Trajectory Tracking and Vibration Control of Flexible Beams in Multi-Axis System

In this paper, an X-Y position stage simulates flexible loads completing handling or detection tasks in industrial applications are studied. The platform is driven by permanent magnet synchronous motors (PMSM) servo system, which has flexible beams with different natural vibration frequencies on the X-axis and Y-axis. The controller is designed to suppress the vibration of the flexible beams with different frequencies and reducing the contour error. The Euler-Bernoulli beam theory is adopted to obtain the mode shapes and natural frequencies of the flexible beam with clamped and endpoint mass boundary conditions. Analysis shows that the first-order vibration mode contributes the most to the displacement of the flexible beam. The trajectory motion profile based on time-shifted cosine jerk central angle interpolation (CJCI) contains prefilter to suppress low vibration frequencies in the two beams, which does not cause distortion of the actual contour. The linear phase lead iterative learning control (ILC) combined with the contour of CJCI is proposed to reduce the tracking errors of each axis, thereby reducing the overall contour error. The analysis and design process of ILC in frequency domains, which is applied to alleviate noise and disturbance effects. Comparison experiments confirm the effectiveness of the proposed method.