A novel single-axis motion control system using solenoid electromagnet actuators is built and successfully controlled using a non-linear real-time control algorithm. Procedures for defining and modeling the electromagnetic actuator are established and implemented. Discrete-time nonlinear control law with global asymptotic stability and zero steady-state error is designed and numerically optimized. Stable operation with small-signal 0dB crossover frequency of 370 Rad/sec and positioning RMS steady-state error of better than 4 micron is achieved. Time domain parameters are verified on a working prototype. A step reference response positioning a 0.35 Kg mass payload over 1 cm travel in under 30 milliseconds is demonstrated.