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Structural Mode Significance using INCA
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3346
Frank H. Bauer*, NASA/Goddard Space Flight Center
John P. Downing’, NASA Goddard Space Flight Center
Christopher J. Thorpe( Fairchild Space Company
TIROS-N (ATN) [l] weather satellite series, and
the Cosmic Background Explorer (COBE)
spacecraft and instruments.
Structural finite element models are often too
large to be used in the design and analysis of
control systems. Model reduction techniques
must be applied to reduce the structural model to
manageable size. In the past, engineers either
performed the model order reduction by hand or
used distinct computer programs to retrieve the
data, to perform the significance analysis and to
reduce the order of the model. To expedite this
process, the latest version of INCA has been
expanded to include an interactive graphical
structural mode significance and model order
reduction capability.
The Interactive Controls Analysis (INCA)
program was developed at NASA’s Goddard
Space Flight Center (GSFC) as a computer aided
control system design tool primarily for use by
engineers in the Guidance and Control Branch.
Initial development of the INCA program began
in 1982 with the first release of the program to
members of the Guidance and Control Branch in
1983.
Since then, INCA has been used
extensively to design or analyze control systems
for all of Goddard’s spacecraft programs.
Numerous flight proven designs have been
developed or validated using INCA’S analytic
capabilities. These include the Earth Radiation
Budget Satellite (ERBS) spacecraft, the Advanced
*Head, Project Support Section,
Guidance & Control Branch, Member AIAA
‘Physicist, Member AlAA
#Svstern Prowammer. Member AIAA
Copyright
1990 by the American Institute of Aeronautics
and Astronautics, lnc. N o copyright is asserted in the
United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under
the copyright claimed herein for Governmental purposes.
All other rights are reserved by the copyright owner.
285
In 1985 INCA was first delivered to COSMIC [2],
NASA’s computer program dissemination source,
for general distribution.
Its excellent user
interface, versatile graphics system, and robust
controls algorithms have made INCA a popular
tool for use in universities, private industry and
the government. Since it is a public domain
program with source code provided, user
enhancements are possible. A number of the
user enhancements have been incorporated in the
COSMIC version of INCA; the most notable
enhancement in this category is the describing
function analysis capability which was developed
by Dr. Bong Wie and Mr. Tobin Anthony of the
University of Texas at Austin [3].
INc4 overview
INCA was developed for use on VAX/VMS
computers. The program was written primarily in
Pascal; however the matrix and multivariable
control algorithms, obtained from the SAMSAN
[4] subroutine package, are written in
FORTRAN. Since INCA was written to perform
control system design analysis on very expensive
spacecraft and instruments, emphasis was placed
on doing the analysis right the first time. Thus,
the program. utilizes algorithms which strive for
numerical accuracy and attempt to prevent ill
conditioned situations. These algorithms may be
less efficient than others available, but when
expensive spacecraft are at stake accurate results
are of supreme importance.
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3346
Figure 1 illustrates the program interface. INCA
incorporates a menu driven command structure.
These commands can be used to access the
graphic and editor modes, query the help library,
retrieve data from input files, and create and
manipulate transfer functions and matrices. Plots
are displayed on local graphics terminals and can
be printed using standard hard copy capabilities.
Using INCA the controls engineer can quickly
generate system models. INCA provides the
capability to analyze continuous, sampled-data
and hybrid (continuous/sampled-data) systems.
Systems with computational delays or transport
lags can be analyzed via the modified z-transform.
The resultant linear models can then be
manipulated to modify the design or can be used
to determine system stability, parameter
robustness or control system performance.
Standard filter and control law templates have
also been included to expedite the system design.
INCA provides a comprehensive host of standard
classical controls analysis techniques including
Root Locus, Frequency Response (Bode, Nichols,
Nyquist) and Linear Time Response. Frequency
response analyses of nonlinear systems can be
performed using the describing function method
[3]. Analysis results can be presented in graphical
or tabular form. Figure 2 is a sample design
analysis plot generated by INCA.
