1. Aerodynamic Attitude Control for CubeSats
Samir Rawashdeh, Anthony Karam, Daniel Erb, David Jones, James E. Lumpp, Jr.
University of Kentucky
Abstract
Torque Profiles and Stiffness
Performance Design Space
The plots below show the design space highlighting the effect of the design variables on the pointing performance.
The equal-stiffness curves show panel length and deployment angle combinations that have equal performance in steady state. It is evident that a deployment angle of 50 degrees makes most efficient use of a certain panel length. Longer panels increase the pointing accuracy, while also increasing the average cross-sectional area making the satellite experience greater drag that reduces orbit life.
Atmospheric density changes exponentially with altitude, thus making the performance of the design concept very sensitive to altitude. It becomes prohibitively difficult to design an aerodynamically stabilized satellite above 500 km.
To compare the performance of different designs, torque profiles representing the amount of aerodynamic torque the satellite experiences as a function of its attitude were generated. Zero-crossings with a negative slope represent stable points, as evident in the plots below, the design concept oscillates around a stable point flying forward, experiencing a correcting negative torque for a positive error angle, and vice versa.
It was found that a deployment angle of 50 degrees is most efficient. Longer panels increase the amount of stiffness (slope through the zero crossing) linearly.
The CubeSat standard poses volume, mass, and power limitations of all components and modules within the satellite. Passive techniques such as Aerostabilization present low risk and simple alternatives to stabilize small satellites such as CubeSats. Aerodynamic drag can be utilized to provide stabilization in a ram-facing attitude. Aerodynamic stability acts in pitch and yaw to maintain a ram-facing attitude while leaving roll uncontrolled. Stability of light-weight satellites using drag fins can be achieved for altitudes below 500 km. This poster highlights research at the Space Systems Laboratory at the University of Kentucky on Aerostabilization of a 3-U CubeSat. The main questions addressed are what panel length and deployment angles would be most effective in a shuttlecock design of a CubeSat with deployable side panels..
Torque Profiles for 20 cm panels at 400km
Stiffness Plots
Design Concept
Equal -stiffness Curves at 400 km
Effect of Altitude
Aerostabilization has not been demonstrated for CubeSats in orbit yet. However, the feasibility has been demonstrated by PAMS (Passive Aerodynamically Stabilized Magnetically Damped Satellite), which is similar to CubeSats in size and weight. Other related research shows the ability to stabilize a satellite using aerodynamic torques for orbit altitudes below 500km where the atmospheric density is sufficient to provide aerodynamic authority over other disturbance torques.
The image is of the design concept of an aerodynamically stable 3-U CubeSat. Simulations show the feasibility of this shuttlecock design to provide ram-facing stability. The trailing fins are side panels that are deployed after launch.
Simulation Results
Sample Runs at 400km and Simulation Results.
Type
Description
Sample Run A
Sample Run B
Unit
Initial Conditions
Pitch (φ)
120
Tumbling rate 5
°/s
Satellite Description
Moment of Inertia
0.045
0.049
kg.m2
Drag Panel Length (λ) 20 25 Cm
Panel Deployment Angle (θ) 30 50
Ram-Facing Area
0.05
0.0866 m2
Results
Settling Time 70
100
Orbits
Steady State Error
+/- 5
+/- 2.5
Pitch Angular Rates (body- frame)
Orbit Life
(No panels: 3 years)
16.8
10.2
Months
Satellite Attitude Propagation
Optimization Variables
In order to estimate the performance of an attitude stabilization or control technique under perturbing torques, an attitude propagator with models for the major disturbances is required. The Orbital Environment Simulator by the Space Systems Laboratory at the University of Kentucky simulates Gravity Gradient, Hysteresis Material, Permanent Magnets, and Aerodynamic effects.
The main satellite body is a 3-U CubeSat with a 10x10 cm2 cross section and 30 cm in length. The deployable side panel length, and the deployment angle, were varied to study their effect.
The approach was to calculate the amount of aerodynamic torque affecting the satellite as a function of its attitude, by modeling the atmosphere using free-molecular concepts. This was done for a wide range of panel length and deployment angle combinations.
The designs are compared based on their torque profiles. Then the performance of a design is evaluated in an attitude propagator that predicts the satellite’s behavior under external disturbance torques such as gravity gradients and magnetic torques.
The table and plots show the response of two sample runs at 400km.
Sample Run A is of a satellite with 25cm panels deployed at 50 degrees. The result is a steady-state error of 2.5 degrees. That design has a large average cross-sectional area and therefore a short estimated orbit life of 10.2 months.
Sacrificing pointing accuracy with a less efficient design (Sample Run B) that has shorter panels deployed at 30 degrees, the estimated orbit life increases to 16.8 months.