Design and Implementation of. Robust Decentralized. Control. Laws for the ACES Structure at Marshall. Space Flight Center. Emmanuel. G. Collins,. Jr., Douglas.
NASA
Contractor
Design Robust Laws
Report
and Implementation of Decentralized Control for the ACES
at Marshall
Space
Emmanuel
Jr.,
and
G. Collins,
David
Harris
under
Florida
for Research Contract
Center NAS1-18872
National Aeronautics and Space Administration Office of Management Scientific and Technical Information Division
1990
Flight
Douglas
J. Phillips,
C. Hyland
Aerospace
Melbourne,
Langley
Structure
Corporation
Government
Prepared
4310
Systems
Division
Center
Abstract
Many mance
large space system
requirements
it is imperative based
vibration Space
that
Flight
especially
the benefits This
Investigator control
report
The
the study
accuracy.
of active
The
results The
structure
of line-of-sight
of this
be practically
conducted experiment
testbed
is the
is dynamically control
control
to satisfy
for these concepts
control
an experiment
structure.
ACES
active vibration In order
vibration
describes
Program.
for a flexible
Center.
allows
will require
such as line-of-sight
experiments.
CSI Guest
concepts
traceable
to become
successfully
as part
perfor-
operational
demonstrated
by Harris
ACES
critical
in groundof the NASA
demonstrate
structure
at NASA
to future
space
active Marshall
systems
and
issues.
iii PRECED]F,]G PAGE
BLAI',]Rix;OT FILMED
I_'_.L-L_INIENTIONALLY
8tANg
Table
1.0
Introduction
2.0
Description
3.0
Modeling
5.0
................................
of
the
ACES
Procedure
3.1
Choosing
3.2
Model
4.0
of Contents
the
Control
Structure
for
the
Modeling
Development
Design
1-1
ACES
the
the
ACES
4.1
Design
Process
for the
Detector
4.2
Design
Process
for the
Base
4.3
Design
Process
for the
LMED
Performance
of
the
Realization
Structure
..................
to IMC
Force
to Pulse
Disturbances
5.2
Response
Due
to to an
RCS
5.3
Response
Due
to a Crew
5.4
Some
Gimbal
4-1
Loops
to Accelerometer
4-1 ............
Loops
4-2
..........
4-3
.................
5-1
....................
Disturbances
Disturbances
5-1
..................
5-2
....................
Implementation
Results
5-2 .............
5-2
7.0
References
.................................
7-1
8.0
Appendix
.................................
8-1
BLANK
Conclusions
3-3
Closing
PAGE
and
.......
6.0
PRECEDING
Remarks
Algorithm
................
Controller
Due
on the
Loops
to AGS
Response
Remarks
3-1 3-1
Eigensystem
5.1
Final
...............
......................
Gyro
Integrated
2-1
Structure
Procedure Using
for
....................
NOT
FILMED
.....................
6-1
_L..._.._NIEN]IOttALL'_
BL_K
List of Tables 5.1.1
Det-X Response Improvement to a BET-X As the Controllers Were Combined
Pulse
................
5-3
5.1.2
Det-Y Response Improvement to a BET-Y As the Controllers Were Combined
Pulse
................
5-4
List 1.1
The Maximum Entropy/Optimal Design Equations
The ACES
Test Article
of Figures
Projection
..................
1-3
...........................
2-5
AGS-X to BGYRO-X: FE Model Bode Plot
Magnitude vs. FRF
Comparison
of
................
3-4
3.1.2
AGS-Y to BGYRO-Y: FE Model Bode Plot
Magnitude vs. FRF
Comparison
of
................
3-5
3.1.3
AGS-X to BGYRO-X: Phase Comparison FE Model Bode Plot vs. FRF
3.1.4
IMC-X to DET-Y: Magnitude Comparison FE Model Bode Plot vs. FRF
of
.................
3-7
3.1.5
IMC-Y to DET-X: Magnitude Comparison FE Model Bode Plot vs. FRF
of
.................
3-8
3.1.6
Pattern of Strong and Weak in the System Dynamics
Iterative
Procedure
Final Steps in Model AGS-X to BGYRO-X
for System
of
Interactions
3-6
....................
Identification
Development and AGS-Y
..................
3-9
..................
3-10
for ..................... to BGYRO-Y Loops
3-11
vii PRECEDING
PAGE
BLANK
NOT
FILMED
I__NRNTIONALL_
BLANK
3.2.3
Final Steps in Model Development for IMC-X to DET-Y and IMC-Y to DET-X
.................... Loops
3.2.4
AGS-X to BGYRO-X: Magnitude ERA Model Bode Plot vs. FRF
Comparison
of
.......
3.2.5
AGS-Y to BGYRO-Y: Magnitude ERA Model Bode Plot vs. FRF
Comparison
of
................
3.2.6
AGS-X to BGYRO-X: Phase Comparison ERA Model Bode Plot vs. FRF
3.2.7
.........
3-13
3-14
..................
3-15
IMC-X to DET-Y: Magnitude Comparison ERA Model Bode Plot vs. FRF
of ..................
3-16
3.2.8
IMC-Y to DET-X: ERA Model Bode
of ..................
3-17
4.1.1
Disturbance Tracking to DET Loops
..................
4-5
4.1.2
DET-X Response to a BET-X Pulse: ..................... Open Loop vs. Closed Loop with the IMC to DET
Controller
DET-Y Response to a BET-Y Pulse: ..................... Open Loop vs. Closed Loop with the IMC to DET
Controller
4.1.3
of
3-12
Magnitude Comparison Plot vs. FRF
Problem
for the IMC
4-6
4-7
4.2.1
Influence of Maximum Entropy Region for the AGS to BGYRO
Design on Phase Loops
4.2.2
Influence of Maximum Entropy Region for the AGS to BGYRO
Design on Magnitude Loops
4.2.3
Maximum Entropy Design Robustified the Notches for the High Frequency Modes
4.2.4
DET-X Response to a BET-X Pulse: ..................... Open Loop vs. Closed-Loop with the AGS to BGYRO
..o
VIII
in the Performance
in the Performance
...................
.......
4-8
.....
4-9
4-10
4-11 Controller
4.2.5
4.2.6
BGYRO-Y
Response
Open
vs.
DET-Y Open
4.2.7
4.3.3
4.3.4
Loop
Response Loop
vs.
to a BET-Y
Response
Open
Loop
vs.
Block
Diagram
for LMED
Feedback
Response vs.
Closed
ACCEL-1X
Response
Open
vs.
Closed
ACCEL-2X
Response
Open
vs.
Loop
Closed
4.3.5
BGYRO-X Open Loop
4.3.6
ACCEL-1Y
Response
Open
vs.
4.3.7
5.1.3
5.1.5
5.1.6
5.1.7
CIosed
Response
Open
vs.
Loop
DET-X
Closed
Response Loop
vs.
Response
Open
vs.
Response
Open
vs.
Closed
ACCEL-2X
Response
Open
vs.
DET-Y Open
Loop
Response Loop
with
vs.
Closed
Loop
with
Loop
with
with
Loop
with
Loop
with
with
Loop
with
the
the
4-16
Controller
the
LMED
4-20
4-21
Controller
..................... Integrated
5-5 Controller
...................
