力回饋壓電加速規即時控制系統

Abstract

本論主要設計及製作一壓電加速規，推導其電壓╱加速度驅動、電壓輸出的完整數學模型，並建構一實驗平台，根據力平衡控制法設計控制器，進行壓電加速規的回饋控制。 在壓電加速規的機械結構部分，本文製作出形狀簡單的三層複合式壓電懸臂樑，此懸臂梁具有感測及驅動能力。在數學模型建立的部分，我們以壓電力學進行動態模型的理論推導，並比較數值模擬軟體ANSYS的模擬結果及實驗使用都普勒量測儀(Laser Doppler Velocity)的量測結果。理論推導、數值模擬、實驗數據三者結果大致相符。 力平衡控制法乃是利用回授控制產生一平衡力，使得懸臂樑在受到外力（加速度）的狀況下仍能維持不動，藉由所產稱的平衡力來推算待感測的加速度。因此在力平衡控制的實驗部分，我們首先對壓電加速規做系統鑑別，再利用MatLab對所設計的P及PI控制器進行模擬。最後利用C-code與DSP來實現系統的即時回授控制。模擬及實驗結果顯示，本文成功的改善此壓電加速規的低頻響應，並增加感測頻寬40Hz。 本論文完成一力平衡加速規的設計、製作、數學模型推導。由於時間限制，僅能針對力平衡加速規的性能響應進行初步的探討。許多的研究項目列於「未來工作」中，繼續探討。

This thesis presents a design, modeling, and control of a piezoelectric accelerometer. The fabricated piezoelectric accelerometer features built-in sensor and actuator so that it can perform the force-balance measurement when feedback control applies. The fabricated accelerometer was well calibrated. The calibration methods and a complete setup for the force-balance feedback controls are also presented in this thesis.

This piezoelectric accelerometer is designed to be a sandwich-structure cantilever beam with piezoelectric materials on the top and bottom, and a copper layer in the middle. The piezoelectric layer on the top and bottom are divided into two sections: one for actuation and one for sensing. The top and bottom piezoelectric layers form a bi-morph structure. Meaning that, this accelerometer uses a bi-morph piezoelectric structure to bend the copper layer, and a bi-morph piezoelectric structure to sense the deflection of the cantilever beam.

A theoretical model is derived to describe the dynamic behaviors of this voltage-in/acceleration-in and voltage-out accelerometer. To verify the feasibility of this model, not only did finite element simulations, but also experimentally data were obtained using the Laser Doppler Vibrometer. The results from the theoretical model, FEM simulations, and experimental data are consistent with each other.

To experiment on a force-balance control piezoelectric accelerometer, we first did the system identification to obtain system model. Secondly, we verified simple P and PI controllers using MatLab tools. Lastly, this controller was implemented using C-codes on a DSP platform. The simulation results and experimental results show that the proposed force-balance control can increase the system bandwidth by 40Hz, especially in improving the low frequency response.

This thesis completes the design, fabrication, and modeling of a force-balance piezoelectric accelerometer. However, due to time limitation, only some preliminary results were obtained for the force-balance control. More research items are listed in the future work.