This relates to a control mechanism for keeping a solar panel at optimum angles to the sun. It is really more of a thought problem than a practical solution I just found this to be the best example for building a model. I am not really looking for a better solution as much as I am trying to solve this one. So any answers should be based on something operated with freon gas pressures reacting with the sun. I will try and state the problem along with thoughts on it the best I can.
A couple of cylinders big enough to pivot and rotate the panel by simply going in and out would be installed and it would respond to somewhere between two and three gas filled containers . the containers would be positioned so they they did not get the same amount of sunlight and heated up (higher pressure) at different rates. So I am assuming that the valve would have to operate on a differential of pressures. I can’t figure out how to configure a control valve that would do this.
I’ve going to avoid the term “cylinder” since that’s ambiguous.
Here a much simpler idea:
Connect one gas supply tank to one pneumatic push-only actuator on the e.g. east side of the south-facing panel. Put an identical arrangement on the west side in mechanical opposition. As one actuator extends to rotate the panel, the other must retract. Place the supply tanks such that when the panel is aligned with the sun they are equally in the shade of the panel. As the sun moves, so does the panel’s shadow. Which causes one supply tank to move out of the shadow and heat up in the direct sun and supply increasing pressure to its actuator while the other tank moves more deeply into shadow, cools, and reduces pressure to its actuator. Which differential pressure in the two opposing actuators causes the panel to rotate to once again center the two tanks in its shadow. Thus you get accurate and completely passive solar tracking. With no valves at all.
You will need a reset mechanism, perhaps a spring, to pull the panel back to its easternmost orientation overnight. Once the sun has set pretty quickly the two tanks will cool equally and there’ll be no net force on the panel rotation. If it takes the spring 10 hours to slowly drag the panel back to face eastwards, that’s plenty good enough. So it doesn’t need to be all that strong. The westward tank and actuator would need to be slightly oversized versus the eastern one to overcome the asymmetric pull of the spring during the day. But that’s just a matter of fine tuning.
In reality none of this will work because the net pneumatic forces are far too small to move anything big enough to matter. Far smarter to use electric motors and some sort of electronic shadow sensor or even a computer with a clock and an ephemeris. After all, it's a solar panel; there will be electricity right close at hand all day every day.
If their were only about 1# differential pressure you could use a 9 sq in diaphragm operated piston and get 9# push on it. That should be enough to slowly rotate something that is counter balanced.
It’s actually a little more complex than I described.
The tanks would have to be mounted on a base that rotates with the panel. So the tanks, their base, and the panel rotate as a unit to track the sun. The end of the actuators that are not attached to the yoke that rotates that assembly would be attached to the non-moving ground nearby.
Designing something of industrial scale for outdoor long term use with little maintenance that also responds to very light forces is quite a challenge. I conveniently ignored wind. Which is a non-trivial issue for solar panel installations whether moving or fixed.
Many, many solar installations are fixed because the incremental cost and complexity of sun-tracking doesn’t produce enough extra power to pay for itself over the life of the panel. It’s cheaper and far more reliable & low-maintenance just to install a few more panels.