PID Control Algorithm for a Nuclear Magnetic Resonance Gyroscope
摘要
This paper presents a novel proportional-integral-derivative (PID) control algorithm for a nuclear magnetic resonance gyroscope (NMRG). In practice, the random fluctuation of the NMRG’s rotation rate results in random Larmor precession frequencies of the 129Xe and 131Xe nuclei. To maintain the nuclear magnetic resonance state, the PID algorithm in this paper forms a feedback control loop that tracks these varying frequencies in real time. The system employs lock-in amplifiers to detect the extremely weak precession signals of the two noble gas isotopes. The phases of the nuclei are then computed in real time from the outputs of the in-phase/quadrature demodulators. The PID controller adjusts the frequencies of the applied alternating current magnetic fields based on the deviation of these phases from zero, thereby locking the spin precession frequencies of 129Xe and 131Xe to their respective resonance frequencies. The gyroscope’s angular velocity is subsequently derived from the resulting Larmor frequency shifts. This approach provides servo control for the spin precession frequencies of 129Xe and 131Xe without concerning the disturbance of the main field. Experimental results demonstrate that the proposed PID algorithm successfully tracks the noble gas precession frequencies with an accuracy of up to 0.005 Hz. Furthermore, the gyro turntable experiment result shows that NMRG prototype is able to effectively detect the input angular velocity of the gyroscope turntable increasing from 0° /s to 12° /s, reversing to −12°/s, and returning to 0°/s.