Transcript Typical TF from Horizontal Actuator to Geophones

Modal Analysis and Feedback
Control of HAM MEPI
Lei Zuo
Osamah Rifai
Samir Nayfeh
Oct 16, 2002
LIGO-G030187-00-D
Page 1
Overview
• Review of loop transmissions vs. modal data
• Preliminary look at control
– Multiple lightly damped modes close to crossover make
control difficult
• Approaches
– Modal control may decrease the relative magnitudes of
the flexible modes.
– Easiest approach to robust performance: structural
damping.
– Optimal MIMO Control can improve the performance,
but requires a good model
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Typical TF from Horizontal Actuator to Geophones
10
Magnitude
Magnitude (dB)
Horizontal Actuator 1 to All Horizontal (solid) and Vertical (dashed) Velocities
10
10
18.4Hz
8.6Hz
16.4Hz
14Hz
0
-2
-4
10
0
10
1
300
200
Phase
Phase
40dB/dec
20dB/dec
blue 1
red 2
mage 3
green 4
100
0
-100
180°-15°
-200
-300
10
0
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Frequency (Hz)
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Typical TF from Vertical Actuator to Geophones
10
Magnitude
Magnitude (dB)
Vertical Actuator 3 to All Vertical (solid) and Horizontal (dashed) Velocities
10
10
18.5Hz 27.7Hz
14Hz 19.1Hz 29.2Hz
9.6Hz
0
-2
-4
10
0
10
1
blue 1
red 2
mage 3
green 4
300
200
Phase
Phase
40dB/dec
20dB/dec
100
0
-100
180°-85°
-200
-300
10
0
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Frequency (Hz)
10
1
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Observation of this two typical TFs
• The horizontal-horizontal coupling is very strong, so
is vertical-vertical coupling. The vertical -horizontal
coupling is very strong at around 3Hz, 19Hz and
28Hz
• The actuator-sensor pairs seems to be collocated well
• For control consideration, the critical modes are the
two modes around 19Hz, and two modes around
28Hz. (The modes around 14Hz are also critical)
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Modal Analysis
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Typical Measurement (x)
15.7Hz 18.9Hz
18.3Hz
13.4/13.7Hz
20.38/20.41Hz
8.4/9.3Hz
9.9/10.9Hz
6.8Hz
5.0Hz
4.4Hz
27.5/28.7Hz
2.95Hz
1.68Hz (2.5Hz)
1.3Hz
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Typical Measurement (y)
15.7Hz
18.3Hz
18.9Hz
20.38/20.41Hz
8.4/9.3Hz 13.4/13.7Hz
27.5/28.7Hz
4.4Hz
6.8Hz 9.9/10.9Hz
(5.0Hz)
(2.95Hz)
2.5Hz
1.68Hz
(1.3Hz)
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Typical Measurement (z)
18.3/18.9Hz
27.5/28.7Hz
15.7Hz
13.4/13.7Hz
9.3Hz
6.8Hz
5.0Hz
8.4Hz 9.9/10.9Hz
20.38/20.41Hz
1.3Hz 2.95Hz
2.5Hz
4.4Hz
(1.68Hz)
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Critical Modes
13.37Hz, in-plane bending + twist 13.71Hz, in-plane bending (local)
15.75Hz, in-plane bending
In-plane Beam Bending
18.32Hz, in-plane bending
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Critical Modes
18.85Hz, out-of-plane twist
Twist
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Critical Modes
27.45Hz, tank
28.74Hz, tank
Tank Related
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Mode Summary
• Modes at (2.5),3.0, 4.4, 5.0, 6.8, 8.4, and 9.3 Hz are
rigid-body modes (compare with Dennis’s modeling?)
• Modes at 13.4, 13.7, 15.7 Hz, and 18.3 Hz are
associated with in-plane bending
• Mode at 18.9 Hz is related to twist
• Modes at 27.5 and 28.7 Hz are associated with tank
motion
• Two modes around 20.4 are out-of-plane (vertical)
bending
• Modes at 1.3 and 1.7 Hz seems to be tank
motion+frame rigid body (measurements is not so
reliable at so low freq)
• Modes at 9.9, 10.9 are
rigid-body plus some bending
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Feedback Control of HAM
Fd
V
G(s)
T(s)=
=
Fd
1+G(s)H(s)
G(s), HAM
dynamics
+-
F
V
H(s), sensing
and control
• |G(jw)H(jw)| >>1 at low frequency, T(jw)1/H(jw)
•
|G(jw)H(jw)| <<1 at high frequency, T(jw) G(jw)
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-1
|H(s)|
A Control Loop (Concept Design)
-2
-1
1
10
|G(s)H(s)|
Loop Gain
-2
0
10
+1
-1
+1
10
|G(s)|
-2
10
-3
|T(s)|
10
Closed Loop
+2
+1
0
1
10
10
15 reduction 1-3Hz
300
250
200
150
100
50
0
-90°
-50
-100
-150
-200
0
10
-180°
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Phase Margin
180-15-90+=75°1
10
Page 15
(The low-frequency characteristics of geophones is not good  Position feedback will be used for <0.5Hz)
FdV and X0X
| T ||
V
|
Fd
V
sX

