Interplanetary travel, much like early earth exploration, is an advent that produces not only tremendous public interest but ground breaking technology as well. The capability of active pointing on a CubeSat is an essential part of an interplanetary mission. Using simulation methods, to implement a control scheme, we present a 3u CubeSat with the capabilities of pointing to within +/- 0.1 degrees bore-sight, with body rate control by implementing momentum wheel and magnetorquer actuation. The active sensory and actuator system is expected to cost around $100,000, which is considerably lower than previous works. Through the development of an accurate and inexpensive active pointing system, interplanetary CubeSat travel is made more accessible.

http://sdsl.club.asu.edu/Authors

Aaron M. Goldstein

Christopher T. Kady

The Sun Devil Satellite 1 (SDS-1), and

The Flare Initiation Doppler Imager (FIDI)

SensorsReaction Wheels

Sinclair Interplanetary – RW-0.01-4

Actuators

Actuator Modeling

Specs:Nominal Torque: 1 mNmMomentum Storage:

10 mNm-sec @ 3410 RPM

Specs:Nominal Dipole:0.2 Am2

Torque Rods

Satellite Services Ltd.

Specs:

Accuracy:

+- 0.1 deg

Field of View:

+- 70 deg

Fine Sun SensorSinclair Interplanetary – SS-411

Specs:

Rate Gyro

Accuracy: 0.02 deg

Drift: <= 0.2 deg/min

Range: +- 150 deg/s

Inertial Measurement Unit

Micro Aero Solutions – MASIMU-02

Specs:Total Error:

1.56% Applied Field

Resolution:

120 ugauss

Magnetometer

Honeywell – HMC1043

Simulation Results

Modeling Overview

Active Pointing, on a Budget

The Sun has been imaged in great detail in a multitude of wavelengths, however high time resolution data of solar flares is still somewhat lacking. The Flare Initiation Doppler Imager, as its name implies, aims to obtain doppler images of the Sun during increased solar activity, at a time resolution of 1s.

The FIDI instrument consists of two co-aligned EUV telescopes that form two images side-by-side on the same focal plane array. The two telescopes image the solar disk in two bandpasses, centered to the red and blue sides of Fe XVI 335 Å. The difference of the two images provides a measure of the Fe XVI 335 Å Doppler shift with a sensitivity to shifts of 25 km/s and greater. The two images will be formed side-by-side and captured by the same focal plane array, a thinned back-illuminated CMOS sensor. To achieve consistent and clean capture of the Sun, the FIDI will have to be pointed with an accuracy of +/- 0.2º, at less than 0.1º/s.

Model Details

The SDS-1 CubeSat

The FIDI Instrument

The SDS-1 is the CubeSat platform that will support the FIDI instrument. Mounted within the SDS-1 structure, the FIDI will occupy the front half of the satellite, and will point in a parallel direction with two deployable solar panels. To properly obtain the data rate necessary, the SDS-1 will downlink twice a day using a 2.4GHz patch antenna. To achieve these critical mission requirements, the SDS-1 places significant emphasis on its 3-axis attitude control subsystem.

Abstract

Reaction Wheels

Torque Rods

Control Mode (Control Mode Select)The SDS-1 enters 1 of 2 control modes, every clock cycle, depending on the reaction wheel momentum status:

Mode 1: Utilize the torque rods, applying a moment in the reverse direction of the current reaction wheel stored momentum to desaturate the reaction wheels.

Mode 2: Turn torque rods off, allowing reaction wheels to maintain full attitude control.

Upper Momentum Limit

timeRW

m

om

entu

m

Lower Momentum Limit

Mode 2 Mode 1 Mode 2

Introduction Torque Determination (Hardware Response)

An ideal torque desired (1.) is determine from the controller gains selected. This desired torque is fed intro the Hardware Response block where it is subtracted from the torque rod torque (2.), depending on the Control Mode, and the rest of the torque is applied through the reaction wheels (3.).

The simulation conducted was developed in MATLAB Simulink. It follows a typical 3 input, 3 output, feedback control loop format. The control law selection and determination blocks, or the Control Mode Selector, and Hardware Response blocks, feed into a plant model, or the Rigid Body Dynamics block, which determines the SDS-1's current euler angles. These angles are fed back through a sensor distoration, or Sensor Dynamics and Kalman Filter block,

Modeling the reaction wheels is accomplished through specifying a maximum and minimum torque value (+/- 1 mNm), as well as a maximum and minimum stored momentum value (+/- 1 mNm-sec). When the limiting torque value is reached, the model simply uses the corresponding limiting torque value. However, when the limiting momentum value is reached, the model drives the available torque to 0 mNm.

timeTotal Desire Torque

Torque RodTorq

ue

3. Reaction Wheel Torque1. Total Desired Torque2. Torque Rod Torque

The moment required from the torque rods is simply limited by a maximum and minimum dipole contribution of +/- 0.2 Am2 from each torque rod. In simulation a desired torque rod moment direction is found first, then utilizing magnetometer readings, a possible dipole vector is found, which is then used to determine an available torque rod moment.

