| A robust control profile is generated which suppresses all the high frequency vibrations in a flexible dynamic system. This robust control profile is the shifted time-limited version of the functions that optimally achieve the energy concentration property. The robust control profile is designed by considering the first resonance frequency. In practical system, a lower resonance frequency mode may exist which is located far from the high frequency resonance modes. In this case, a robust control profile is generated which suppresses one specific resonant mode in a flexible dynamic system. This robust control profile is a smooth function which can be used as a robust velocity profile, or as a robust shape filter to an arbitrary control command. The robustness can be arbitrarily improved, which brings about a smoother profile. Combination of high frequency vibration suppression control profile and low frequency vibration suppression control profile generates a robust vibration suppression control profile that is able to suppress all the resonant dynamics in a flexible dynamic system. The technique can be applied to both open-loop and closed-loop systems. |
