Design Parameters forSampled-Data Drives for CNCMachine Tools

A mathematical analysis ofatypical sampled-data servo- drive forcomputer numerial control (CNC)machine tools ispresented withtheobjective ofproviding thecontrol engineer withuseful design charts fortheselection ofsystemparameters. A mathematical model isfirst developed whichfacilitates theevaluation oftherelation between servo-loop gain andcomputer sampling rate. Thequestion of stability isreviewed, anda solution forthetimeresponse ofthe sampled-data systemispresented. Different performance criteria are discussed including: selection ofdesired damping factor; maximum overshoot; integral ofspeed square-error; position steady-state error; andtheabsolute value oftheerror. Thelatter criterion hasbeenchosen asthemostuseful approach. Systemperformance evaluation is presented intheformofdimensionless charts. A final design procedure isrecommended whichutilizes adimensionless chart toselect sample rateandgaininorder toachieve anoptimal performance consistent withallowable contouring accuracy andclosed-loop bandwidth.