The major components of a design and operational flight strategy for flexible structure control systems are presented. In this strategy an initial distributed parameter control design is developed and implemented from available ground test data and on-orbit identification using sophisticated modeling and synthesis techniques. The reliability of this high performance controller is directly linked to the accuracy of the parameters on which the design is based. Because uncertainties inevitably grow without system monitoring, maintaining the control system requires an active on-line system identification function to supply parameter updates and covariance information. Control laws can then be modified to improve performance when the error envelopes are decreased. In terms of system safety and stability the covariance information is of equal importance as the parameter values themselves. If the on-line system ID function detects an increase in parameter error covariances, then corresponding adjustments must be made in the control laws to increase robustness. If the error covariances exceed some threshold, an autonomous calibration sequence could be initiated to restore the error enveloped to an acceptable level

Mettler, Edward

Milman, Mark

English

NASA Technical Reports Server

tN87- 16 040
SYSTEM IDENTIFICATION AND MODELING
FOR CONTROL OF FLEXIBLE STRUCTURES
Edward Mettler
and
Mark Milman
Jet Propulsion Laboratory
California Institute of Technology
Pasadena, California
First NASA/DOD CSI Technology Conference
November 18-21, 1986
419
https://ntrs.nasa.gov/search.jsp?R=19870006607 2020-03-20T12:04:32+00:00Z
LARGESPACESTRUCTURESACTIVECONTROL
High performance control systems for flexible structures which provide
adequate robustness require synthesis techniques that incorporate the
interdependencies between performance objectives and model fidelity. Such levels
of fidelity are not possible to achieve via ground testing alone. This is due to
the fact that differences in ground and space environments can significantly
change the measuredparameters. In addition, the time-varying nature of the space
environment requires real-time "tracking" of key structural parameters.
An on-orbit ID function can provide the real-time knowledge of plant
characteristics which greatly influence control performance, such as flex-body
parameters, self-generated disturbances, shape distortions, actuation and sensing
dynamics, etc. This information is then available for updating the controller
plant model, and mayserve as the data base from which a control function can make
adjustments to autonomously tune the system performance and stability margins. I
In this discussion, the focus will be on those identification and modeling
aspects primarily associated with large space structure dynamical control.
QUASI TATIC
• STIFFNESS
• INERTIA/CM
• DEFORMATIONS
ADAPTIVE_
• PARAMETERERRORS
• MODELTRUNCATION DYNAMIC
• NONLINEARITIES
CONTROLSYSTEMS
I
EMBEDDED I IDYNAMI CAL I
MODELS I
j,_SYSTEM IDENTIFICATIONt_
DYNAMIC
• MODAL FREQIDAMPINGI
I • MODE SHAPES
I CONTROL •TRANSIENTDIsTURBANcEsANDSTOCH STIC
LFIGURE
• SURFACE DEFORMATIONS
• RELATIVE ALIGNMENTS• DISTURBANCE SUPPRESSION
• VIBRATION DAMPING
• LOS STABILIZATION
420
GENERALFLEXIBLESTRUCTURECONTROLMETHODOLOGY
In general, the high frequency dynamicsof LSSwill not be well
known and the order of the dynamics will be too large to design an effective
wideband control system. Newmethods are required to control the low
frequency modeswithout exciting the higher frequency dynamics inherent
in the structure and to constrain the control gains from spill-over into
the higher modescausing instabilities or performance loss. This area is
a major thrust in the extension of modern control theory and the emerging
cross-discipline technology of active structural control covers a wide
range of interrelated design and system functions.
As depicted below, the general structure control methodology is to
phase stabilize modes lying within the control bandwidth (in-band modes) and
to gain stabilize structurally damped modes lying outside the control band-
width. Such active control methods require very precise knowledge of the
locations of the in-band modes in order to allow correct phase stabilization
(such sensitivities are even more pronounced when actuators and sensors
are non-colocated). Because such precise knowledge of system dynamics is
not possible via ground testing alone, on-orbit system identification is
required.
dB GAIN
"--DI STURDANCE BANDWIDTH--"I _TRANs ITION__I
I REGION I
IN-BAND MODES 1 }
• A • I
. _ FREQUENCY-_-I,-
= CONTROLBANDWIDTH_-_ "_ I_ U!" -C OUT OF BAND MODES
= PHASE STABLE ---I= GAIN STABLE---,,-
(PRECISE KNOWLEDGEOF IN-BAND MODES
NEEDEDFOR PHASE STABILIZATION)
421
DISTRIBUTED PARAMETER MODELING, APPROXIMATION AND CONTROL
Control design for distributed parameter systems introduces a number of
complexities that are either not present or relatively innocuous in the design
process for lumped systems. A most fundamental issue is selecting an appropriate
