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This thesis formulates the vibration control of a rod with the tip mass in transfer function models. Since the model is established without mode-truncation,instability caused by spillover is avoided. Several boundary controls are presented for stabilizing the vibration of the rod without damping. The asymptotic or uniform stability can be checked by the locations of the poles. Hence, finding a controller to stabilize the system uniformly is easier with the transfer function approach than previous study.
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