You can write nonlinear model equations using force balance equations. Then linearise it using Taylor series considering only the first order terms at the equilibrium point (where net force is zero). Or else if arrangement is available you can incorporate a stabilizing controller (May be PD ) by making it close loop to make the close loop stable. Then you can carry out system identification by exciting the system by some standard excitation signal like (PRBS) then using the I/P and O/P data you can find a linearised model using MATLAB System Identification Toolbox. For more you may see any book on how to identify a O/L unstable system.
You may consider non-stationary setup: magnetic field between two ems has a point where the second derivative over the distance is zero. This is the area there the field is the most linear. Changing the strength of em currents you can shift this area up and down. Doing this periodically with high enough frequency you may get quasi-linear mean magnetic field in a larger area. Just an idea, may not work.