Abstract: Zero-point deviation and drift are technical challenges that all tilt sensors face. This paper delves into the leveling principle of the sensor using the ancient method of rotating a bubble level 180°, establishing a theory and method for automatic zeroing of tilt sensors. An automatic zeroing servo tilt sensor is designed and implemented using stepper motor and microcontroller control technology, effectively solving problems such as zero-point deviation, time drift, and temperature drift, thus improving the performance of the tilt sensor and possessing significant application value. I. Introduction Tilt sensors are devices that measure the tilt angle relative to a horizontal plane, and have wide applications in engineering fields such as civil engineering, hydrogeology, weaponry, aerospace, and biomedicine. There are many types of tilt sensors, which can be classified into three types according to their working principle: solid pendulum, liquid pendulum, and gas pendulum. Research on solid pendulum tilt sensors is relatively mature and their applications are widespread, but they are susceptible to external interference, such as mechanical vibration and shock. Liquid pendulum tilt sensors, on the other hand, possess high sensitivity, corrosion resistance, and moisture resistance, but their fatal flaw is that temperature changes severely affect their operating characteristics, thus limiting their development and application. Gas pendulum tilt sensors have a simple structure and strong vibration and shock resistance, but they are greatly affected by ambient temperature, resulting in low testing accuracy. In short, improving the accuracy of existing tilt sensors requires significant investment and suffers from problems such as zero-point deviation, time drift, and temperature drift. To address these issues, this paper designs an automatic zero-adjustment servo tilt sensor based on automatic zero-adjustment theory. Its basic idea originates from the ancient method used by carpenters and builders to level the surface using a bubble level rotating 180°, and it is designed and implemented using stepper motors and microcontroller control technology. This automatic zero-adjustment servo tilt sensor effectively solves problems such as zero-point deviation, time drift, and temperature drift, improving the performance of the tilt sensor and possessing significant application value. II. Theoretical Basis The automatic zeroing servo tilt sensor is designed to correct zero-point deviations and drifts from various sources. Its basic idea originates from the ancient method used by carpenters and builders to level the surface of an object by rotating a bubble level 180° on it. If the bubble level shows the same result, it indicates normal operation; otherwise, it indicates an error equal to half the difference in the bubble's apex position. In this application, the servo tilt sensor is located on a rotating disk with its input axis IA parallel to its surface. When performing offset correction, it can be directly rotated 180° to the opposite position of the disk, as shown in Figure 1. The zero-point deviation of the servo tilt sensor is independent of the sensor's position. Therefore, when the sensor attached to the horizontal rotating disk rotates to two different positions, its output will not change. [align=center][img=274,143]http://www.e-works.net.cn/images/128110620316093750.GIF[/img] Figure 1 Zero position deviation of servo inclinometer independent of sensor position[/align] The output of the inclinometer at zero input (the base of the inclinometer is on an absolutely horizontal surface) consists of two parts: (1) Offset error VB is defined as the output independent of the position of the inclinometer. (2) Misalignment error angle e is mainly caused by the inclinometer base not being absolutely parallel to the measurement axis. This results in an output voltage Ve proportional to the misalignment angle (for very small angles, sine≈e). If the rotating base in Figure 1 is on an absolutely horizontal plane, it is clear that the sum of the offset error output VB and the misalignment error output Ve of the inclinometer at the two positions is: Vo=VB+Ve (1) Assuming that the rotating base is tilted by an angle φ relative to the Y-axis, the analysis process is as follows, as shown in Figure 2. [align=center][img=262,89]http://www.e-works.net.cn/images/128110620711875000.GIF[/img] Figure 2. Rotating the sensor at opposite diameter positions will produce equal electromagnetic fields with opposite polarities.[/align][align=left] It is clear that when rotating the sensor as shown in Figure 2, the angle φ is the same at both positions. Obviously, the directions of the input axes are opposite, so the polarity of the output voltage Vφ is also opposite. The voltage outputs at positions 1 and 2 overlap: V1=Vo+Vφ=VB+Ve+Vφ (2) V2=Vo-Vφ=VB+Ve-Vφ (3) Finally, subtracting the outputs at positions 1 and 2 (V1-V2=2Vφ) yields the result: [/align] [img=131,41]http://www.e-works.net.cn/images/128110513413125000.gif[/img][align=left] Generally speaking, it can be seen from the equation that offset error and misalignment error can be completely eliminated, thus obtaining the true angle. In fact, this is the function of automatic zeroing. To apply these theories to practice, the following basic conditions must be met: (1) The surface of the rotating disk at position 2 must be parallel to the surface at position 1. (2) Since the tilt sensor is actually an accelerometer, the instrument must be stationary when performing error correction operations, and vibration should be avoided as much as possible. (3) The reading at the measurement position should be taken when the output of the tilt sensor reaches a balanced state. III. System Working Principle and Structure Based on the theoretical foundation of automatic zeroing mentioned