The original motivation for TREETOPS was to build a generic multi-body simulation and remove the burden of writing multi-body equations from the engineers. The motivation of the enhancement was twofold: (1) to extend the menu of built-in features (sensors, actuators, constraints, etc.) that did not require user code; and (2) to extend the control system design capabilities by linking with other government funded software (NASTRAN and MATLAB). These enhancements also serve to bridge the gap between structures and control groups. It is common on large space programs for the structures groups to build hi-fidelity models of the structure using NASTRAN and for the controls group to build lower order models because they lack the tools to incorporate the former into their analysis. Now the controls engineers can accept the hi-fidelity NASTRAN models into TREETOPS, add sensors and actuators, perform model reduction and couple the result directly into MATLAB to perform their design. The controller can then be imported directly into TREETOPS for non-linear, time-history simulation

Kumar, Manoj N.

Vandervoort, R. J.

English

NASA Technical Reports Server

N90- 23047 -_
Enhanced Modeling Features Within
TREETOPS
R. J. VanderVoort
and
Manoj N. Kuma:
Dynacs Engineering Co., Inc.
Clearwater, FL 34623
August 16, 1989
_8
https://ntrs.nasa.gov/search.jsp?R=19900013731 2020-03-19T22:15:39+00:00Z
MOTIVATION
The original motivation for TREETOPS was to build a generic multi-body
simulation and remove the burden of writing multi-body equations from the
engineers. The motivation of the enhancement was twofold: ])to extend the
menu of built in features (sensors, actuators, constraints, etc) that did not
require user code and 2)to extend the control system design capabilities by
linking with other government funded software (NASTRAN and MATLAB).
These enhancements also serve to bridge the gap between structures and
controls groups. It is common on large space programs for the structures
groups to build hi-fidelity models of the structure using NASTRAN and for
the controls group to build lower order models because they lack the tools
to incorporate the former into their analysis. Now the controls engineers
can accept the hi-fidelity NASTRAN models into TREETOPS, add sensors
and actuators, perform model reduction and couple the result directly into
MATLAB to perform their design. The controller can then be imported
directly into TREETOPS for non-linear, time-history simulation.
549
SUMMARY OF ENHANCEMENTS
TREETOPS is more than a time-history simulation. It is a suite of programs
oriented toward design and analysis of embedded control systems for flexi-
ble spacecraft. The enhancements to TREETOPS can be divided into two
categories. Internal enhancements add to the menu of time history simula-
tion features and External enhancements provide links to other software and
provide stand alone utility features.
Internal Enhancements
• Orbital Environment-Standard NASA models of the earth's magnetic field
and atmosphere have been added to TREETOPS. You can specify the
"shape" of each body and appendage, the orbit and certain atmospheric
paramenters and TREETOPS will in turn compute the aerodynamic
drag forces. You can also include gravity gradient moments on each
body in your model through a simple menu option. The magnetic field
operates through magnetic actuators to produce controllable moments
at any point on the structure.
• Actuators-The new actuators include reaction wheels, single gimbal con-
trol moment gyros (SGCMG), double gimbal CMG's (DGCMG) and
seven variations of motor drive actuators.
The previous actuators were simply input devices that applied a force
or moment. The reaction wheels, SGCMG's and DGCMG's have their
own dynamics that are closely coupled to the structure dynamics. Fur-
thermore, you can select friction models for the gimbals, such as the
DaM friction model, that are described by non-linear differential equa-
tions. When you select one of the actuators from the menu TREE-
TOPS will form the associated differential equations augment them to
the structure equations and simultaneously solve the complete set.
The motor drive actuators simulate a wide variety of electric motors
driving through gear trains. These models include gear train com-
pliance, backlash, coulomb friction and no-back-drive options. Seven
varieties of motor drive actuators have been added to TREETOPS
representing different degrees of complexity.
550
• Devices-the new devices include cables, brakes and locks.
A cable is connected between any two nodes on the structure and con-
strains the distance between the two nodes to be less than or equal to
the cable length. An alternate way of looking at a cable is that node
2 is constrainted to be within or on a sphere centered at node 1. The
sphere radius is equal to the cable length.
A brake is a device that mounts on a hinge degree of freedom and
produces a force that can inhibit motion but not cause motion. The
