Download - LTP dynamics and control
D. Bortoluzzi, M. Da Lio, S. Vitale 1Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
LTP dynamics and control
D. Bortoluzzi, M. Da Lio, S. VitaleUniversity of Trento
D. Bortoluzzi, M. Da Lio, S. Vitale 2Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
The LTP basic mode of operation
D. Bortoluzzi, M. Da Lio, S. Vitale 3Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
DOF Dc-force compensation
TM-stabilisation
Drag-free in measurement
bandwidth
Drag-free at low
frequency
Test-mass 1
x
y
z
Test-mass 2
x
y
z
D. Bortoluzzi, M. Da Lio, S. Vitale 4Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Force noisemodel
Mq -1 1/s2
Electrostaticreadoutmodel
IS noise
Electrostaticsuspension
Laserreadoutmodel
Interferometernoise
fnoiseq*q*
..
factuation
Kh
Spacecraftmotion
Spacecraftdistortion
CSC
Mu
nSC
u..
LTP modelS/Cmodel
fho,fLTPo
Sensit. to noise(Bfhf,BfLTPf)
Fsc
Fsc
Drag free control and actuation system
KLTP
q
CLTP
LTPdistortion
nLTP
-
Bfhf
BfLTPf
q
q̂
q
LTP is an autonomous dynamical system
D. Bortoluzzi, M. Da Lio, S. Vitale 5Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
drag free ,x
S / C,xS / C n 2
Fx x
M
Requirements given for S/C control
DOF Readout noise Thrust noise Total relative displ.
xS/C
y2S/C
y1S/C
z1S/C
z2S/C
1S/C
TM-S/C relativedisplacement
Readout noiseExternal forces on S/C
suppressed by drag-free control loop
91.8 10 m / Hz 94.7 10 m / Hz 95 10 m / Hz
91.8 10 m / Hz 947 10 m / Hz 947 10 m / Hz
91.8 10 m / Hz 966 10 m / Hz 966 10 m / Hz
918 10 m / Hz 947 10 m / Hz 950 10 m / Hz
918 10 m / Hz 966 10 m / Hz 969 10 m / Hz
965 10 rad / Hz 9235 10 rad / Hz 9243 10 rad / Hz
3 210 Hz f 3 10 Hz
D. Bortoluzzi, M. Da Lio, S. Vitale 6Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
LTP Multibody model• Inertial reference frame• Spacecraft body fixed reference frame• S/C-LTP mechanical interface
reference frame• Optical bench body fixed reference
frame• Electrode housings reference frames• Test masses body fixed reference
frames
Defined frames
• Spacecraft (Inertial Frame)• Test mass 1 (S/C frame)• Test mass 1 (EH frame)• …
Coordinates
* * * * * * *1 1 1 1 1 1 1q x , y , z , , , u x, y, z, , ,
1 1 1 1 1 1 1q x , y , z , , ,
D. Bortoluzzi, M. Da Lio, S. Vitale 7Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
DistortionsDisplacements of H1, H2 (readout references) frames due to distortions occurring:A) within the spacecraft (S/C-mechanicalinterface frame)
(in S/C frame)
B) within the LTP (mechanical interface frame-optical bench frame-electrode housings frames)
D. Bortoluzzi, M. Da Lio, S. Vitale 8Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Forces and torquesPicture of forces
fe1 fe2te1 te2
fLTP1 fLTP2
tLTP1 tLTP2
f12f12
t12
t12fh1
th1 fh2 th2
FSC
TSC
•Fsc, Tsc: total force and torque (in SC frame) applied by LTP onto the S/C•fe, te: total force and torque of environmental origin on TMs•fLTP, tLTP: total force and torque on TMs originated within the LTP or the S/C•f12, t12: force and torque between TM1 and TM2•fh, th: total force and torque on TMs caused by the interaction between TMs and their housings (it includes actuation force and torque)