Integrated
5-8
Controller
..................... Integrated
5-7
Controller
...................
Integrated
5-6
Controller
...................
Integrated
ix
4-19
Controller
...................
Pulse: the
4-18
Controller
...................
Pulse: the
4-17
Controller
LMED
Pulse: the
Pulse: with
...................
...................
Pulse:
to a BET-X Loop
4-15
...................
Pulse: the
to a BET-X Loop
4-14 Controller
...................
LMED
Pulse: with
Controller
Pulse: ................... the LMED Controller
to a BET-Y Loop
to BGYRO
LMED
Pulse: the
4-13
to BGYRO
LMED
Pulse: the
4-12 Controller
...................
AGS
Pulse: the
to BGYRO
..................... AGS
Loops
to a BET-Y Loop
...................
AGS
Pulse: the
to a BET-X
to a BET-Y Closed
the
to a BET-X
to a BET-X
Closed
ACCEL-1X Loop
Loop
to a BET-X Closed
BGYRO-Y Loop
to a BET-X
Response to a BET-Y vs. Closed Loop with
ACCEL-2Y
Open 5.1.4
Loop
to a BET-Y with
Open
Pulse: the
Pulse: with
Closed-Loop
BGYRO-Y
Loop
with
Closed-Loop
BGYRO-X
Loop
to a BET-X
Closed-Loop
5-9 Controller
5.1.8
5.1.9
5.1.10
BGYRO-X
Response
Open
vs.
Loop
to a BET-Y
Closed
ACCEL-1Y
Response
Open
vs.
Loop
ACCEL-2Y Open Loop
RCS
Loop
the
to a BET-Y
Closed
Loop
Response vs. Closed
Disturbance
Pulse:
with
...................
Integrated
Pulse:
with
the
...................
Integrated
Profile
BGYRO-Y
Response
Open
Loop
vs.
Crew
Disturbance
DET-X Open
Response Loop
vs.
..........................
to a BET-X
Closed
Loop
Profile
with
RCS the
Loop
Crew with
the
5-12
5-13
Disturbance: Integrated
................ Controller
..............
5-14
5-15
Controller
..........................
to a BET-X Closed
5-11
Controller
to a BET-Y Pulse: ................... Loop with the Integrated Controller
DET-X Response to a BET-X RCS Disturbance: Open Loop vs. Closed Loop with the Integrated
5.2.3
5-10
Controller
5-16
Disturbance: Integrated
x
............... Controller
5-17
1. INTRODUCTION Many
large space system
performance
requirements
roughness.
In order vibration
discusses
an experiment
results
Figure
primary
reduction
of the
cantly
the beam
reduced-order
and
law implementation
The
Section
3, the strong
involving
actuators
eight
The jection
primary Approach
simultaneous controller
Entropy/Optimal high performance, (Figure
1.1) consist
equations MEOP
interaction
two of the feedback
paper
Program.
space
missions,
testbed,
shown
in
that the
provide
limitations
substantial
controllers
to signifi-
on controller
simplicity
reduction
in control
on throughput
of even
design
at NASA
by designing
design
[12-13].
by using
As will be described
in the dynamics
decentralized
was facilitated
of the ACES
control
more
fully in
structure
laws for selected
the
allowed
system
loops
Optimal
Pro-
and eight sensors.
for Uncertain
Systems
for control
robustness
Projection robust
versus (MEOP)
control
of four coupled
control
design
(OPUS)
of four fundamental
was used to develop approach
benefits
This
Investigator
Complexity
for control
patterns
in this experiment
[1-10].
The
issues in control system
law design matrix
equations
design
actuator
A subset
[2-6] which
for flexible
OPUS
design:
performance.
methodology
when the plant is known perfectly
projection
the
(MSFC).
was also placed
architectures).
used
developed
chosen
and
Center
required
due to stringent
models
methodology
trade-off order
interest
system
and weak
the control
emphasis
that
The
controllers
of this objective
controller
Algorithm
us to approach
to design
surface
to future
structure.
Flight
on rms
processors.
of the
Realization
was
Space
critical
experiments.
traceable
for a flexible
Particular
decentralized
qualified
development
Eigensystem
vibration.
it is imperative
directly
to satisfy
constraints
in ground-based
Marshall
satisfaction
is of paramount
space
control
at NASA
The
operational
features
of this experiment
LOS errors.
and
as part of the NASA CSI Guest
has
vibration
control systems
accuracy
demonstrated
which
structure
(LOS)
to become
by Harris
active
attenuate
state-of-the-art
concepts
experiment,
objective
active vibration
as line-of-sight
conducted
2.1, is the ACES
will require
be practically
demonstrate
The
(i.e.,
control
of this
successfully
such
for these
of active
The
concepts
is the process
sizing, sensor
of OPUS
was developed
structures.
The
is the
MEOP
design
specialize
to the standard
and a full order
controller
is desired.
[7-8] was used to develop
vibration
control
loops. 1-1
suppression.
laws for a tracking
accuracy, Maximum
particularly
which
laws for active
allows for the
to allow equations
LQG
In this experiment
The discrete-time problem
Riccati
associated
optimal with
The paperis organizedas follows.Section2 describesthe basicACES configuration.Section 3 then discusses the finite elementmodelprovidedby MSFCand the developmentof the models actually usedfor control design. This sectionalsomotivatesthe decentralizedapproachchosen for the control design. Next, Section4 describescontrol designfor eight systemloops which wereselectedby analysisof test data collectedfrom the structure. Section5 then presentsthe experimentalresults. It is seenthat very significantperformanceimprovementis achievedwhen the eight feedbackloopsareclosed.Finally,Section6 presentsclosingremarksandconclusions.
1-2
0=
A_Q
+ QA T + Vt -
QZ'Q
+ r±Qy_,Qr
T
P
P
+ Z
a2AiQAT
+ Z
i:I
0 = ATp
a2AiQAT
i=I
+ PA T + R1 - PZP
+ rWp_Pr±
P
P
+ _ _ ATPA,+ _ 4 ATPA, i=i
0 = (A_ -
_P)Q
+ Q(A_
0 = (A_ - Q2)TP
_"= c2P(_P)
Figure coupled
1.1 The MEOP by a projection
flexible
structures.
-
i=1
Z'P)
+ Q_,Q
-
+ P(A_ - QF_,) + P£P P = rank
QP
T
- rTpZPr±
rank
_) :
#,
(.)# denotes the group generalized
design matrix
rank
r±QZ'Qr
:
nc
inverse.
equations consist of four modified Riccati and Lyapunov equations, r and allow high performance, robust control law developement for
1-3
2.
DESCI_IPTION The
ACES
ployable,
built
(JPL). The
form
The
approximately
of the beam
Inc.
It was supplied
which
is triangular
properties.
When
continuously
the beam
basic
test
article
is a de-
is a spare
Voyager
and is very lightly
damped.
section.
its full length. each having
the Astromast
article
Labora-
in cross
along
test
by the Jet Propulsion
5 pounds)
into 91 sections
fully deployed,
The
to MSFC
(about
beam
divide
The
lightweight
and extend
its shape,
MSFC.
