1. Hardware Design of Tilt Angle Measurement System
The hardware part of the tilt angle measurement system mainly consists of MEMS sensors (including dual axis tilt angle sensors and temperature sensors), SoC circuits, data processing and transmission, and other auxiliary circuits. The composition diagram of the inclination measurement system is shown in Figure 1.
1.1 MEMS tilt sensor interface
The MEMS tilt sensor adopts SCA100T-D01 from VTI Technologies' SCA100T series in Finland, with a measurement range of ± 30 °. The SCA100T series is a high-resolution dual axis tilt sensor manufactured using Micro Electro Mechanical Systems (MEMS) technology. The digital output resolution of SCA100T-D01 is 0.035 °/LSB, and the analog output resolution is 0.0025 °. The resolution of analog output is much higher than that of digital output, so this design adopts its analog output. Analog output will involve complex analog signal processing. If the analog signal is not processed properly, the resolution and accuracy of the system will be greatly reduced, and sometimes even inferior to digital output. One of the methods to ensure system accuracy is to use a reasonable analog signal processing circuit.
SCA100T-D01 has a built-in temperature sensor that can read temperature values through its built-in SPI digital interface and perform corresponding temperature compensation in the processor. This is another method to ensure system accuracy.
1.2 Impedance matching and amplification
The output impedance of SCA100T-D01 is 10 k Ω. In order to ensure the effective transmission of the signal output by the MEMS tilt sensor SCA100T-D01, which requires minimal attenuation, an impedance matching circuit was designed using a field-effect transistor operational amplifier TL081 with high input impedance. The same phase input was used to improve the input impedance.
The signal amplification circuit is completed using ICL7653 chopper stabilized zero operational amplifier, as shown in Figure 2. ICL7653 has extremely low offset voltage and bias current, high operational stability, and excellent high-precision amplification function. When using the ICL7653 chopper stabilized zero internal clock, add a 0.1 μ F low discharge, high stability polyester or polypropylene capacitor between the CA, CB, and CR terminals. Simultaneously filter and decouple at the dual power supply connection end.
1.3 Differential Conversion and Drive
As shown in Figure 3, the differential conversion circuit uses AD8138AR as the core to convert single ended signals into differential signals, which can improve the common mode rejection ratio, effectively reduce the influence of common mode signals, and drive the 24 bit differential Sigma Delta analog-to-digital converter inside the SOC. The AD8138AR has a wide analog bandwidth (320 MHz, -3 dB. When the gain is 1), and it is a surface packaged device with a small size, which allows the ADC to be very close to the signal input point, greatly reducing the influence of external noise.
1.4 SOC microcontroller resource allocation
This design uses Silicon Labs' C8051F350 as the processing core. C8051F350 is a truly independent system on chip (SOC) that comes with 8K bytes of Flash memory and can be programmed in the system; Integrated with one fully differential 24 bit Siva Delta analog-to-digital converter (ADC), which has on-chip calibration function, and two independent digital extraction filters can be programmed to a sampling rate of 1 kHz; It has 2 UART and 1 SPI interfaces. Compared with other types of microcontrollers that require a combination of multiple chips to achieve the same functionality, C8051F350 not only reduces system costs and volume, but also greatly improves system reliability.
In the design, a 24 bit Sigma Delta analog-to-digital converter using C8051F350 is used for analog-to-digital conversion of system signals, SPI interface is used for temperature acquisition of MEMS tilt sensors to achieve temperature compensation of the sensors, and UART is used as a serial LED display interface. To ensure stable operation of the analog-to-digital converter, an external reference source is used.
1.5 ADC reference source and sensor power supply
When the inclination angle of the MEMS tilt sensor SCA100T is 0 °, the analog output is 1/2 of its power supply voltage. If the power supply voltage of the tilt sensor fluctuates, its output will produce corresponding fluctuations. Therefore, during design, the output of the reference source will be provided to the analog-to-digital conversion circuit (as shown in Figure 4), and after improving the driving capability, it will be provided to the MEMS tilt sensor SCA100T as a power source (as shown in Figure 5). On the one hand, the reference source has minimal output ripple and stable performance; On the other hand, the reference source of the analog-to-digital converter and the power supply of the MEMS tilt sensor SCA100T change in the same direction simultaneously, offsetting the impact of zero drift caused by the power supply on the MEMS tilt sensor.
The 2.5 V voltage output from the reference source LM236 is processed by a tracking circuit consisting of a rail to rail operational amplifier OPA340, which increases the driving capability. It serves as the reference source for the analog-to-digital conversion circuit and also provides the center voltage for the differential conversion circuit, as well as the power input for the MEMS tilt sensor SCA100T.
