Using continuous function shaping to reduce vibration for flexible systems

The control of vibration reduction for flexible systems is a significant field of study. Numerous control schemes have been proposed to solve the challenging problems. This paper presented a novel method, called continuous function (CF) shaping, which uses a continuous function to shape the original command for vibration reduction in flexible systems. Unlike previous command shaping strategies, a continuous function is used as the controller to shape the original command. Then, the CF-shaped command should be a smooth profile to suppress vibration. The effectiveness of the CF shaper for robustness is explored and quantified. The theoretic analysis shows that the CF shaper acts like a combination of low-pass and multi-notch filters, which benefits vibration reduction for multi-mode systems. Experimental results from a small-scale double-pendulum bridge crane transporting distributed-mass payloads validate the simulated dynamic behavior and the effectiveness of the new method.