本論文針對一具有未知時變參數並且持續受到外在環境干擾之磁浮系統，提出一適應控制器，其係利用函數近似法(Function Approximation Technique, FAT)將系統之未知時變參數以有限項的正規直交函數近似，並配合Lyapunov法則來證明系統的穩定性，以改善傳統適應控制必須假設未知參數為常數及強健控制需確切知道系統未知項邊界值的限制。此外，經由實驗結果與PID控制器的比較，可得到良好的追蹤性能。

In this paper, a function approximation based adaptive controller is designed to a magnetic levitation system. The system dynamics is assumed to be with time-varying uncertainties so that traditional adaptive controllers fail. The proposed controller uses function approximation technique to represent those uncertainties as finite combinations of the basis functions. A Lyapunov function candidate is then designed to find update laws to the coefficients of the approximating series. Experimental results are performed to test its feasibility, and good results are obtained.

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