本文採用之壓電陶瓷馬達具顯著之非線性摩擦特性，本論文將對摩擦模型進行探討，並針對模型不確定性進行修正。然而摩擦模型仍存在一些不確定性與時變特性，因此本文中採用一適應控制器，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之，並以Lyapunov法則為基礎設計適應更新律，並證明系統的穩定性。本研究採用兩種控制器設計方法，第一種控制器係在知道系統模型與部份參數時，利用FAT函數近似法解決模型之估測誤差與系統時變特性；第二種控制器係在不知道系統確切模型時，如何利用FAT控制器來設計，解決不易取得適當模型與參數的困擾。

In this paper, the friction model of a X-Y table actuated by linear-piezoelectric motors is investigated. This positioning table has slowly nonlinear friction properties, especially at the slow motion phase. Since the friction behavior is time-varying and difficult to model, any friction model will has modeling error or system uncertainty. An adaptive controller is then proposed to deal with these problems. This controller employs the function approximation technique to simulate this modeling error and uncertainty. It is expanded into finite combinations of orthonormal basis functions. Adaptive laws and system stability can be derived based on the Laypunov-like design strategy. This paper presents two controller design methods. One is employed the FAT scheme to deal with modeling errors and time-varying properties accompanied with estimated system dynamics model and friction models. The other is to use the FAT scheme to design a model free controller, when the estimated system model is not properly. Experiment results are used to evaluate the control performance of the proposed control strategies.

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