本文所採用的壓電陶瓷馬達致動定位平台具有顯著的非線性摩擦特性，首先利用基因演算法的技術針對摩擦模型的參數作最佳化鑑定，並對模型的不確定性進行修正。接著以model-based的方法設計適應性滑動控制器以及探討摩擦模型參數未知時的back-stepping適應性滑動控制器之設計，並經實驗來測試機台運動的穩定性，比較兩種控制器的優劣。
本研究的第一種控制器是以model-based方式設計的適應性滑動控制器，以基因演算法估測出的模型為基礎並使用正交函數的有限組合對系統時變時之未知擾動量進行近似補償。由於正交級數的係數為常數，所以可經由設計適當的Lyapunov函數理論來推導適當的參數調整率，確保輸出的結果是漸進穩定的。第二種控制器則是當模型參數不確定時，由back-stepping的方式來選定Lyapunov函數並推導設計未知參數的參數調整率，解決未知參數的困擾。

In this paper, the friction model of an X-Y table actuated by linear-piezoelectric motors is investigated. This positioning table has slowly nonlinear friction properties, especially at slow motion phase. Firstly , Genetic Algorithm is employed to estimate the parameters of a LuGre friction model. Secondly , a model-based adaptive sliding mode controller was developed based upon the estimated model and a back-stepping adaptive sliding controller with unknown model parameter was designed.
The first controller, orthogonal series function is employed to approximate the unknown disturbance terms of the friction model. Then the adaptive sliding mode controller is designed based on the GA estimated model and function at uncertainly. Since the coefficients of the function approximation are time –invariant, control strategies and updated laws can be easily derived from Lyapunov approach to guarantee the boundaries of output signals. The second controller, a back-stepping method is adopted to design an adaptive sliding control based on design the unknown parameters update law of friction model.

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