Command shaping for flexible systems: A review of the first 50 years

The control of flexible systems is a large and important field of study. Unwanted transient deflection and residual vibration are detrimental to many systems ranging from nano-positioning devices to large industrial cranes. Thousands of researchers have worked diligently for decades to provide solutions to the challenging problems posed by flexible dynamic systems. The work can roughly be broken into three categories:1) Hardware design, 2) Feedback control, and 3) Command shaping. This paper provides a review of command-shaping research since it was first proposed in the late 1950's. The important milestones of the research advancements, as well as application examples, are used to illustrate the developments in this important research field.