We describe the design and performance of the digital servo and motion control system for the 6-meter parabolic antennas of the Submillimeter Array (SMA) on Mauna Kea, Hawaii. The system is divided into three nested layers operating at a different, appropriate bandwidth. (1) A rack-mounted, real-time Unix system runs the position loop which reads the high resolution azimuth and elevation encoders and sends velocity and acceleration commands at 100 Hz to a custom-designed servo control board (SCB). (2) The microcontroller-based SCB reads the motor axis tachometers and implements the velocity loop by sending torque commands to the motor amplifiers at 558 Hz. (3) The motor amplifiers implement the torque loop by monitoring and sending current to the three-phase brushless drive motors at 20 kHz. The velocity loop uses a traditional proportional-integral-derivative (PID) control algorithm, while the position loop uses only a proportional term and implements a command shaper based on the Gauss error function. Calibration factors and software filters are applied to the tachometer feedback prior to the application of the servo gains in the torque computations. All of these parameters are remotely adjustable in the software. The three layers of the control system monitor each other and are capable of shutting down the system safely if a failure or anomaly occurs. The Unix system continuously relays the antenna status to the central observatory computer via reflective memory. In each antenna, a Palm Vx hand controller displays the complete system status and allows full local control of the drives in an intuitive touchscreen user interface. The hand controller can also be connected outside the cabin, a major convenience during the frequent reconfigurations of the interferometer. Excellent tracking performance (~ 0.3′′ rms) is achieved with this system. It has been in reliable operation on 8 antennas for over 10 years and has required minimal maintenance.