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In the ConstantActuator model the force F is strictly proportional to the current i as indicated by the converter constant c. However, there is an additional non-linear force component in such an actuator that is due to the dependency of the coil inductance L on the armature position x. The inductance increases as the armature moves into the stator. The total force is

    1  2 dL
F = - i  --  + c i
    2    dx

Both force components are properly considered with a simple permeance model as shown in the figures below. Figure (a) illustrates the dimensions of the axis-symmetric moving coil actuator that are needed in the permeance model. Figure (b) shows partitioning into flux tubes and the permanent magnetic field without current. G_ma and G_mb both are the permeances resulting from a series connection of the permanent magnet and air gap sections. The field plot of the coil-imposed mmf is shown in figure (c) without the permanent magnetic mmf (H_cB=0). The placement of the magnetic network components in figure (d) retains the geometric structure of the actuator. In figure (e), the permeance model is restructured and thus simplified.