braking force is an input command, just like other actuators, and when
the velocity goes to zero a constraint is instituted just like a coulomb
damper.
Locks are like brakes except that they mount between two nodes rather
than on a hinge axis.
• Manipulators-Two enchancements have been made t o facilitate the sim-
ulation of manipulators. The first is a grapple option where the ma-
nipulator tip can attach to another point on the structure and create
a closed tree topology. The second option is a contact option where
the manipulator tip makes contact with a surface producing equal and
opposite forces but does not form a closed loop constraint.
• Cut joints-A cut joint facilitates the modeling of dosed tree topologies. It
lets you constrain any combination of the relative degrees of freedom
between two nodes and is specified just like a TREETOPS hinge. A
"closed loop constraint" can be thought of as a subset of cut joints
because it constrains all 3 relative translations between two nodes but
allows all 3 relative rotations.
• Flexibility-Previous versions of TREETOPS had a restriction that the
deformation of any flexible body must be zero at the attach point node.
This restriction has been removed.
.561
External Enhancements
As stated previously, TREETOPS is a suite of programs for performing anal-
ysis, design and simulation of spacecraft control systems. By linking TREE-
TOPS with NASTRAN and MATLAB, the job is now much easier. All thrce
programs were developed under government funding and are available free or
at low cost. Furthermore, all 3 programs run on UNIX workstations which
brings the cost of performing complex design tasks down to an acceptable
level.
• TREEFLEX-A new program that links NASTRAN and TREETOPS.
Each flexible body in a TREETOPS simulation has certain volume
integrals that are required and others that are optional. TREEFLEX
will read data from a NASTRAN output file, compute all required vol-
ume integrals and write them in the proper format. All data files are
in an ASCII format to facilitate transfer of data from one computer to
another or from one subcontractor to another. Options are available
in TREEFLEX to specify the NASTRAN modes that will be retained,
the number of optional terms that will be retained and the damping for
each mode. In addition, the computation of augmented modal data has
been further automated makingit easier to "augment" the modes of
inboard bodies to account for the mass and inertia of outboard bodies.
• TREESEL- A model reduction program. A common problem in multibody
systems is that the number of system modes which is equal to the sum
of individual component modes becomes very large. TREESEL uses a
modified Component Cost Analysis (CCA) method to rank individual
component modes based on their contribution to overall system costs.
The modes having the least impact on system response are then deleted
using TREEFLX. In other words, the substructure modes are selected
based on system level cost criterial All model reduction is done in
physical coordinates.
• Link to MATLAB-MATLAB is a public domain program, developed under
government funding. It provided the basis for several well-known com-
mercial controls analysis programs. We have incorporated the public
domain version into the TREETOPS suite because the user interface
is well-known and widely accepted. Portability and low cost were em-
phasized in this link. An ASCII file format was adopted to store linear
552
system data (ABCD matrix quadruples). TREETOPS writes linear
plant models in this format and reads controller models in the same
format from the same file. The link to MATLAB wascompleted by
simply adding two functions, onefor reading quadruplesand the other
for writing them.
• TREEFREQ-Frequency domain analysis. This is a post-processorthat
readslinearsystemdataandperformsfrequencydomainanalysis. Poles
and zerosare computed, frequencyresponsein computed and plotted
in Bode, Nicholsor Nyquist format.
• Utility Function-Each of theseutilities operateson linear systemdata.
- EIGEN computesand prints system Eigenvalues.
- LINC will combineseverallinear systemsinto one.
- BL2M convertsa block diagram controller into matrix form.
- SPRT producesa pretty printout of ABCD Systemquadruples.
553
EXAMPLE PROBLEM NO. 1 - AXAF
The Advanced X-ray Astrophysics Facility (AXAF) is a proposed NASA
spacecraft for the 1990's. It is a multi-body spacecraft.
Two different models of the spacecraft were used for two different con-
troller design Tasks. The first task was basic attitude or pointing control
in the presence of external disturbances. A three body model was chosen
with a rigid core body and two flexible solar panel appendages as sketched
in figure 1. A simple proportional-derivative controller, defined in block dia-
gram form, used reaction wheels for actuators and attitude and rate sensors
for feedback. Disturbances included aerodynamic drag, gravity gradient and