reduced order model so that system performance objectives can be met. As is
well known, a poor selection can severely degrade performance and in some cases
yield closed loop instabilities. Under reasonable hypotheses on the finite
dimensional approximation schemes, the distributed parameter LQG design approach
utilizing a functional gain convergence criterion achieves a correct match
between model order and desired performance 2. In addition, LQG also has the
desireable property that new physical objectives are easily incorporated into
the design process through the state-cost functional.
We have successfully applied this distributed parameter LQG design
methodology to large-scale simulations of control systems for flexible struc-
tures. The chart below contains time history plots of controller performance
based on this approach. Because a functional gain convergence criterion is used,
these controllers are very near optimal for the full distributed parameter system.
SENSORS
ACTUATOR_
M_ !Si-I
BEAM
0.50
0.25
ZO 0
<,.,-
wCI:
.jIM
-0.25
Z
< -O,5O
0
DISTRIBUTED PARAMETER ANTENNA POINTING
AND VIBRATION CONTROL SYSTEM
WITHOUT RMS SURFACE
ERROR CONTROL
RMS
_"_ = RIGID BODY ANGLE
[ t [ [ I I I I I
1 2 3 4 5 6 7 8 9 10
S6¢
0.50
0.25
o<_
uj(X:
.j IM -0.25L_
Z
< -0.50
CONTROLLING RMS
SURFACE ERROR
RMS
\
0 = RIGID BODY ANGLE
I I I I I I I I I
0 1 2 3 4 5 6 7 8 9 10
$ec
422
ON-ORBITSYSTEMDYNAMICSIDENTIFICATIONMETHODOLOGY
The need for developing a system identification (ID) on-orbit methodology is
driven by practical considerations. The post-launch changes in a physical
system's characteristics must first be identified before the mission operations
proceed with confidence; structural dynamics identification is essential for
accomplishing active vibration control of large structures; and system
characterization in space is required to verify the accuracy and adequacy of
ground-based models for predicting and modifying in-flight performance.
The technical challenges involved in performing on-orbit identification are
significant. As opposed to ground testing which involves elaborate test beds with
virtually unlimited sensing, excitation, and computational resource, the on-orbit
situation is constrained to only a few sensors, operationally viable excitations,
and restricted computational resource. 3 The diagram below illustrates the
integrated systems approach for on-orbit dynamics identification. The methodology
involves a multi-stage identification process starting with robust nonparametric
survey methods, and progressing to more refined parameter determination
algorithms.
I
'MODEL WITH UNKNOWN
PARAMETERS
_,_, (_, n
I THRUSTER
EXCITATION
T PROOF-MASSACTUATORS
i
DYNAMIC
DI STURBANCE
?t'
SYSTEMI _ r*k
RESPONSE _/
i
I FFT I
1 I,l,l,lll,I,
PRELIMINARY ID
AND FILTERING I
INITIAL II IllES IMATES J I I
_ _ .
TIME DOMAIN L,_FREQUENCY DOMAIN
HOPTIMAL' POTDES'O"
lANDSENSO,_PLACEMENT/
o_ - FREQUENCY
,_ - DAMPING
- MODE SHAPE
n - MODEL ORDER
423
IDENTIFICATION EXPERIMENT CONSTRAINED INPUT DESIGN
On-orbit identification of modal frequencies of a 15 degree-of-freedom Power
Tower model of the Space Station was considered using maximum likelihood
estimation. Low frequency modes can successfully be identified by the proper
application of multi-directional thruster inputs in the form of force and torques
in orthogonal spaces. Higher frequency modes, however, are insufficiently excited
to permit accurate estimation due to thruster power and bandwidth limitations.
Among the inputs considered, it is concluded that staggered pulse sequences are
superior for obtaining a more accurate estimate of the unknown parameters. When
staggered thruster pulses are used the identification process may toleratean
initial parameter estimate error of up to 50% of the nominal values for the lower
frequency modes. Further research is needed for the identification of modal
dampings.4,5, 6
n
n
.... .I-....
MODE I, 0.129 Hz MODE 2, 0.163 Hz
_Z-
MODE 4, 0.178 Hz MODE 5, 0.343 Hz
MODE 3, 1.172 Hz
I
MODE 6, 0.357 Hz
3O
¢Y
0
,,, 20
W
I--
10
0
' ' ' STAGGERED PULSE
STAGGERED DOU BLET
WHITE NOISE
- r_
!'/
I 2 3 4 5 6 7 8 9 10 11 12
MODE NUMBERS
424
ROBUSTNESSENHANCEMENTOFLQGCONTROLLERS
Our initial approach to control design utilizes infinite dimensional LQG
theory to design compensators that are robust with respect to errors introduced by
model truncation. A second error source that requires accommodationare those
errors introduced by parameter error. At the present time two approaches have
been developed and validated to improve the robustness characteristics of LQG
compensators with respect to parameter error. The first approach synthesizes
structured uncertainty and loop transfer recovery techniques to achieve a
systematic process for making trades between performance and robustness 7. In
terms of synthesis, the method involves adjusting the weighting matrices in both
the regulator and estimator portions of the LQGdesign problem in a way that
reflects the structure and magnitude of the modeling uncertainties. This
