Simulating Magnetic Hysteresis Damping

CubeSats have caused a renewed interest in magnetic control of satellites, and passive hysteresis damping in particular. Modeling actual hysteresis rods on a satellite is not trivial, and generally requires empirical data on the properties of the rods selected. Our newest CubeSat simulation demonstrates damping using rods in LEO. A permanent magnet is modeled using a constant dipole moment, and we expect the satellite to align with the magnetic field and damp. We evaluate the results by plotting the angle between the dipole and the Earth’s magnetic field and the body rates.

First, let’s verify the magnetic hysteresis model in the toolbox using the bulk material properties in orbit. We use a dipole model of the Earth’s magnetic field. The nice hysteresis curves below confirms that we are computing the derivatives of the magnetic field correctly in the body frame, which requires careful accounting of rotating coordinates. Also we stay within the saturation limits which means our magnetic flux derivatives are correct too.

Hysteresis curves from simulating magnetic hysteresis in orbit

Hysteresis curves from simulating magnetic hysteresis in orbit

We will assume the rods are 1 mm radius and 95 mm length, with rods placed perpendicular to each other and the permanent magnet. Three rods are used per axis. The apparent rod parameters are taken from the literature. The actual rods will not reach saturation while in orbit, so we will see a minor loop.

Minor loops from damping rods

Minor loops from damping rods using apparent properties

The rods produce only a small amount of damping per orbit, so we have to run for many orbits or days to see significant damping – in some passive satellites, the total time allotted for stabilization is two months! In this case we test the rods’ ability to damp the torque induced by turning on a torque rod with a dipole of 1 AM2 and allowing the CubeSat to align itself with the magnetic field, starting from LVLH pointing.

Damping in LEO using hysteresis rods

Damping in LEO using hysteresis rods

Simulating the rods is time-intensive, with a timestep of about 4 seconds required – which makes a simulation of several days on orbit take several minutes of computation. Once performance of the rods has been verified, a simple damping factor can be substituted.

This new simulation along with the functions for hysteresis rod dynamics will be in the new version of our CubeSat Toolbox, due for release in June!


  1. F. Santoni and M. Zelli, “Passive magnetic attitude stabilization of the UNISAT-4 micro satellite”, Acta Astronautica,65 (2009) pp. 792-803
  2. J. Tellinen, “A Simple Scalar Model for Magnetic Hysteresis”, IEEE Transactions on Magnetics, Vol. 34, No. 4, July 1998
  3. T. Flatley and D. Henretty, “A Magnetic Hysteresis Model”, N95-27801 (NASA Technical Repoets Server), 1995

6U CubeSat to Mars

We’ve been working on Asteroid Prospector, a 6U CubeSat to explore Near Earth Objects, for the past two years. It is quite a challenge to pack all the hardware into a 6U frame. Here is our latest design:



The nadir face has both an Optical Navigation System camera and a JPL designed robot arm. The arm is used to grapple the asteroid and get samples. The camera is used both for interplanetary navigation and close maneuvering near the asteroid.

Our fuel load only allows for one way missions but could be increased for sample return missions by adding another xenon tank, making it more of a 12U CubeSat. With that in mind, we wondered if we could do a Mars orbital mission with our 6U. It turns out it is possible! We would start in a GPS orbit, carried there by one of the many GPS launches. The spacecraft would spiral out of Earth orbit and perform a Hohmann transfer to Mars. Even though we are using a low-thrust ion engine, the burn duration is a small fraction of the Hohmann ellipse time making a Hohmann transfer a good approximation. We then spiral into Mars orbit for the science mission as seen in a VisualCommander simulation.


The low cost of the 6U mission makes it possible to send several spacecraft to Mars, each with its own instrument. This has the added benefit of reducing program risk as the loss of one spacecraft would not end the mission. Many challenges remain, including making the electronics sufficiently radiation hard for the interplanetary and Mars orbit environments. The lifetime of the mechanical components, such as reaction wheels, must also be long enough to last for the duration of the mission.

We’ll keep you posted in future blogs on our progress! Stay tuned!

SCT Seminar – Sheffield UK

Yosef and Amanda are giving a seminar on our Spacecraft Control Toolbox in Sheffield, England on October 1, 2013. This event has been arranged through our UK distributors, MeadoTech Ltd. A big thank you goes out to Dr. Mohamed Mahmoud and Ruth Jenkinson!

