Vibrations of machines subjected to digital force control

When a robot has to interact with the environment, force control of the contact between its actuator and the workpiece may be required. Force control tries to maintain a prescribed contact force. Basic text books often call the attention for the destabilizing digital effects, like sampling, in these systems. In this paper, the stability limits are presented in the parameter space of the sampling time, control gains and mechanical parameters. The least force error and the fastest settling force signal is calculated with simple closed form formulae. These analytical results have a central role in understanding the technical phenomena and in forming the common sense in design work.