Matrix data in various ASCII and binary file
formats can be easily merged in the INCA data
base. Supported matrix arithmetic operations
include addition, subtraction, multiplication,
inversion, transpose and exponentiation.
Standard linear algebra routines are also available
to the user including eigenvalue/eigenvector
computations, solving the determinant of a
matrix, trace computations and singular value
decomposition calculations.
Controls specific MIMO capabilities include
transfer function t o s t a t e variable
transformations, state variable to transfer
function matrix computations, and a structural
finite element model reduction capability.
The mode significance module was designed to
expedite the model reduction process from
loading the finite element data through to
generating reduced order flexible body plant
transfer matrices.
Structural dynamic models, such as that provided
by the NASA Structural Analysis program,
NASTRAN, [5] can be described in the following
form:
m + D X + K x = F (1)
The present multivariable capabilities
incorporated in INCA perform rudimentary
Multi-Input-Multi-Output (MIMO) analyses.
Additional MIMO enhancements will follow later.
INCA will accept real or complex matrices.
INCA’s dynamic transfer function capability has
been extended to include matrices. The dynamic
matrices work like a spreadsheet. As an
independent variable changes, the matrix is
recomputed to incorporate this change. INCA’s
MIMO extension accepts arrays of 1st order
(vectors), 2nd order (standard mxn matrices), 3rd
order (mxnxo arrays) and beyond.
where M, D, and K represent the system mass,
damping and stiffness matrices respectively, x
represents the flexible system’s translation and
rotation degrees of freedom, and F represents the
external forces and torques which act on the
body.
Using the modal coordinate
transformation:
where 4 represents the mass normalized
eigenvector matrix, the system finite element
model of equation (1) can be expressed as:
q t Cq
+ Xq = 4’F
(3)
where x is the diagonal matrix of system
286
eigenvalues (the square of the modal
frequencies), C is the diagonal matrix
representing the modal damping and +T is the
transpose of the mass normalized eigenvector
matrix defined in (2).
The mode significance analysis in INCA relies on
the system modeling and modal coordinate
definitions described in equations 1-3. Data input
to INCA includes
, C, and the sensor and
actuator locations defined in x. Row vectors +s
and 4A,representing the respective sensor and
actuator locations to be analyzed, are obtained
from the eigenvector matrix of equation (2).
Since each column of
represents a specific
structural mode, the numeric data in the i'th
column of the row vectors cPs and +A represent
the participation or influence of mode i to the
sensor or actuator in question. The significance
of each structural mode is then computed in
INCA for each requested sensor/actuator pair
using the above row vectors and the model
reduction criteria selected.
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3346
+,
+
where s=jiz and 8 is the transfer function
obtained from the rigid body modes such that:
R
8 =
C.
+si +Ai
(7)
i=l
Where R represents the number of rigid body
modes kept in the analysis.
The modal significance criteria for the Gregory's
model reduction criteria is computed for each
sensor/actuator pair using the following formula:
+
Several model reduction techniques are available.
The simplest analytic technique is the modal gain
criteria [6]. For the modal gain criteria, the
significance of each mode, oi is computed for a
specific sensor/actuator pair as follows:
Frequency weighted criteria include the Peak
Amplitude criteria [7l and Gregory's model
reduction criteria [7l [8]. For the peak amplitude
criteria, the significance of each mode, oi is
computed at the frequency for which the
amplitude of each mode is a maximum. This
frequency is:
where wi is the flexible mode's natural frequency,
and r is the structural damping. Thus, the
significance for each modal frequency becomes:
287
User-defined frequency weighting criteria such as
sensor dynamics frequency shaping or control
bandwidth shaping can be used to augment the
criteria described above.
Mode significance analysis results can be
displayed through the use of two and three
dimensional color plots (figure 3) or by viewing
the results in tabular form. These results can
then be used to automatically or manually select
the modes to keep in the model. Commands
have been included to automatically generate the
plant transfer matrices from the reduced order
model.