45 feet in length.
is extremely
configuration
the Astromast appendages
(Figure 2.1) consists
tip and the pointing creates
the
frequency
Research,
at NASA
Three
The
cross members,
equal
exhibits
longerons
length
and mass
a longitudinal
twist
of
260 degrees.
The ACES
Overall,
is located
is a symmetric
elastic
STRUCTURE.*
approximately
Astromast
give the beam
and similar
the
"nested"
structure
modes
configuration study
beam,
Astromast
ACES
testbed
by ASTRO
the corners
which
THE
experimental
lightweight
Astromast tory
OF
is very
(more
modal
and
40 modes traceable
and counterweight
arms at the Astromast
frequencies
flexible
than
is dynamically
gimbal
of an antenna
characteristic
lightly
under
damped.
10 Hz).
to future
space
base.
The addition
of Large
It contains
Space many
As illustrated
systems
legs appended of structural
Structures closely
by Figure
and is particularly
to
(LSS).
spaced,
2.1, the
low
ACES
responsive
to the
of LOS issues. The precise
voltage
input
Variable servo
motion
to the BET
Differential
controllers
adjust
of the Base Excitation servo control
Transformer
compare
the position
system. whose
the commanded
input
of the BET.
The closed-loop
limitations
of the hydraulic
to be position
commands
to the BET.
two pointing
Motion
gimbals,
Figure
1.1 shows
control
design
gimbals
the
Compensation
location
are each
* This description
positioned
detector
of each
of the
the laser beam on the
of the ACES
movements
are monitored
LVDT
consists
and associated components
in the center
a commanded by a Linear
signals
and
the disturbances
of a 5-mW electronics, of the
primarily
from
and two power
The detector
to increase
[11]
The
the
within
are chosen
two 12-inch
IMC system.
of the detector. appendage
laser,
The
automatically
allows any type of BET movement
In this experiment
System
2-1
by supplying
to the
controller
is taken
is obtained
are fed back to the servo controllers.
voltage
end of a flexible
testbed
BET
outputs
system.
(IMC)
a four quadrant
is to position
The
(LVDT)
the frequency
The Image
Table (BET)
mirrors, supplies.
goal of the and pointing
difficulty
of the
control problem. The the controller
design
lack of information (i.e., there
about
the
appendage
is no accelerometer
motion
also adds
or gyro at the location
complexity
of the
gimbals
to
or the
detector). In addition Gimbal
to the two IMC gimbals,
System
applications, provides
(AGS),
which
torque
control
of 27 amps servo
which
outputs
can generate
azimuth
torquer
however,
torquers,
be set manually
of azimuth
freedom.
of-10
that
designed
gimbal
in the
azimuth.
AGS
receives
Astromast.
The
to +10 volts.
causes
of generating
13.8 ft-lbs
allows
the
5 degrees test
range
torque
from
system)
the
in the
a current
limit
the AGS
command
the
signals.
used in the SSC labora-
range
± 30 degrees.
of _ 5 degrees.
at any position to any
system
to the current,
of approximately
to be rotated
gimbal
Because
proportional
over an angular
of rotation
article
measure.
to produce
pointing
commands
represents
and servo amplifiers
over an angular
The
This saturation
torque
the Advanced
accuracy
acquisition
be designed
of torque
i
for high
data
an applied
must
also include
as a protective
with the power supply
to allow
This
system
servo amplifier
in the COSMEC
is capable
actuators
a third
of the
into the AGS
37.5 ft-lbs
control
on an HP 9000 via the COSMEC
a current
used
gimbal
with
base
over the range
The AGS gimbal tory,
at the
is built
algorithms
two-axis
augmented
(implemented
inputs
amplifier
control
has been
actuation
algorithm
form of analog
a precision,
the available
about
The It can,
the 360 degrees
position
desired
without
remounting. Linear apply
Momentum
forces
having
and measure
orthogonal
(LVDT's). These
The
axes,
were
modes.
Y axes of the
inertial
to the structure
and
(LMEDs)
packages
and
the Astromast
a colocated
Each
frame
the
accelerometer
sensor/actuator
LMED
package
Variable
at intermediate
ability
is at rest, shown
colocated
two Linear
are positioned
to maximize
reference
provide
accelerations.
two accelerometers,
selected
When
Devices
the resulting
two LMED
locations
structural
Exchange
of these
in Figure measures
2.1.
points
package
The
along
Transformers the
is aligned applies
which
two LMEDs
to control
LMED
the resulting
contains
Differential
devices
each LMED
pairs
Astromast.
the
dominant
with the X and a horizonal
acceleration
force
at the actuator
location. The LMED applied travels
is linear permanent
to the structure along
coil which
a single
extends
as a reaction shaft
inside
magnet
motor
against
on a pair of linear the magnet
assembly
whose
magnet
the acceleration bearings. from
2-2
functions
of proof mass.
The armature one end.
as a proof mass.
The
The
magnet
of the motor
magnet
assembly
Force is assembly
is of a hollow moves
along
the shaft on each
with respect end
by a bracket
accelerometer the proof
which
is mounted
mass with
In addition and LVDT's gyros
to the coil which is fixed to the LMED
in line with
respect
rate
package
small
angular
digital
converter
period
of approximately
card
rates The
dynamic
for warmup, the
power
included
on board
The signals
time
reduces
the instrument
package.
One channel
of each pair
to that
and negative
the
As in the
cases
COSMEC
system.
As mentioned
to 12-bit ATM
requires
rate
Rate
and the
of
accelerometers
include
Gyros.
signals binary
three-axis
rate
However,
since
and
They
were not
words
during
are designed
of an ATM
gyro packages
1.5 amps
ASTROMAST provide
requires
are
rate
gyro
by the
analog-to-
require
a warmup
warmup
0.9 amp
measured
resolution
1.2 amps
per package.
are different
require
and then
1.25
The
by two identical
finer than
0.0001
approximately
at 28 Volts
from the ATM
of the accelerometer carries
by a decrease
previously
position
DC.
20 minutes After
accelerometer
g and a
warmup
electronics
are
Two channels
are
package.
acceleration
of the other
A linear
devices.
output
of 25 to 30 Hz. They
package
of the synchronization
acceleration
the
implementation
(ATM)
analog
The
tip of the
from the accelerometers
carries
Mount
package
to about
of freedom
identical
Each
each
for each degree
channel
mass.
at the tip and base.
measurement
The accelerometers
required
other
is constrained
to measure
devices
for controller
is converted
of ± 3 g with a bandwidth
requirement
proof
IMC System
measurement
The
system.
and
packages.
which
magnet
at 28 volts DC.
at the base
during
to the
is utilized
accelerometers
Telescope
signal
COSMEC
both
accelerometer range
the available
precisely.
40 minutes.
accelerations
three-axis
very
force
with the
only the remaining
analog
of the
amps after stabilization, The
associated
at the base are Apollo
is ± 45 volts.
