拘束調整修正模態超音波致動器之設計與應用

Design and Application of a Constraint-Tuning Modified-Mode Ultrasonic Actuator

賴明宏(Lai, Ming Hung)

指導教授 ： 歐陽敏盛 ； 周懷樸

國立清華大學/原子科學院/工程與系統科學系/博士(2012年)

摘要

本論文提出具有拘束調整修正模態（Constraint-Tuning Modified-Mode: CTMM）機制的單片壓電振動子，並設計一新型薄盤超音波致動器推動線性平台加以驗證之。透過具模態參與係數的模態擴充技術及拘束波Green Function的理論推導，獲得內部拘束薄圓板修正模態的估測公式，可用來解釋此新型致動器的作動機制。將正確分佈的四只螺絲施加於單片壓電薄盤上，超音波修正模態的致動機制會被產生及傳播。入平面振動模態（In-plane vibration modes）可被施加在壓電振動子上的螺釘拘束修正及調整。為了實現此致動器雙向平衡的結構力，導入結構阻尼概念，利用有限元素分析軟體ANSYS的自然模態、強迫諧振及阻抗比較來設計拘束分佈，解決理論模態加入多重拘束不易獲得數值解的困擾。因此，選擇兩個不同修正模態可與壓電材料產生機電共振者，做為此致動器的驅動模態，以提高機電轉換效率。將所設計的致動器及單相雙頻LC諧振驅動電路，取代推動光學台車的DC馬達及其齒輪組並保留原光碟機控制器，輔助光學致動器尋軌及讀取光碟片資料與播放影片均可獲得想要的功能。另依據施加在CTMM超音波致動之驅動電壓及預力的變化，探究其機電共振頻率偏移及推動平台時不工作區（dead zone）響應的非線性現象，這些非線性行為可藉由具輸出biases的PID型順滑模態控制器（SMC）抑制補償。使用系統鑑別法獲得線性平台的近似二階模型，提供PID-based SMC等效控制項的設計。透過模型誤差的估測，切換控制項的設計可被使用來補償在機電耦合下振動子共振頻率偏移的特性。於線性平台軌跡追蹤實驗中，使用目標命令塑形函數（shapping function）來匹配系統的響應速度，實驗結果顯示PID-based SMC控制器使所提之CTMM致動器雙向移動線性滑軌位置具有抗雜訊能力，定位解析度可達微米等級，其行程可達mm級之長程控制的能力，驗證了CTMM致動器的理論、設計與實現的一致性及可控性。此CTMM超音波致動器厚度僅3 mm，採用此型致動器可協助開發須薄形化的致動裝置。

關鍵字

拘束調整修正模態 ； 超音波致動器 ； 入平面模態 ； 順滑模態控制器

並列摘要

Using a piezoelectric unimorph vibrator with constraint-tuning modified-mode (CTMM) mechanism, a novel design of a thin-disc ultrasonic actuator was developed and validated to drive a linear slider. The theoretical estimation of in-plane wave propagation on a thin disc was introduced to explain the novel actuating mechanism, via a modal expansion technique, modal participation factors and derived green functions of planer waves. Applying four screws at the exact distribution of angles on the thin-disc vibrator, the actuating mechanism of ultrasonic modified modes is generated and propagated. The in-plane vibration modes could be tuned by these desired screw constraints on the piezoelectric vibrator. To implement the equilibrium structure force in bilateral directions, natural and forced harmonic analysis as well as impedance comparison with structural damping of FEM software ANSYS are also introduced into the constrained design. Hence, computing complexities in mathmatics to solve these multiple constraints in a thin disc could be avoided. There are two kind of modified modes chosen at the different resonant frequencies within the electromechanical coupling of piezoelectric material to pursue more efficiency in energy conversion. Experimental results have demonstrated that the proposed ultrasonic actuator with an adapted single-phase, bi-frequency LC resonant driving circuit is able to directly drive the optical sled in rightward and leftward movements to help the optical actuator to retirve the data in the optical storage dick. Based upon the driving variation of voltage amplitude and the preload on the CTMM ultrasonic actuator, the nonlinear phenomena, such as the frequency shifting in electromechanical resonance and the dead zone in moving response, could be suppressed completely by the PID-based SMC controller with output biases. Using system identification technique, an approximate second-order model of the linear stage could be obtained for the equivalent control term of the PID-based SMC controller. Through an estimated model error, the design of the switching control term was used to compensate for the shifting property of resonant frequencies under electromechanical coupling. A target-command-shaping function matched the responding speed of the system during tracking experiments. The SMC controller has the capacity for noise rejection to control the slider positioning in bilateral tracking motions pushed by the CTMM actuator. Its resolution is sufficient to approach the accuracy within a micrometer level and the controllable proficiency in the long moving distance of millimeters. Therefore, the theory, design, and implementation for CTMM actuators have the excellent agreement and controllability. A CTMM actuator, with the thickness of only 3 mm, is very suitable to develop the thin and slender driving mechanism.

並列關鍵字

constraint-tuning modified mode ； ultrasonic actuator ； in-plane mode ； sliding-mode controller

參考文獻

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