Mode Sigm-
EjcMtple
The GOES (Geosynchronous Operational
Environmental Satellite) I/J/K/L/M satellite
series, scheduled for first launch in June 1991,
contains two instruments which observe at
infrared and visible wavelengths: the Imager and
the Sounder. See figures 4 and 5. The
instrument design represents a challenging
structural-control interaction problem due to the
tight jitter and pointing accuracy requirements
imposed to meet the needs of the National
Weather Service.
The instruments are
functionally similar in design and both scan the
Earth by positioning their mirrors using a twoaxis gimbal pointing system. See figure 6 . EastWest scans across the Earth are performed using
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3346
the elevation gimbal. North-South motion is
performed by rotating the azimuth gimbal. The
pointing performance specifications result in
instrument bandwidth requirements on the order
of 50 Hz.
A detailed NASTRAN model with over 8,000
degrees of freedom was developed to emulate the
instrument scanner dynamics. See figure 7. A
cursory model reduction was performed by first
reducing the degrees of freedom to include only
actuator and sensor grid points required to
perform the controls analysis. Structural modes
above 3 KHz were also deleted from the model.
The resultant model containing 125 modal
frequencies and 8 degrees of freedom was
specified in an eigenvector and eigenvalue format.
All structural modes were initially specified with
a 0.1% damping ratio (r = .001). This model was
retrieved by INCA and used to perform the
significance analysis.
Once the instrument
engineering model frequency response tests were
completed, the damping ratio and frequency of
each mode was fine tuned to provide better
correlation with the test data. These adjustments
are reflected in the presented mode significance
analysis.
Model reduction for the instrument was
accomplished interactively using Gregory’s model
reduction criteria. Two structural models were
generated for the GOES instruments. A high
fidelity, high order model was developed to
design the controller and determine system
stability margins. A lower order structural model
was incorporated in the instrument nonlinear
simulation to determine system performance. A
cutoff significance of 1% was chosen for the high
fidelity model and a significance of 10% was used
for the lower order model. These criteria
reduced the high and low order models to 17
modes and 8 modes respectively. Figure 8 lists
the 17 modes selected for the high fidelity model.
Figure 9 is a graphical plot of the significance
results for the first 30 modes. This plot is used
in INCA to interactively select structural modes
or to change the significance criteria.
For GOES, the mode significance analyses for
the azimuth and elevation gimbal axes were
288
merged together to form a single “pool”of modes
from which the plant model was generated. The
plant transfer matrix was computed and stored in
the INCA database for future design analysis
support. Bode plots of the elevation (figure 10)
and azimuth gimbal axes were generated. This
plant transfer matrix was used in INCA to
perform the scanner control system design
analysis, structural mode compensation and linear
performance studies.
Futwe P h
The structural mode significance and model
reduction capability described in this paper is
incorporated in the latest version of INCA.
Enhancements planned beyond this version
include extending the multivariable and mode
significance capabilities. A PC and Macintosh
derivative of INCA is also under development at
NASA Goddard called ASTEC (Analysis and
Simulation Tools foe Engineering Controls).
ASTEC, is planned for release to COSMIC in
1991.
The Interactive Controls Analysis (INCA)
program couples a user friendly interface with
excellent, well conditioned computational
algorithms to provide control system engineers
with tools which are simple to use, quick, and
provide accurate results.
The program’s
algorithms are quite robust and have been
spaceflight proven. The latest version of INCA
includes an interactive graphical structural mode
significance and model order reduction capability.
As shown in the GOES instrument servo control
system example, the INCA model reduction
capability allows the controls designer to reduce
a complex high order structural model to a
manageable size.
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3346
1.
Bauer, F. H. and Downing, J. P., "Control
System Design and Analysis using the
INteractive Controls Analysis (INCA)
Program", AIAA Guidance, Navigation and
Control Conference Paper 87-2517, 1987.
2.
Bauer, F. H. and Downing, J. P., "INteractive
Controls Analysis (INCA) Version 2.0",
Program Number GSC-12998, COSMIC,
University of Georgia, Athens GA., 1985,
updated to Version 3.13, 1989.