An LVDT
at the tip are not available
we will describe
The rate gyros to measure
detector
centering
The
assembly.
as well as three-axis
gyros
used for evaluation,
the shaft.
with the LMEDs,
at the tip and base
the three-axis
a small
to the LMED
to the two-axis
associated
provides
package.
a 2.4-kHz
information. channel,
the computer
these
square Zero
positive
in frequency
instruments,
package,
system
2-3
i.e., six channels
acceleration acceleration
signal,
is represented by an increase
by a hardware
of an HP 9000 digital
and the
by a signal in frequency,
to the synchronization
are monitored
consists
per accelerometer
wave synchronization
as compared
signals
rate gyros.
channel. card
in the
computer
inter-
facedwith the COSMECInput/Output system.The HP 9000performsthe controlalgorithm,data storage,real-timeplotting, andthe strapdownalgorithm(describedin the next section).The HP 9000is a 32-bitmachinewith an 18-MHzclockrate. It includesan HPIB interfacecard,two 16-bit parallelinterfacecards,512kbytesof extra memory,anda floppydiscdrive. The benchmarktest timesfor processingthe presentcontrol andstrapdownalgorithms,plotting, andstorageare .010 to .013millisecondsper sample. The COSMECis a highlymodifiedAIM-65microcomputersystemusedforI/O processing.The primary purposesof the COSMECare to processthe sensorinputs, to provideforce and torque commandsfor the actuators,and to off-loadcontrol and sensordata to the computersystem. Currently, the COSMECperformsthesetaskswith 25 sensorinputs and nine actuator outputs, whilemaintaininga 50-Hzsamplingrate. Thecycletime for COSMECoperationis approximately 5 milliseconds. In our controldesignandimplementationweused8 controlinputsand8 measurement outputs. The inputswerethe X andY torquesof the IMC gimbals,the X andY torquesof the AGSgimbals andthe X and Y forcesof the two LMED packages.The measurements consistedof the X and Y detector(DET) positionoutputs,the X andY basegyro (BGYRO)rate outputsandthe X andY outputs of the LMED accelerometers.
2-4
/
o
=,.2.
N_
© g m_ _._
_.-
2-5
_
3.
the
MODELING
PROCEDURE
The first critical
step in control
process
that
procedure
that
the system 3.1
identification
Initial
designer
has
model
development
for flexible
model
design
and validation.
models
Realization
(FEM)
structures
by using
Algorithm.
that
the
three data
FEM
Below, we describe
a system
We then
identification
present
details
data
collected
(i) modify
an appropriate
which is in some sense a hybrid
based on the finite element
by comparing
is inadequate
options:
using
is usually
is evaluated
from input-output
essentially test
STRUCTURE
development
control
the Eigensystem
Procedure
shows
input-output
our
Modeling
gleaned
comparison
ACES
of
procedure.
finite element
information
this
the
the
model
The initial with
upon
THE
design is model
led us to of develop is based
Choosing
FOR
from the actual
FEM,
system
of the FEM
its time and frequency
for control the
system
identification developed
physical
design,
(ii) develop
and models
approach.
apparatus.
then
a new
algorithm
responses
the
model
If
control based
on
or (iii) develop
using system
a
identification
techniques. In this noise,
experiment
sine-sweeps
system
modes
to limitiations inputs
the
inputs
or delta-functions.
were
on the length
system
finite element DET-Y,
loops
model.
(ii) IMC-Y
As evidenced ent frequency
contain
1.4 Hz mode
the FEM
predicts
trends
than
FRF's
that
yielded
which
of Figures
lower frequency to generate
real behavior
that
the broad-band in the
response
(iv) AGS-Y
the FEM
finite
bode
TO
loop.
for the AGS-X
3-1
Also notice
to BGYRO-X
(FRF's)
plots
of the
(i) IMC-X
to
BGYRO-Y. differ-
For example,
Figure
model
that
time
significantly
the open loop LOS performance.
to BGYRO-Y
due
random
functions
predicted
to some of the modes
the
allowable
loops:
the structure. element
about
this is primarily
for four system and
random
information
dynamics
frequency
testing
loop the
peaks corresponding
for the AGS-Y
most
broad-band
with the corresponding
3.1.1-3.1.5,
by actually
influenced
the
and the fact that
to BGYRO-X,
to BGYRO-X most
allowed
show this comparison
(iii) AGS-X
to be either
We conjecture
were compared
those obtained
AGS-X
positive
inputs
was used
3.1.1-3.1.5
do not show the large magnitude shows analogous
data
and these
for the
chosen
the dominant
by the comparisons
that
the
test
to DET-X,
3.1.1 shows
were
and delta-functions.
excite
Figures
responses
system
of the time-histories
The input-output
of selected
The
the sine-sweeps
did not significantly
windows.
to the
past
Bode
plot does
The
FEM's
not also
8 Hz. Figure
3.1.2
as seen by Figure
3.1.3
loop, while the
FRF reveals
that between2 Hz and4Hz the phaselags-90° by as muchas 25° (evenwhen the computational delaydueto the 50 Hz samplerate is not takeninto account).This phaselag is probablydueto actuatorandsensordynamics. The FRF's ofthe IMC-X to DET-Y andIMC-Y to DET-X loops,shownrespectivelyin Figures 3.1.4and3.1.5,revealthat theseloopsareinfluencedverylittle by the flexiblemodesof the structure. It followsthat the IMC gimbalsarenot capableof controllingflexiblemodesto improveLOS performance.Thus,if oneconsidersthe four actuatorinputs(IMC-X, IMC-Y, AGS-XandAGS-Y) andthe four sensoroutputs(DET-X, DET-Y, BGYRO-X,BGYRO-Y), it is not necessary to feed backthe BGYRO outputs about
the behavior
outputs
of the flexible
do not contain
much
provided
by the BGYRO's.
the DET
outputs
by Figure above DET-Y,
were
and
above
the
loops
comparable
analysis FRF's
four
IMC-Y
In summary,
and accounting
should
account
space
of their
of the LMED's
data
cannot
outputs
contain
information
In addition,
gimbals
that
be improved
the decentralized AGS-Y
the DET
is not already by feeding
to the AGS gimbals.
to BGYRO-X,
performance finite
back
As illustrated
structure
described
to BGYRO-Y,
models
IMC-X
and actuator
and actuator
was in transition.
useful
system
actual
dynamics
sensors
loops. and
control some
to
test data.
described
four dominant
structure.
Also,
of the trends design
design.
Thus,
seen
studies,
the
in the
the
FEM
it was necessary
Modifying
to
the finite element
would have been a very time-consuming
to use the Eigensystem
Realization
It is important
actuators,
models
Algorithm
to note that generated
(ERA)
since all test
from
this data
dynamics.
input-output
In addition,
showed
involving
for preliminary
control
a model based upon
and actuators
structure
a centralized
and was thus adequate
the control
masses.
control
model
of the four dominant
obtaining
for the four sensors
with
element
and thus we decided
for the sensor
proof
that
for high performance
by using
We had difficulty itations
control.
for the AGS
that within
AGS-X
primarily
cannot
performance
also revealed
the
for the sensor
process
were collected
information
with a decentralized
the FEM or develop
state
IMC's
or the BGYRO
achievable
by the test
model
the
of the test data revealed
although
as a model
and expensive
useful
loops:
performance
that
modify
data
dominant
which
the achievable
of test data
to the
either
to develop
Thus,
analysis
revealed
was inadequate
(if any)
since the BGYRO's
to DET-X.
