彎曲模態與扭轉模態是撓性結構中主要的兩種振動模態，由於其模態振型有顯著差異，既有研究大多僅針對彎曲模態進行進階振動控制探討、或是以多組致動器配置法與單一致動器斜交角(Skew Angle)配置法進行激發與抑制扭轉振動響應探討；目前能夠僅以單一致動器同時抑制這兩種振動響應、並依隨機出現之任一種模態進行有效抑制之相關研究仍是付之闕如。本論文為基於壓電電極配置法就智慧撓性樑之彎曲模態與扭轉模態開發新型多模態主動振動控制法之研究探討。為分析不同電極配置模式於欲探討模態下之激振效果，本研究首先透過有限元素分析軟體進行致動效能分析，證實了全電極模式與切割電極模式能夠各自有效地激發懸臂樑之彎曲模態與扭轉模態。本研究以正位置回授控制作為單模態主動振動控制之基本控制架構作為基礎，接著基於電極配置法提出兩種全新的多模態主動振動控制架構，分別為：(1)控制輸入疊加法；與(2)電極切換控制法。控制輸入疊加法係根據疊加原理將彎曲與扭轉模態之控制輸入疊加作為實際給予壓電致動器之控制輸入，進而達到同時抑制此兩種模態之共振行為。至於電極切換控制法則是結合了單模態主動振動控制之基本架構與本研究所開發之電極切換配置模組，並透過設計之電極切換控制器在任意時間根據結構系統的工作環境與狀態即時切換對應模態的控制律與硬體上的電極配置模式。本研究亦加入一平滑切換函數進行控制器切換，並分析不同的平滑切換函數與其設計參數對結構系統控制效能之差異。透過多模態主動振動控制實驗，結果證實本研究基於壓電電極配置法所開發之新型多模態主動振動控制架構能夠提供良好的彎曲/扭轉多模態主動振動控制效能。本文所提之新型主動振動控制架構應用甚廣，除了一般結構系統外，亦可應用於撓性機械手臂定位控制或工具機加工振顫抑制等撓性結構之關鍵技術研發、大幅提升系統效能與經濟效益。

Bending mode and torsion mode are two important vibration modes in flexible structures. Due to their inherently-different mode shapes, most existing research has focused either on active control of bending mode vibrations using advanced controls, or on torsion mode excitation and suppression using multiple actuators and sensors placement and control or using a single actuator with skew angle configuration. Unfortunately, research that merely applies a single actuator to address both vibration modes is still lacking. This thesis presents novel bending-torsion vibration suppression control methods of smart flexible beam based on piezoelectric electrode configuration. Modal analysis shows that applying the electrode configurations including “full electrode configuration” and “segmented electrode configuration” can effectively enhance the excitation efficiency of a piezoelectric cantilever beam at bending mode and torsion mode frequencies. Using the above designed electrode configurations, this study proposes two novel multimodal vibration control schemes integrated with positive position feedback (PPF) control as fundamental controller to address the coexisting bending-torsion vibrations, i.e., (1) Superposition Control and (2) Electrode Switching Control. The first control scheme that superposes control inputs of bending mode PPF controller and torsion mode PPF controller has an extremely beneficial effect on simultaneous suppression of these two vibrations. The electrode switching control scheme, on the other hand, is developed with our designed electrode configuration switching circuit module and fundamental PPF control algorithms to handle real-life examples of time-varying single modal vibrations (either bending mode or torsion mode) in real-time. Comparative experiments and analysis demonstrate that the proposed new multimodal vibration control schemes can effectively suppress simultaneous bending-torsion vibrations and time-varying bending/torsion vibrations. The proposed multimodal vibration control schemes have a great advantage of saving extra costs of used actuators and may be applied to a broad range of applications in which the discussed structural system contains both bending mode and non-bending mode vibrations.

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