(Dr. William Singhose, advisor)
"Investigation and Development of Reference Commands for Vibration Reduction"
The shape of a reference command can have a significant impact on system performance. Input shaping is one type of command generation scheme for reducing residual vibrations in computer-controlled machines. This technique consists of convolving a sequence of impulses, an input shaper, with any desired system command to produce a shaped input that is then used to drive the system. The time locations and amplitudes of the input shaper are determined by solving a set of constraint equations. Most often, the reference command is a step function because it yields the fastest rise time. This choice, however, is often debated. Some researchers claim that smooth commands are more appropriate to drive flexible systems because they tend not to excite the flexible modes as much.
The research conducted in this thesis addresses two main topics. First, a new approach is proposed on interpreting smooth command profiles such as S-curves or trigonometric transition functions as input-shaped functions. This leads to fundamental frequency analysis results and common comparison criteria. It also creates a platform for creating new commands that benefit from both input-shaping and smooth transitioning. Experimental results from a large robotic arm demonstrate the key results.
The second type of problem under study in this thesis relates to saturation issues. Input shaping is based on linear system theory, although in some instances, it has proved robust for nonlinear systems. Because of their nature, step inputs sometimes yield actuator saturation, making the system nonlinear. The classical solution consists of avoiding saturation. This work instead revolves around developing input shapers that take into account saturation. This method benefits the system in settling time and avoids adding complexity to the input shaper design.