For a project we have to make a balance system for a plate which is about 0.15 m². The plate will be attached to a driving and turning system which will have to go over bumps and other small obstacles (glasses or beer coasters). On the plate there will be ten glasses (total weight of plate and glasses around 4 kg). Our plan for the balance system is to use a gyro sensor for balance in one axe. We want to sent the data from this sensor to a arduino system which sends output data to a hydraulic actuator which compensates the movements caused by the bumps and obstacles.

My question to you is wether there is a existing code for the arduino and wether it is capable of doing as above described. We do not have a lot of experience with programming this kind of systems.

I doubt if you will find anything that specific.

What about the passive approach and have the tray mounted on a gimbal of some sort - or just some kind of damped suspension or mount the tray on a universal joint, with a counterweight hung underneath to keep it level.