Check out what our MATLAB toolboxes have to offer!
Core Control Toolbox
Aircraft Control Toolbox
CubeSat Toolbox
Spacecraft Control Toolbox

Asteroid Prospector Orbiting Apophis

Asteroid Prospector is a 6U CubeSat designed to survey asteroids. It uses a Busek Ion engine to spiral out of earth orbit and rendezvous with an asteroid. It then uses its reaction control thruster system, which employ ECAPS green propellant thrusters, to perform near-asteroid operations. Here is a picture of the spacecraft in circular orbit mode.

The simulation is running in our Simulation Framework. The graphical display uses our VisualCommander client on the Mac.

The flight software is implemented in our ControlDeck C++ class library. Both the simulation and control software are available as part of our Aero/Astro vehicle control products.

You can see a movie of the spacecraft on our YouTube channel:

We presented our Asteroid Prospector mission concept on Tuesday Aug 13th, 2013  the Small Satellites Conference in Logan, Utah in Session VI: Strength in Numbers. A copy of our paper is available here.

SmallSat Conference in the Cache Valley!

PSS attended the Small Satellite Conference in Logan, Utah, Aug 12-15. The conference site, on the campus of Utah State University, couldn’t have been more beautiful!
View from the SmallSat venue, Logan Utah

The technical program, conference organization, and venue were all outstanding!  I bumped into several PSS MATLAB Toolbox customers and representatives from companies PSS has teamed with on past projects.

SmallSat signs guiding the way!

I also had the pleasure of connecting with a number of new companies and teams working on advanced small satellite projects. We presented our Asteroid Prospector paper as part of the Strength in Numbers Session. The presentation was well received and we had a number of individuals express interest and provide feedback on the concept afterwards.

Amanda on the last day of the conference

On Wednesday evening, I was able to take advantage of the organized group activities and participated in the hike in Logan Canyon. It was a great week! Hope to see you all again next year!

Is that a spaceship in your pocket?

I remember the day my dad brought home our very first VCR. It was a glorious invention. No longer were our family outings constrained by the TV Guide. This nifty VCR would magically record our favorite shows and allow us to play them back whenever we wanted. It wasn’t long before we had a cabinet full of unlabeled tapes — most of which were never watched again, except while searching for something we accidentally recorded over. But still, it was cool.

That first day, my dad and I watched “The Empire Strikes Back”. Twice! Being just five years old, this was my first “real” movie. I remember in the opening scenes, the huge imperial star destroyer floating ominously across the screen. It seemed to go on forever. Okay, so this is a spacecraft.

Fast forward 32 years. Everything seems to have gotten… smaller.

We can now manage our DVR, record our own digital movies, tweet, text and call from that little smartphone in our pocket. And those huge spaceships from 1980’s fiction? They are now about the size of that first VCR.

We’ve recently designed a 6U CubeSat capable of escaping Earth orbit, rendezvousing with an asteroid, and returning to Earth. Its called “Asteroid Prospector”. It’s shape is 12 x 24 x 36 cm, which is about 5 x 10 x 15 inches, and it weighs about 40 lbs. In other words: its a 1981 VCR. But it goes a lot faster.

Earth departure spiral for the Asteroid Prospector

Earth departure spiral for the Asteroid Prospector

The Asteroid Prospector is propelled through space using a Busek Bit-3 ion thruster. It uses electric power to accelerate ions out the nozzle at high speed, pushing the spacecraft in the opposite direction of the ion stream. This gives us a small thrust of 1.9 mN, but it can operate for nearly 3 years on just 5 kg of propellant! We are presenting the spacecraft design, mission analysis and example asteroid rendezvous simulations at the upcoming SmallSat conference.

Fast forward another 32 years. Is that a spaceship in your pocket?


Getting Started with the CubeSat Toolbox

The CubeSat toolbox is a set of MATLAB functions, including a subset of the Spacecraft Control Toolbox, designed to facilitate CubeSat design. The best place to start is to run the example scripts in CubeSat/Demos, including AttitudeProfileDemo, OrbitAndSensorConeAnimation, CubeSatSimulation, and TwoSpacecraftOrbitSimulation.

Orbit animation with sensor cones

Contact us for your free demo today!