uncertainty information could be obtained from the covariance analysis provided by
an on-line identification process. An alternative approach that has also been
developed consists of a sensitivity optimization of the eigenvalues of the closed-
loop system8. A nominal LQGcompensator is used to initialize the nonlinear
programmingproblem associated with the optimization. Constraints in the form of
stability margins are imposed in the optimization to insure adequate trades
between performance and robustness. On the models to which these methods have
been applied, both approaches have yielded substantial improvement in robustness
over o+o_A_rdLQGcontrollers.
The chart below illustrates the overall design methodology, and how the
sensitivity optimization method can increase observer bandwidth in an LQG
compensator and simultaneously increase its robustness properties.
SYSTEM MODEL
PERFORMANCE
OBJECTIVES
HIGH PERFORMANCE ROBUST DESIGN
DESIGN METHODS METHODS
, ,
• DISTRIBUTED I
i PARAMETER
CONTROL • STRUCTURED UNCERTAINTIES
=' THEORY UNCERTAINTY •
FREQUENCY
• MODEL • DAMPING
REDUCTION • SENSITIVITY • MODE SHAPES
OPTIMIZATION
I © I
jvL HIGH PERFORMANCE/ROBUST CONTROLLAW
25
>-
¢J
Z
Lu 20
,o
g,.
,_ 15
Z
0
z
_ 10
0
_ 5
z
OPTIMAL
BANDWIDTH
f I I
0.5 1.0 1.5
OBSERVER BANDWIDTH, 1/uB¢
I
2.0
425
IDENTIFICATIONANDCONTROLFLIGHTEXPERIMENTS
A natural progression of technology development, from analysis and simulation
through laboratory physical test beds to full scale flight experiments, is basic
to major CSI research initiatives. The COFSprogram and the ATSE(Antenna
Technology Shuttle Experiment) provide the meansto space test and enable
application readiness of advanced identification and control technologies.
The objectives of the ATSEin identification and control have the underlying
theme of an integrated system capability to support robust precision
stabilization/control of the MSAT(2nd generation 20-meter dish). This can be
further described by the following criteria which include operational constraints,
system design limitations, in-situ performance maintenance, and synergistic use of
identification/control techniques:
a) Integration of identification with active structure control
for LOSstabilization
b) Identification in operational mission time
c) Design for flight system hardware limitations
d) Input design for controlled excitation 9,10
e) Unify frequency and time domain techniques for in-flight
support
I
I
I
FIRST FEED-BOOM MODE (1.01 Hz)
FIRST REFLECTOR-BOOM MODE (2.26 Hz)
/
SECOND FEED-BOOM MODE (6.60 Hz)
SECOND REFLECTOR-BOOM MODE (9.52 Hz)
426
POINTINGJITTER CONTROL EXPERIMENT
The objective of this experiment is to control the dynamic motions
of both feed boom and reflector boom in order to maintain precision pointing
of the feed to dish llne-of-slght. Distributed accelerometer signals
are processed onboard by selected algorithm options to actively control
boom dynamics via proof-mass actuators located at mldspan and tip of each
boom. Parameter updates from identification processing at the payload
operations control center (POCC) are used to tune the controller-embedded
reduced order plant models. Both regulation and tracking control policies
are to be evaluated in a sequence of sub-experlments.
LOS JITTER CONTROL
COMPUTATION
MEASUREMENT KAL/ViANFILTER/ PROOF-MASS
SYSTEM OPTIMAL CONTROL ACTUATION
FEEDBOOM
REFLECTOR
BOOM
ON ORBIT
ON GROUND
HHI STORY
_= _ +KZ I
1
A,K,C
POCC
GROUND-BASED
PARAMETER
IDENTIFICATION
X = STRUCTUREDISPLACEMENT
Y = PROOF-MASS DISPLACEMENT
427
SUMMARY
We have presented the major components of a design and operational
flight strategy for flexible structure control systems. In this strategy
an initial distributed parameter control design is developed and implemented
from available ground test data and on-orbit identification using sophisticated
modeling and synthesis techniques. The reliability of this high performance
controller is directly linked to the accuracy of the parameters on which the
design is based. Because uncertainties inevitably grow without system moni-
toring, maintaining the control system requires an active on-line system
identification function to supply parameter updates and covariance information.
Control laws can then be modified to improve performance when the error
envelopes are decreased. In terms of system safety and stability the covariance
information is of equal importance as the parameter values themselves. If
the on-line system 1D function detects an increase in parameter error covar-
iances, then corresponding adjustments must be made in the control laws to
increase robustness. In one scenario for example, if the error covariances
exceed some threshold, an autonomous calibration sequence could be initiated
to restore the error envelope to an acceptable level.
GROUND TESTING
LAUNCH/DEPLOYMENT/
CALIBRATION
ON-LINE
IDENTIFICATION
428
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7.
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429


System identification for modeling for control of flexible structures

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