Equation for Spin Stabilization ?

[killm2]

Equation for "Spin Stabilization"?

So I'm working on a project by myself, and I've already built it, but I need a certain number to hone in on the efficiency.

What is the equation for spin stabilization? The object spinning is a thin disk (cylinder).

I am going in early tomorrow to have 3 physics teachers help me, but I asked today and none of them knew the equation or had heard of such a thing. I would like the equation if anyone knows it, because I already have the teachers to help me.

Just to clarify, this is NOT homework. I'm doing this for fun actually haha

 

[Mordred]

How many degrees of freddom are involved?

if its a free spinning object it can have upwards to 6 degrees of freedom. more if you count every radian as a degree of freedom. Most examples I red about in ballistics rockets etc usually only deal with a few degrees of freedom. You could probably find what your looking for and adapting one of their calc's to aid you I personally don't know the calc's, that include multiple degrees of freedom simultaneously but if your spinning in one direction you can calculate the centrifical force of that spin then apply a counter force equal to it but over a length of time. To handle the latter Proportional control formulas could help you.
The reason I mention the proportional control is that its designed to reach a desired setpoint over a period of time to prevent overshoot of a set point. Its mathematics decide how much to open the thrusters if its in a high full spin open thrusters all the way. if its a spin halfway from max spin rate open half way etc.
This is often referred to as Fuzzy logic.
I would look at PI calculations to control your stabilizers in conjunction with the centrifical force laws.

 

[xts]

What do you mean by "equation for spin stabilization?"
What exactly such equation should express?

There are many equations more or less related to stabilisation of rotating objects, but none of them is called such...

 

[Mordred]

I'll send a PM to you for a site that deals with PID on a regular basis its another Forum and they are used to dealing with degrees of freedom and controlling spin of shafts bearings etc.
They can probably help you with a suitable controller either PC or PLC based.

To describe why PID is probably needed in your example. Say your moment of inertia is X the amount of force to stop that moment of inertia being N m/s^2

If you apply that amount of force in the opposite direction the object will not instantly stop as it takes time for the cylinder to slow down. As its slowing down if you continue to use the same setpoint for your thrusters as the orignial moment of intertia you will overshoot the spin causing it to spin in the opposite direction. Now let's run a couple of examples.
Say its spinning at 10 revolutions per min if you apply the oposing force all at once and until the object comes to zero ( your setpoint) you will spin in opposite direction.
However if you break the steps down use full thrust to start then sample the rate at say 1 second then recalculate how much force is needed to offset the error of direction, then repeat this sampling every second again at each step recalculating the amount of force needed you will gradually bring the cylinder to rest without overshooting the setpoint.
This process is called fuzzy logic and is something PID is designed to deal with However your not going to be ale to pick this up over night so the site I sent on PM has ppl there that can aid you in this aspect of implemtimenation.

 

[killm2]

How many degrees of freddom are involved?

if its a free spinning object it can have upwards to 6 degrees of freedom. more if you count every radian as a degree of freedom. Most examples I red about in ballistics rockets etc usually only deal with a few degrees of freedom. You could probably find what your looking for and adapting one of their calc's to aid you I personally don't know the calc's, that include multiple degrees of freedom simultaneously but if your spinning in one direction you can calculate the centrifical force of that spin then apply a counter force equal to it but over a length of time. To handle the latter Proportional control formulas could help you.
The reason I mention the proportional control is that its designed to reach a desired setpoint over a period of time to prevent overshoot of a set point. Its mathematics decide how much to open the thrusters if its in a high full spin open thrusters all the way. if its a spin halfway from max spin rate open half way etc.
This is often referred to as Fuzzy logic.
I would look at PI calculations to control your stabilizers in conjunction with the centrifical force laws.

I plan on just printing this full page, because I honestly don't understand much of this (at least I'm honest)

Here are some assumptions to make:
Assume the disk (thin cylinder) is free floating.
Assume the disk is in this position from the side: "\" and I want to make it flat "--" ~45 degrees from goal.
Assume that the force that is causing the disk to spin is at the exact center of the disk.
Assume there are not outside factors. It's in a vaccum.

Does this information help?

Also, I don't need to reach the exact point of spin stabilization, I actually plan to overshoot it. I need to know what to shoot for though.

 

[Mordred]

Details needed

1) mass of object
2) number of possible movements (if the cylinder is on a shaft it only has one possible movement or degree of freedom.
3) circumference of the object
4) method of controlling the spin (rockets magnets etc?
5) output power of the stabilizer at a given supply power.

If you have overshoot you will never reach your setpoint. It will always go above and below that setpoint but never stay on set point.

http://en.wikipedia.org/wiki/PID_controller on the right is a graph representing a PID action to set point you can see the overshoot and undershoot gradually reach the setpoint. This is with PID, Unfortunately this is what in control terms we call a quarterly amplitude decay
Meaning that it has 4 sets of overshoot and undershoot. In most applications this is fine.
If you need to arrive at set point with no over/undershoot we term that it Critically dampened.

Meaning that the initial curve comes smoothly to the desired set point.
without regular sampling and readjusting the stabilizer you would have an overshoot and undershoot curve that looks like a sine wave with same amplitude all the time.

Now to simplify it to terms you can relate to

P =proportional (amount of force needed to reach setpoint)
I =integral error ( or sampling rate)
D= derivitave THis one is hard to explain in laymens but essentialy its a kind of look ahead prediction value that prevents the first two values from going too high.

For your application PI only is needed. When you sample your rate you will need the amount of force needed to correct that parts easy.
The sampling rate is how to cause that slow down in a desired amount of time. Each time you sample calculate the amount of force needed to bring to a stop then calculate the amount of energy your thrusters can deliver/per percentage of the amount the thruster valve is opened.. do this for every sample point.

What will happen is that the thruster/stabilizer will open a little less at each sample point sort of like using less gas on your car gradually to come to a stop.

 

[killm2]

I'm not quite sure I understand the concept of overshooting a setpoint?
In my project, let's pretend the disk is a frisbee.

Are you trying to say that if I spun a frisbee TOO fast to wouldn't remain level?
As far as I know, you can throw a frisbee as terribly as you want as long as you put enough spin on it and it will level out.

Am I wrong to make this comparison?

 

[Mordred]

Look at the graph on the Wiki link I provided. The blue peridicular line is your setpoint.
What they call the reference signal. WIKI doesn't explain it well.

where the bell curve goes above the reference signal is overshoot where it falls below the reference signal is undershoot. Normal PI math leads usually to 4 overshoots and 4 undershoots unless you critically dampen it then there is no over/undershoot but a smooth bell curve to setpoint.

Most PID controllers use the Zeigler-Nickols calculations this always gives a quarterly amplitude decay.
however further fine tuning can remove that decay.

 

[killm2]

Look at the graph on the Wiki link I provided. The blue peridicular line is your setpoint.
What they call the reference signal. WIKI doesn't explain it well.

where the bell curve goes above the reference signal is overshoot where it falls below the reference signal is undershoot.

Will print out this page and that wiki.
I will return tomorrow and let you guys know how it went.

 

[Mordred]

After your meeting with your 3 Physics teachers please let me know what they thought of my recommended methodology.