Model Aircraft Controls Mixing Unit: Find a Tricky Function

[Cyrus]

I am trying to model a controls mixing unit on an aircraft and I need a special function to do this and I can't think of one for the life of me!

I have a ruddervator, which serves as a rudder and elevator. Basically I need the following:

- For a pure rudder input, I get a linear change in rudder +/- 20 deg.

- For a pure elevator input, I get a linear range in elevator for +/- 20 deg.

- For any combination of elevator and rudder, the two need to be mixed (by what amount depends on the function you give me). Ideally, they are weighted equally for equal amounts of inputs. BUT, you cannot exceed 20 degrees deflection of the surfaces, that is their physical limits! So your function has an upper and lower bound.

The last one is easy, its having the simultaneous requirement of the first two points which makes life difficult! If you can't satisfy all three as linear, just give me whatever you got anyways - it might stimulate some ideas in that space between my ears.

 

[Xitami]

$$\frac{20x}{\sqrt{1+x^2}}$$

WolframAlpha

 

[Phrak]

I'm not sure what Xitami's getting at...

Here's a starting point.

$$\theta_{left} = \frac{1}{2}(\theta_{elevator} +\theta_{rudder})$$
$$\theta_{right} = \frac{1}{2}(\theta_{elevator} - \theta_{rudder})$$

 

[Cyrus]

Ah, but the trick is that its not a left and right control because we didn't test it like that. You have to combine pure elevator and pure rudder to get a combination of the two, while not saturating the system.

 

[Ynaught?]

How about using the equation for a circle and setting limit of the control input to equal the radius? Since the deflection is +/- the same degree, the degree doesn't need to come into play. Assuming (x,y) are rudder and stick position, set movement of the rudder pedals left/right cause opposite up/down movement of the left and right control surfaces (equal to increase/decrease of 1/2 x). Set aft/fore movement of the stick to cause an increase/decrease of "y" to both the left and right control surface.

 

[Phrak]

Ah, but the trick is that its not a left and right control because we didn't test it like that. You have to combine pure elevator and pure rudder to get a combination of the two, while not saturating the system.

I'd thought I'd understood your question, or perhaps not. See if this is right:

You have the two standard input controls; stick and rudder. You wish these to be mixed to control a left ruddervator and right ruddervator, presumably arranged in a noninverted "V".

How is that?