在許多產業中都有懸臂樑結構的應用，在工作環境中難免會有許多外在因
素的干擾，這些干擾可能造成懸臂樑的振動，影響其工作效率與精度，因此許
多學者研究如何利用主動控制的方式抑制振動。壓電材料是主動控制元件最常
見的一種，有響應快、能量轉換率高等特點，非常適合當作感測器與制動器使
用，許多學者在此研究領域中利用壓電材料結合不同控制方法，研究個理論抑
振的效果及優缺點。
當外部干擾使懸臂樑產生振動時，其產生的振動效應是由第一共振模態至
無窮共振模態的總和，且產生的振動隨模態遞增而遞減，因此多數學者在懸臂
樑建模時，只考慮第一與第二共振模態，但實際上干擾可能引起其餘共振模態
的振動，若用使用此模型設計控制器控制效果有限，因此將懸臂樑考慮越多模
態並以此設計控制器越能近似實際懸臂樑振動情況，並增加控制效果。
本論文使用激振器產生一干擾訊號同時引起懸臂樑第一到第四共振模態的
振動，在懸臂樑建模時考慮第一到第四個共振模態，結合卡曼濾波器與線性二
次調節器(Linear Quadratic Regulator, LQR)，分別使用一到四對壓電片感測器與制動器抑振系統，並利用實驗驗證模擬結果。限制控制電壓小於20 v且同時有四種共振頻率干擾的環境下，利用四對壓電片感測器與制動器以兩不同電壓控制，模擬可以達到36.8%的抑振效果，實驗可以則可達到23.4%抑振效果。

It is common to see cantilever beam structures applied in industry. When some disturbances appear in environment, they will cause cantilever beam vibrations and sometimes will affect productivities. Due to this reason, many experts studied how to suppress the vibrations using active control. Piezoelectric material is a common component with fast responses and high energy-conversion rates. Thus, this study uses the material to be sensors and actuators.
The vibration of the cantilever beam can be regarded as the sum of model vibrations and the vibration amplitudes decreases as the mode number increases. Therefore, many experts only assume the first and second mode to design the controller. Actually, the disturbance might cause the vibrations excited by higher modes. Accordingly, the more modes are considered in modeling, the more similar to an actual cantilever beam system the model is, so the designed controller has better performances.
In this thesis, a shaker is used to generate the first four model vibrations, and the first four modes are considered to design the Kalman filter and the linear quadratic regulator. Different combinations of piezoelectric sensors and actuators are considered to suppress the vibrations. The simulation and the experiment results show that four pairs of piezoelectric sensors and piezoelectric actuators with two different voltages have 36.5% of suppressions in simulation results and 23.4% of suppressions in experimental results.

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