以Inverse Preisach模型補償磁滯效應在壓電結構上所造成之誤差

Error Compensation on Hysteresis Effects of Piezoelectric Structures by Inverse Preisach Model.

陳鈞賀(Chun-Ho Chen)

指導教授 ： 趙昌博 ； 黃健生

中原大學/工學院/機械工程研究所/碩士(2006年)

https://doi.org/10.6840/cycu200600883

摘要

本文主旨是針對雙層壓電片懸臂樑進行微觀建模後，利用Inverse Preisach Model來消除磁滯效應在壓電片定位上所造成的誤差。首先在壓電材料的微觀建模方面，利用壓電方程式（constitutive equations）中加入反應磁滯效應的極化值 （polarization term），並且以Inverse Preisach model 來描述其磁滯效應。以此修正後的壓電方程式，透過有限元素法推導出壓電懸臂樑包含極化值之運動方程式。接著透過實驗鑑別與插值方程式(Interpolation Functions)建立位移與電壓相對應之資料庫(Database)，利用微觀上推導出之線性化動態方程式得到極化值。並可藉由此方程式輸入之位移量經過Inverse Preisach model後而反求得到補償電壓值，進而消除磁滯效應在壓電片定位上所造成的誤差。最後，透過模擬與實驗結果，顯示經由Inverse Preisach model結合有限元素法能有效建立壓電材料的磁滯效應之微觀模型。

關鍵字

磁滯 ； 插值方程式 ； Inverse Preisach model

並列摘要

This study presents inverse Preisach model via finite element method for the piezoelectric cantilever beam to eliminate the error on positioning. First, to perform the microscopic modeling on hysteresis, the constitutive equations of a general piezoelectric material are modified to include the hysteresis effect by adding a polarization term in one of the constitutive equations. Inverse Perisach model is employed to prescribe the hysteresis effects through polarization. Equations of motion of the piezoelectric beam are next derived through the utilization of the finite element method based on modified constitutive equations. Second, to build the database which contain voltages corresponding the desired displacements by the identification process and Interpolation functions. Subsequently, we use linearization of dynamic motions through finite element method to obtain polarizations and compensative voltages. Finally, both simulations and experimental results show the effectiveness and efficiency of the microscopic hysteresis model established via the inverse Preisach modeling.

並列關鍵字

Interpolation Functions ； hysteresis ； inverse Preisach model

參考文獻

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