Robust vibration suppression control profile generation

Abstract

Scope and Method of Study:

The control of flexible structures has been extensively studied in recent years. Flexible structures such as high-speed disk drive actuators require extremely precise positioning under very tight time constraints. Whenever a fast motion is commanded, residual vibration in the flexible structure is induced, which increases the settling time. One solution is to design a closed-loop control to damp out vibrations caused by the command inputs and disturbances to the plant. However, the resulting closed-loop response may still be too slow to provide an acceptable settling time. Also, the closed-loop control is not able to compensate for high frequency residual vibration which occurs beyond the closed-loop bandwidth. An alternative approach is to develop an appropriate reference trajectory that is able to minimize the excitation energy imparted to the system at its natural frequencies.

Findings and Conclusions:

A robust vibration suppression 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.