Analysis and design of fast input shapers for the control of flexible structures

In the control of flexible structures there are many methods that are used to reduce residual vibration from the excitation of flexible modes. Input shaping, a feed-forward method, typically convolves the input with a sequence of impulses that is independent of the system maneuver. While reducing the residual vibration, input shaping also extends the duration of the maneuver command by the length of the input shaper. Various input shaping methods can be applied depending upon the number of modes that need to be cancelled and the robustness to parameter variation that is desired. This dissertation analyzes the length of input shapers from different methods to see what can be done to decrease their length and thus increase the speed of the maneuver.; First some of the conventional input shaping methods are analyzed and compared to determine which shaper methods result in a faster shaper for different combinations of modes. Next a new approach is taken that creates shaped commands of equal length by applying increased control authority. General conditions for which an equal length shaped command will reduce vibration are analyzed and presented, and then an equal length shaped command is applied to a tape head tracking system to demonstrate a 35% reduction in settling time. Lastly the idea of adaptive input shaping is explored and two methods are presented: one that tunes the shaper between maneuvers and one that tunes the shaper during a maneuver. These methods are demonstrated to have large regions of convergence and to be less computationally complex than other approaches.