After minimizing the coupling effects, I created a 1 DOF Simulink Model to test whether the setup is stable in the vertical direction. Below appears the model. We have not included yet Eddy Current Damping (simulations showed no great changes).

We create noise with a pulse generator and recorded the step response of the system with the oscilloscope, which appears at Output (1). 

The behavior of the system appears stable and so we tried to levitate the plate starting from AC3. The plate would jiggle back and forth back after some time the DAC would saturate. Going back to the Simulink Model, the relationship between saturation limits and noise amplitude seem to determine the stability of the system as well. Looking at other factors that might affect our system, we consider the following:

• The force of the gain directly depends on the location of the plate. The coils are not strong enough and the magnetic field created is non-uniform around the plate. Prior to this summer, Haixing had acquired measurements for the correlation between the plate's distance from the coils and the force exerted on it and we intend to use this information in our model.
• ADC and DAC background noise may limit the sensitivity of our system
• We need a more precise measurement of the system's rigidity. For a linear degree of freedom, such as the vertical direction, the rigidity can be measured as F/distance. Haixing's measuremts of the force exerted as a function of the distance from the plate will be used.