Control Engineering Coursework Questions

[meyra31]

Hi guys..
I am here to really beg for an help.. I have a coursework due on Friday and im stressed big time for it.. I tried it hours weeks and ages but i can't get anywhere.

Please i would really really appreciate if someone can help me solve it..

Attaching a picture for the questions..

 

[BradtheRad]

Speaking for myself, I don't get the parameter called 'quadcopter height'. Is it the height of the craft? I don't think it is.

Or is it altitude? Altitude isn't calculable, unless it has to do with predicting altitude after a known length of time while rotating the prop at a constant speed? You would need to know rate of climb or descent.

Or does the text say height when it really means vertical speed?

Anyway it seems to me that hover rpm is the chief parameter of interest, requiring a certain prop speed. From knowing that, you can calculate climb or descend rates based on various prop speeds.

I also don't get that the 'Thrust' arrow points upward.

 

[CataM]

Hi,

I am able to answer only the first question because I haven't studied z Transform yet... sorry.

Newton seconds law is like this: Sum of all forces applied to an object = mass of that object·acceleration of that object. (Note that this is a vectorial equation not a scalar one)

On the height direction (I am not going to put the vectors, just the module of the vectors because I have already said that I am going to work on the height direction).

\[Ft-Mg=M\frac{{d}^{2}x }{d{t}^{2}}\]
Replacing "Ft" by "kt·v" you have v=f(x) what was required (Mg is a constant)

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I also don't get that the 'Thrust' arrow points upward.

For the height x arrow: That means that is the "positive way", theres the origin of displacement. Like the X axis in Math. When I started studying Automation and Control it took me a while to get used to the way they place the problem

Fot the thrust Ft: The force to elevate the copter is going in that way, opposed to the gravity.

 

[BradtheRad]

It states, propeller thrust is proportional to its rpm. I believe that's supposed to be a hint. From the given data, you are supposed to derive a certain value, or scaling coefficient, or formula. I think the idea is for you to be able to predict what height (or change in height) will result from a given propeller speed. It appears each timeframe is 100 mSec.

It may or may not be necessary for you to distinguish between mass and weight. Gravity pulling down on the craft causes it to have weight. Weight is measured in different units from mass. Mass determines how quickly the craft changes velocity in response to a change in prop speed.

I can't be certain but this exercise appears designed to make you generate a vertical maneuverability envelope, so that you know how much, and when, you need to change prop speed, in order to (for instance), (1) make the craft rise at a rapid rate, then (2) stop before it hits the ceiling, and (3) hover stationary.

 

[BradtheRad]

Similarly, when descending via thrust = 180g, and you want to stop short of the floor, then you need to increase prop speed momentarily.

You cannot simply switch to hover rpm, because then inertia (mass) would send the craft overshooting into a crash. You must first counteract inertia by speeding up the prop for a moment, just long enough to stop descent. Then you switch to hover rpm.

You can apply 500 g of thrust for 0.8 sec, then hover.
Or 1000 g of thrust for 0.4 sec, then hover.
Or 2000 g of thrust for 0.2 sec, then hover.
Etc.

I believe that's what the formulas are about. They allow you to forecast what prop speed you must apply during the next 100 mSec, after you determine all contributions from inertia, and gravity, and prop speed, and thrust, during the previous 100 mSec.

 

[CataM]

I believe that's what the formulas are about. They allow you to forecast what prop speed you must apply during the next 100 mSec, after you determine all contributions from inertia, and gravity, and prop speed, and thrust, during the previous 100 mSec.

Of course, they gave you those formulas to model the system, to tell the system all variables that interfere. He needs to do a system (draw the block diagrams required and the feedback) in order to achieve stability to a reference height (Xref). So the system will think and adjust itself. The smoother or not will be depending on how well the PID controller is.

You can apply 500 g of thrust for 0.8 sec, then hover.
Or 1000 g of thrust for 0.4 sec, then hover.
Or 2000 g of thrust for 0.2 sec, then hover.

That will be done by the PID controller.