Decreasing infinite-mode vibrations in single-link flexible manipulators by a continuous function

Unwanted vibrations caused by the commanded motions degrade positioning accuracy and safety in flexible link manipulators. There are an infinite number of vibration modes in a single-link flexible manipulator. The contribution of the first mode is fundamental, but the high modes might also have some impacts on the overall system dynamics. A continuous function is designed to control the vibrations of the total modes by smoothing the driving commands. Comparison between the new continuous function and input shaper, which is a series of impulses, is also explored and evaluated. Numerous simulations and experiments for a wide range of working conditions and modeling errors are performed to validate the effectiveness of the new continuous function.