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A mathematical analysis of a typical sampled-data servo-drive for computer numerical control (CNC) machine tools is presented with the objective of providing the control engineer with useful design charts for the selection of system parameters. A mathematical model is first developed which facilitates the evaluation of the relation between servo-loop gain and computer sampling rate. The question of stability is reviewed, and a solution for the time response of the sampled-data system is presented. Different performance criteria are discussed including: selection of desired damping factor; maximum overshoot; integral of speed square-error; position steady-state error; and the absolute value of the error. The latter criterion has been chosen as the most useful approach. System performance evaluation is presented in the form of dimensionless charts. A final design procedure is recommended which utilizes a dimensionless chart to select sample rate and gain in order to achieve an optimal performance consistent with allowable contouring accuracy and closed-loop bandwidth.
Date of Publication: May 1978