球型壓電馬達具備高角度解析度和多軸向輸出等優點，因此廣泛應用於機器人關節和精密定位系統，然而，現有研究偏向實現多軸向力矩輸出，卻忽略了對馬達轉子的姿態控制方法。大部分球型壓電馬達系統僅能實現在坐標系中的 xyz三軸旋轉，僅有少數系統能達到多軸向運動，但通常受限於單一平面或缺乏清晰定義的實際軸向範圍，且大多採用開迴路控制，缺少基於模型的控制方法。為了解決上述問題，本研究以一自行開發的三定子球型壓電馬達作為研究對象進行姿態控制與合成軸向研究。此系統採用壓電電極配置法激發定子側向振動模態以此提升單一壓電片下的致動效 能；同時藉由改變定子與轉子間接觸點位置來產生相反轉向的驅動力矩，結合線性疊加概念便可達到轉子全軸向的操作。為了處理奇異點問題，本文使用四元數作為系統狀態建構轉子動態模型，藉由計算力矩法得到命令力矩並分解此力矩決定各個定子需要的驅動力矩，最終實現馬達轉子的姿態控制。球型馬達在不同應用場合中欲達成的運動目標不盡相同，經過分析球型轉子所有可能的運動行為，我們提出了三種運動模式：定位、自旋和混合模式，分別為姿態定位控制、角速度控制和兩者同時進行控制。通過對這些馬達運動行為的歸類，可幫助我們了解在各種情況下最適合的運 動模式，使馬達在姿態控制上有更高的應用價值。本馬達系統根據不同的定子與轉子接觸點位置產生期望的合成軸向，在三定子的組合下能夠產生八組軸向空間從而達到全軸向空間，因此進行轉子運動控制時需先判別輸出軸向所屬的軸向空間後方能切換接觸點位置給予正確的驅動力矩。為了減少多次切換接觸點造成的可能動態影響，我們提出基於切換優先級概念的接觸點切換演算法以便優化切換時機。透過電腦模擬轉子動態結果，我們成功地驗證所提出的姿態控制器和切換接觸點演算法的有效性。本文所提出之全軸向轉子閉迴路運動控制架構具備極佳泛用性，除了壓電馬達系 統外亦可結合新型機構設計開發成本較低之球形電磁式馬達系統，值得學者們持續深入探討其應用潛力與多自由度運動系統控制效能。

Spherical piezoelectric motors (SPM) have been applied to multi-DOF robot joints and precision positioning systems due to the advantages of high resolution and multi-axis output. However, existing research mainly focuses on realizing multi-axis torque outputs while overlooking methods controlling the motor's rotor orientation. Most existing SPM systems can only achieve three-axis rotations (xyz) in the coordinate system. Although there are a few reported systems capable of generating multi-axis motion, the rotor orientations are often limited to a single 2D plane and the ranges of the actual axial movements are not well defined. As a result, open-loop control systems are often applied to implement rotor attitude control for prototype evaluation and the system positioning accuracy and robustness still remains a great challenge for precision motion control. This study proposes a feedback control framework for rotor attitude control of a three-stator based omni-directional SPM using the technique of electrode configuration to enhance stator excitation efficiency under lateral mode resonance. The driving torques of the rotor are designed to achieve omni-directional capability with a linear combination of six elementary torque orientations by adjusting the contact point positions between the stators and the rotor. This study employs a quaternion based dynamic model to avoid singularity issues in manipulating omni-directional rotors and derives the decomposed control commands to each stator from a computed torque based control law. This study applies the proposed rotor attitude control framework to general motion control applications categorized into three groups, including positioning, spinning, and hybrid modes. The control goal of these motion modes is to implement desired 3D space position control, angular velocity control, and a combination of both. Because the orientation configuration space is composed of eight vector spaces for the proposed SPM system, it is mandatory to identify the belonging vector space of the desired orientation outputs to devise the required torque commands for rotor motion control. A priority level based switching algorithm is developed to facilitate torque trajectory generation and reduce the dynamic effects caused by switching rotor contact positions. Simulation results on these three motion modes are finally conducted to validate the proposed rotor attitude control algorithm and SPM system.

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