An electro-mechanical control system for controlling all of the movements of one or more slides on a single workhead grinding machine. A programmable controller is interfaced with a digital to analog converter or feed control which in turn controls a drive motor that is directly connected to a screw actuator means that directly controls the movements and positions of a slide. The positioning accuracy of the control system is derived from the accuracy of the electronic control components and the stability of the machine. The control system can control the operative movements of each slide in a compound slide assembly, simultaneously or independently, for a part of a grinding machine cycle. The compound slide assembly may alternatively carry a rotating grinding wheel or a workhead that is reciprocated at high speed for a grinding operation on a workpiece.