[AR] Re: Probalistic model of solid rocket motor thrust curve?
- From: "Ed LeBouthillier" <codemonky@xxxxxxxxxxxxx>
- To: <arocket@xxxxxxxxxxxxx>
- Date: Mon, 11 Apr 2016 18:12:29 -0700
I'm interested in using state-space tracking techniques to try to improve
position tracking for a rocket, but I need a process model for the motor.
Are you tracking the rocket from the ground or from the vehicle?
In either case, the general technique used is often the Kalman filter [
https://en.wikipedia.org/wiki/Kalman_filter ;].
In general, models which include probabilistic variance are called Stochastic
models [
https://en.wikipedia.org/wiki/Stochastic ;].
You can generally take the differential equations and turn them into linear
models suitable for practical use.
I have the manufacturer thrust curve and a measure of variability, but
modeling the variability as noise doesn't really make sense because thrust
from moment to moment shouldn't be statistically independent of the previous
moment, it should be roughly the same and change only slowly.
For a good general overview of stochastic state space models, my favorite is
Optimal Control and Estimation by Stengel.
http://www.amazon.com/Optimal-Control-Estimation-Dover-Mathematics/dp/0486682005
You can find PDF copies floating around on the web.
But, generally, the noise is considered to be independent and white riding over
the predicted values.
What kind of model might be appropriate?
Without knowing more about the accuracy you’re trying to attain, it’s hard to
suggest a one-size-fits-all model.
There are numerous models with differing degrees of fidelity.
However, you can work out the various relationships using first-order
approximations.
For example, there is the rocket thrust equation:
https://www.grc.nasa.gov/www/k-12/airplane/rockth.html
Using that, you can model the nozzle effects as the rocket ascends through the
atmosphere.
A good site for general solids rocket propulsion is Richard Nakka’s site:
http://www.nakka-rocketry.net/
If you look there, you can find numerous equations for modeling the burn of
solids. Perhaps the most relevant one might be:
http://www.nakka-rocketry.net/th_thrst.html
You can use the combustion equations for determining the thrust over time.
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