Reference voltage (VREF) output. The operational amplifier circuit composed of low drift and high stability OPA340 provides power to the tilt sensor SCA100T, ensuring small power ripple and stable operation.
2. Mathematical processing of signals
2.1 ADC accuracy control
The C8051F350 has two independent extraction filters (SINC3 filter and fast filter) and one programmable gain amplifier inside. According to the reference SINC3 filter, the RMS noise is small and the accuracy is high, but the disadvantage is that the output rate is low, while the fast filter is the opposite. This design requires low speed but high accuracy, so SINC3 filter is chosen. The typical RMS noise of SINC3 filter is shown in Table 1. From Table 1, it can be seen that higher extraction ratios require longer conversion periods, resulting in lower output word rates but lower noise. According to the reference, when using the SINC3 filter, the actual resolution of the analog-to-digital converter is: According to formula (1) for the actual resolution, when the extraction ratio is 1920 and the output word rate is 10 Hz, the actual resolution can be obtained as approximately 20.00 bits based on formula (1) for the actual resolution. The sensitivity of the SCA100T sensor is 70mV/(°), the resolution is 0.0025 °, and the ADC reference voltage VREF is 2.5V. Therefore, the minimum signal that needs to be detectable is 0.0025 ° x70mV/°=0.175 mV. According to 0.175 mV/2.5 V="1"/14 286, the number of ADC bits should be at least 14, that is, 214=16 384>14 286. According to the requirements of the derating design, 20 bits are taken, so this design fully meets the design requirements.
2.2 Temperature compensation
According to the reference, the temperature error curve of SCA100T-D01 is shown in Figure 6. Through curve fitting, the equation of the curve is: after the signal is collected by the analog-to-digital converter and converted into angle output, the temperature value at the SCA100T tilt sensor collected in real-time can be used to compensate for the corresponding angle value based on the temperature compensation curve, minimizing the impact of temperature on tilt measurement.
2.3 Curve fitting
Due to the non-linear relationship between the output of SCA100T series sensors and the tilt angle (non-linear error of 0.11 ° within the measurement range), it is not conducive to analyzing and processing the measurement results. Therefore, corresponding linearization measures must be taken to compensate for the nonlinearity introduced by the sensor. Most traditional methods use hardware methods, which are complex to implement and difficult to control for stability and reliability.
Due to the known nonlinear characteristics of the SCA100T series sensors, corresponding correction functions can be used for compensation. Due to the strong functional and data processing capabilities of microprocessors, the required calibration functions can be easily implemented through programming methods. This design uses SOC to correct nonlinearity through software programming.
In the design process, the measurement range of the SCA100T-D01 sensor is further subdivided, such as dividing the curve with a tilt angle of 3 ° into 2.5 ° to 3.5 °, and modifying the fitted curve into the following equation: where XIN is the sample value obtained by filtering the output value of the analog-to-digital converter through the internal SINC3 filter, TER is the real-time temperature compensation value of the SCA100T sensor, and PI is the pi. The above equation corrects both the nonlinearity of the sensor output and the influence of temperature on the sensor.
3. Actual measurement data
The inclination measurement system was calibrated and performance tested on the MC019-J2 digital 2 "optical indexing head standard instrument. The MC019-J2 digital 2" optical indexing head is a precision optical metrology instrument used for angle calibration or inspection of workpieces clamped on its spindle, with a display equivalent of 1 ". The test data is shown in Table 2.
From the test data, it can be seen that the deviation of each test point is positive and negative, mainly because the curve fitting of these test points is independent and does not affect each other. In addition, the maximum absolute error is at 30 °, with a maximum absolute error of 0.0044 °, and the maximum relative error is at 1 °, with a ratio of 0.0018/1 ≈ 0.018%.
4. Conclusion
This article uses the analog interface of the MEMS tilt sensor SCA100T as the output, and its digital interface is used to achieve temperature compensation. At the same time, a reference source and operational amplifier are used as the power supply for the sensor, which improves the accuracy and stability of the sensor output; During signal processing, low drift operational amplifier processing circuits and differential analog-to-digital conversion circuits are used, effectively improving the signal-to-noise ratio and common mode rejection ratio of the signal; The use of sine curve fitting effectively improves the linearity of signal output. After various signal processing and optimization, the maximum absolute error of the system within the measurement range is 0.004 4 °. And the system has high integration, small size, and low cost, which can meet engineering applications such as geological and petroleum exploration, equipment installation, road and bridge construction, as well as automatic horizontal adjustment applications for robot control, tank and ship artillery platform control, aircraft attitude control, and other systems.