Sensor ModelingFine Sun Sensor

Conversion to Discrete Voltage

Euler Angles

+

+

Uniform Error

To Coupled

& 1D Kalman

The sun sensor was modeled by defining the line of sight of the sun sensor, and then by reading in the Euler angles. These readings were discretized, and uniform noise representing random error was added to the signal.

Magnetometer

NOAA World Magnetic Model [1]

Conversion to Discrete Voltage

+ +

+

Uniform Linear Error

Gaussian Noise

To 1D Kalman

For a particular orbital position, MATLAB’s ‘wrldmagm’ function was utilized to lookup a predicted value of magnetic field. To mimic a reading, noise and error was added according to the HMC 1043 specification.

Inertial Measurement UnitEuler

Anglesddt

Body Rates Transformation

+

+

Drift Error

To Coupled Kalman

The IMU was modeled by transforming the Euler angles from the rigid body dynamics to body rates. Then, error was included by considering the resolution and drift present in the device.

Conversion to Discrete Voltage

Kalman Filtering1D Kalman

The magnetometer data, and the z axis body rate were cfiltered using 1D Kalman filter methods.

Coupled KalmanThe body rates in the x and y axes were filtered with x and y angles in a coupled kalman filter.

Interplanetary travel, much like early earth exploration, is an advent that produces not only tremendous public interest but ground breaking technology as well. The capability of active pointing on a CubeSat is an essential part of an interplanetary mission, however cost and design work can be difficult to overcome. Using modern simulation and design methods to implement a control scheme, we present a 3u CubeSat with the capabilities of pointing to within +/- 0.2 degrees bore-sight, with body rate control by implementing momentum wheel and magnetic torque rod actuation. The active sensory and actuator system is expected to cost around $100,000, which is considerably lower than satellites of a similar pointing accuracy commercially available. Much of the cost incurred in the production of an attitude control subsystem (ACS) is in engineering costs related to design, simulation and testing. Using modern computational techniques, this process can be largely simplified, and easily repeated. Through the development of an accurate and inexpensive active pointing system, interplanetary CubeSat travel is made more accessible.

Environment Modeling

Dec

linat

ion

[d

eg]

Right Ascension [deg]

Using Keplerian orbital mechanics, 1 full day of the mission of SDS-1 was simulated, consisting of approximately 16 orbits. This data was used to generate the environmental disturbance predictions, predict the magnetic environment, and was largely an input to the attitude control simulator.

Aerodynamic DragThe most significant component of the disturbance environment was the aerodynamic drag and torque, since the orbital altitude is approximately 350 [km]. The 1976 Standard Atmosphere Model [2] was used to determine the mean atmospheric density at this altitude. In order to determine the aerodynamic torque, it was necessary to determine the moment arm between the center of pressure and center of mass. This was determined by considering the silhouette of the satellite was a flat plate. The angles at which the silhouette was oriented was determined to be proportional to the angles between the sun vector and wind velocity vector.

Other DisturbancesThere are numerous other disturbances to consider, but many were much smaller in magnitude than the Aerodynamic drag. For instance, since the satellite is always sun pointed, the solar pressure will produce very little or no torque due to an extremely small moment arm between the solar center of pressure and the center of mass. The gravity gradient is also a torque commonly considered, but due to the relative symmetry present in the inertia tensor, the gravity gradient is very small compared to the aerodynamic disturbance.

References[1] NGA, , NGDC, and BGS. "World Magnetic Model." Provided By, NGDC & NOAA WMM.

(2005): n.pag. Web. 28 May 2012. <http://www.ngdc.noaa.gov/seg/WMM/DoDWMM.shtml >.

[2] NOAA, NASA, USAF. U.S. Standard Atmosphere, 1976. Washington, D.C.: 1976. Print. <http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/ 19770009539_1977009539.pdf>.

At a final estimated hardware cost of ~$100,000 is considerably less than those of similar accuracy specifications. This is largely due to the use of ‘off the shelf’ hardware, and implementing computational design techniques. Through the use of the MATLAB/Simulink suite, the design of an active pointing system can be accomplished with relative ease. Future work may include the implementation of a MATLAB GUI to assist in the modeling and design process.

The ACS system was designed such that it could be scaled up or down, depending on the need. For instance, replacing torque rods which depend on the Earth’s magnetic field with cold gas thrusters could be simply implemented in the ACS simulator model.

Conclusion

Abstract

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heel M

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Magnetic F

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Y-dir

Z-dir

Attitude Response

The plots above depict the attitude of the satellite over approximately 16 orbits, or 1 full mission day. The attitude is shown in the x and y planes to be holding a constant reference, and in the z plane to follow a moving reference.

Hardware Response

The hardware response of the actuators over the full mission day are shown above. Modes 1 and 2 can be observed above, mode 1 occurs when torque rods are generating an applied torque.

Environment

Above shows the sum total disturbance torque applied throughout the mission day.

Shown above is the simulated magnetic field present.