Introduction
Due to the extremely limited size and payload capacity of MAVs, reducing the size and weight of the flight control and navigation system is particularly important. This paper designs a dual-axis inclinometer based on a MEMS accelerometer. This device is highly accurate and lightweight, meeting the attitude angle measurement requirements of MAVs, and can also be used in other inclinometers requiring small size and light weight.
MEMS accelerometer
The ADXL202 is a state-of-the-art, low-gravity acceleration biaxial micromachined accelerometer that outputs both analog and pulse-width modulated digital signals with extremely low power consumption and noise. Surface micromachining allows for high integration of the accelerometer sensor and signal processing circuitry onto a single silicon chip. Like all accelerometers, the sensor unit is a differential capacitor, whose output is proportional to the acceleration. The accelerometer's performance depends on the sensor's structural design. The differential capacitor is constructed from a cantilever beam, which consists of many alternating pairs of finger-shaped capacitor electrodes. A single pair of finger-shaped capacitor electrodes can be simplified as shown in Figure 1. The capacitance of each finger electrode is directly proportional to the overlap area between the fixed and moving electrodes and the displacement of the moving electrode. Clearly, these are very small capacitors, and to reduce noise and improve resolution, a differential capacitance that is as large as possible is actually required.
The motion of the cantilever beam is controlled by the polycrystalline silicon springs supporting it. The masses of these springs and the cantilever beam obey Newton's second law: for an object of mass m, acceleration a due to a force F, then F = ma. The deformation of the spring is proportional to the magnitude of the force, i.e., F = kx, so x = (m / k)a, where x is the displacement (m); m is the mass (kg); a is the acceleration (m/s²); and k is the spring stiffness coefficient (N/m).
Therefore, only two parameters are controllable: the stiffness of the supporting spring and the mass of the cantilever beam. Reducing the spring constant seems like an easy way to improve the sensitivity of the cantilever beam, but the resonant frequency of the cantilever beam is proportional to the spring constant. Therefore, reducing the spring constant leads to a decrease in the resonant frequency of the cantilever beam, and the accelerometer must operate below the resonant frequency. Furthermore, increasing the spring constant makes the cantilever beam more rigid. Therefore, if the spring constant is kept as high as possible, only the mass parameter of the cantilever beam is variable. Generally, increasing the mass means increasing the sensor area, thus increasing the cantilever beam size. In the ADXL202, a novel cantilever beam structure was designed. The finger electrodes constituting the variable capacitors of the X and Y axes are integrated along a square cantilever beam, thereby reducing the overall sensor area. Moreover, the shared large mass of the cantilever beam improves the resolution of the ADXL202. The spring suspension system located at the four corners of the cantilever beam is used to minimize the sensitivity coupling of the X and Y axes.
Inclination measurement principle
The ADXL202 is most typically used for tilt measurement, using gravity as the input vector to determine the orientation of an object in space. It is most sensitive to tilt when gravity is perpendicular to its sensing axis, exhibiting the highest sensitivity to tilt angles at this orientation. When the sensing axis is parallel to gravity, the change in output acceleration per 1° tilt is negligible. When the accelerometer's sensing axis is perpendicular to gravity, the change in output acceleration per 1° tilt is approximately 17.5 mgn, but at 45°, the change is only 12.5 mgn, and the resolution decreases. Table 1 shows the output of the X and Y axes when tilted ±90° in the vertical plane.
When the X and Y axes of the accelerometer are both perpendicular to the direction of gravity, it can be used as a dual-axis tilt sensor with roll and pitch angles. Once the accelerometer's output signal is converted into an acceleration, this acceleration will be between -1 gn and +1 gn. The tilt angle, expressed in degrees, can be calculated using the following formulas: θ = arcsin(AX / gn) γ = arcsin(AY / gn), where θ and γ are the pitch and roll angles (°), respectively; AX and AY are the X-axis and Y-axis outputs of the accelerometer, respectively, in gn.
Inclination measurement circuit
The block diagram of the measurement circuit is shown in Figure 2. The voltage output by ADXL202 is first filtered by a low-pass filter and then impedance matched by a voltage follower. When both the X and Y axes are in a horizontal position, the two output voltages are divided by a voltage divider to 1.2V. When the X and Y axes rotate from -90° to +90° respectively, the amplified voltage changes from 0V to +2.4V to meet the needs of the A/D converter of the C8051F002 microcontroller. Then, the microcontroller performs linearization and temperature compensation, and outputs analog quantities from the D/A converters DAC0 and DAC1 respectively, with θA representing the pitch angle and γB representing the roll angle. At the same time, the pitch and roll angles are converted into digital quantities and output as digital measurements from the RS232 serial port, namely θD and γD respectively.
Experimental results
After linearization and temperature compensation of the inclinometer, measurements were performed within its range. The equipment used was a coordinate measuring machine (CMM) table as the horizontal reference, and a 200mm sine bar and micrometer gauge as angle generators to produce reference angles. The inclinometer was connected to a computer via a serial port to display the measured angles. Because the levelness of the CMM table and the angle accuracy generated by the sine bar and micrometer gauge were sufficiently high, the resulting angle error was considered minimal and could be taken as the expected angle value. The measurement results are shown in Table 2.
From Table 2, we can calculate that the maximum tilt angle error is -0.26° to 0.25°, while the average angle error is ±0.135°, which are 0.57% and 0.30% of the full scale, respectively.
in conclusion
This paper presents a dual-axis inclinometer designed using a MEMS dual-axis accelerometer. The inclinometer is small in size and lightweight (approximately 10 g). Measurement results after linearization and temperature compensation show that within the measurement range of ±45°, the maximum error is 0.57% of the full scale and the average error is 0.30% of the full scale.
This inclinometer perfectly meets the roll and pitch angle measurement requirements for MAV attitude control. Furthermore, it can also be used in other measuring equipment requiring small size and light weight.
Edited by: He Shiping
