One of the most common goals in manufacturing is to improve the quality and accuracy of the parts being fabricated without reducing productivity. Aiming at this goal, many different manufacturing processes have been developed. Among them, machining plays a major role in increasing product accuracy. As an important machining process, grinding is a vital step that can produce both fine finish and dimensional accuracy for applications in which the workpiece material is either hard or brittle. Currently, the ball screw is the most frequently used setup for grinding machine tool feed drive. However, the existence of transmission components induces wear, high friction, backlash, and also lower system stiffness; therefore, applications of conventional feed drives for high speed and high accuracy machining are very limited. As a promising technology, a linear motor feed drive discards the transmission system; therefore, it eliminates transmission induced error, such as backlash and pitch error, and avoids stiffness reduction as well. As a result, a linear motor drive can achieve both high speed and high accuracy performance. A linear motor feed drive will be subject to external disturbances such as friction, force ripple and machining force. Due to the lack of a transmission unit, the tracking behavior of a linear motor feed drive is prone to be affected by external disturbances and model parameter variations. Thus, in order to deliver high performance, a controller should be capable of achieving high accuracy in the presence of external disturbance and parameter uncertainty. This dissertation proposes a general robust motion control framework for the CNC design of a linear motor feed drive to achieve high speed/high precision as well as low speed/high precision. An application to the linear motor feed drives in grinding machines was carried out. One of the developed algorithms is the HSMC, which combines the merits of a reaching law based sliding mode control and a modified disturbance observer for precision tracking to address the practical issues of friction, force ripple, and grinding force disturbances. Another algorithm presented is ASMC, which combines the reaching law based sliding mode control with adaptive disturbance estimation to achieve an adaptive robust motion control.