NASA Technical Reports Server (NTRS) 20050215317: Study of a 30-M Boom For Solar Sail-Craft: Model Extendibility and Control Strategy

0.47 MB·English

by  NASA Technical Reports Server (NTRS)

2004

NASA FACULTY FELLOWSHIP PROGRAM

MARSHALL SPACE FLIGHT CENTER

THE UNIVERSITY OF ALABAMA
THE UNIVERSITY OF ALABAMA IN HUNTSVILLE
ALABAMA A&M UNIVERSITY

STUDY OF A 30-M BOOM FOR SOLAR SAIL-CRAFT:
MODEL EXTENDIBILITY AND CONTROL STRATEGY

Prepared By: Leehyun Keel

Academic Rank: Professor

Institution and Department: Tennessee State University
Center of Excellence in Information
Systems & Department of Electrical
Engineering

NASA/MSFC Directorate: Transportation

MSFC Colleague: Dr. Mark Whorton

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Introduction

Space travel propelled by solar sails is motivated by the fact that the momentum exchange that
occurs when photons are reflected and/or absorbed by a large solar sail generates a small but
constant acceleration. This acceleration can induce a constant thrust in very large sails that is
sufficient to maintain a polar observing satellite in a constant position relative to the Sun or
Earth. For long distance propulsion, square sails (with side length greater than 150 meters) can
reach Jupiter in two years and Pluto in less than ten years.

Converting such design concepts to real-world systems will require accurate analytical models
and model parameters. This requires extensive structural dynamics tests. However, the low mass
and high flexibility of large and light weight structures such as solar sails makes them unsuitable
for ground testing. As a result, validating analytical models is an extremely difficult problem. On
the other hand, a fundamental question can be asked. That is whether an analytical model that
represents a small-scale version of a solar-sail boom can be extended to much larger versions of
the same boom. To answer this question, we considered a long deployable boom that will be
used to support the solar sails of the sail-craft. The length of fully deployed booms of the actual
solar sail-craft will exceed 100 meters. However, the test-bed we used in our study is a 30 meter
retractable boom at MSFC. We first develop analytical models based on Lagrange’s equations
and the standard Euler-Bernoulli beam. Then the response of the models will be compared with
test data of the 30 meter boom at various deployed lengths. For this stage of study, our analysis
was limited to experimental data obtained at 12ft and 18ft deployment lengths. The comparison
results are positive but speculative. To observe properly validate the analytic model,
experiments at longer deployment lengths, up to the full 30 meter, have been requested. We
expect the study to answer the extendibility question of the analytical models.

In operation, rapid temperature changes can be induced in solar sails as they transition from day
to night and vice versa. This generates time dependent thermally induced forces, which may in
turn create oscillation in structural members such as booms. Such oscillations have an adverse
effect on system operations, precise pointing of instruments and antennas and can lead to self
excited vibrations of increasing amplitude. The latter phenomenon is known as thermal flutter
and can lead to the catastrophic failure of structural systems. To remedy this problem, an active
vibration suppression system has been developed. It was shown that piezoelectric actuators used
in conjunction with a Proportional Feedback Control (PFC) law (or Velocity Feedback Control
(VFC) law) can induce moments that can suppress structural vibrations and prevent flutter
instability in spacecraft booms. In this study, we will investigate control strategies using
piezoelectric transducers in active, passive, and/or hybrid control configurations. Advantages and
disadvantages of each configuration will be studied and experiments to determine their
capabilities and limitations will be planned. In particular, special attention will be given to the
hybrid control, also known as energy recycling, configuration due to its unique characteristics.

UTF Mast Load-Deflection/Load Deflection Cut Wire Test Configurations

Figure 1 shows UTF mast load-deflection cut wire test configuration. The displacement data
collected from the tip position of the boom was used for preliminary model comparison.
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Accel Xlf/18’
Accel Ylf/18’
Accel Xlf/12’ LVDTX/18’
UTF 12’ Accel Ylf/12’
Accel Xhf/12’
AccelYhf/12’
LVDTX/12’
Accel Xlf/12’
Accel Xlf/6’ Accel Ylf/12’
Accel Ylf/6’ Accel Xhf/12’
Accel Xhf/6’ AccelYhf/12’
AccelYhf/6’ LVDTX/12’
LVDTX/6’
UTF 18’
Top View
Accel Xlf/Base Accel Xlf/6’
Accel Ylf/Base Accel Ylf/6’
LVDT Torsion -X Accel Xhf/Base Accel Xhf/6’
AccelYhf/Base AccelYhf/6’
LVDTX/Base LVDTX/6’
Accel lf X Torsion
Y Accel lf Y Torsion
LVDT Torsion X Accel hf X Torsion
Accel hf Y Torsion Accel Xlf/Base
Accel Ylf/Base
LVDT Torsion -X Accel Xhf/Base
Load A AccelYhf/Base
LVDTX/Base 18’ Test
LVDT Torsion X Accel lf X Torsion
Cannister Load A (+ load = tension) Accel lf Y Torsion
Accel hf X Torsion
X Accel hf Y Torsion
LVDT Torsion -X
LVDT Torsion X
Load A

Figure 1: UTF Mast Torsion Load-Deflection Test/Cut Wire Torsion Load-Deflection Test
Configurations

Analytical Models

Consider a beam in transverse vibration. Under the assumption that the cross-sectional
dimensions are small compared with the length of the beam, both the shear and rotary inertia
effects can be neglected. Then kinetic energy T(t) and potential energy V(t) are:

1 L⎡∂y(x,t)⎤2 1⎡∂y(L,t)⎤2
T(t) = ∫ m(x)dx+ m (1)
2 ⎢⎣ ∂t ⎥⎦ 2⎢⎣ ∂t ⎥⎦ p
0
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1 L ⎡∂ϕ(x,t)⎤2
V(t) = ∫EI(x) dx (2)
⎢ ⎥
2 ⎣ ∂x ⎦
0
To determine the transverse displacementy(x,t), we assume separation of variables, that is,
n
y(x,t) = ∑φ(x)q (t). (3)
j j
j=1
Remark: The beam is assumed to be uniform, that is, EI(x)=constant, m(x)=constant.
Substituting for the expressions above in Lagrange’s equation, a state space model was
developed and (A,B,C,D) matrices were computed for both 12ft and 18ft boom lengths under the
following assumptions.
Model 1: Though inconsistent with eq. (1), we derived mode shape functionsφ(x)assuming (for
j
simplicity) the boom is an Euler-Bernoulli beam with no tip mass.
Model 2: To improve the accuracy of the model (Model 1), we derived alternative mode shape
functions φ(x) assuming the boom is an Euler-Bernoulli beam with a short tip massm .
j p

Results

Two different EI values were used for each boom length. EI = 20x106 lb-in2 was read from the
graph provided by the boom manufacturer, ABLE, Inc. Another value of EI used was estimated
from experimental data. Figure 2 shows the response comparison (analytical model predictions
and experimental data) of the 12ft booms for each EI value.
Response to Initial Conditions Response to Initial Conditions
0.02 0.02
Experimental Experimental
Analytic Analytic
0.015 0.015
12ft Boom 12ft Boom
0.01 0.01
0.005 0.005
Meters) 0 Meters) 0
ment ( −0.005 ment ( −0.005
Displace −0.01 Displace −0.01
Tip Tip EI=20E6 (provided by ABLE)
−0.015 −0.015
EI=4.62E6 (obtained from experiment)
−0.02 −0.02
−0.025 −0.025
−0.03 −0.03
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time (Secs) Time (Secs)
Figure 2. Responses of 12ft boom
Similarly, Figure 3 shows the response comparison (analytical model predictions and
experimental data) of the 18ft booms for each EI value. In both cases, the EI values estimated
from the experimental data yielded an analytical model predicted response that is closer to that of
the experimental data. The results are not conclusive and more data at longer beam lengths is
needed to reach firm conclusions. Note that all Figures are based on Model 1.

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Response to Initial Conditions Response to Initial Conditions
0.04 0.04
Experimental Experimental
Analytic Analytic
0.03 0.03
0.02 0.02
Meters) 0.01 Meters) 0.01
ment ( 0 ment ( 0
Tip Displace −0.01 Tip Displace −0.01
−0.02 −0.02
EI=8.24E6 (obtained from exp data)
EI=20E6 (obtained from plot provided by ABLE)
−0.03 −0.03
−0.04 −0.04
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time (Secs) Time (Secs)
Figure 3. Responses of 18ft boom

Control Configuration Using Piezoelectric Transducers

A theoretical study of active, passive, and energy recycling (hybrid) control configuration has
been conducted. Since the structure does not permit excessive added weights due to cabling,
mass, and/or an external power source, the energy recycling control configuration may be the
“best” if feasible. Laboratory studies are needed to confirm capabilities, limitations and
feasibility of this approach.

Resources

The project requires one software tool. Matlab with appropriate toolboxes was the main software
tool for verification of models. A laboratory engineer at MSFC provided the experimental data
from the boom.
Future Works

More experiments at longer boom lengths have been requested. Once the data is available, the
response comparison procedures will be repeated and we expect more conclusive evidence will
be found. To evaluate the control strategy, a new test-bed consisting of a long rod with
piezoelectric transducers will be constructed. Using that test-bed, the capabilities and limitations
of each potential control configuration will be studied. Eventually, the “best” control
configuration will be installed on the 30 meter boom for ground testing.

Acknowledgements

The author would like to thank Dr. Mark Whorton of TD54 for providing an opportunity to
participate in cutting edge research at NASA, and many hours of valuable discussion and
guidance.

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