achievable
generated
modes
to the IMC gimbals
3.1.6, analysis
there
to the IMC gimbals
early
In particular,
data
from the
in the project MSFC
3-2
in joint
LMED's
the internal consultation
due to the stroke control
lim-
configuration
with the guest
inves-
tigatorsdecidedto havethe springsremovedfrom the LMED's andreplacedby internal position loops.The uncertaintyregardingthe dynamicsof the LMED's ledus to delaycontroldesignactivities involving thesedevices.Ultimately,it wasdecidedto simplyfeedbackthe colocatedLMED accelerometers to the corresponding LMED forceaxisandto determinesimpledynamicsfor these controllersby usingcrudemodelsof the loops,developedby informationprovidedto us by MSFC andour knowledgeof proofmassdevices.Aswill be seenin Section5,thesecolocatedLMED loops did providesignificantperformanceimprovement. 3.2
Model
Development
The collection usually steps
procedure
in developing
design
17th and DET-Y
the
for the
19th order and IMC-Y
implementation
filters
AGS-X
were effective
loops.
to BGYRO-X models.
model.
because
Figures
for control
first-order
all-pass
for the computational
delay.
AGS-Y
The control
discrete-time to design
maturity
to BGYRO-Y
design
models
design
design
models.
The
were
control
were respectively
Ideally,
directly
using
the AGS to BGYRO
in the theory
is
the final
filters
for the loops
the controller
We chose to design
of a greater
models
3.2.2 and 3.2.3 show
Note that
and
it is better
Algorithm
high fidelity
3.2.1.
loops to account
algorithm
models
IMC-X
for digitial discrete-
feedback
and software
to
loops
development
setting. show
from
the ERA
by Figure
were both 4th order
of the system
3.2.4-3.2.8
generated
show that
loops
of a control
for the continuous-time
FRF's
to BGYRO
Realization
to obtain
for the four major
to DET-X
using continuous-time
Figures
of test data
continuous-time
time representations
Eigensystem
as illustrated
models
into the AGS
models
the
and manipulation
an iterative
incorporated
Using
comparisons
the test data.
models
closely
in emulating
The resemble
of the
ERA
magnitude
plots
the FRF's.
the computational
3-3
models
of the
of Figures
As illustrated
delay
four
system
3.2.4,
3.2.5,
by Figure
in the system.
loops
with
the
3.2.7, and 3.2.8
3.2.6, the all-pass
AGSoX 10 0
TO BGYRO-X
....................
10-1
FIE MODEL
10-2 Z 10-3
10-4
......
AGS-X
10o
_02
TO BGYRO-X
FRF 10"i
ud
I
.j'
10 "4
W"
il',,t t l,( ti
i
E -i I
I t,-
10.5 I 10-2
,
10-1
10o FREQ
Figure
3.1.1
BGYRO-X (which sponding
A comparison
loop most
shows
influences
to some
of the
that
of the the
LOS higher
finite
,
FRF
data
element
performance) frequency
and model
and
does
modes.
3-4
h
10 i
10 2
IN HZ
finite
element
neglects not
show
the
Bode contribution
the
large
plot
for
the
of the magnitude
AGS-X 1.4
to
Hz mode
peaks
corre-
10 0 _
AGS-Y
10-I
FINITE
TO BGYRO-Y
ELEMENT
MODEL
10-4
10-5_ 10-2
.............. 10-:
...............101 FREQ IN HZ
AGS-Y
TO BGYRO-Y
10 o FRF lff t
10-2
10-3
10-4 ¸
......
10-2
'10_l FREQ
Figure
3.1.2
BGYRO-Y (which sponding
A loop
most
comparison shows
influences
to some
of the
that
of the the
LOS higher
finite
......
101
FRF
data
element
and model
performance)
and
frequency
modes.
does
3-5
'102
IN HZ
finite
element
neglects not
show
the
Bode contribution
the
large
plot
for of the
magnitude
the
AGS-Y
to
1.7 Hz
mode
peaks
corre-
AGS-X 2OO
,
TO BGYRO-X ,
v
,,v.
,
i
,i,.,
150 100
m
50 0 -50
a.
-I00
-150
FE MODEL
"2_2
FREQ
AGS-X
......
_02
......
102
IN HZ
TO BGYRO-X
200 150 100 u2 t_
5O 0 -50 -100
......................................................
-150
-201! .2
10-1
10 ! FREQ
Figure behavior
3.1.3 while
For the
the AGS-X FRF reveals
to BGYRO-X that between
loop 2 Hz
25 ° .
3-6
the and
IN HZ
finite 4 Hz
element loop predicts positive real the phase lags -90 ° by as much as
IMC-X 10 3
TO
DET-Y
..................
10 2 gd
FE
MODEL
10 x
ERE
_
x_
FREQ
Figure
3.1.4
A comparison
of the FRF data
loop shows that the finite element and the dominance of the IMC-X much
higher
and finite
IN HZ
element
Bode plot for the IMC-X
to DET-Y
model correctly predicts the small influence of the flexible modes mode but predicts much lower damping in the gimbal mode and
loop gain.
3-7
IMC-Y 10 3
TO
DET-X
i
i
t
t
!
t
A
I
I
I
L
I
J
i
A
I
10 2
101
10 0
10-1 1(_ 2
i
I
I
A
I
I
i
I
I
10-1
i
I
I
I
I
I
I
10 o FREQ
IN HZ
Figure 3.1.5 A comparison of the FRF data and finite element Bode plot for the IMC-Y to DET-X loop shows that the finite element model over estimates the influence of the flexible modes.
3-8
l
101
0
._
E
e_
Q
o_
o_
0
U
3-9
r,D
C
0 Wla_ C _0
"U
c.D 0
0
u_
0
O'9 cW
rru.l
O_
C_
3-10
(I)
AGS-X
TO
13 ERA
BRATE-X
STATES
-1 STATE
LOST
+4 STATES
FOR
+1 STATE
FOR
17 th ORDER
(IV)
AGS-Y
IN CONVERTING HIGHER ALL-PASS
FROM
FREQUENCY
DISCRETE-TIME UNMODELED
TO EMULATE
CONTINUOUS-TIME
TO MODES
COMPUTATIONAL
DESIGN
CONTINUOUS-TIME
DELAY
MODEL
TO BRATE-Y
17 ERA
STATES
-1 STATE
LOST
-2 STATES +4 STATES +1 STATE 19 th ORDER
FOR FOR FOR
IN CONVERTING DELETED HIGHER ALL-PASS
HIGH
FROM
DISCRETE-TIME
FREQUENCY
FREQUENCY
CONTINUOUS-TIME
MODES
COMPUTATIONAL
DESIGN
Figure 3.2.2 The final steps in developing control and AGS-Y to BGYRO-Y loops yielded respectively
3-11
CONTINUOUS-TIME
MODE
UNMODELED
TO EMULATE
TO
DELAY
MODEL
design models for the AGS-X to BGYRO-X 17th and 19th order continuous-time models.
