Comparison of residual-vibration and energy-minimizing control methods for command generation

There are numerous methods for controlling unwanted vibration in machines. One possible approach is to design reference command profiles that move the system without inducing significant residual vibration. Many approaches have been proposed for designing such low-vibration commands. Some of these methods design the command profiles by minimizing the residual energy, while others minimize the residual vibration amplitude. Given that energy functions are naturally quadratic in nature, problem definitions using residual energy are generally easier to solve than those based on residual vibration. However, minimizing residual vibration, rather than residual energy, is the more direct approach to achieving the desired goal. So, the question naturally arises as to whether minimizing residual energy is a good approach to minimizing residual vibration. This paper explores this issue and demonstrates that minimizing residual energy is not necessarily a good approach to minimize residual vibration of multi-mode systems.