Stability of turning processes subjected to digital PD control

Abstract

Stabilization of turning processes with a digital proportional-derivative feedback controller is analyzed. A one-degree-of-freedom model of the turning process is considered. The control force is assumed to be acting directly on the tool. The sampling effect and the delay of the digital controller are involved in the model. The governing equation is a periodic delay-differential equation, which includes a continuous point delay due to the regenerative effect of the material removal process and a discrete delay (i.e., a term with piecewise constant argument) due to the sampling effect of the controller. The principal period of the system is the sampling period. The stability analysis is performed using different implementations of the semi-discretization method. A series of stability diagrams are presented for different proportional and derivative control gains.