Design and implementation of a controller for optical pathlength compensation on a flexible structure is presented. Nanometer level pathlength control is demonstrated in the laboratory. The experimental results are in close agreement with performance predictions

Rahman, Zahidul H.

Spanos, John T.

English

NASA Technical Reports Server

v , _
N93°18842
Optical Pathlength Control
on the JPL Phase B Interferometer Testbed
John Spanos and Zahidul Rahman
Jet Propulsion Laboratory, California Institute of Technology
Pasadena, California 91109
Abstract
Design and implementation of a controller for optical pathlength compensation on a
flexible structure is presented. Nanometer level pathlength control is demonstrated in
the laboratory. The experimental results are in close agreement with performance pre-
dictions.
Introduction
Many future space missions will require major advances in the areas of controlling,
aligning, and pointing optical instruments mounted on large flexible structures. One
of the most challenging applications is optical pathlength control for stellar interfer-
ornetry [1]. Figure 1 shows one possible configuration of a long baseline interferometer
with six collecting telescopes mounted on a free flying truss structure. The optics are
designed such that any two collectors can be used as a stand-alone interferometer. For
the interferometer to perform its mission successfully, the variations in the length of the
path traveled by light through a pair of collectors to the detector (see Fig. 2) must be
no more than a few nanometers [1].
Achieving nanometer level pathlength control becomes more difficult as optical el-
ements are mounted on larger, more flexible structures. Loosely stated, the larger the
distance separating the collecting apertures the better the astrometric accuracy of the
interferometer. However, a longer baseline translates into a more flexible structure which
in turn implies a more severe interaction between the structure and the feedback control
system.
To meet the control structure interaction challenge, the Jet Propulsion Laboratory,
in conjunction with a NASA-wide Control Structure Interaction (CSI) program, has
developed the Phase B Testbed [2] in order to explore, develop, and validate emerging
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technologies and design methodologies. In particular, JPL has initiated efforts toward a
multilayer control approach involving (1) piezoelectric active member structural control,
(2) active isolation control of on-board disturbances, and (3) direct control of optical ele-
ments. This paper addresses the optical control layer, presents the control system design
methodology, and discusses the experimental results achieved.
The JPL Phase B Testbed
In order to address the control structure interaction problem associated with opti_
cal pathlength control, the Jet Propulsion Laboratory has developed a ground testbed
facility known as the Phase B testbed (Fig. 3). This is an eight foot tall truss struc-
ture cantilevered at the base and equipped with an optical motion compensation sys-
tern.* The optical compensation system is framed in a rectangular shaped trolley and
attached firmly to the truss structure. A voice coil actuator and a piezoelectric (PZT)
actuator provide high bandwidth pathlength control. Earlier control experiments con-
ducted by O'Neal and Spanos [3] using an optical configuration that isolated most struc-
rural motion from the optical path demonstrated closed loop performance to the level
of tl nanometers rms. This paper describes the control system design and implementa-
tion for a new optical configuration that introduces a larger degree of coupling between
structural motion and optical pathlength.
344
Figure 4 represents the current optical configuration and shows how laser interferom-
etry was implemented in our experiment. Retroreflector and plane mirror interferometry
were combined in such a way that the optical alignment is maintained under X and Z
lateral motions and X, Y and Z rotational motions. This optical configuration is consid-
erably less sensitive to alignment errors induced by structural vibration than either plane
interferometry or retroreflector interferometry alone. In this setup the two laser beams
are placed very close to each other and the returning beam is directed to the receiver
by an additional plane mirror. Note that the laser beam passes eight times through the
trolley as compared to two times with retroreflector interferometry or to four times with
