本論文目的在於研究核磁共振陀螺儀的運作模式以及載具角速率檢測的誤差分析。理論上，核磁共振陀螺儀具有低成本、高精度、小尺寸，以及輸入載具角速度不受限等特性，這些特性優於現役陀螺儀，值得吾人深入探討。論文首先介紹核磁共振陀螺儀的運作原理及數學模型，再依據物理參數及數學模型進行開迴路以及閉迴路系統的模擬與誤差分析。
　　核磁共振陀螺儀是以原子核作為轉子，原子核的旋轉運動包含自旋、章動和進動，這些運動類比於傳統陀螺儀的運動模式，因此吾人可以利用原子核磁矩進動的相位角速率去檢測載具的角速率。核磁共振陀螺儀是以 Bloch 方程式作為其數學模型，吾人可以利用此數學模型分析開迴路及閉迴路系統的動態響應。不論是開迴路，還是閉迴路響應，都是由原子核磁矩的相位變化率去估測載具的旋轉角速率。兩者的差別在於開迴路系統的磁矩振幅大小無法維持固定，不利於磁矩相位角速率的測量。閉迴路系統則透過訊號回授，可穩定磁矩的振幅，利於相位的測量。

The purpose of this thesis is to study the operation mode of the nuclear magnetic resonance gyroscope and the error analysis of the angular rate detection of the vehicle. In theory, the nuclear magnetic resonance gyroscope has low-cost, high-precision, small size, and the angular velocity of the input vehicle is not limited. These characteristics are better than the active gyroscope, which is worthy of further discussion. The paper first introduces the operation principle and mathematical model of the nuclear magnetic resonance gyroscope and then carries out simulation and error analysis of the open-loop and closed-loop system based on physical parameters and mathematical models.

The nuclear magnetic resonance gyroscope is a nucleus with a nucleus as the rotor. The rotational motion of the nucleus contains spin, nutation, and precession. These motions are analogous to the motion modes of traditional gyroscopes. Therefore, we can use the phase angular velocity of the nucleus magnetic moment precession to detect The angular rate of the vehicle. The nuclear magnetic resonance gyroscope uses the Bloch equation as its mathematical model. We can use this mathematical model to analyze the dynamic response of the open-loop and closed-loop systems. Whether it is an open-loop or a closed-loop response, the phase rate of change of the nuclear magnetic moment is used to estimate the rotational angular rate of the carrier. The difference between the two is that the amplitude of the magnetic moment of the open-loop system cannot be maintained fixed, which is not conducive to the measurement of the angular rate of the magnetic moment. The closed-loop system transmits feedback through the signal, which stabilizes the amplitude of the magnetic moment and facilitates phase measurement.

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