D. Bortoluzzi, M. Da Lio, S. Vitale 9Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Dynamics 1: test-masses
Dynamics 2: reaction on spacecraft
Readouts
TM-S/C couplingTM-S/C relative displacementTM-EH couplingTM-EH relative displacementInverse of mass matrix
TM-EH space-independent coupling
TM-EH relative displacementCapacitive readout cross-talk
Capacitive readout noise
Stray forcescapacitive actuationMass matrix
OB-S/C relative position
S/C motion
TM-S/C space-independent coupling
Optical readout cross-talk
TM-EH relative displacementOptical readout noise
D. Bortoluzzi, M. Da Lio, S. Vitale 10Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Symbolic form (for instance: inertia)
Numeric form (for instance: stiffness & cross-talk)
Matrices provided
D. Bortoluzzi, M. Da Lio, S. Vitale 11Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Noisea ,x
drag free ,x
S / C,x1/ 2 14 2xp,xnoise,x n 22
Fm fS 3 10 @1mHz a xm Ms Hz
D. Bortoluzzi, M. Da Lio, S. Vitale 12Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Example: x(t) signal obtained from given x readout noise
spectral density
Example: force noise spectral density obtained from
sampled signal
D. Bortoluzzi, M. Da Lio, S. Vitale 13Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
D. Bortoluzzi, M. Da Lio, S. Vitale 14Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
© A s t r i u m9 0 S m a r t - 2 F i n a l P r e s e n t a t i o n 1 2 / 0 7 / 2 0 0 2
F r e q u e n c y A n a l y s i s – X a x i s a c c e l e r a t i o n ( 1 o f 3 )
1 0- 4
1 0- 3
1 0- 2
1 0- 1
1 0- 1 4
1 0- 1 3
1 0- 1 2
x 1
H z
ms
-2/H
z0
.5 o
r s
-2/H
z0
.5
P S D t o t a leF x 1 fo r c e n o is eF y 1 fo r c e n o is eF z 1 fo r c e n o is eT h e t a 1 fo rc e n o is eE t a 1 fo r c e n o is eP h i1 fo r c e n o is eF x 1 re a d o u t n o is eF y 1 re a d o u t n o is eF z 1 re a d o u t n o is eT h e t a 1 r e a d o u t n o is eE t a 1 re a d o u t n o is eP h i1 r e a d o u t n o is e
Simulation results
D. Bortoluzzi, M. Da Lio, S. Vitale 15Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
© A s t r iu m9 4 S m a r t - 2 F in a l P r e s e n t a t i o n 1 2 /0 7 /2 0 0 2
F r e q u e n c y A n a l y s i s – R e m a in i n g a x e s
• R e m a in in g l in e a r a n d R o t a t io n a l a x e s m e e t f r e q u e n c y r e q u i r e m e n t s
1 0- 4
1 0- 3
1 0- 2
1 0- 1
1 0- 1 4
1 0- 1 3
1 0- 1 2
Y 2
H z
ms
-2/H
z0
.5 o
r s-2
/Hz
0.5 P S D t o t a l e
F xF yF zT xT yT zS T t h e t aS T E t aS T p h i
1 0- 4
1 0-3
1 0- 2
1 0- 1
1 0- 1 3
1 0- 1 2
1 0- 1 1
1 0- 1 0
Z 1
H z
ms
-2/H
z0
.5 o
r s
-2/H
z0
.5
P S D t o t a leF xF yF zT xT yT zS T t h e t aS T E t aS T p h i
1 0- 4
1 0- 3
1 0- 2
1 0- 1
1 0-1 2
1 0-1 1
1 0-1 0
1 0-9
1 0-8
T h e ta 1
H z
ms
-2/H
z0
.5 o
r s
-2/H
z0
.5
P S D t o t a leF xF yF zT xT yT zS T th e t aS T E t aS T p h i
1 0- 4
1 0- 3
1 0- 2
1 0- 1
1 0 - 1 2
1 0- 1 1
1 0 - 1 0
1 0- 9
1 0- 8
E t a 1
H z
ms
-2/H
z0
.5 o
r s
-2/H
z0
.5
P S D t o t a leF xF yF zT xT yT zS T t h e t aS T E t aS T p h i
1 0 - 4 1 0 - 3 1 0 - 2 1 0 - 11 0
- 1 2
1 0- 1 1
1 0- 1 0
1 0- 9
1 0 - 8P h i 1
H z
ms
-2/H
z0
.5 o
r s
-2/H
z0
.5 P S D to t a leF xF yF zT xT yT zS T t h e t aS T E t aS T p h i
1 0- 4
1 0- 3