(I)
IMC-X 6 ERA
TO DET-Y STATES
-4 SPURIOUS +1 DELAY
STATES STATE
+1 FILTER 4th ORDER
(II)
IMC-Y USED
(DISCRETE-TIME)
DISTURBANCE
STATE
DISCRETE-TIME
DESIGN
MODEL
TO DET-X IMC-X
TO
DET-Y
DESIGN
MODEL
(THE OPEN LOOP GAIN AND THE DAMPING OF THE DOMINANT MODE WAS MODIFIED, HOWEVER)
Figure IMC-Y
3.2.3 The final to DET-X loops
steps in developing control design models yielded 4th order discrete-time models.
3-12
for the
IMC-X
to DET-Y
and
AGS-X
TO BGYRO-X
10 o
10-I
ERA
MODEL
\
10-3
10 4
10-5 10-2
............... 10-1
i_ FR_Q
AGS-X
............... 101
io_
IN HZ
TO BGYRO-X
10o FR_ 10-I
t
10.2
10-3
10-4
10-5 10-2
10-1
10o FREQ
Figure generated
3.2.4 from
The
ERA
test
data.
model
for
the
AGS-X
x
IN HZ
to
3-13
BGYRO-X
loop
closely
resembles
the
FRF
AGS-Y 100
TO BGYRO-Y
....................
10-I
ERA
MODEL
t_ t
0.2
_
10.3
10 4
1@5 10-a
,
10-1
10 o FREQ
AGS-Y
10 o -
l
,
i
101
L
,
10 a
IN HZ
TO
BGYRO-Y
10-1
10.2
10-3
10-4
10-5 10. 2
...... FREQ
Figure generated
3.2.5 from
The
ERA
test
data.
model
for
the
AGS-Y
_0 2
IN HZ
to
3-14
BGYRO-Y
loop
closely
resembles
the
FRF
AGS-X 2OO
,
TO
,
,
,
BGYRO-X
,,,
,
,
,
,
,,,
150 100 50 0 U3
/ i
-50 J -100 ERA
-150
MODEL
10-1
°2Op(y2
10 o FREQ
AGS-X
101
lo 2
IN HZ
TO BGYRO-X
200 150
50
io
1
-50
-_oo_
............................................ '_
"150 t -2
010_
2
10.1
i
,
_
,
10 o
,
,_1
FREQ
Figure
3.2.6.
As
shown
modeled
the
computational
here delay
for
the
AGS-X
by using
to
all-pass
3-15
IN HZ
BGYRO-X filters.
loop,
the
ERA
models
effectively
IMC-X
TO
DET-Y
101 i
i
i
i
i
i
i
i
i
i
i
/,?-_
.J
ERA
MODEI_ .............................
"
FRF
10°
10-1 10-2 FREQ
Figure 3.2.7 The ERA from test data.
model
for the IMC-X
IN I--IZ
to DET-Y
3-16
loop closely
resembles
the FRF
generated
IMC-Y
TO
DET-X
10 z
Z
101 _
10 o 10-2
I
I
t
I
f
I
I
I
I
I
[
L
ERA
model
for the
I
i
I
I
I
t
t
I
l
L
I
10 0 FREQ
Figure 3.2.8 The from test data.
I
10-1
IMC-Y
3-17
loop
closely
1
]
101
IN HZ
to DET-X
I
resembles
the
FRF
generated
4.
CONTROL
DESIGN
Once
settled
we had
structure
of the
a three
step
IMC gimbal
(ii)
design
of the AGS gimbal
(iii)
design
of the LMED
Below,
we give details
scribing
the
resultant
THE
design
integrated
delayed
Section
5. The sample
4.1
Design The
Process
design
essentially
processes
identical.
as a disturbance white
noise process
as the
positive
parameter
the low frequency synthesized
IMC-X
a filter
(i.e., modes
[7-8] by minimizing J(e)
the
along
to DET-Y
loop
with
data
controller
Loops
with
ACES
the
paths
IMC-Y
1/(z-
to be tracked
1-{-e), which
zero.
This filter accounted
below
1.5 Hz).
the quadratic
Optimal
loops
closed)
is
was 50 Hz.
to DET-X problem
loop were
was formulated by filtering
a discrete-time
for the system
Projection
de-
performance
w_ was modeled
approximates
data
the
all feedback
feedback
and
experimental
describing
4.1.1, for each loop the control
The disturbance
e approaches
modes
step
Experimental
to IMC
by Figure
problem.
wl through
for each
(i.e.,
Detector
As illustrated
for the
loops.
rate for each of the three
for the
tracking
procedures
controller
for the
design
and
accelerometer
improvement.
of the
control
loops,
to base gyro loops,
performance
architecture,
process:
force to colocated
of the
STRUCTURE
controller
to detector
improvement until
ACES
on a decentralized
was essentially
(_) design
FOR
control
a
integrator
biases
and
laws H(z)
also were
cost function
= lim E[qW(e)q(e)-{-
puW(e)u(e)],
p > 0.
/c---* oo
The
controllers
trollers
implemented
contained
integrators
both loops the design controller
gains
models
were the limiting which
were 4th order
are given in Appendix
The resultant
performance responses
to the x and
y axes
of the Base
eliminate
system
biases
as e --_ 0. Thus,
to effectively
eliminate
while the controllers
the
the implemented line-of-sight
implemented
con-
biases.
For
were 3rd order.
The
A.
improvement
loop and closed-loop
the
were able
controllers
is illustrated
by Figures
of the x and y axes of the detectors Excitation
and also improved
Table.
Notice
that
respectively the
the LOS performance
tracking. 4-1
4.1.2-4.1.3
feedback
which
show open-
to pulse
commands
loops
by providing
were
able
low frequency
to
4.2
Design
Process
The design quently
processes
to be referred
design
Entropy
of varying
only the modes
The Maximum
controllers
which
yielded
the ME approach Figure
varies
over
loop transfer
and were unstable region
robustness
Figure full-order
4.2.2
than
implication
controllers.
is that
of the compensator
two highest by Figure
authority
frequency 4.2.5,
implying several
when implemented.
the
in the
those
In practice,
The higher
interval,
ME design
shown was able
were then
In our control
designs
LOS perfor-
in developing
implemented.
on the
The phase
the
times.
stable
The utility
of
of a full-order
LQG compensator
plot of the expect,
the ME designs
Thus
phase
of the
Nyquist
As one would
However
region.
yield
Notice
corresponding
these
became
the ME designs
notched in the
design that
designs
positive
provided
robust
controllers actually
on the
were real in
the needed
performance
that
provide
insight
reduced
the high frequency
modes
models
to robustify
4-2
of Figures
the controller
magnitudes
reduced
order
into the choice
of the
controllers.
had high gain, i.e., the
3.2.4 and notches.
of a
An-
order that
shape
robustness.
are effectively
aid in synthesizing
ERA
magnitude
the ME compensator
thus providing
ME designs
and is a numerical
modes
that
compensators,
the ME designs
controllers
continuous-
controllers
to be crucial
design
of ME uncertainty
performance
the full-order
that
region.
influence
of the LQG
the modes
the open-loop
when
3 Hz).
rate feedback.
in the performance describes
improvement
(i.e., less than
toward
These
dominate
proved
influenced
4.2.1-4.2.3.
the origin
tending
compensator
are smoother
order
encircles
most
for the
mode.
prewarping.
of ME uncertainty
region
that
for the Y-loop
and robustness.
design
performance
modes
3, the
model
was used to synthesize
with frequency
robustness
influence
this frequency
function
the performance stability
the
the
(subse-
in Section
while the design
Similarly,
synthesis
authorities
by Figures
in the performance
widely
nonrobust
describes
model
3 Hz since these modes
(ME)
significant
modes.
to BGYRO-Y
As mentioned
For the X-loop
(MEOP)
control
less than
is illustrated
4.2.1
compensator
continuous-time
transformation
Entropy
loop and the AGS-Y
1.7 Hz and 2.3 Hz bending
Projection
orders,
Loops
were very similar.
model.
were
by using the bilinear
we penalized mance.
continuous-time
Optimal
Gimbal
to BGYRO-X
was a 17th order
LOS performance
time controllers discretized
to AGS
were 1.4 Hz and 2.4 Hz bending
most influenced Maximum
Gyro
to as the X and Y loops)
was a 19th order
LOS performance
Base
for the AGS-X
model for the X-loop
Y-loop
other
for the
3.2.5.
