Rotating Belt control system

Hi all,
I need materials and advices to design a control system for a one direction rotating belt. The goal of this system is to sustain an object in an unstable equilibrium position. The problem resembles a lot to Inverted pendulum or the Self-balancing unicycle

The system is shown in the figure. Its is composed of two rotating belts among which one is planar and rotates continuously without interruption while the second has a slope of about 40 degree. This belt receives periodically objects from the first one and tends to transport them to the top point of the belt such that a robot arm can catch them. Objects are solids with different weights. A scale (see figure) is used as a sensor to detect if the object reached or not the top point of the belt.
The belt rotates in one direction to bring the object to the desired direction.
When the object is exactly in the top the scale indicated a maximum of weight forcing the belt to stop.

I find the control system difficult to implement since one direction control is involved and because the weight measured by the scale will have a bell shape which maximum has to be determines in real time.

Please refer me to the appropriate materials.

Thanks in advance.

I think that if the belt only moves in one direction the system is underactuated. Unless gravity or other forces can bring back the object if it overshoots the position, there is no way to control it in an unstable position.
You may use an optical or proximity detector to stop the object just before reaching the top. Then it would be in a stable position and no control system is required.
Or redesign the belt with an horizontal plane at the top.

Hi alber32,
Yes, as you said, the one direction rotation and the absence of the restoring force are what make the system complicated to control. I modified the figure by adding a second slope to provide the restoring forse needed for stability.
Can you refer me to materials dealing with equivalent systems ?
Thanks in advance.

Sorry but I dont see how the second slope can do that. I would rather drive the object to an horizontal plate which may have the scale sensor. So the object just sits there waiting for the robot to pick it up. It is much simpler.

The subject of inverted pendulum is covered in any book of feedback systems like like the classics by Kuo or Åström but they are very complicated in math.
The simplest approach that I have seen is here:
https://ww1.microchip.com/downloads/en/AppNotes/00964A.pdf

Thank you Albert22. I will try to find this book. I hope to find in it something not complicated that I can understand.