Fd
k ( X  Xo )
-1/dec


V
Fd
X

V
s
Xo

Fd
k
|
X
|
Xo
1

LIGO-G030187-00-D
-2/dec
Page 16
Further Consideration
• The previous concept design is for vertical
channels based on the assumption of low
plant uncertainties.
• See the previous control loop again:
* Multiple crossing, not robust (unstable!)
* PM is 15°, not 75° (add lead? no)
• See horizontal channels
* Multiple crossing, not robust
* PM is only 5°
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Vertical Loop (Concept Design)
-1
|H(s)|
-2
Multiple Crossings
-1
1
10
|G(s)H(s)|
Loop Gain
-2
0
10
+1
-1
10
|G(s)|
-2
10
-3
|T(s)|
10
0
1
10
Closed Loop
10
15 reduction 1-3Hz
After Structure
Modification
300
250
200
150
100
50
0
-90°
-50
-100
-150
-200
0
10
-180°
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(Position feedback will be used for <0.5Hz)
Phase Margin
180-15-90+=75°180-75-90+=15°1
10
Page 18
-1
|H(s)|
Horizontal Loop (Concept Design)
-2
Multiple Crossings
-1
1
10
|G(s)H(s)|
-2
0
Loop Gain 10
+1
-1
10
-2
10
|G(s)|
10
|T(s)|
-3
Closed Loop
0
1
10
10
15 reduction 1-3Hz
After Structure
Modification
300
150
100
200
50
100
0
0
-50
-90°
-100
-100
-200
-150
0
10
-180°
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(Position feedback will be used for <0.5Hz)
Phase Margin
10
180-85-90+=5°1
Page 19
Suggestion for Feedback Control
* Modal Decomposition SISO Control.
Questions (SISO):
1) how good is the
decomposition?
|·|
1
Other rigid-body modes from
non-perfect decomposition
X
Xo
Dominant rigid-body mode
Flexible modes
2) how large are the
peaks of flexible
modes?
V
Fd

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Suggestions on Structure Modification
(to make control easier)
• Add constrained layer (viscoelastic) damping to
the beam structure (to damp the bending modes)
• Make the joints stiffer; add some damping to the
joints; or add another beam
• Reduce the coupling between tank and the frame.
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Conclusions
• Multiple lightly damped modes close to crossover
make control difficult
– Instability
– Amplification of disturbances
• Modal control may decrease their relative
magnitudes.
• Easiest approach to robust performance: structural
damping.
• Optimal MIMO Control can improve the
performance, but requires a good model
LIGO-G030187-00-D
Page 22
Other Control Schedules Discussed
• Osamah: low frequency crossing with high order
controller
• Dave: notch filter
• Rich, David and Denis: high frequency crossing
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Appendix
LIGO-G030187-00-D
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Typical TF from Horizontal Actuator to Positions
Horizontal
Actuator 1 to All Horizontal (solid) and Vertical (dashed) Positions
-1
Magnitude
Magnitude (dB)
10
10
10
10
-2
-3
-4
10
0
10
1
500
Phase
Phase
0
-500
-1000
-1500
-2000
10
0
LIGO-G030187-00-D 10
Frequency (Hz)
1
Page 25
Typical TF from Vertical Actuator to Positions
Vertical Actuator 3 to All Vertical (solid) and Horizontal (dashed) Positions
Magnitude
Magnitude(dB)
10
10
10
10
-1
-2
-3
-4
10
0
10
1
500
Phase
Phase
0
-500
-1000
-1500
-2000
0
10
1
LIGO-G030187-00-D
Frequency (Hz)
10
Page 26
Out-of-Plane Bending Modes
20.38Hz
20.41Hz
Out-of-Plane Beam Bending Related
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Mode Shapes
1.3Hz
1.7Hz
(low-freq, measurement isLIGO-G030187-00-D
not reliable)
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Mode Shapes
2.50Hz
2.97Hz
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Mode Shapes
4.41Hz
4.99Hz
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Mode Shapes
6.86Hz
8.33Hz
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Mode Shapes
9.25Hz
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Mode Shapes
9.82Hz
10.9Hz
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