Stability Analysis of a One Degree of Freedom Robot Model with Sampled Digital Acceleration Feedback Controller in Turning and Milling

Abstract This study is interested in the stability of robots in machining. The goal is to improve the dynamic performance of robots using an additional acceleration signal fed back through the conventional built-in proportional-derivative controller provided by the manufacturer. The structure of the robot is modelled with a simple one degree-of-freedom lumped model and the control signals are fed back via a linear spring and damping. The time delays of the feedback controllers are considered as zero-order holds, which results in sawtooth-like time-periodic time delays. The resulting equation of motion is an advanced delay differential equation. The semidiscretization method is shown for such systems having multiple sampled digital delays and continuous delays. First, we establish the stable regions in the plane of the sampling delay and the gain of the acceleration signal without machining. Then, we show the possibility to improve stability in turning and milling using the additional acceleration feedback controller compared to the cases without any controller or using only the built-in proportional-derivative controller.