1 0- 2
1 0- 1
1 0 - 1 2
1 0- 1 0
1 0- 8
1 0- 6
y S C
1 0- 4
1 0- 3
1 0-2
1 0-1
1 0- 1 1
1 0- 1 0
1 0- 9
1 0- 8
1 0- 7
z S C
1 0- 4
1 0-3
1 0- 2
1 0-1
1 0- 1 2
1 0- 1 0
1 0- 8
1 0- 6
1 0- 4
T h e t a S C
Simulation results
D. Bortoluzzi, M. Da Lio, S. Vitale 16Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
1. ´ 10- 6 0.00001 0.0001 0.001 0.01
10
100
1000
10000
parasitic
Gk
frequency[Hz]
Compensating negative stiffness kp= 10-7 N/m and dc forces
10-10N/10-7 N/m 1 mm
Low frequency suspension
D. Bortoluzzi, M. Da Lio, S. Vitale 17Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Single input single output control laws
Actuation cross-talkLow frequency suspension laws matrixCapacitive readout
D. Bortoluzzi, M. Da Lio, S. Vitale 18Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
4*1y o
1yo
4*2z o
2zo
4*1 o
1o
G s sKm s s
G s sKm s s
G s sKI s s
Dc force compensation only
Parameter Value so 10-5s-1
K1y 0.0075 s-2
K2z 0.015 s-2
K1 0.0012 s-2
D. Bortoluzzi, M. Da Lio, S. Vitale 19Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
+ TM stabilisation
2 2 2 2 2 21 1 1 2 2 2 3 3 3
2 2 2 2 2 24 4 4 5 5 5 6 6 6
s 2 s s 2 s s 2 sG s K
s 2 s s 2 s s 2 s
D. Bortoluzzi, M. Da Lio, S. Vitale 20Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Optimised control
Robust against knowledge of parameters
D. Bortoluzzi, M. Da Lio, S. Vitale 21Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
nk
k njk 1
nj j 1 j
jj 1
a s Ah s A
s sb s
j
tn ms t'
j jj 1 j 10
y t A x t A e x t t ' dt ' A x t y t
x(s) h(s) y(s)
j j j
ts t s t ' s t
j j j j j0
y t t e y t A e x t t ' dt ' e y t x t A t
jj
1for t<<s
Numerical implementation of control laws
D. Bortoluzzi, M. Da Lio, S. Vitale 22Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
1
1
1
1
1
1
s t1 1 1
s t2 2 2
s t3 3 3
s t4 4 4
s t5 5 5
s t6 6 6
y n 1 y n Ae 0 0 0 0 0y n 1 y n A0 e 0 0 0 0y n 1 y n A0 0 e 0 0 0 x[n 1] ty n 1 y n A0 0 0 e 0 0y n 1 y n A0 0 0 0 e 0y n 1 y n A0 0 0 0 0 e
ARMA basic step
m
jj 1
y n 1 y n 1 A x n 1
D. Bortoluzzi, M. Da Lio, S. Vitale 23Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
TM motion after a force step 10-11 N
Low frequency suspension control
Numerical implementation of control is good
Very long damping time
Stiffer TM actuation needed for emergency
D. Bortoluzzi, M. Da Lio, S. Vitale 24Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Limits of the low-frequency actuation:
•Low damping
•Low maximum force
x omax,x
K df2
Limit to stiffness
Limit to maximum force
Different operational mode (accelerometer mode) is defined in which larger maximum force can be exerted with larger stiffness (up to hardware limit)
D. Bortoluzzi, M. Da Lio, S. Vitale 25Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
x1,…,x6
Transfer functions
parameters upload
Threshold detector
DC force offsets
Fd1,…, Fd6
DC comp. a
DC comp. b
TM stabiliz a
TM stabiliz b
SCIENCE MODE
Suspension c
Suspension d
ACCELEROMETER MODE
LARGE AMPLITUDE MODE
TBC
Transfer functions selection
External command
Low frequency sine wave
Charge measurement
dither
Poles, zeroes, gain
Suspension switch
Caging command
Charge measurement
command
Channels combinator
Ch1, ch2,…
Calibration parameters
upload
