and base isolation) Cycles must be performed very quickly
System dynamics become important Time delays – due to data communication and computation Time lags – due to actuator dynamics
NumericalCalculations
Apply Displacement
Measure RestoringForces
Base Isolation MR Damper
Effects of Time Delays and Time Lags Systematic errors that propagate throughout experiment Introduces energy negative damping Problems arise with
structures with low damping experiments with large hydraulic actuators
Measuredxm
Desiredxd
MeasuredResponse
ActualResponse
t
x
x
f
Multi-Metric Feedback Rate-dependent specimens are sensitive to velocity and
acceleration trajectories Sensors measuring higher-order derivatives can be
incorporated into model-based actuator control for RTHS Better estimate of model states Improved tracking of higher-order derivatives Improved frequency bandwidth
Base Isolation MR Damper
ACTUATOR DYNAMICS AND COMPENSATION
Model of Actuator Dynamics
-+xm
fpic
s
Natural velocity feedback
Kprop
-+u e xv
QL ApL
A
Controller ServovalveDynamics
Servovalveflow
Actuator Specimen
( )v vG s k' '
L q v c LQ K x K p 1
4t
le
VC s
2
1
t tm s c s k
Because of the “natural” velocity feedback, the dynamics of the experimentalcomponent directly affect the response of the actuator (Dyke et al., 1995).
Gyu(s)
am
sUs
sUsAsX
syum1
m
m YG
Actuator Dynamics Compensation Actuator dynamics produce effects on both magnitude
and phase lag Actuator transfer function dependents on the attached
specimen (i.e., actuator-specimen interaction) Models of actuator dynamics are used to develop model-
based compensation strategies
Framework for Actuator Dynamics Compensation
-+
xm
fpxd
PID-+
u e icQL
Servo-controller
Compensator for actuator dynamics
Servovalve Actuator Specimen
Control algorithm
Gyu(s) Inner-loop controlOuter-loop control
► Goal: to make measured displacement xm and acceleration am as close as
possible to the desired displacement xd and acceleration ad
(minimizing phase lag and amplitude changes)
Natural vel. feedback
am
ad
Express servo-hydraulic system model in state space:
Assume ideal system with perfect tracking:
Create deviation system:
Define tracking control as combination of feedforward and feedback terms:
CzyBAzz
m
u
m
m
d
dmd a
xax
yye
dm yzCyBzAz
u
mmm~~~
yyy
zzz
uuu ezCyBzAz
~~
~~~
m
u
FBFF~ uuuuu
Tracking Control through Regulator Redesign
Feedforward Component Open-loop control, processes the reference signal
directly to produce the ideal response Allows combining knowledge of the command/plant to
improve the system response
Design of a feedforward compensator is in essence a calculation of the inverse of a dynamic system (Åström and Wittenmark, 1984)
GFF(s) Gxu(s)uFF xmxd
Feedforward Controller
Servo-Hydraulic
System
Feedforward Component Linearized poles-only model
1. Implement improper inverse by adding a low-pass filter (Carrion and Spencer, 2007)
2. Higher order derivatives can be pulled from numerical integration of structure
N
ii
xu
ps
KsUsXsG
1
K
ps
sRsUsG
N
ii
1
FF
tratratratratratu NN 3210FF
Identified System Model Inverse
Inverse in Time Domain
Model-Based Feedforward-Feedback Control Use LQG regulator design Reduces effect of
Innacuracies in the modeling or identification of the plant Variations of the plant dynamics during the experiment (e.g.,
specimen yielding or MR damper changes)
GFF(s)
LQG Gxu(s)e uFB
uFF
u
Feedforward Controller
Feedback Controller Servo-Hydraulic Dynamics
+
‒+
+r x
Multi-Metric Feedback Include acceleration measurements
Better state estimates Add LQG weighting to acceleration
LQGuFB
uFF
u
Feedback Controller Servo-HydraulicDynamics
+
+
sGFF
Feedforward Controller
sG yu+ ‒
+ ‒
r x
r
xxe
xe
Large-Scale Experimental Setup@ the University of Illinois
556 kN Actuator±152 mm Stroke
Shear KeyShear Key
Reaction AngleReaction Angle
Block and Wedge
Block and Wedge