rotating machinery vibrations. Note that no user supplied code is required
and the problem is completely defined by the .INT and .FLN files. A typical
line-of-sight disturbance response is shown in figure 2.
The second task was to design a closed loop controller for calibrating the
optical system. A two body model was used with the optical bench and solar
panels combined to form the first rigid body and the High Resolution Mirror
Assembly (HRMA) formed the second body as shown in figure 3. Six motor
drive actuators in a tripod configuration gave control of all 6 relative degrees
of freedom. Relative attitude and rate sensors simulated the optical sensors
which are not yet defined. A user controller was incorporated to illustrate
the technique of incorporating user supplied code. The pointing system was
operating in parallel with the optical calibration system. The .INT file and
user controller listing completely defines this problem. The same system
model was used to design the actuator servo loop and then to design the
controller loops. Figure 4 shows the relative velocity frequency response
between two motor drive actuator end points in response to a force input.
As you would expect the transfer function is approximately l/ks and the
effect of the other 5 actuators constraining the 6 relative degrees of freedom
is negligible for this particular example.
EXAMPLE PROBLEM NO. 2 - SPACE STATION
This example demonstrates the NASTRAN/TREETOPS interface and model
reduction procedures as they apply to large dimension, real-world problems.
The NASTRAN model known as the MB-1 configuration was developed
by the structures group at NASA Langley Research Center and is shown in
554
figure 5. The NASTRAN model has 1062degreesof freedom but only the
first 89 modesfor each body were computed within NASTRAN giving us
the first rough cut model reduction. In the secondstageof model reduction
TREEFLEX wasusedto arbitrarily selectthe first 15modesfor body 1 and
the first 50 modesfor body 2. This produceda baselineTREETOPS model
with 72 DOF's. (6 Rigid body for hinge 1, 15 flex for body 1, I rigid for
hinge 2 and 50 flex for body 2). The third step was to perform component
cost analysisusingTREESEL and selecta reducedsubsetof modesbasedon
relative importance. This step reduced the model from 72 to 41 degreesof
freedomand further reduction is quite likely for the control designproblem.
A comparison of the transient responsefor the 72 and 41 DOF models is
presentedin figure 6.
IMPORTANCE OF WORK TO COMMUNITY
For many years government funded software has been available to model, an-
alyze and design complex spacecraft systems. Now these software codes have
been integrated. With NASTRAN you can create and analyze complex fi-
nite element models. TREETOPS can combine these NASTRAN single body
models into a multi-body model, add sensors and actuators and linearize the
total for use in MATLAB. The controller can be designed in MATLAB and
passed back to TREETOPS for verification via non-linear simulation.
Strict adherence to FORTRAN 77 standards enhances TREETOPS porta-
bility. All software has been installed on engineering workstations.
No user supplied code is required.
FUTURE DIRECTION
The major complaint against generic, multi-body simulations is run time. We
are currently using three approaches to reduce run time: Order-N algorithms,
symbolic programming and parallel processing. Order-N and symbolics can
be done without compromising portability but parallel processing requires
the proper hardware. Two orders of magnitude reduction in run time is
feasible without resorting to approximate solutions. This puts a large class
of problems in the realm of real time simulation.
The second area of advancement is graphical interfaces. A menu/mouse
555
method of building models is very desirable but hardware dependent. NASA
funded software is already available for 3-D solid modeling and building NAS-
TRAN input files. The same 3-D model built with the graphical preprocessor
can be used in a graphical post processor to produce movies from your sim-
ulation. The simulation merely supplies the coordinate transformation for
each of the graphic objects created with the preprocessor.
Last, but not least, a collection of MATLAB macros is being collected to
solve the common controls problems.
556
Body #2
Flexible Solar Panel
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Magnetic
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Error
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Magnetic
Actuator
Commands
• Rate
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Pointing I
Control
System
Body #3
Flexible Solar Panel
Figure I A 3-body representationof the AXAF spacecraft,.
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Figure 3 A 2-body representation of the AXAF spacccrat't.
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Enhanced modeling features within TREETOPS

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