Ways to control height in a flexible model

In last post simulations showed that a rigid model will have a better behaviour (its equilibrium height is much lower and there are no problems related with rubber burst). In addition, if a system with controlled volume could be easily (and lightly) built, that problem would be solved.
Unfortunately that’s much easier to say than to actually do, besides a rigid model would me much heavier, so I’ll have to manage with a flexible one.

I’ve been thinking in a way to control height without consuming energy (that’s an important issue all the time, but especially at night), and I thought on the following system:

It’s a piston than can compress and expand the gas it contains (helium, for example). When ‘x’ increases, the rest of the gas has more space to fill, so the pressure drops and hence its radius decreases. That increases the system’s density and its lift is much lower. The opposite happens when ‘x’ decreases.

To check its performance in a simulation first is important to create some kind of law to relate ‘x’ as function of current radius, velocity, position and whichever other factors.

One control function can be the following (remembering the formula x=1/2*a*t^2):

Being:
h_des=desired height
h= current height
v=current velocity
a=current acceleration
a_crit=desired acceleration

a_crit=(2.*(h_des-h-v*10.)/100.) (making t=10)

And the condition (in pseudocode):
If a>a_crit then increase x
else decrease x
With x between (0,L)

With that control system I run the simulation. First of all it randomly assigned a desired height between 0 m and 9000 m, and tried to reach it. When it’s stabilized at that height it changes the desired height to another one.

The result is shown in the following graph, where both height and diameter were adimensionalized with it’s maximum value so that it’s represented d/dmax and h/hmax as function of the time in hours (max height 8000.09 m and max diameter 3.710571 m.). Since the desired height is chosen randomly in any other simulation the max values may differ.

That system of control seems to work, but further study has to be carried out.