I believe your using the wrong equations for your transfer function. The equations that you are referencing to in the above article are for levitating a soft magnetic material (such as steel). If you are using a hard magnetic material (such as a permanent magnet) the equations are going to be different. The reasoning is that the mechanism that generates force is different. The soft magnetic material's force is due to the change in inductance vs change in position. Whereas the permanent magnets flux couples with the coil and the force mechanism is the change in magnetic flux vs the change in position.
In addition, a permanent magnet has the same permeability as air, so the inductance that the coil sees does not change with respect to the position of the magnet. Steel has a permeability around 2000 times that of air. Hence the inductance changes when the object gets closer or further from the coil.
The amount of flux that couples with the coil is going to change with respect to the position of the coil you are using. I would highly recommend modeling your system in FEMM and solving for the flux linkage at several magnet positions.