Vibration control of a flexible beam driven by a ball-screw stage with adaptive notch filters and a line enhancer

For a low-stiffness beam driven by a ball-screw stage, the lateral vibrations cannot be adequately controlled by a collocated compensator based on rotary-encoder feedback alone. Acceleration signals at the tip of the flexible beam are measured for active vibration control in addition to the collocated compensator. A second-order bandpass filter (a line enhancer) and two notch filters are included in the acceleration-feedback loop to raise modal dampings for the first and the second flexible modes without exciting higher-frequency resonances. A novel adaptation algorithm is devised to tune the center frequencies of the notch filters in real time. It consists of a second-order low-pass filter, a second-order bandpass filter and a phase detector. Improvement of the control system is elaborated progressively with the root-locus and bode-plot analyses, along with a physical interpretation. Extensive testings are conducted on an experimental device to verify the effectiveness of the control method.