本論文針對欠驅動振動系統提出一適應控制器，達到減振效果。由於一般振動系統受到外力頻率改變時，傳統被動式減振器的抑制效果不佳。若系統參數具有時變、非線性行為時，該減振器更難以得到期望的性能。本文依據外部動態行為設計FAT適應控制器，雖然可以有效抑制系統振動，但無法規範減振器之振幅。為了限制減振器本身的振動，提出以Olfati轉換，將系統化為一標準串接結構，據以設計適應多面滑動控制器(Adaptive Multiple Surface Sliding Control, AMSSC)，以掌控系統與減振器之動態行為。最後，利用電腦模擬驗證控制器的可行性。

Traditional passive vibration absorbers are very effective for systems with known dynamics and known excitation sources. They are not capable of giving acceptable performance when the system contains uncertainties. This thesis proposes adaptive strategies for uncertain vibration systems. Firstly, a FAT-based controller is designed for the external dynamics. The output error can be proved to be uniformly ultimately bounded, while the magnitude of the internal states can only be bounded. This implies that some unacceptable large vibration in the absorber dynamics might appear. The Olfati transformation is therefore proposed to represent the system in a special cascade from without internal dynamics. However, various system uncertainties will enter the new system dynamics in a mismatched fashion giving difficulties in controller designs. Here, we suggest to apply the adaptive multiple-surface sliding controller to deal with the mismatched system uncertainties. It is proved that we may still arrive at the uniformly ultimately bounded performance for the system states both in the original space and the transformed space. Computer simulation cases are performed to show effectiveness of the proposed schemes.

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