3,
Anthony, T., Wie, B., and Carroll, S., "PulseModulated Controller Synthesis for a
Flexible Spacecraft", AIAA Paper No. 893433, 1989.
4.
Frisch, H. P., and Bauer, F. H., "Modem
Numerical Methods for Classical Sampled
Systems Analysis (SAMSAN Version 2)
User's Guide", Program Number GSC- 12827,
COSMIC, University of Georgia, Athens,
GA., 1984.
5.
"The NASTRAN Theoretical Manual",
NASA SP-221-(06), COSMIC, University of
Georgia, Athens, GA., January 1981.
6.
McGlew, D. E., "MODESIG, a Computer
Program to Determine the Significant
Flexible Modes", GSFC Guidance and
Control Branch Report No. 324, November
1982.
7.
Class, B. F., Bauer, F. H., Strohbehn, IC,and
Welch, R. V., "Space Infrared Telescope
Facility/Multimission Modular Spacecraft
Attitude Control System Conceptual Design",
AAS Paper No. 86-031, AAS Guidance and
Control Conference, 1986.
8.
C. 2.Gregory, "Reduction of Large Flexible
Spacecraft Models Using Internal Balancing
Theory," J. Guidance and Control, Vol. 7,
NO. 6, NOV-DW1984, pp. 725-732.
289
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3346
INCA Data & Command Flow
INCA
-1
DATA OUTPUT
DATA SAVE (inpuffoutput) FILES
Figure 1
m
=
58d8
n
1.416 92 Hz
Y= 2.869588 Hz
0dB
HACN I Tk
U= 164.3621 Hz
-58dB
I
Y= 2392.361 Hz
- 188d
I
Frequency Response Example
Figure 2
290
MODE SICNIflCANCE
S I RTF/MMS
A
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3346
6
Sensor/Torquer
Pair
Structural Rode Number
3-D Mode Significance Plot
Figure 3
GOES I/J/K/L/M Satellite
Figure 4
291
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SOUNDER SENSOR ASSEMBLY
IMAGER SENSOR A
GOES Imager and Sounder Instruments
Figure 5
Instrument Scan Assembly
Figure 6
292
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Scan Assembly NASTRAN Model
Figure 7
Mode
---3
4
5
6
7
18
20
63
65
66
67
68
98
113
115
118
119
59.00
56.65
96.00
111.72
174.90
621.60
536.00
1601.94
1500.00
1681.18
1681.18
1650.00
1679.97
2665.88
2710.12
2761.65
2765.09
0.0010
0.0010
0.0010
0.0010
0.0200
0.0010
0.0030
0.0010
0.0070
0.0010
0.0010
0.0010
0.0070
0.0010
0.0010
0.0010
0.0010
100.00
3.69
12.16
7.97
1.29
3.22
1.03
10.17
14.21
100.00
38.69
2.11
12.19
1.44
2.02
61.22
8.33
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
SELECT
---- ---------- ------ ------ ........................
Mode Significance Results
Figure 8
293
A z i m u t h
E l e v a c l o n
0 . 1 0 -
0 . 5 0
0 . 5 0 -
1.00
1 . 0 0 -
2.00
I C
..
1 2
2 . 0 0 -
5 . 0 0
5 . 0 0 -
1 0 . 0 0
1 0 . 0 0 -
2 0 . 0 0
2 0 . 0 0 -
5 0 . 0 0
1 3
1 4
1 5
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1990-3346
1 6
I
"
1 9
2 0
2 1
2 2
U H D . d l
c a i n
2 3
G r . 9
2 4
o r y
s
2 5
A m p l l t d d .
2 6
I f
2 d
2 9
3 0
3 1
3 2
2
1
1 . 1
e
5
0
1
GOES Instrument Mode Selection Plot
Figure 9
1.23
-189
19-JUN-1998
--
dB
-158
18
188
frequency ( Hz 1
Bode Plot of Instrument Elevation Axis
Figure 10
294
1090
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