結合Ｈ∞與順滑模態控制器於移動平臺單軸撓性臂之應用

Abstract

本篇論文結合Ｈ∞與順滑模態設計法提出一個改進的頻域補償順滑模態 控制器。頻域補償順滑模態控制器是透過補償器動態系統產生一組切換順 滑平面來達到頻域補償的功能。補償器動態系統雖可由極點安排法(pole- placement)來設計，但卻難以看出頻域補償的情形。本文藉由Ｈ∞控制器 合成方式依成本函數(cost function)來調整權重函數(weighting function) 並據此看出補償和削減的頻域。此種控制器除了保有傳統順滑 模態控制器消除匹配性擾動的能力、當系統在切換順滑平面作理想滑動時 消除非匹配性擾動的能力及系統整體的逼近與順滑的條件亦在文中討論之 。在受控系統選擇上我們採用移動平台單軸撓性臂。除因這個系統在航太 方面應用日廣，另外數學模型上利用有限維度模型來合成適當控制器上其 困難點就在未模型成份(unmodel part)極多，再加上外界入的大振幅低頻 擾動－即平台移動對臂上撓性成分的影響，受控系統非線性與不確定成份 耦合就更複雜且難以控制。故使用此系統作控制更能驗證控制器的穩健性 。文中亦對線性最佳化控制與增益調變可變結構控制器其方法和使用條件 做一簡略描述，再將這四種控制器應用於移動平台單軸撓性臂上。 A modified approach, combining sliding-mode and Ｈ∞ techniques, of frequency shaping sliding-mode controller is proposed in this thesis. The design methods which permit shaping frequency through introducing a class of switching surfaces generated by compensator dynamics. Although the compensator can be design by pole-placement method, the locations of poles is hard to associate with its phenomenon of frequency shaping. According to the cost function, we adjust the weight function in order to compensate or penalize one specific frequency domain by Ｈ∞ control synthesis. This controller retains the ability in eliminating the matching type disturbance. We also discuss the capability of eliminating the mismatching type disturbance and the reaching and sliding conditions. While selecting the plant, we choose the moving-based single flexible arm system. In spite of the diverse application in aerospace, designing a suitable controller is difficult because the unmodelling components of finite dimensional model approximation is large. Moreover, the large amplitude and low frequency disturbance, generated by the movement of base, increase the problem of control. The robustness of controllers can be verified by employed into the plant.