雙晶壓電梁的定位控制

Abstract

本研究探討雙晶壓電梁致動器應用於微米尺度的精密定位技術，首先以漢彌爾頓定理推導壓電梁振動的理論模型，利用黏貼於梁上下表面的兩枚應變規，構成半橋式量測系統，量測壓電梁的軸向動態應變。由壓電梁最低的兩個共振頻率響應的波德圖，以系統識別得到動態結構的轉移函數。利用比例積分控制及相位領先補償等古典控制法則對壓電梁共振響應進行即時補償，使梁末端之橫向位移能達到精密定位的性能。壓電梁的遲滯與潛變特性對系統之影響亦ㄧ併討論。

A technique of precision position control in sub-micrometer scale using piezoelectric bimorph actuator is presented in this thesis. Mathematical model for structural vibration of the piezoelectric bimorph is derived by Hamilton’s principle. A half-bridge system measuring the axial, dynamic strain of the bimorph is composed of two strain gauges mounted on the top and bottom surfaces of the bimorph to get rid of thermal expansion effect. Physical transfer function of the piezoelectric bimorph is determined through system identification from Bode diagram of the lowest two flexural resonant modes. Classical control theories including proportional-plus-integral control and phase-lead compensator are used to real-time compensate the resonant response occurring in lateral deflection at the tip of the bimorph. The influences of creep and hysteresis in piezoelectric bimorphs on the system response are also well discussed in the study.