445 kN Load Cell
Internal AC LVDT
Tie Down
Tie Down
Accelerometers
Tracking Performance:Frequency Domain, Passive-Off
0 5 10 15 20 25 30 35 40 45 500123456
Frequency (Hz)
Mag
nitu
de
3rd Poly 8ms Lead Comp 8ms G
FF,0.0A + LP G
FF,0.0A
0 10 20 30 40 50-40
-20
0
20
40
Frequency (Hz)
Pha
se (
)
0 10 20 30 40 50-5
0
5
Frequency (Hz)
Tim
e La
g (m
sec)
0 5 10 15 20 25 30 35 40 45 500123456
Frequency (Hz)
Mag
nitu
de
3rd Poly 8ms Lead Comp 8ms G
FF,0.0A + LP G
FF,0.0A
0 10 20 30 40 50-40
-20
0
20
40
Frequency (Hz)
Pha
se (
)
0 10 20 30 40 50-5
0
5
Frequency (Hz)
Tim
e La
g (m
sec)
0 5 10 15 20 25 30 35 40 45 500123456
Frequency (Hz)
Mag
nitu
de
3rd Poly 8ms Lead Comp 8ms G
FF,0.0A + LP G
FF,0.0A
0 10 20 30 40 50-40
-20
0
20
40
Frequency (Hz)
Pha
se (
)
0 10 20 30 40 50-5
0
5
Frequency (Hz)
Tim
e La
g (m
sec)
0 5 10 15 20 25 30 35 40 45 500123456
Frequency (Hz)
Mag
nitu
de
3rd Poly 8ms Lead Comp 8ms G
FF,0.0A + LP G
FF,0.0A
0 10 20 30 40 50-40
-20
0
20
40
Frequency (Hz)
Pha
se (
)
0 10 20 30 40 50-5
0
5
Frequency (Hz)
Tim
e La
g (m
sec)
Tracking Performance:Frequency Domain, Passive-On
0 5 10 15 20 25 30 35 40 45 500123456
Frequency (Hz)
Mag
nitu
de
3rd Poly 10ms Lead Comp 10ms G
FF,2.5A + LP G
FF,2.5A
0 10 20 30 40 50-40
-20
0
20
40
Frequency (Hz)
Pha
se (
)
0 10 20 30 40 50-4-20246
Frequency (Hz)
Tim
e La
g (m
sec)
0 5 10 15 20 25 30 35 40 45 500123456
Frequency (Hz)
Mag
nitu
de
3rd Poly 10ms Lead Comp 10ms G
FF,2.5A + LP G
FF,2.5A
0 10 20 30 40 50-40
-20
0
20
40
Frequency (Hz)
Pha
se (
)
0 10 20 30 40 50-4-20246
Frequency (Hz)
Tim
e La
g (m
sec)
0 5 10 15 20 25 30 35 40 45 500123456
Frequency (Hz)
Mag
nitu
de
3rd Poly 10ms Lead Comp 10ms G
FF,2.5A + LP G
FF,2.5A
0 10 20 30 40 50-40
-20
0
20
40
Frequency (Hz)
Pha
se (
)
0 10 20 30 40 50-4-20246
Frequency (Hz)
Tim
e La
g (m
sec)
0 5 10 15 20 25 30 35 40 45 500123456
Frequency (Hz)
Mag
nitu
de
3rd Poly 10ms Lead Comp 10ms G
FF,2.5A + LP G
FF,2.5A
0 10 20 30 40 50-40
-20
0
20
40
Frequency (Hz)
Pha
se (
)
0 10 20 30 40 50-4-20246
Frequency (Hz)
Tim
e La
g (m
sec)
RTHS Study ofSDOF Structure Numerical substructure
20,000 kg mass 2% damping 0.5, 1, 5, 10, 20, and 30 Hz models
Experimental substructure Passive-off (0.0 Amps)
200kN MR damper Input
0 to 50 Hz BLWN ground acceleration Numerical Integration
CDM at 2000 Hz
gx
0 10 20 300
50
100
150
Dis
p E
rror
(%
)
0 10 20 300
5
10
15
20
25
Dis
p E
rror
(%
)
0 10 20 300
50
100
150
200
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
10
20
30
40
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
100
200
300
400
500
600
Acc
el E
rror
(%
)
0 10 20 300
20
40
60
80
100
Acc
el E
rror
(%
)
RMS Tracking Error Norm During RTHS
0 10 20 300
50
100
150
Dis
p E
rror
(%
)
0 10 20 300
5
10
15
20
25
Dis
p E
rror
(%
)
0 10 20 300
50
100
150
200
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
10
20
30
40
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
100
200
300
400
500
600
Acc
el E
rror
(%
)
0 10 20 300
20
40
60
80
100
Acc
el E
rror
(%
)
0 10 20 300
50
100
150
Dis
p E
rror
(%
)
0 10 20 300
5
10
15
20
25
Dis
p E
rror
(%
)
0 10 20 300
50
100
150
200
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
10
20
30
40
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
100
200
300
400
500
600
Acc
el E
rror
(%
)
0 10 20 300
20
40
60
80
100
Acc
el E
rror
(%
)
0 10 20 300
50
100
150
Dis
p E
rror
(%
)
0 10 20 300
5
10
15
20
25
Dis
p E
rror
(%
)
0 10 20 300
50
100
150
200
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
10
20
30
40
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
100
200
300
400
500
600
Acc
el E
rror
(%
)
0 10 20 300
20
40
60
80
100
Acc
el E
rror
(%
)
0 10 20 300
50
100
150
Dis
p E
rror
(%
)
0 10 20 300
5
10
15
20
25
Dis
p E
rror
(%
)
0 10 20 300
50
100
150
200
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
10
20
30
40
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
