本論文針對單自由度振動系統進行適應性控制之研究。當系統參數未知而且具有非線性行為時，傳統被動減振器的減振效果不佳。本文以函數近似法(Function Approximation Technique, FAT)設計適應控制器，並結合傳統減振器提出兩種控制架構來抑制系統的振動。本論文更進一步提出無被動減振器的控制架構。最後由模擬證明，無被動減振器之控制架構具有良好的性能表現。

Traditional passive vibration absorbers are designed based on its linearized model and precise knowledge of system parameters. Once the system contains strong nonlinearities and/or uncertainties, most passive designs fail to give satisfactory performance. Active vibration absorbers, however, can frequently provide adequate performance when the system has additional effects other than its linear dynamics. The robust active absorber is very effective when the variation bounds of the nonlinearities or uncertainties are available. The adaptive active absorber, on the other hand, is useful when the nonlinearities or uncertainties are linearly parameterizable into a known regressor and an unknown constant parameter vector. However, if the system includes general uncertainties (i.e., time-varying and the variation bounds are not available), then both the robust or adaptive designs are infeasible. Here, in this paper, we would like to investigate the problem for the design of an adaptive vibration absorber for the system containing general uncertainties. The function approximation technique (FAT) is applied to represent the uncertainties using finite-term basis function first, and then update laws can be found by the Lyapunov-like analysis. The closed loop system is proved with rigorous mathematics to be uniformly ultimately bounded. Simulation cases show the efficacy of the proposed design.

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