Time-Optimal Trajectory Generation for Machine Tool Feed Drives and Implementation by Contouring Control

Time-optimal trajectory planning for mechanical systems has been widely studied thus far because of its effectiveness to reduce the time required for many industrial tasks. However, in general, because the time-optimal trajectory is generated based on ideal dynamics of controlled systems, it may be difficult to implement the obtained trajectory to actual systems with vibration mode that is neglected in the trajectory generation. In other words, high-speed motion based on the time-optimal trajectory may cause the vibration of the real system. Hence, in this paper, we propose to employ the contouring control developed by the authors, which enables to reduce controller gain magnitudes while contouring performance are maintained. First, this paper presents a method of generating the time-optimal trajectory for machine tool feed drives. The presented method considers viscous friction that is significant in high-speed motion of mechanical systems and has an advantage that the number of variables required for the optimization is reduced compared to the conventional method. Next, the contouring controller is applied to implement the time-optimal trajectory to an actual machine tool system. The effectiveness of the proposed method and the contouring controller is demonstrated by comparative experiments with the conventional method.