plane mirror interferometry.
Control Law Design
The frequency response functions (FRF) for the two input one output system were
measured with a Tektronix 2630 Fourier analyzer and are shown in Figure 5. Sine sweep
* A detailed description of the Phase B testbed is given by Eidred and O'Neal [2].
and band limited white noise inputs wereused to generatethe FRF's with high coher-
encelevels. The PZT actuator to laserpathlength FRF is not affectedby the dynamics
of the flexible structure due to the fact that the massof the PZT mirror is small and
the balanced PZT stack providesmomentum compensation. Note that while the magni-
tude is relatively constant acrossthe measuredfrequencyband, the phasedrops linearly
with a constant slopecorrespondingto 70microsecondsof pure time delay. This delay
is associatedwith the time it takes to measurethe optical pathlength and output the
measurement from the computer to the spectrum analyzer.
The voice coil to pathlength FRF is significantly affected by structural flexibility. The
dominant peak at 0.7 Hz is due to the flexure that attaches the trolley to the truss. All
other peaks in the frequency response function correspond to structural modes of the
truss. Observe that the peaks and valleys (i.e., poles and zeroes) in the FRF are alter-
nating up to 80 Hz which guarantees that all the modes below this frequency will in-
teract stably with a controller of the phase tead type. Beyond 80 Hz the phase drops
rapidly while modal density and plant uncertainty increase considerably. As a result, we
have chosen to limit the bandwidth of the voice coil controller to a frequency lower than
80 Hz.
The architecture of the two-input one-output optical pathlength control system is
shown in Figure 6. Bode's classical control design methods [4] were used to shape the
open loop response in the frequency domain. We point out that, unlike most modern
control design methods, this design methodology does not require an explicit paramet-
ric model of the plant using instead the FRF measurement directly to synthesize robust
controllers.
The control system architecture is similar to that of Colavita [5] in the sense that the
output of the PZT controller drives both the PZT actuator and the voice coil controller.
The objective of this configuration is to desaturate the limited stroke PZT actuator in
the low frequency range where disturbances tend to have large amplitudes. Note that
in Fig. 6 we have modeled the PZT-to-pathlength transfer function as unity while the
measurement in Fig. 5 shows it to be approximately 4.5 dB or 1.7. We shall compensate
for this simplification later by dividing the PZT controller K1 (s), and multiplying the
voice coil controller K2(s) by a factor of 1.7 after the two control laws are designed.
The open loop transfer function for the system of Fig. 6 is
L = K1 (1 + h_2G2) (1)
345
The objective is to design the two compensatorsK, (s) and K2(s) such that the closed
loop system is stable and the total loop gain ILl is as large as possible over the largest
achievable bandwidth. The design requirements are placed on ILl since the disturbance
rejection is inversely proportional to ILl when ILl is much larger than unity. The follow-
ing three properties are observed from (1):
1. When II'22G2]>>1, ILl_ IK,KeG21
2. When IK2G2I<<1, ILl_ IK,[
3. When IIC=G=I= 1, ILl _ ¢ II:,1
where ¢ = angle(K2a2) + zc and angle(K2G2) is the phase angle (in radians) of I£2G2 at
the frequency where 1I:2G21= 1. Clearly, when the voice coil loop gain is large, the total
loop gain is the product of the voice coil loop gain and the PZT loop gain. The total
loop gain also approaches the PZT loop gain as the voice coil loop gain approaches zero.
Also at the voice coil loop gain crossover frequency the total loop gain is the product of
the PZT loop gain and the phase margin ¢ associated with the voice coil loop.
The control laws were designed one loop at a time. First, the voice coil controller was
designed to stabilize the system assuming that it is driven directly by the laser path-
length measurement (i.e., K, (s)=l) and the PZT actuator is disconnected. Using fre-
quency domain loop shaping techniques, a voice coil controller with the following trans-
fer function was obtained:
/:2(s) = (0.117) _-_+3-_s+3092 s2__4_-2_T[,0052 _ _l-0-0s__-5-_: )
LEAD LOW PASS NOTCH
The controller consists of (1) a second order lead filter that provides more than 30 de-
grees of phase at the gain cross over frequency, (2) a second order low pass filter that