Capacitive actuation functional block diagram
D. Bortoluzzi, M. Da Lio, S. Vitale 26Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
x1,…,x6
Transfer functions
parameters upload
Threshold detector
DC force offsets
Fd1,…, Fd6
Capacitive actuation functional block diagram
DC comp. a
DC comp. b
TM stabiliz a
TM stabiliz b
SCIENCE MODE
Suspension c
Suspension d
ACCELEROMETER MODE
LARGE AMPLITUDE MODE
TBC
Transfer functions selection
External command
Low frequency sine wave
Charge measurement
dither
Poles, zeroes, gain
Suspension switch
Caging command
Charge measurement
command
Channels combinator
Ch1, ch2,…
Calibration parameters
upload
Capacitive actuation functional block diagram
D. Bortoluzzi, M. Da Lio, S. Vitale 27Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
x1,…,x6
Transfer functions
parameters upload
Threshold detector
DC force offsets
Fd1,…, Fd6
Capacitive actuation functional block diagram
DC comp. a
DC comp. b
TM stabiliz a
TM stabiliz b
SCIENCE MODE
Suspension c
Suspension d
ACCELEROMETER MODE
LARGE AMPLITUDE MODE
TBC
Transfer functions selection
External command
Low frequency sine wave
Charge measurement
dither
Poles, zeroes, gain
Suspension switch
Caging command
Charge measurement
command
Channels combinator
Ch1, ch2,…
Calibration parameters
upload
Capacitive actuation functional block diagram
D. Bortoluzzi, M. Da Lio, S. Vitale 28Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Accelerometer mode: high damping, large force
2 2
122 2 2 1a o 2
2 212
2
sss ss
max2
F m0.15m s
TM motion after a force step 10-7 N
Accelerometer mode control
damping time shorter
D. Bortoluzzi, M. Da Lio, S. Vitale 29Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Transition to-from accelerometer mode requested to damp long term transitory
Needs adjustment of long term behaviour
TM subjected toforce step
Accelerometermode threshold
TM motion arrestedTM moved towards EH center
Passage to low frequency suspension law
D. Bortoluzzi, M. Da Lio, S. Vitale 30Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Dc-force dominate
Low frequency suspension and accelerometer mode asyntotic behaviour must be the same to avoid overshoot at handover
lfslfsj
lfsj
accaccj
accj
lfsns t jlfs lfs lfs
j j j dc s tj 1
accns t jacc acc acc
j j j dc s tj 1
A ty e y A tx f x
1 eA t
y e y A tx f x1 e
lfs acc
lfs accj j
lfs accn nj j acc lfs 2 2
s t s t s 0 s 0j 1 j 1
A t A tLimh s Limh s 10 s
1 e 1 e
Adjust low frequency gain
D. Bortoluzzi, M. Da Lio, S. Vitale 31Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Capacitive actuation
1
Carrier waveform synthesis
3
ISFEE DAC
4
TM
Fd1,…, Fd6V1,…, V12
V1(t)..V12(t)
Capacitive model equation
parameters upload
Carrier waveform parameters upload
x1,…,x6
F to V conversion
2
F to V conversion
2
Switch
Optical metrology
Capacitivesensing
Switch
forces
ADC
ADC
Com
man
d
Command
D. Bortoluzzi, M. Da Lio, S. Vitale 32Penn State, 20th-24th July 2002
4TH INTERNATIONALLISA SYMPOSIUM
Summary:
•LTP dynamics mathematical model •Capacitive actuation control laws: low frequency suspension and accelerometer mode•Noise models•Simulations results of a drag-free and attitude control system matching the requirements given