That
As illustrated
is, the controller
notcheswereincreasedin both width anddepth. The controllerswhich yieldedthe best performancewhenimplementedwerea 4th order controller for the X-loop and a 6th ordercontrollerfor the Y-loop. The controllergainsarepresented in AppendixA. The resultantperformanceimprovementis shownin Figures4.2.4--4.2.7 which showopenand closedloop responses of the detectorsandbasegyrosto pulsecommandsto the x andy axesof the BaseExcitation Table.Noticethat significantperformanceimprovementwasachievedin both the detectorandbasegyroresponses 4.3
Design
Process
of the
In this subsection to as LMED-1 The
control
and hereafter
while
design
the corresponding
LMED
the
two-axis
was based LMED
Force
the two-axis LMED
proof-mass
axis.
(ii) LMED-1Y
LMED-2Y
to ACCEL-2Y.
It was assumed
assumed
dynamics
From LMED
4.3.1
controller
it follows
and along
that
device
closest
to the
Thus
closest
to the base will be referred
tip will be referred
that H(s)
the open
loops is shown
the transfer
for control
(iii) LMED-2X
of each
in each loop. in Figure
function
from
a given axis) to the force applied
outputs
design
to ACCEL-2X,
loop dynamics
can be utilized
to as LMED-2.
accelerometer
the four loops utilized
to ACCEL-1Y,
for each of the feedback
Figure
location
the same
LMED
Loops
back each of the four colocated
to ACCEL-1X,
so that
device
on feeding
LMED-1X
was identical
to Accelerometer
of the
A block
to
were (i) and
(iv)
four loops
diagram
of the
4.3.1.
the
beam
(by the LMED
velocity along
(at the
the same
given axis) is
/_5¢ = H(s)s 2 + Ds + k._kd _p s 2 + D--s+
The
design
frequency
goal was to choose (say around
10 Hz) in order objectives
stroke
limitations
low frequency, filter.
could of the
low frequency
damping
LMED
stroke
proof
positive
above
Thus,
transfer
real to some
by simply mass
even this controller a first order
the
to the beam
be accomplished
is not implementable.
Unfortunately,
such that
1 Hz) and remains
to provide
design
H(s)
devices,
modes
choosing
H(s)
this controller,
the stroke
high pass filter was then 4-3
significantly
in this frequency
H(s) was initially
caused
function
chosen limitations
cascaded
= 1/s 2. which
is positive higher
real at low
frequency
band.
In theory
However, has very
with the second
the
due to the high
to be a second-order to be violated.
(say
gain
at
low-pass To limit the
order low pass
filter. The resultantcontrollerwasthus of the form ks H(s) The
low and
high pass portions
transformation control
gains
The Figure
with
It is seen that
more
the LMED
clearly
closed
in Figures
seen if Figures
of the
4.3.5-4.3.7 disturbance.
AGS gimbals,
the LMED frequency
in the
controllers
and was then
beam
performance
4.3.3
and 4.3.4 which
frequency
which When
vibration
that
harmonics
integrated
damping
to a BET-X
significantly ACCEL-1Y
with the feedback
the LOS performance
in the detector
responses.
4-4
loops.
The
to the higher
pulse
even
and ACCEL-2X.
of the responses
reduced.
Similar
and ACCEL-2Y
especially
frequency
is demonstrated
magnitude
controllers
4.3.2.-4.3.7.
pulse disturbance.
of ACCEL-1X
both the peak were
the bilinear
of the
in Figures
to a BET-X
show the responses
reveal
in each
is demonstrated
in providing
improvement
by using
A.
of BGYRO-Y
aided
show the BGYRO-Y,
loops improved
implemented
vibration
especially
responses
separately
are given in Appendix
loop
higher
pulse
of the higher
controller
were discretized
and closed loop responses
loop accelerometer
influences
BET-Y
prewarping
loop attenuation
The
The closed the
frequency
4.3.2 shows the open
harmonics.
of the controller
of the discretized
closed
= (s + _)(s _ + 2_,_,,s + w_,)"
involving by reducing
results
responses the IMC
and are to a and
the influence
..,._
l wt
r'
FILTER
z -
--_=_
H (z)
- CONTROLLERS
J(e)
Figure
4.1.1
The
loop was formulated
_=_
--
control
lim
SYSTEM
1+ •
LOW
as a disturbance
w, _- white
DESIGNED
E[qW(e)q(e)
problem
for both tracking
ACCOUNTS
1
,,@--=-=
WERE
white noise
problem.
4-5
AND
FREQUENCY
MODES
noise
BY
MINIMIZING
+ 9uW(e)u(e)]
the IMC-X
BIASES
FOR
to DET-Y
p > O.
loop and the IMC-Y
to DET-X
OPEN
LOOP
RESPONSE
5.0
STFIRT CONTR, }L
71
^10
TO BET-X
m
PULSE
1/
ON
4.0 m-
3.0
_,..'_t/'_,_-
y
I
,IIll Igl
Lr--
1.0
'dIlUI '
Z -.0 B B m
_EC
m
,
l
-5-_.
0 '
I
• :7;
,
,
.6
I
,3
z
Ii
12
At
I_
II
18
:'
TIME (SECS)
RESPONSE
S.0 2X10
WITH
IMC
TO DET
FEEDBACK
LOOPS
iS
-I m
4.0
m m
X E
...... lii"
"wl,._
z 1,0 rm
m
I XI ) -5-_.
Figure addition
0 '
I
I
• :2',
4.1.2. The IMC to bias correction
I
.6
I
I
,
,
_.4
,3
to DET feedback loops to improve the DET-X 4-6
were able to provide response to a BET-X
I
,
,
t7.7
low frequency tracking pulse disturbance.
,
:3,D
in
OPEN
5.0
LOOP
RESPONSE
TO BET-Y
PULSE
m
-×i0
1:21
-I .0
-e. o
E-'.-:-_-:. 0 LO
'_ , I_"
_ii*',,
-4.
1 I
I
I
TIME
RESPONSE
WITH
-t
IMC TO DET
START' COI4TR')L
-1 m
LOOPS
I I ,"16/09 Oil P
1:21 Irr
IlL)1,
-
, t! _.i_,,
tl
. 71 m m
-5.
