I Transfer Function relating momentum and force

[thoraxepi]

Hey all,

I hope this is the correct forum section to post this in.
I heard about this problem from a youtube video but I've not been able to simulate it because the video was meant only for an introduction into PID control.

Here's the problem:

A remote control helicopter is hovering just above the ground (0 m). It is desired that the helicopter hover at 50 m. Develop a transfer function that takes an input from the controller and outputs height in meters. The measurement block has negligible dynamics (Gm=Km=1).

What assumptions are necessary?

~~~

My assessment:

The function could be something like dp/dt = Fl(t) - Fg

where p is linear momentum in kg*m/s, Fl is lift force in N (or kg*m/s^2) and Fg is force due to gravity in N.
I need to develop a transfer function that might be in the form H(s)/Fl(s) but I'm not sure how to get there from my differential eqn.

Any help is much appreciated!

-thoraxepi

 

[RPinPA]

Laplace transform both sides of your differential equation. The Laplace transform of dp/dt is -sP(s) - p(0). The differential equation becomes an algebraic equation.

See here for instance on how differential equations are solved by transforming them.
http://tutorial.math.lamar.edu/Classes/DE/IVPWithLaplace.aspx

 

[thoraxepi]

Thank you for the reply.
I think my main issue is finding a transfer function that describes a real system whose output must be height. Upon further review, I find that the problem statement doesn't provide enough information to create a full transfer function without deciding on information about the system.

For example, we could decide that the controller sends an output signal to an electric motor that tells the motor how fast to spin (rpm) and the rpm of the propeller determines the lift force (N) and the lift determines the altitude of the RC helicopter. The equations for propeller force are beyond the scope of the digital process controls course I'm in, so I don't think it would be worth it to relate propeller speed with lift.

If anyone has any comments that might simplify this system, please feel free to share.

-thoraxepi