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MODEL AND RESULT ANALYSIS OF DRAG SAIL
MODULE EARLY TESTING
ANSHUMAN SHUKLA,
C.P. Vidya Niketan, Kaimganj, UP 209502, India
PRANAV M. SAWANT,
Army Public School, Pune, MH 411041, India
PROF. R.P. SHIMPI,
Former Adjunct Professor, Dept. of Aerospace Engineering, IIT B., MH 400076, India
Abstract—An inverted stepper motor assembly was
previously proposed in a design of a satellite deorbiting
module incorporating the drag sail method by the authors.
Following it, tests were conducted on an embodiment of
the module over an adjusted version of a deployment
sequence. The results from these tests were compared and
reproduced using a numerical model of the stepper motor.
A need was identified to produce a model of the tension
varying throughout the deployment sequence.. Curve
fitting technique was employed to generate from the data
obtained during test runs. Moreover, additional results
from test runs are discussed in the paper.
Index terms: Curve-fitting, Analytical Model, Motor
Drives, Drag Sail, Control System
I. INTRODUCTION
The need and feasibility of a plug and play, scalable drag
sail module was overviewed in [1]. Since then, early tests
have been done on an early prototype of AirDragMod
(ADM) obtaining important data in the process. This
prototype had four degrees of freedom. It consists of an
embodiment of the deployment mechanism described in
[1] with adequate sensors to obtain necessary data needed
to iterate the mechanism and derive an analytical model of
tension force at the motor drive during the deployment
sequence.
The primary components of the system are the rotator, aid
masses, and the sail deployment drives. The rotator,
controlled by said mechanism, generates the necessary
rotation in sync with a pre-defined sequence. The aid
masses are released first; due to the sail being connected to
these masses at free end, the tension created causes
elongation of the sail. The motor units drive the sail,
essentially “spewing it out”, at a constant rate upto
complete extension.
In the setup, the deployment sequence was normalized
down to 184 seconds with 120 seconds of sail deployment.
The data obtained will be used to develop an active control
system for perturbations caused to the system during this
deployment. To perform accurate dynamic modeling of the
forces at the base of the sail extension (at motor drives), an
analytical model is needed. In the paper, the analytical
model of tension caused due to centripetal force acting on
sail petals is derived with the help of flex sensors at the
same in the experimental setup. Additionally, interpolation
of angular velocities is performed, the data for which was
obtained using IMUs. Additionally, vibration data from the
system derived is visualized on a surface plot with the
derived model. This helps identify the periods of amplified
vibration during the sequence.
II. BACKGROUND
Equation of motion (domain equation) for extended sail
petal is [2]
(1)
This equation along with its boundary values and initial
values forms the initial value boundary problem [2] and
can be used to model the motion in Simulink®. in
the equation is a function of tension varying with position
on the petal. The sail petal can be assumed to be a
continuous mass distribution; mass of sail spread over the
length of the petal. Figure 1 provides a representation of
the location where tension data is recorded. Using
Newton’s second law and definite integration over a small
mass element, can be found to be:
(2)
Here, is the linear mass density; for a sail the
linear mass density for a petal is if
material chosen were Aluminized Kapton® Polymer [3].
Here, position is a function of time; the rate at which
motor drive units release the petals. This rate is dependent
upon deployment time and sail petal length to be extended.
For a sail, this rate for the 120 second sail release
period (for the setup mentioned prior) is .
is the angular velocity of the rotator unit. The model of
the physical system i.e. the ADM module in Simulink® is
shown in Figure 2. This model forms the physical system
over which active control is to be achieved.
Figure 1: Location of flex sensor recording tension
Figure 2: SimScape Physical System Block Diagram
III. NUMERICAL MODEL SETUP
Owing to hardware limitations, the force models do not
account for lateral forces on sail petals during deployment,
nor are the disturbance models computed in the y-axis of
the system as setup was placed on a surface and not in a
simulated microgravity environment. The force and
acceleration profiles are two dimensional but consistent
with the expected three dimensional model. Hence, the
current modeling can be extended into three dimensions.
The general setup along with axes are shown in figure 3.
Sail placeholders were used in the setup. Testing using
actual sail material would yield the lateral force profile.
The configuration geometry is novel to the design,
however, the number of deployment motor drives can be
varied with a minimum of 4. The setup consisted of 4 such
motor drives. The release rate was kept as mentioned
earlier. The tension data recorded at prototype was at the
base of motor drive units during the sail petal release
period of the deployment sequence. Theoretically, tension
would increase initially, then decrease to attain a constant
value. The axes for the setup are shown in Figure 3. Roll
axis for the setup is the y-axis; angular velocity is
measured around it. Ideally, there should not be any
movement in other axes, however, perturbations would be
caused and thus need for an active control system.
Figure 3: Setup CAD model with local axes
IV. RESULTS
The curve-fit of tension force data was done in
MATLAB®.The best fit model equation obtained is given
below with the coefficient values given in Table 1.
(3)
Table 1: Curve-fit coefficient values
Figure 4 shows the curve-fit plot along with the residuals
plot for the given fit is shown in Figure 5.
The Tension values are normalized moving means of
values recorded over multiple test runs.
The interpolation of angular velocity recorded using IMU
in x-axis is displayed. The cubic spline interpolant in is
a piecewise polynomial over p, where is normalized by
mean 92.03 and standard deviation 53.02 and p is a
coefficient structure. From plot Figure 6, it can be inferred
that some periodic disturbance of oscillation nature is
caused in the x-axis. This disturbance needs to be
controlled by the control system under development.
Figure 6 shows a surface and contour plot of time, angular
velocity and tension values obtained from the numerical
model (3).
Figure 4: Curve-fit of Normalized Tension Values vs. Time
Figure 5: Residuals Plot of Curve-fit in Figure 4
Figure 6: Interpolant of Angular Velocity in X-axis vs. Time
Figure 7: Surface Plot with Time as X-axis, Angular Velocity as Y-axis, and Tension as Z-axis
V. FUTURE WORK
Future work towards refining the models of disturbance
and formulas of motion should follow. Development of an
active control system is the next milestone towards the
development of AirDragMod. More tests with accurate
hardware and sail material should be done to obtain the
model of lateral forces. The result of these tests would also
be improved and rectified formula (2) modified.
Eventually, the active control system would need to be
tested out on a full scale AirDragMod.
VI. CONCLUSIONS
The curve-fit model of tension varying on a sail release
motor drive is useful dynamic modeling of such
microgravity release systems. The model derived using
data and numerical model in two dimensions was
visualized using surface plot matching closely with the
scatter plot obtained further testifying the accuracy. The
vibration data interpolation obtained is needed to
understand the intervals of increased disturbance and thus
help in development of the active control system. The
models obtained can be further extended to create three
dimensional models with tests improvised according to
results of said models. Additional refinement in formulas
would help refine models.
Future work would involve further testing and extensions
of setup degree of freedom into 4 to help in three
dimension modeling.
REFERENCES
[1] Shukla, Anshuman & Sawant, Pranav & Mohite, KC.
(2022). Scalable PnP Drag Sail Module Deorbit System for
LEO Satellites. 10.13140/RG.2.2.17377.38244/1.
[2] Daniel. S. Stutts (2000),
https://web.mst.edu/~stutts/PRESENTATIONS/ModalAnal
ysisofaTightString.pdf
[3]
https://www.dupont.com/content/dam/dupont/amer/us/en/p
roducts/ei-transformation/documents/EI-10142-Kapton-Su
mmary-of-Properties.pdf