壓電懸臂樑之精密定位控制設計與實作驗證

Precision Position Control and Experiment Verification of a Piezoelectric Cantilever Beam

林昆瑩(Kun-Ying Lin)

指導教授 ： 趙昌博

中原大學/工學院/機械工程研究所/碩士(2003年)

https://doi.org/10.6840/cycu200300369

摘要

本文主旨針對單片壓電懸臂樑（Piezoelectric Cantilever Beam）設計精密定位控制器。系統之動態模型由兩種方法獲得，第一種為考慮壓電懸臂樑本身之物理行為與壓電方程式，利用漢米頓原理（Hamilton’s principle）推導出完整的統御方程式，並利用有限元素法得到系統之轉移函數；另一方法為利用實驗鑑別出系統之轉移函數，比較並分析兩模型的精確性。並以壓電懸臂樑作為光碟機之致動器為例，利用輸入電壓控制使懸臂樑末端的位移達到所要求的高度。控制器設計方面，利用古典控制的 加上落後領先補償器作初步的設計，進而考慮光碟機因碟片旋轉時所產生的振動以及對於系統模型的不確定性設計具有強健性之H∞ 定位控制器。最後利用dSPACE即時控制之人機介面，將所設計之控制器以實作驗證。

關鍵字

精密定位控制 ； 強健控制

並列摘要

This study performs precision position control of the piezoelectric cantilever beam with consideration of nonlinearity. Two different dynamic models were obtained. The first one is derived in the forms of linear systems through application of basic physic laws of piezoelectric material, Hamilton’s principle and modeling technique of finite elements. The second one is established as in through experimentally-obtained frequency responses. With theoretical models in hand, the controllers aimed to perform precision positioning of the piezoelectric cantilever beam are next designed to work for a pickup actuator in optical disc drives, which ought to suppress the vibratory disturbance caused by the rotation of the disc. Two types of controllers, PI-and-lag-lead compensator and H∞ controller, are synthesized herein to perform the precision positioning due to the simple structure of the PI-and-lag-lead one and the robustness achieved by the H∞ one. Note that the H∞ controller designed herein would able to work against plant uncertainty, sensor noise and the extraneous disturbance caused by the eccentric rotation of the disk. Simulations are performed to validate the performance expected by previously-designed controllers. Finally, experiments are conducted to verify the effectiveness foreseen by simulations.

並列關鍵字

Robust control ； H∞ control

參考文獻

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