attenuates the high frequency Iighly damped structural modes, and (3) a second order
notch filter that attenuates the peak at 80 Hz so that the gain margin of the correspond-
ing mode is approximately 6 dB. The low pass and notch filters are essential in ensuring
a stable control structure iteration. The compensated voice coil to laser pathlength frequency
response function is shown in figure 7.
Similarly, the transfer function of the PZT controller was designed:
K,(s) = (3,137)(s+378) ( s+4,000 )s 2 + 440s + 394,784
LAG LOW PASS
346
The first order lag keeps the total loop gain high at low frequencies for good disturbance
rejection. On the other hand, the second order low pass filter enforces a steep gain roll-
off while maintaining adequate phase margin for stability robustness. Although the PZT
actuator has very high bandwidth, the PZT loop bandwidth is limited by high frequency
noise, digital implementation time delay, and phase lag from the power amplifier.
Figure 8 shows the loop transfer function L as well as the PZT controller K1. The
effects of time delays due to the computer implementation have been taken into account.
The frequency responses are clearly in agreement with the three properties described
earlier.
Both control laws were discretized using the bilinear transformation and prewarping
was used to match them to their analog counterparts at the respective gain crossover
frequencies. The low bandwidth voice coil controller and the high bandwidth PZT con-
troller were implemented at 2,000 Hz and 12,000 Hz respectively. The phase lags associ-
ated with the zero order hold and the computational delay were modelled as pure time
delays since the sampling frequencies of both controllers are much higher than their re-
spective bandwidths.
Experimental Results
Two closed loop experiments were carried out. The objective of the first was to reject
the ambient laboratory disturbance environment and to establish the noise floor of the
closed loop system. The objective of the second was to reject a sinusoidal disturbance
tuned to the frequency of the fundamental truss mode (i.e., 5.3 Hz). The sinusoidal dis-
turbance was induced by a proof-mass type shaker attached to the midspan of the truss
via a stinger.
In both experiments, the open loop optical pathlength histories were recorded for the
first 5 seconds at which time the control loop was closed and the closed loop pathlength
histories were recorded for an additional 5 seconds. The results from the experiments are
shown in Figures 9 and 10.
Figure 9 shows the optical pathlength variation reduced to 24 nanometers rms from
an open loop ambient disturbance of I5 micrometers rms. This corresponds to 56 dB re-
jection of the ambient disturbance. It is emphasized that in these experiments the laser
beam makes 8 passes through the trolley optics which implies that the equivalent path-
347
348
length error for a space interferometer (i.e., Figures 1 and 2) would be 3 nanometer rms.
Spectral analysis of the open and closed loop signals indicates that the achieved con-
troller bandwidth is approximately 500 Hz and that a large part of the closed loop error
is due to noise at frequencies beyond the controller bandwidth.
Figure 10 illustrates the forced response experiment. The impact of the 5.3 Hz sinu-
soidal disturbance on the pathlength is clearly shown during the first 5 seconds of the
time history. The closed loop response indicates that the disturbance is attenuated by
more than 70 dB which is in close agreement with the total loop gain of Figure 8.
Conclusions and Future Work
We have successfully designed and implemented a two input one output optical path-
length control system on an experimental flexible structure. The control design was car-
ried out in the frequency domain by directly shaping the measured actuator-to-sensor
frequency response function and did not require a parametric model of the system. Ex-
periments were conducted to reject the laboratory ambient disturbance environment and
also shaker induced disturbances tuned to the fundamental structural frequency. The re-
sults we have obtained so fax indicate that nanometer level control of optical pathlength
is feasible in space.
Presently we are reconfiguring the optical path in order to introduce a stronger cou-
pling between the optical pathlength and the structure. The laser beam will be reflected
back from an additional point on the structure where large structural motion has been
observed. We are also in the process of introducing additional layers of control (i.e., pas-
