Design of 0°～360° inclination sensor based on MAD2020E acceleration

Abstract: The basic principle of the 0°～360° inclination sensor based on the MAD2020E accelerometer is introduced. Combined with the characteristics of actual acceleration sensing, the dual-axis non-temperature compensation method is used to design the hardware and software. Experimental verification shows that the inclination acceleration sensor has achieved compact size, high accuracy and intelligence.
Keywords: accelerometer; inclination measurement; non-temperature compensation; MAD2020E

1 Introduction
At present, most of the inclination sensors used in domestic fields are applied to system level measurement. According to the working principle, the inclination sensors can be divided into four types: "same body pendulum", "liquid pendulum", "gas pendulum" and "acceleration". Most of them are angle sensors with a biased frame structure, which have low process accuracy and poor reliability. Although the new quartz flexible accelerometer has high measurement accuracy, it has poor seismic resistance and is easy to damage. MEMSIC accelerometer MAD2020E is not only small in size, high in accuracy, but also has high impact resistance. It is particularly suitable for occasions such as mines and locomotives where the inclination measurement conditions are relatively poor. Therefore, a design scheme of a 0°~360° inclination sensor based on MAD2020E accelerometer is proposed here.

2 Working principle of inclination measurement
2.1 Working principle of inclination measurement by accelerometer
The accelerometer determines the inclination angle of an object by sensing the magnitude of the component of gravity acceleration g on its measuring axis. When the MEMSIC accelerometer is placed horizontally (the two sensitive axes are parallel to the horizontal plane), it is most sensitive to changes in position or inclination. When placed vertically (the two sensitive axes are perpendicular to the horizontal plane), the sensitivity to changes in position or inclination will decrease. Figures 1 and 2 describe the corresponding changes in the output values ​​of the X-axis and Y-axis of the MEMSIC accelerometer during the tilt process from +90° to 0°. Please note that when the output change of any axis (for every 1° of tilt) is small, the output change of the other axis is large. The principle of mutual compensation of the changing characteristics of these two axes is used to design a high-precision inclination sensor.

To measure the tilt angle, calculations are required because the output of the accelerometer only acts on the gravity acceleration value on the sensing axis. The relationship between the output of a dual-axis accelerometer and gravity when placed horizontally is:

Where Ax and Ay represent the output of the accelerometer, g is the acceleration due to gravity, and α and β are the tilt angles. To calculate the tilt angle, use the inverse sine equation:

2.2 Introduction to MAD2020E Accelerometer
The MAD2020E accelerometer is a complete dual-axis acceleration measurement system based on a single-chip COMS process. Like other accelerometers with gravity blocks, the MEMSIC device uses a movable thermal convection air mass as a gravity block. The device measures acceleration by measuring the change in internal temperature caused by acceleration. The mass block in the MEMSIC sensor is gas. The MAD2020E accelerometer is a device that determines acceleration by measuring the principle of temperature change. The output signal of the MAD2020E accelerometer sensor is 2 PWM (duty cycle) signals. When the accelerometer sensor outputs a PWM signal, the duty cycle of the PWM signal is proportional to the acceleration signal.

3 Design of a dual-axis 0°～360° inclination sensor without temperature compensation
3.1 Overall system design
In applications where the inclination angle does not exceed ±60° based on the horizontal position, a dual-axis accelerometer can be used to measure the inclination on both axes. When it is necessary to measure an inclination angle greater than 90°, the X and Y axes of the accelerometer are combined to obtain a better resolution within the 360° range. This requires a dual-axis accelerometer sensor to measure the single-axis inclination angle. Figure 3 shows
an accelerometer based on a vertical initial position, a single-axis inclination measurement placed at an angle, and a good resolution of ±360°.

When the acceleration and the tilt angle are:

Here, (δ+γ)=90°, and the value of δ or γ can be easily obtained. Therefore, Ax can also be written as: Ax=g·sin(-γ+90°)=g·cos(γ). γ can be obtained by the inverse tangent equation: γ=tan-1(Ax/Ay).
In addition to providing better tilt angle resolution, the vertical frame also provides two output errors that are offset by Ay divided by Ax. Therefore, after performing this conversion process, there is no need to perform temperature compensation on the accelerometer. Because the sensitivity of the thermocouple accelerometer has a repeatable temperature characteristic, the output change amplitude of the two axes is the same, so the change in sensitivity with temperature has no effect on the calculation of the contrast value.
The design of the dual-axis tilt sensor system without temperature compensation is based on the above principle, with the dual-axis PWM input of the PIC16F873 microcontroller as the core, and the idea of ​​compensating the zero temperature drift by pre-setting the zero bias value. The hardware schematic diagram of the temperature compensated dual-axis tilt sensor system is shown in Figure 4.

The RC3 and RC2 terminals of the PIC16F873 are set to select and calibrate the zero point. When the PIC16F873 reads in, the 0 g calibration and sensitivity calibration are performed through the circular selection of the buttons.
The output of the MAD2020E accelerometer sensor is 2 PWM (duty cycle): T1/(T1+T2), then the acceleration output is:

There are three timers in PIC16F873. Time1 can be used to calculate the time of PWM high and low pulse widths.
According to the relationship between the input and output of the MEMIC accelerometer, the output expression of the signal is:
AOUT(α)=AOUT(0)+SENSITIVITY×SIN(α) (5)
The method to achieve the inclination of 0°～360° is to first place the MEMIC accelerometer vertically, then adjust it to get AOUT(0), and then use the ARCTAN function:

This method does not require temperature compensation. 0 g calibration is achieved by presetting an offset angle (AngleOffset), and then adding the offset angle to AOUTX each time to complete 0 g calibration.
The main program flow of the system software is shown in Figure 5.

3.2 Experimental results
According to the above inclination measurement principle and circuit design, data measurement was carried out on the actual rotation angle test platform. The measurement angle error is shown in Figure 6. The measurement error result is no more than ±0.1°. The experiment proves that the method of measuring inclination has good accuracy, thus realizing the measurement of dual-axis 0°~360° inclination without temperature compensation.

4 Conclusion
The acceleration and inclination sensor design using the PIC16F873 microcontroller cleverly utilizes the sensitivity of the thermocouple MEMSIC accelerometer MAD2020E sensor with repeatable temperature characteristics. The outputs of the two axes have the same change amplitude. The inverse tangent operation eliminates the sensitivity error. At the same time, the 0 g deviation is achieved by using a pre-set angle offset, thereby avoiding the angle measurement error caused by zero drift, and realizing high-precision and intelligent measurement of the dual-axis acceleration 0°~360° inclination without temperature compensation.