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

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:

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

IlliniSat-2 Bus

Payload

55

Operational Sequence

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.

0 1 2 3 4 5 6 7

-50

0

50

Euler Angles vs. Time

Roll

[ ]

Time [hr]

0 1 2 3 4 5 6 7

-50

0

50

Pitch [

]

Time [hr]

0 1 2 3 4 5 6 7

-50

0

50

Yaw

[]

Time [hr]

Satellite Dynamics LQR Magnetic Torquers

+

TGG TAD

Duty Cycle

Direction

Torque

Typical single run Euler angles and rates are shown below.

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-5

0

5

Angular Body Rates

R

oll [ /

sec]

Time [hr]

0 1 2 3 4 5 6 7-6-4-2024

P

itch [

/sec]

Time [hr]

0 1 2 3 4 5 6 7

0

2

4

Y

aw

[ /

sec]

Time [hr]

Robustness Testing Results

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.40

50

100

150

200

250

300

350

Detumbling Time (1000 runs)Mean = 1.23 hrs STD = 0.28 hrs

Detumbling Time [hrs]

Fre

quen

cy

0 1 2 3 4 5 60

50

100

150

200

250

Tracking Time (1000 runs)Mean = 2.70 hrs STD = 1.27 hrs

Tracking Time [hrs]

Fre

quen

cy

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.

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: 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

The sail is assumed to be traveling in a sun-synchronous terminator orbit.

Sail is oriented with its edge to the orbital velocity direction. Deviation away from the local vertical is ignored and only out-of-

plane deflection is considered. The governing equations can be written as:

Steady-State Shape of the Sail

Deflections due to Solar Radiation Pressure are relatively small.

Maximum out-of-plane deflection is approximately 18 m. Final angle away from the local vertical are

approximately 15º.

Out-of-plane deformations along the sail length for varying pitch angles

-15 -10 -5 0 5 10 15

0

50

100

150

200

250

l sail [

m]

[deg]

Increasing Sat

Increasing Sat

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

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

0

50

100

150

200

250

l sail [

m]

[deg]

Increasing Sat

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1

x 10-4

0

50

100

150

200

250

l sail [

m]

T [N]

Increasing Sat

Tension along the sail length for varying pitch angles

Questions?