傳統LQ控制器可以在時域上對一線性系統進行最佳控制，頻率塑型控制器則可以在頻域上對該系統提供最佳性能。然而，當系統具有未知量時，這兩種控制器都不再有效。本論文提出一適應控制器，使得未知機械系統在頻域下仍能得到最佳控制。其中關鍵在於採用函數近似法，將未知量以基底函數展開之。同時，由於該法的特性，讓此控制器得以處理未知的非線性項，使得其應用更為廣泛。另外，本文亦以Lyapunov-like的方法來確保輸出的收斂性，以及內部訊號的有界性。最後再以雙行程平台為範例，進行實驗研究，以測試所提出控制器的性能。在Tomizuka設計的基礎上，本文提出了三種新版的性能指標，以改善參數調整性。其性能皆得到實驗驗證。

The traditional LQ controller can give optimal performance to a known linear system in the time domain, while the frequency shaped LQ controller is able to provide optimal performance to the same class of systems in the frequency domain. When the system contains uncertainties, both of these two approaches fail. In this thesis, an adaptive controller is proposed to an uncertain mechanical system such that LQ performance can be achieved in the frequency domain. The function approximation technique is applied to represent the uncertainties into a finite combination of a set of known basis functions. This allows the system to be with various nonlinearities without significant impact on the design procedure. The Lyapunov-like analysis is used to ensure convergence of the system output and boundedness of the internal signals. A dual stage is built to evaluate the performance of the proposed scheme experimentally. Tomizuka’s design is implemented in its adaptive version proposed in this thesis as a formal behavior of the traditional frequency shaped LQ. An adaptive controller based on a new performance index is then presented with different characteristics in parameter adjustments and frequency domain behaviors.

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