sive/active damping, and disturbance isolation) to improve the overall performance of
the pathlength compensation system.
Acknowledgernents
This research was performed at the Jet Propulsion Laboratory of the California Insti-
tute of Technology under a contract with the National Aeronautics and Space Adminis-
tration sponsored .by the ONce of Aeronautics and Space Technology, Code RM.
References
[1] Laski n R.A., and San Martin A., "Control/Structure System Design of a Spaceborne
Optical Interferometer", AAS/AIAA Astrodynamics Specialist Conference, 1989.
[2] Eldred D. B., and O' Neal M. C., "The JPL PhaseB TestbedFacility", ADPA Active
Materials & Adaptive Structures Symposium& Exhibition, 1991.
[3] O'Neal M. C., and Spanos J. T., "Optical Pathlength Control in the Nanometer
Regime on the JPL Phase B Interferometer Testbed" SPIE Intl Symposium on Op-
tical Applied Science and Engineering, 1991.
[4] Bode, H. W., Network Analysis and Feedback Amplifier Design, Van Nostrand, NY,
1945.
[5] Colavita, M. M., et al, "Prototype High Speed Optical Delay Line for Stellar Interfer-
ometry", SPIE Intl Symposium on Optical Applied Science and Engineering, 1991.
349
Figure 1. CSI Focus Mission Interferometer
350
BLAC,N AND WHITE r-"HOTOGRAP_
UGHT
SIDEROSTAT \ FROM \
_f.._ eTIP/TILT (COARSE)• RETROREFLECTOR
MOUNTED IN CENTER
LIGHT
\FRq
COLLECTING SCOPE
• 0.5 m APERTURE 3 THREE TIER TROLLEY 3'
•OFFSEYSECO.OAR* • V_CEC_L:2. RA.GE ,2.II \]
•_ STACK:,..*.GE _i I_l_._
• REACTIONLESS
S _MING BELT,,,,
r -1 C._'HH'H'H'H'''"" .7;HH.(.)
I FRINGE TRACKER
I _ PATHLENGTH _i I "
I IANGLE TRACKERI I
I I A WAVETILT I _ '.....
L. J COMB,,,NGOPTICS
• BEAM SPLITrER AT BEND 9
• UP TO BENDS8 AND 8', BOTH BEAMS
EXPERIENCEIDENTICAL (NOT SYMMETRICAL)
REFLECTIONS
DETECTOR
Figure 2.
L
RXED TROLLEY
• MIMICS UGHT BENDS
OF MOVING TROLLEY
Optical Layout of an Interferometer
351
CSi FOCUS MISSION INTERFEROM
Figure 3. JPL CSI Phase B Testbed
6 INCH PARABOLIC
PRIMARY MIRROR--
RETROREFLECTOR --
SECONDARY
MIRROR
. FLEXURE \ ,. "_ _. \ \ -. -- , ..,.,, • , -. ,, ,. . . -\\,
fl__=_, _--_-_-_-................. __
_ _r__-::==: .................
- VOICE COIL J
E
ACTUATOR _ PZT ACTUATOR --LASER PATH
...
LASER
t RECEIVER
jINTERFEROMETER
OPTICS
PLANE
MIRROR
OP_CALBENCH
•"_ 2NO LASER BEAM
Figure 4. Optical Pathlength Compensation System
352
PZT TO PATHLENGTH TF
8 I
E
<
7 2
i i! _ii_,_
1-
30r
VOICE COIL TO PATHLENGTH TF
120 .......
2o'-
10 r
m 0
_ -ioi
m -20
v
N -3o:
< -401_
_" -501
-6o!
_70 T
loo 2OO 3OO 400 5OO 6OO 7OO 8OO 9OO IOO0
100p
.-.. 80
60_
40
_ 2o
Z
< 0
-20
-40
-60
l, oi- _
, .50_-
I I
i f---70 MICROSECONDS ] G -100!
, / / TIME DELAY i
_ -2oo_
_ J
m -250 k
_, -3OO_-
i -350
l .,_oo[
10 -1
FREQUENCY (HZ)
-\
\i "_,
, iI 1 i _t:_
! i !t i ,I I illi!_!
10° 101 102 103
FREQUENCY (HZ)
Figure 5. Identified Frequency Response bSanctions
353
PZT CONTROL
COMMAN5 j(__ KI(S)J
LASER/PZT
XFER FN
=1 1 1
LASERNC
VC CONTROL XFER FN
DISTURBANCE
+_ LASER+( "T.-_,,-I PATHLENGTH
+
Figure 6. Control System Architecture
VOICE COIL
CONTROL
I
_. K 2 (s) j
LASERNOICE COIL DISTURBANCE
TRANSFER FUNCTION LASER
G2(s) I +A
PZT
K2(s ) = (0.117) 1,oo  s2+ 371s+ 3092 _2+ 402_+ 1,0052 \_ g _5- _--65-2]
% Y ,4% Y ,/'% Y •
LEAD LOW PASS NOTCH
Z
<
30
40 F- \@i "\\x
2
lOI I0 o l0 = l0 s 10 J
FREQUENCY (tlZ)
0,
d0
-100
E
-_0
I0 a IO o tO'
FIIEQLrENCY (WZ)
10 7 I0_
Figure 7. Voice Coil Loop Gain and Phase
354
140
120
.--, 100
80
Z 6O
.<
40
2O
0
-2(
-50
-100
-150
< -200
-250
-300
10-1
L
Kl
l i I L I t i i i 1 _J,_&.l I
Kl
L
/
I I I I I [ I I I I h 1 _
?
I 1 I I t 1111 I I 1 1 t t II I I I I t I I I II I I I I I t [ J
10 o 101 102 10 3
FREQUENCY (HZ)
Figure 8. PZT and Total Loop Gain and Phase
355
DISTURBANCE: LABORATORY ENVIRONMENT
OPEN LOOP: 15.2481 um RMS
80 100 CLOSED LOOP: 23.9999 nm RMS
60
40
20
0
-20
0
03 50
©
-50
Z
' -100
5 10 6 7 8 9
SECONDS SECONDS
10 4
[
101 =
10-2
lO-I
OPEN LqOP !solid) VS C LgSED LO9P (dashed) '
i i I i ! ! ! i i i ! i
,I
I I l"IO III." "I I l I PIII#I ' , III , IIII I l__L__l I tlll I I l I_..I_L_
10 o 10 _ 10 2 10 3 10 4
FREQUENCY (HZ)
Figure 9. Closed Loop Optical Performance with Ambient Laboratory Disturbance
356
DISTURBANCE:
SINUSOID TUNED TO FREQUENCY OF FIRST STRUCTURAL MODE
500
0'3io
O
-500
-1000
0
Figure 10.
bance
OPEN LOOP: 443.386 um RMS 400 CLOSED LOOP: 101.257 nm RMS
200
O
Z_-200
-400--
5 10 6 7 8 9
SECONDS SECONDS
Closed Loop Optical Performance with Shaker Induced Sinusoidal Distur-
357



Optical pathlength control on the JPL Phase B interferometer testbed

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