Servo control using ferromagnetic core material and electrical windings is based on monitoring of winding currents and voltages and
inference of
magnetic flux, a force indication; and magnetic gap, a position indication.
Third order nonlinear servo control is split into nested control loops: a fast nonlinear first-order
inner loop causing flux to track a target by varying a
voltage output; and a slower almost linear second-order outer loop causing magnetic gap to track a target by controlling the flux target of the
inner loop. The
inner loop uses efficient switching regulation, preferably based on controlled feedback instabilities, to control
voltage output. The outer loop achieves damping and accurate convergence using proportional, time-integral, and time-derivative
gain terms. The time-integral feedback may be based on measured and target solenoid drive currents, adjusting the magnetic gap for
force balance at the target current. Incorporation of permanent
magnet material permits the target current to be zero, achieving
levitation with low power, including for a
monorail deriving propulsion from the
levitation magnets. Linear magnetic approximations lead to the simplest controller, but nonlinear analog computation in the
log domain yields a better controller with relatively few parts. When
servo-controlled solenoids provide actuation of a pump
piston and valves, electronic LC
resonance measurements determine liquid volume and
gas bubble volume.