above, to achieve automatic zeroing of the tilt sensor, the tilt sensor needs to rotate precisely 180°. After comparing various micro-motors, a stepper motor, which is easy to control precisely, was selected to rotate the platform. The tilt sensor is then precisely mounted on this platform. The readings of the tilt sensor at two opposite positions need to be converted using an A/D converter with sufficient bit depth, accuracy, and response speed. Finally, the final result is stored and calculated using a microcontroller. The digital output is output via RS-232 or other formats, as shown in Figure 3. [align=center][img=269,100]http://www.e-works.net.cn/images/128110621212031250.GIF[/img] Figure 3. Design structure diagram of the automatic zeroing servo tilt sensor[/align][align=left] IV. Experimental Results 1. Temperature Drift Test After studying the automatic zeroing principle of the tilt sensor, an automatic zeroing servo tilt sensor prototype was designed and implemented. In order to verify the automatic zeroing and drift elimination characteristics of the automatic zeroing servo tilt sensor, high and low temperature tests were conducted on this tilt sensor. The temperature test results are shown in Table 1, where V0 and V180 are the readings directly obtained by the internal tilt sensor at two measurement positions during the automatic zeroing calibration operation, while Vout is the calculated result after zeroing calibration (the same below). [align=center]Table 1 Zero-point temperature test results (1V/°) [img=308,141]http://www.e-works.net.cn/images/128110623888125000.gif[/img][/align] The results were then corrected for data analysis. The corrected results are shown in Table 2. The temperature change-output change characteristic diagram is shown in Figure 4. It can be seen that within the temperature range of -40℃ to 60℃, the output V0 of the internal tilt sensor has a maximum temperature sensitivity of 0.135V. After offset correction, the output Vout of the tilt sensor has a maximum temperature sensitivity of 0.01V. That is to say, the zero-point temperature coefficient of this tilt sensor is less than 0.0001°/℃, and its zero-adjustment accuracy reaches 0.01°, achieving the purpose of automatic zeroing and meeting the requirements of the testing equipment. [align=center]Table 2 Corrected Results[img=308,131]http://www.e-works.net.cn/images/128110624347031250.gif[/img][/align][align=center][img=194,158]http://www.e-works.net.cn/images/128110628192500000.GIF[/img] Figure 4 Output Variation Characteristics of Zero-Point Temperature Test[/align] [align=left] 2. Zero-Point Repeatability Test Zero-point repeatability refers to the change in tilt angle when the tilt sensor deviates from zero and then returns to zero. The data recording results are shown in Table 3. Analysis of the data records shows that the zero-point repeatability of the automatic zeroing servo tilt sensor is 0.001°. Table 3 Zero-position repeatability experiment record table [img=312,78]http://www.e-works.net.cn/images/128110625090937500.gif[/img][/align] 3. Error analysis The tilt sensor was tested at room temperature (20℃) within the range of -10° to 10°, and V0, V180, and Vout were recorded respectively. Based on the measured data, the linearity graph of this tilt sensor at 20℃ can be obtained as shown in Figure 5. [align=center][img=216,166]http://www.e-works.net.cn/images/128110628831875000.GIF[/img] Figure 5 Linearity graph of sensor output at room temperature (20°)[/align] Based on the measured data above, the nonlinearity error of the tilt sensor output Vout over the full range can be calculated to be 0.02°, which meets the requirements of the testing equipment. 4. Vibration Test: The tilt sensor was placed on a vibration table for a vibration test. The technical conditions for the vibration test are shown in Table 4. The zero-point outputs V0, V180, and Vout of the tilt sensor were recorded before and after the vibration test. The test data are shown in Table 5. Table 4 Vibration Test Technical Conditions [align=center] [img=318,77]http://www.e-works.net.cn/images/128110626381562500.gif[/img][/align] Table 5 Vibration Test Data [align=center] [img=393,157]http://www.e-works.net.cn/images/128110626597656250.gif[/img][/align] After analyzing the above data, a comparison diagram of Vout before and after vibration was drawn, as shown in Figure 6. As shown in the figure, the automatic zeroing servo tilt sensor has good vibration and shock resistance, meeting the requirements of the testing equipment. [align=center][img=180,134]http://www.e-works.net.cn/images/128110629891875000.GIF[/img] Figure 6 Comparison of output Vout before and after vibration[/align] [align=left] 5. Continuous Working Test The continuous working test refers to powering on the automatic zeroing servo tilt sensor and making it work continuously for 24 hours, recording its data output values ​​V0, V180, and Vout every hour. Based on the continuous working test records, its output change graph during continuous working can be drawn, as shown in Figure 7. [align=center][img=196,151]http://www.e-works.net.cn/images/128110630197187500.GIF[/img] Figure 7 Output variation graph of continuous operation test[/align] V. Test Results After testing the automatic zeroing servo tilt sensor prototype, its technical parameters were finally measured as follows: [b]VI. Conclusion[/b] Zero-position deviation and drift are technical problems that all sensors need to solve. This paper studies the model and method of automatic zeroing and the algorithm of compensation, establishes a set of theories and methods for automatic zeroing of tilt sensors, designs and implements an automatic zeroing servo tilt sensor prototype, and proves through tests that it has good automatic zeroing characteristics and can eliminate drift problems, which has very important application value.