Regards

Abhijith Janardhan

Im using dsPIC microcontroller and want to create a state feedback controller on the dsPIC. I understand the control law is

Torque (T) = torquer dipole moment (M) x earths magnetic field (B)

where M = NIA, therefore T = NIABSIN(x) where x is the angle between M and B.

How do i get the controller to achieve the proper torque needed and turn this into a current to be fed through the torquers?

Using two torquers the torque equation would be T = MxBy - MyBx where Mx is dipole creates from the x-axis magnetorquer

My is the y-axis dipole

Bx is x-component of earths magnetic field ]]>

Great to see the progress. Thanks for allowing us to look in on the project.

I note that in the ADCS section you estimate the altitude of the cubesat to be

330km and the period of an orbit to be 100 minutes.

A quick look at the physics suggests that a satellite at that altitude will have a period

close to 90 minutes. Also, most cubesats to date have been launched into orbits

around 600 - 700km. These differencies may be important to your data transfer

rate (longer access) and to your comm's link budget. (weaker signal at higher

altitude)

Good luck.

Also, to correct for the sine term multiply all times by SQRT[2] (inverse RMS of sine)

Dan

]]>To work out omega correctly, find the torque for your loop and find the moment of inertia of a cube of total mass 1 kg from tippler (there's a table in there somewhere).

That's pretty much what I did, and then combined it with the equation for the magnetic torque exerted on a loop of wire. The whole thing cancelled down very neatly when I expressed it as a function of voltage.

No reason why we can't scale up the mangetorquers and make our craft more manoevrable, really. Size depends on where we get them from. I'll look into some suppliers over Easter.

We'll need to have three sets of coils, one for each axis. Apart from anything else, the earth's magnetic field isn't a neat circle corresponding to our orbit, it's a dipole. (It'll be an interesting test of our vector algebra when the time comes to write the software for our RCS!) Having three coils would also dodge the sinusoidal fall-off problem, as we can run more than one simultaneously to help the craft turn.

(Oh, and it's phil!)

]]>time to stabilize t= (tumbling rate r)/(angular acceleration omega) = (0.1 rad s^{-1})/(0.0004286 rad s^{-2})

= 2.336 x 10^{2}s

= 3:53.6 minutes

Obviously this is underestimating the time quite a bit since the torque (and thus omega) will sinusoidally approach zero as the satellite approaches it's final attitude. But still, stablilization within one orbit (90 mins) or even within two would be totally acceptable I think.

To work out omega correctly, find the torque for your loop and find the moment of inertia of a cube of total mass 1 kg from tippler (there's a table in there somewhere). Also, why don't we just scale up our magnetorquer from radius=0.5cm to radius=5cm. Btw, who are you?

Daniel

]]>Magnetorquers will produce an angular acceleration proportional to the voltage you put across them. For our cubesat (assuming an internal temperature of 25ºC and a circular 1mmØ copper coil) I reckon the acceleration in rads/sec squared will be:

accel = 8571*Volts*Coil Radius*Ambient magnetic field strength*sin theta

…where theta is the angle between the coil's face and the earth's field. Of course, we'll have multiple torquers, so the sin theta bit won't matter as much. Still, it's not as high as it looks; the earth's magnetic field in low earth orbit at the equator (ie the weakest area) is around 10 microTeslas, which assuming a coil radius of 0.5 cm gives us 0.0004286 rads/sec2 for every volt across the coil. That's rather feeble, it'd take days to change direction. I'd heard rumours to that effect on some of the other satellite webpages.

This is assuming there are no glaring, horrible mistakes with my algebra. It's all on a page in my notebook, if anyone's feeling up to checking. I'm kind of glad I did the equations, though. My exams are on the horizon, it's good practice. I tried to keep the equations as general as possible.

So there you have it. Our craft isn't going to be an olympic acrobat; up high the field's too weak and so are our power systems. And it might be crafty to have an additional form of attitude determination to the magnetoresistors; even though they're essential to the torquers the field they read is irregular by it's very nature.

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