On the relationship between wave based control, absolute vibration suppression and input shaping

The modeling and control of continuous flexible structures is one of the most challenging problems in control theory. This topic gains more interest with the development of slender space structures, light weight aeronautical components or even traditional gears and drive shafts with flexible properties. Several control schemes are based on the traveling wave approach, rather than the more common modal methods. In this work we investigate the relationships between two of these methods. The Absolute Vibration Suppression (AVS) controller, which was developed for infinite dimension systems, is compared to Wave Based Control (WBC) which was designed primarily for lumped systems. The WBC was first adjusted to continuous systems and then the two controllers, whose algorithms seem different, are compared. The investigation shows that for the flexible shaft these two control laws are actually the same. Furthermore, when converted into an equivalent open loop controller they appear as an extension to continuous systems of the Input Shaping (IS) methodology. ► Three wave based control methods for flexible system are compared. ► When adapting WBC to structures it is identical with AVS. ► Both WBC and AVS can be viewed as extensions of closed loop input shaping.