A review of command shaping techniques for elimination of residual vibrations in flexible-joint manipulators

Abstract

Command shaping is an important open-loop control method for improving the settling time and positioning accuracy. This technique also minimizes residual vibrations. Shaped command profiles are formed by convolving a sequence of impulses or solving special functions for the desired command signal. To determine the input shaper controller commands, estimated values of the system natural frequency and damping ratio are required to make the necessary calculations. However, real systems cannot be modelled precisely, while robustness of the shaper to modelling errors is an important design consideration. Many robust input shapers have been developed and reported in the literature. It has been observed that the robust shapers typically have longer travelling time durations that lead to slow system response. This makes a relationship between shaper rising/travelling time and robustness. This paper presents a review of command shaping methods and analyses the compromise between duration of motion and shaper robustness for positive and smoothly shaped reference commands.