Method and apparatus for determining magnetic flux and magnetic force in a solenoid assembly

A solenoid assembly comprising:

• a solenoid actuator having a core;
• a coil configured to be wound at least partially around the core such that a magnetic flux (ϕ) is generated when an electric current flows through the coil, the coil defining a coil turn number (N);
• an armature configured to be movable based on the magnetic flux (ϕ), the armature defining a position (x) and an armature velocity (dx/dt);
• a controller operatively connected to the coil and having a processor and tangible, non-transitory memory on which is recorded instructions, execution of the instructions by the processor causing the controller to:
• obtain a plurality of model matrices, including a first model matrix (A0), a second model matrix (B0) and a third model matrix (C0);
• obtain a coil current (i1) and an eddy current (i2) based at least partially on an applied coil voltage (V) and at least two of the plurality of model matrices;
• obtain the magnetic flux (ϕ) based at least partially on the third model matrix (C0), the coil current (i1) and the eddy current (i2);
• and
• control operation of the solenoid actuator based at least partially on the magnetic flux (ϕ).