Theory And Design Strategies Of High Precision Inductive Edge Displacement Sensor

The mirror of large astronomical telescopes is usually made up of a large number of hexagonal sub mirrors.In order to accurately control the surface shape of the mirrors,it is necessary to install displacement sensors at the edge of the sub mirrors to measure the relative displacement changes,and then feed back to the controller and adjust the position of the sub mirrors through actuators accurately.As a new type of edge sensor,inductive sensor has overriding advantages of large range,high resolution,good temperature stability,and high tolerance for harsh environments,therefore receiving attention from foreign research teams.Inductive sensor is expected to be applied to large astronomical telescopes newly built.This paper focuses on the research topic of a high-precision inductive edge displacement sensor applied to the mirror splicing of large astronomical telescopes.The system design and construction of the sensor are introduced in detail,and the design method for sensor probes and circuits are provided to improve the performance indicators such as resolution,sensitivity and stability.This paper also provides a sensor temperature drift compensation method.The performance test results of the designed inductive edge displacement sensor system show that the performance of the sensor meet the design requirements.The main work and contents of this paper are summarized as follows:1)The basic working principle and differential output scheme of the inductive edge displacement sensor are introduced,and the circuit model of the sensor probe is established.A theoretical method for calculating the self-inductance and mutual inductance of multi-turn rectangular coils based on second-order vector potential and magnetic induction intensity is proposed,which can accurately calculate the mutual inductance and mutual inductance based on the shape,size,and relative position of the coils.Compared to finite element numerical calculation or software simulation,theoretical methods based on second-order vector potential show higher computational accuracy and faster computational speed.The experimental results of coil mutual inductance show that the calculation error of the second-order vector potential method is less than 0.5%while its calculation time is less than 1 s.So this method shows excellent performance and can be used for the design of the sensor coils.2)The parameters of the probe coil are designed and optimized,and the influence of coil parameter changes on the sensor outputs is analyzed.The goal of coil design and optimization is proposed,while the traditional and advanced manufacturing process of the coils is summarized.The optimization results of the coil parameters make the output of the sensor in both Piston and Gap directions have high sensitivity and good linearity,while the coupling error of the measurement in the two directions is significantly eliminated.A mutual inductance calculation method for rectangular coils with nonparallel planes is proposed,and the influence of sensor probe rotation in three directions is quantitatively analyzed.The experimental results of the coils agree very well with the theoretical calculation results.After testing its frequency characteristics,a suitable excitation frequency is selected to make the sensor output have higher sensitivity.3)A novel synchronous demodulation circuit based on gated integrator is proposed.The transfer characteristics of traditional lock-in amplifier demodulation method are analyzed.Aiming at its shortcomings,it is proposed that using gated integrator to partially integrate the waveform can improve the signal to noise ratio of the sensor output signal.The signal transmission characteristics of the gated integrator demodulation circuit are theoretically analyzed and calculated.The results show that compared to the lock-in amplifier,demodulation with the gated integrator achieves greater useful signal output while maintaining the same noise suppression capability,which results in an increase in the signal-to-noise ratio of more than 3.8 dB.Further refined calculation results show that the gated integrator demodulation circuit can also suppress the harmonic components of the output as all harmonics are suppressed to below-55 dB.After the gated integrator demodulation circuit is applied to the sensor,it is found that the output performance is significantly improved.4)The source and influencing factors of sensor temperature drift are analyzed,and a temperature drift compensation method based on convolution calculation is proposed.Compared with compensating directly with ambient temperature,the proposed method can eliminate the residual temperature drift after compensation and further improve the temperature stability of the sensor.The temperature gradient existing in the probe structure can also influence the output of the differential sensor,which is also analyzed and calculated theoretically.The results of variable temperature experiments on an eddy current sensor show that the temperature drift of the sensor is reduced from 34.62 nm/℃to 1.64 nm/℃ using the convolution method after compensation,also less than 1/4 of 7.70 nm/℃ which is the directly compensated result using ambient temperature.The convolution compensation method also shows obvious effects on the proposed inductive edge displacement sensor,which greatly improves the temperature stability.In addition,a temperature drift compensation method using the output of a compensation coil is also developed,which can achieve better temperature drift compensation without additional temperature sensors.5)Based on the application requirements of edge displacement measurement for large astronomical telescopes,the construction of an inductive sensor system is completed,with its performance parameters calibrated and tested.The mechanical structure of the sensor probe is designed,the paste technology of the sensor coils is summarized,and the signal processing circuits adopts mode design.The prototype of inductive edge displacement sensor is fabricated and its main performance parameters are tested.The results show that the output performance of the sensor in both Piston and Gap directions meets the design requirements.