100
200
300
400
500
600
Acc
el E
rror
(%
)
0 10 20 300
20
40
60
80
100
Acc
el E
rror
(%
)
0 10 20 300
50
100
150
Dis
p E
rror
(%
)
0 10 20 300
5
10
15
20
25
Dis
p E
rror
(%
)
0 10 20 300
50
100
150
200
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
10
20
30
40
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
100
200
300
400
500
600
Acc
el E
rror
(%
)
0 10 20 300
20
40
60
80
100
Acc
el E
rror
(%
)
0 10 20 300
50
100
150
Dis
p E
rror
(%
)
0 10 20 300
5
10
15
20
25
Dis
p E
rror
(%
)
0 10 20 300
50
100
150
200
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
10
20
30
40
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
0 10 20 300
100
200
300
400
500
600
Acc
el E
rror
(%
)
0 10 20 300
20
40
60
80
100
Acc
el E
rror
(%
)
Zoom
0 10 20 300
50
100
150
200
Natural Frequency of Structure (Hz)
Vel
Err
or (
%)
No Comp
3rd Order PolyLead CompG
FF + LP
GFF
GFF
+ xLQG
GFF
+ xaLQG
Model-based compensator performs very well, providing accurate
compensation for actuator dynamics
MULTI-ACTUATOR SYSTEMS
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
Multi-Actuator Setup
3
2
1
3
2
1
333231
232221
131211
3
2
1
333231
232221
131211
3
2
1
333231
232221
131211
fff
xxx
kkkkkkkkk
xxx
ccccccccc
xxx
mmmmmmmmm
Equations of motion:
1x
2x
3x Actuator 3
Actuator 1
Actuator 2
3f
2f
1fServo-Controller 1
Servo-Controller 2
Servo-Controller 3
Computer Interface
MIMO System Model
+
− −
Servo-Hydraulic System Gxu(s)
Natural Velocity Feedback
Actuator Specimen
saG sxfG
sA
ssG
Servo-Controllerand Servo-Valve
+u xf
s
s
s
s
00
00
00
k
k
k
sG
A
A
A
00
00
00
A
a
a
a
a
a
a
a
00
00
00
psk
psk
psk
sG
1
33332
3332322
3231312
31
23232
2322222
2221212
21
13132
1312122
1211112
11
kscsmkscsmkscsm
kscsmkscsmkscsm
kscsmkscsmkscsm
sxfG
Servo-hydraulic system model:
ssss
ssss
xf
xfxu GGAGI
GGGG
as
as
Model-Based Multi-Actuator Control
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
ssss
ssss
xf
xfxu GGAGI
GGGG
as
as
1s
1s
1a
11FF
sssssss xfxu GAGGGIGG
Prototype StructureActuator 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
0 10 200
0.5
1
1.5
0 10 200
0.02
0.04
0 10 200
0.02
0.04
TF DataModel
0 10 200
0.02
0.04
Mag
nitu
de
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
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 DataModel
0 10 20-200
0
200
Pha
se (
)
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
Input 1 Input 2 Input 3
Output 1
Output 2
Output 3
5 Hz BLWN Tracking
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-20
2
Dis
p 1
(mm
)
desiredNo CompFF + 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
(mm
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-20
2
Dis
p 3
(mm
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
1
23
Cur
rent
(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 %
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
0 10 20 30 40 50-0.1
-0.050
0.050.1
Time (sec)
Acc
el (
g)
Semi-Active RTHS Results0.12x Northridge
0 2 4 6 8 10 12 14 16 18 20-5
0
5
Dis
p 1
(mm
) 0 2 4 6 8 10 12 14 16 18 20
-100
10
Dis
p 2
(mm
) 0 2 4 6 8 10 12 14 16 18 20
-20
0
20
Dis
p 3
(mm
)
SimFF + FB w / Coupling
0 2 4 6 8 10 12 14 16 18 200123
Cur
rent
(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)
Forc
e (k
N)
-50 0 50-100-50
050
Velocity (mm/s)
Model-based compensator performs well for multi-actuator systems as well as under changing specimen
conditions
CONCLUSIONS
Conclusions A state-of-the-art experimental setup has been
assembled for RTHS The source of actuator dynamics including control-
structure interaction and actuator coupling has been demonstrated and modeled
A framework for model-based actuator control has been developed
Model-based control has proven successful for RTHS Robust to changes in specimen conditions Robust to nonlinearities Naturally can be used for MIMO systems Flexible to include multi-metric feedback
Thank you for your attention