Transcript Structures and Thermal - New York City College of Technology

Attitude Control of the
CubeSail Solar Sailing
Spacecraft
Victoria Coverstone, Andy Pukniel
University of Illinois at Urbana-Champaign
Rod Burton, Dave Carroll
CU Aerospace
ISSS 2010 New York
CubeSail Mission Overview
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Low cost solar sailing demonstration.
Goal is to deploy 20 m2 (80mm x 250m) of film between 2 nanosatellites.
Deployment is to occur into a sun-synchronous terminator orbit above 800km
altitude along the local vertical.
Gravity-gradient aids in deployment and provides sail stiffening.
Secondary payload opportunities are used to reduce cost.
Validation of the dynamical and performance models and subsequent
advancement of the TRL will likely lead to secondary demonstration followed by
possible full-scale UltraSail experiment.
Research Motivation
 Consider two reasons for slow emergence of solar sailing technology:
 Challenges associated with stowage and deployment of large sails and
stiffening structure (booms, masts, stays, etc.)
 High risk combined with high launch costs associated with investment in a
poorly-characterized technology.
Technical Approach
 Stowage and deployment based on the UltraSail concept
 Sail material is stored in long strips wound onto motorized reels
 3-axis stabilized satellite on each blade tip control the deployment and attitude
 Risk and cost reduction is achieved through IlliniSat-2 bus and secondary
launch opportunities
 IliniSat-2 bus provides:
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Active 3-axis ACS achieved via magnetic torque actuation
Deployable antenna and associated communication hardware
C&DH capable of supporting wide range of payloads
Power generation and management system
 Complete bus fits into 10x10x10cm volume
Payload
IlliniSat-2 Bus
Operational Sequence
5
Initial Detumbling and Stabilization
 Initial detumbling and stabilization is posed as a Linear Quadratic problem.
 Two operational modes: detumbling and tracking.
 Cost function depends on the mode and is either:
 the time to reduce angular body rates on all 3 axis below a threshold of 0.1 º/sec
 or the accumulated Euler angle error for values above 5º (figure below)
 Desired performance is achieved with GA-selected Q and R matrices.
Attitude Control Simulator
 Matlab-based simulator is used to test performance.
Duty Cycle
Satellite Dynamics
LQR
Magnetic
Torquers
Direction
TGG
TAD
Torque
+
 Typical single run Euler angles and rates are shown below.
50
0
-50
1
2
3
4
Time [hr]
5
6
50
0
-50
1
2
3
4
Time [hr]
5
6
50
0
-50
0
1
2
3
4
Time [hr]
5
6
0
-5
7
0
1
2
3
4
Time [hr]
5
6
7
0
1
2
3
4
Time [hr]
5
6
7
0
1
2
3
4
Time [hr]
5
6
7
4
2
0
-2
-4
-6
7
Yaw [/sec]
0
5
7
Pitch [/sec]
Pitch []
0
Yaw []
Angular Body Rates
Roll [/sec]
Roll []
Euler Angles vs. Time
4
2
0
Robustness Testing Results
 The attitude control simulator is run 1000 times with randomly varying IC’s to
ensure the selected penalty matrices are robust and the spacecraft can
stabilize from any attitude and worst predicted rates of 5º/sec on all axis.
Detumbling Time (1000 runs)
Mean = 1.23 hrs STD = 0.28 hrs
Tracking Time (1000 runs)
Mean = 2.70 hrs STD = 1.27 hrs
350
250
300
200
150
200
Frequency
Frequency
250
150
100
100
50
50
0
0.4
0
0.6
0.8
1
1.2
1.4
1.6
Detumbling Time [hrs]
1.8
2
2.2
2.4
0
1
2
3
Tracking Time [hrs]
4
5
6
Modeling of External Forces
 Solar Radiation Pressure force model includes effects of:
 Reflection, absorption, and re-radiation
 The non-ideal parameters are given as:
 Aerodynamic Drag force is calculated using the method of accommodation
coefficients and includes variations due to:
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Angle of incidence of incoming molecules
Major atmospheric constituents at altitude
Surface coating material and surface temperature
Semi-diffuse reflection model
Aerodynamic Drag Results
 The Aerodynamic Drag force is computed for an undeformed sail in 2 ways:
 accommodation coefficient method
 classical method of constant coefficient of drag, Cd, of 2.2
 Interestingly, the classical method underestimates the magnitude of the force
for all but high angles of incidence.
 In order to match the force computed using the accommodation coefficient
method, Cd must be varied between 0.9 and 2.9 in the classical equation.
Steady-State Shape of the Sail

Steady-state deformations of the sail are computed by including forces due to:
 Solar Radiation Pressure
 Aerodynamic Drag
 Gravity-Gradient
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The sail is assumed to be traveling in a sun-synchronous terminator orbit.
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Sail is oriented with its edge to the orbital velocity direction.
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Deviation away from the local vertical is ignored and only out-of-plane deflection is
considered.
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The governing equations can be written as:
Steady-State Shape of the Sail
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Deflections due to Solar Radiation Pressure are relatively small.
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Maximum out-of-plane deflection is approximately 18 m.
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Final angle away from the local vertical are approximately 15º.
Out-of-plane deformations along the sail
length for varying pitch angles
0
Increasing Sat
50
lsail [m]
100
150
200
Increasing Sat
250
-15
-10
-5
0
 [deg]
5
10
15
Conclusions
 Optimization of Q and R matrices for the LQR controller
with Genetic Algorithms provides good performance,
robust results.
 Classical treatment of Aerodynamic Drag with constant
coefficient of drag underestimates the force exerted on
the sail.
 Equivalent coefficient of drag (specific to the CubeSail
geometry and deployment orbit) varies between 0.9 and
2.9.
 Out-of-plane, steady-state sail deformation due to solar
radiation pressure are relatively small as compared to the
sail length.
Future Work
 Steady-state shape of the sail with a linearly-varying
pitch (twist) along its length is studied.
 Non-linear gravity-gradient deployment dynamics in the
presence of aerodynamic drag and solar radiation
pressure is examined.
In-plane deformations along the sail length for
varying pitch angles
0
50
lsail [m]
100
Increasing Sat
150
200
250
-1.5
-1
-0.5
0
0.5
1
 [deg]
1.5
2
2.5
3
3.5
Tension along the sail length for varying
pitch angles
0
50
100
lsail [m]
Increasing Sat
150
200
250
6.1
6.2
6.3
6.4
6.5
6.6
T [N]
6.7
6.8
6.9
7
7.1
-4
x 10
Questions?