General Question PMI, RD, and Torque.

[Hlynkacg]

I'm not sure if this is a silly question or if I should be posting this in the "Math & Physics" forum but I'm working on a stack optimization program/autopilot and I need some help.

Basically I want to be able to set a desired angular acceleration. To do this I need to be able calculate how much torque in newton-meters is required to achieve the desired acceleration.

I know that in an idealized situation, Acceleration = Torque / Inertia (mass)

What I am unclear on is how the values returned by "GetRotDrag()" and "GetPMI()" factor into the above.

Once I know how much torque is required, gimbaling the engines or firing the RCS to achieve the desired torque is pretty straight forward.

 

[Urwumpe]

PMI = principal moments of inertia = moments of inertia divided by mass.

The moments of inertia are what you call inertia.

RotDrag is aerodynamic drag, that applies to rotating bodies.

You can also calculate a very close approximation of the ideal engine deflection by a PI or PID controller.

 

[Hlynkacg]

PMI = principal moments of inertia = moments of inertia divided by mass.

The moments of inertia are what you call inertia.

RotDrag is aerodynamic drag, that applies to rotating bodies.

You can also calculate a very close approximation of the ideal engine deflection by a PI or PID controller.

So to make sure I follow correctly...

As far as orbiter is concerned, in the absence of an atmosphere, acceleration around the X axis is X axis torque (in newton meters) / GetPMI ().x ?

You can also calculate a very close approximation of the ideal engine deflection by a PI or PID controller.

That's part of what I'm trying to get to

 

[Urwumpe]

As far as orbiter is concerned, in the absence of an atmosphere, acceleration around the X axis is X axis torque (in newton meters) / GetPMI ().x ?

No, it is:

Torque = Diag(PMI) * Mass * Acceleration

(F = m * a)

Diag(PMI) creates a matrix with the elements of the PMI vector being on the diagonal.

 

[Hlynkacg]

No, it is:

Torque = Diag(PMI) * Mass * Acceleration

(F = m * a)

Diag(PMI) creates a matrix with the elements of the PMI vector being on the diagonal.

Where does the matrix come into this? I thought we were discussing floats rather than vectors?

basically i want a function where f(x) = angular acceleration around a given axis, and x = torque in newton meters. What do I do?

 

[N_Molson]

You can also calculate a very close approximation of the ideal engine deflection by a PI or PID controller.

Hehe I asked the question a couple of time and you gave me that answer a couple of times, but my mind seems very resilient to the concept of PI / PID controller, I understand it is something like cruise control in a car, but still have no idea of the maths/logics/physics behind it

 

[Urwumpe]

Where does the matrix come into this? I thought we were discussing floats rather than vectors?

basically i want a function where f(x) = angular acceleration around a given axis, and x = torque in newton meters. What do I do?

Do you only have one single rotation axis? Then you have a one element matrix = float and one element vectors = float.

So:

Torque = PMI * mass * acceleration

And thus:

acceleration = Torque/(PMI*mass)

 

[Hlynkacg]

Do you only have one single rotation axis?

No but I'm only worrying about one at a time. For instance allowing the roll stability program to operate independently of a pitch and yaw autopilot.

 

[Urwumpe]

Hehe I asked the question a couple of time and you gave me that answer a couple of times, but my mind seems very resilient to the concept of PI / PID controller, I understand it is something like cruise control in a car, but still have no idea of the maths/logics/physics behind it

Well, it is actually rather simple in the beginning and gets a bit more complex later.

P = proportional
I = integrative
D = differential

proportional means you have function:

Steering = constant * error

Integrative means you have a function:

Steering = constant * integral(error)

Differential:

Steering = constant * rate-of-change(error)

PI would be the sum of P and I:

Steering = constant1 * error + constant2 * integral(error).

etc.

error is the difference between target value and current value, eg, target velocity vector vs current velocity vector.

The important thing to know is the behavior of each P, I or D when you have a changed error. But that is something I explain later or let you research it.

 

[martins]

The relationship between angular velocity, angular acceleration, PMI and torque is given by Euler's equations of rigid body rotation. These are the angular equivalent of F=ma.

 

[N_Molson]

The relationship between angular velocity, angular acceleration, PMI and torque is given by Euler's equations of rigid body rotation. These are the angular equivalent of F=ma.

HE has spoken !! :hail: :hail: :hail: I'm going to recitate this 100 times each morning. :hail: :hail: :hail: