A Temperature Disturbance Suppression Method for NMR Sensor Stability Based on Consistent Error Responses

Nuclear magnetic resonance (NMR) sensors have broad research prospects in high precision and miniaturization. The NMR sensor output is obtained by calculating the frequency difference between <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">129</sup><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Xe</i> and <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">131</sup><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Xe</i>. However, the two frequency error responses caused by temperature dynamic disturbances of the vapor cell are different and difficult to be offset, which has a significant influence on the sensor stability. Therefore, a temperature disturbance suppression method based on consistent error responses is proposed by combining the internal model controller (IMC) and the generalized extended state observer (GESO). Firstly, the temperature-induced error models of <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">129</sup><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Xe</i> and <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">131</sup><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Xe</i> are established, and the IMC is built to make the two error responses consistent. Secondly, to address the problem of poor phase stability caused by the small integral coefficient in IMC, the GESO is introduced to estimate and compensate for the temperature-induced phase error. Finally, the established error models are considered in the corresponding GESO with the same bandwidths to offset the consistent error responses of <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">129</sup><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Xe</i> and <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">131</sup><italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Xe</i>. The experimental results show that, compared to the PI control, the root mean square error of sensor output is improved by 19.7 % on average under temperature disturbance. The proposed method effectively suppresses the influence of temperature disturbance on sensor stability.