FEEDBACK
.0
-2.0
-4
:3,0
(SECS)
5.0 E)< i 0
i
e
.¢j
.
_,.yl •/'l
I'_. i',_.. Yt
!
!1,
i 5EC
'
l
.3
,
I
_
.6
[
I
_3
t
!
I "-
t
Xl ) i
1
l. 8
2.
7'.4
I
L
2..7
:3.E_
TIME (SECS)
Figure 4.1.3. The IMC to DET feedback in addition to bias correction to substantially
loops were able to provide low frequency tracking improve the DET-Y response to a BET-Y pulse
disturbance.
4-7
COMPENSATOR
PHASE
IN THE
REGION
PERFORMANCE
SOLID-= W/OUT MAXIMUM DASHED=-WITH
2o8
ENTROPY
MAXIMI]M
ENTROPY
lo8
uu r_
i:i .........
"4
...... '::::--LLLII.I. ""
........... l..i" ,,
-lo8
-20O
I
i
i
i
I
1
2
3
4
5
HZ
Figure positive
4.2.1. Maximum Entropy design real in the performance region.
rendered
4-8
the
compensators
for the
AGS
to BGYRO
loops
COMPENSATOR
MAGNITUDE
i
SHAPE IN THE PERFORMANCE
'l
i
REGION
;
)
SOL/D-= W/OUT MAXIMUM DASHED=-WITH
ENTROPY
MAXIMUM
ENTROPY
102 • / .........
-4 //
J"
,\
/" / _'\
// \
('
,
/ / \'\
,,
"\
10i
/
I
I
I
1
1
2
3
4
5
6
HZ
4.2.2.
For the
AGS
to BGYRO
loops
Maximum
Entropy
design
magnitudes in the performance region, thus providing performance that the robust controllers were effectively reduced-order controllers.
4-9
smoothed robustness
out
the
and
compensator also indicating
COMPENSATOR
NOTCH
103 SOLID= W/OUT MAXIMUM DASHED=
WITH MAXIMUM
ENTROPY ENTROPY
lo 2 \
/
'\
/
\
/
/ /
\ 10 !
10 s
4 I
2
;
8
1o
I
|
x2 I
1',
1;
HZ
4.2.3. high
For frequency
the
AGS modes
to BGYRO by increasing
loops their
Maximum width
Entropy and
4-10
depth.
design
robustified
the
notches
for the
OPEN LOOP RESPONSE 5.0
TO
START CONTR
71 m
4.0 p,m
m
3.0
I/llllil illl liil
2.0
1.0
Ill
-.0
1
.0
TIME (SECS)
RESPONSE
WITH AGS TO BGYRO
5.0 --
m
LOOPS
1/'1(9/98 kJL ON P
START CONTR
-'1
ZXIO
FEEDBACK
In
4.0 L--
X
x-
_2.8
&t
"lfil/Iv
_
1,0
SF'C _.5
o C"t
_-
_
•2_i
,
,
.:7
I
t
.8
,5
t
I .2
_
I ._
i
J
,
1.8
i
t
2.1
l
I
F'.4
TIME (SECS)
Figure 4.2.4. The reduction beam vibrationof the AGS substantially improve the DET-X
response to a BET-X
4-11
to BGYRO
feedback loops was able to
pulse disturbance.
OPEN
LOOP
RESPONSE
TO BET-X
PULSE
0"02 / 0.0151 0.01
_, 0.oo5
+° e_.0.005 -0.01 -0.015
-0.020
1_0
I
t
15
20
25
30
TiME (SECS)
RESPONSE
WITH
AGS
TO BGYRO
FEEDBACK
LOOPS
0"02 I 0.015' 0.01
;>.
II
!
0.005
6 -0.005 -0.01 -0.015 _
-0.020
10
L
15
2'0
9_5
30
TIME (SECS) Figure 4.2.5. For a BET-X pulse a comparison response with the AGS to BGYRO feedback loops of the beam vibration.
4-12
of the open loop BGYRO-Y response to the closed reveals significant closed loop damping
OPEN
LOOP
RESPONSE
TO
BET-Y
0
i- I
-I
-2
1
0 _=. ,.=.
i !,_
ll!!jit
m
El
-4
.0
V
tl'_u1
p
-5
, i
• :3
!3, • 0
.6
TIME (SECS)
RESPONSE
WITH
AGS
TO
BGYRO
5.0 -XIO -I
FEEDBACK
START i CON'rR,
m
LOOPS 9
1/
5:
ON
)L
.0
=- li, l_!
-2.0
-'
l,lll,,l/.ll,
0
%;%(, "%._,,-.
l',jlg',._j' _,l' dr'J"b[ _r"
--4 . E1 I 5Ei-j I
-5,_
•
•
.Ei '
.J
'
.9
11 ,
I
' 1._
1.2
1.8
I
2.
;:'.4
to BGYRO
feedback
c
:3,0
,
TIME (SEem)
Figure
4.2.6.
to substantially
The
reduction
improve
the
in beam DET-Y
vibration response
of the to a BET-Y
4-13
AGS
pulse
disturbance.
loops
was
able
OPEN 0.02 0 • 015'
LOOP
RESPONSE
TO BET-Y
PULSE
i
0.01 0.005
6 0
o -0.005 -0.01
i
lo
_5
i
I
TIME
RESPONSE
WITH
io
2_
3O
(SECS)
AGS TO BGYRO
FEEDBACK
LOOPS
0.02 0.015 0.01 0.005
6
o -0.005 -0.01 -0.015
"0"020
5
i'0
15
2'0
25
30
TIME(SECS) Figure 4.2.7. For a BET-Y pulse a comparison response with the AGS to BGYRO feedback loops of the beam vibration.
4-14
of the open loop BGYRO-X response to the closed reveals significant closed loop damping
fc
kmkd x s/p
p= beam
acceleration
x s/p= relative
velocity
of proof mass
m = mass of proof mass f c = force
applied
k s = position D = inherent k
loop stiffness viscous
rp = position
with
4.3.1. control
The
damping
of the LMED
mkd = motor force constants
H(s) = compensator
Figure
to structure
LMED
designs
transfer
function
command.
assumed
that
this block
law H(s).
4-15
diagram
described
each feedback
loop
OPEN
LOOP
0.02
RESPONSE
,
TO BET-X
1
PULSE ,
0.015 0.01 0.005
6
o
c3 _-O.OOfi
4).01 -0.015
-0.02{
3O
TIME (SECS)
RESPONSE
WITH
COLOCATED
LMED
FEEDBACK
LOOPS
0.02 0.015 0`01 0.005
_-0`005
-0.01 -0.015
-o.02_
}
1'o
io
i_
23
_o
TIME (SECS) Figure
4.3.2.
response with harmonics.
For a BET-X the
LMED
loops
pulse closed
a comparison reveals
some
4-16
of the closed
open
loop
BGYRO-Y
loop damping
response
of the higher
to the
frequency
OPEN
0.6
LOOP
RESPONSE
TO BET-X
PULSE
0.4
0.2
m
0
< -0.2
-0.4
-0.6 0
3O TIME
RESPONSE
0.6
WITH
(SEGS)
COLOCATED
LMED
FEEDBACK
LOOPS
0.4
O.2 X
o
cJ
