Abstract: This paper introduces an aircraft power supply performance parameter testing system based on the VXI bus, and analyzes the gross errors, random errors, and systematic errors present in the system. Through several sampling and data processing, corresponding error handling methods were found and applied in practice. Experiments demonstrate that the error handling methods are effective in improving the accuracy of the aircraft power supply performance parameter testing system.
Keywords: error; test; aircraft power supply In order to verify whether the design and manufacturing of the aircraft power supply system meets the given requirements, it is necessary to conduct a systematic test on its power supply quality [1] . The Key Laboratory of Aircraft Power Supply of Nanjing University of Aeronautics and Astronautics has developed an aircraft power supply performance parameter test system based on VXI bus. The system can perform real-time, high-precision multi-channel signal measurement. In the development process, I participated in the construction and debugging of the hardware system, the compilation of software processing program, and the analysis and processing of system error and random error. Finally, the system has stable performance and high precision, which can meet the measurement work of the aircraft power supply system and provide a basis for the final manufacturing of the aircraft power supply. This article focuses on the error analysis and processing of the test system.
1. Introduction to Aircraft Power Supply Performance Parameter Testing System
The workflow of the aircraft power performance parameter testing system is shown in Figure 1.
The accuracy of this system depends on the input/output interface (conditioning circuit), the accuracy of the A/D converter, and the accuracy of the software processing. Of course, the sampling frequency and sampling period are also decisive factors. Based on the nature and characteristics of the errors, they are generally classified into three categories: gross errors, random errors, and systematic errors. This paper studies the error handling methods for these three types in this system.
2. Handling of Gross Errors
Gross errors in this system may originate from occasional glitches in the aircraft's power system, which significantly affect the accuracy of the measurement results. We employ a first-order difference equation.
x t′ =x t-1 + (x t-1 -x t-2 )In the formula, x <sub>t′ </sub> is the predicted value at time t; x <sub>t-1</sub> is the value of the first sampling point before time t; and x <sub>t-2</sub> is the value of the second sampling point before time t.
As can be seen from equation (1), the value at time t can be estimated by taking the values at times x t-1 and x t-2 . When the data sampling frequency is much greater than the highest frequency of the physical quantity change, this prediction method has sufficient accuracy. We compare the predicted value at time t with the actual data value at time t, and then judge whether the actual data value at time t is a singular term. The criterion for judgment is: Given an error window W, if the actual data at time t is x t , when | x t - x t′ |＞W, then it is considered that this sampled value does not conform to the normal change law and is a singular term. Generally, the size of the error window should be determined according to the sampling frequency of the data acquisition system and the change characteristics of the physical quantity [2] .
Based on the above theory, a program was developed to detect singularities in AC and DC steady-state voltage and current measurement data. With a relative error set at 10%, the predicted value at a given point is calculated using a difference equation and compared with the actual sampled value at that point. If the relative error is greater than 10%, that point is considered a singularity. After detecting a singularity, a data point equal to the predicted value is added at that location.
3. Software processing methods to overcome random errors
In actual measured signals, various noises and interferences often exist, originating from the signal itself, the sensor, electromagnetic interference, or the quantization effect of the A/D converter. Their amplitude and phase change irregularly over time, thus their impact on the measurement results falls under the category of random errors. Here, utilizing microprocessor capabilities and employing specific software processing methods on the measurement results can reduce random errors in the measurement. For n independent, error-free, and equally precise measurements of a measurand, yielding n measurement data x1 , x2 , ..., xn , the most probable estimate of the measurand is the arithmetic mean of all the measurement data. This is known as the arithmetic mean principle.
Repeated measurements based on the arithmetic mean principle can minimize the impact of random errors on the final result.
When calculating the effective values of voltage and current, harmonic content, and voltage modulation parameters, this system strives to increase the sampling frequency and test cycle to minimize random errors.
4. Analysis and processing of systematic errors
4.1 Errors caused by LEM-type current and voltage sensors
The sensors in the circuit of this system include multiple LEM Hall effect current sensors and LEM voltage sensors. The errors generated by the voltage and current sensors are caused by their own accuracy, as well as by the correct use of the sensors and the influence of external magnetic field interference.
LEM Hall voltage and current sensors have good linearity and high accuracy, but improper use can also cause measurement errors. For example, when DC current passes through the primary coil, the sensor is not connected to the power supply, or the secondary coil is open, so that the secondary coil circuit cannot provide the corresponding compensation current, causing the magnetic ring to be magnetized and generating residual magnetism, thus affecting the measurement accuracy.
This system places the LEM module inside a magnetic field shield to avoid interference from external magnetic fields. On the other hand, it strictly adheres to the system testing procedures, ensuring that the entire system can only begin testing when the sensor is powered on, in order to prevent the magnetic ring from being magnetized.
After repeated measurements, the results are shown in Table 1, confirming the existence of systematic errors in the conditioning circuit. These systematic errors originate from several sources: the 5A current sensor error is ±0.5%; the PM3300 power analyzer measurement error is ±0.05%; the sampling resistor accuracy is ±0.1%; and wiring errors, etc. Here, the systematic error is reduced by using the method of input value = output value ÷ (1 - 0.4%) for each output channel. Practice has proven this method to be effective.
4.2 Errors caused by asynchronous sampling
Synchronous sampling refers to sampling the periodic signal f(t) at equal intervals Ts within the time interval [t<sub>0</sub>, t<sub>0</sub>+T], at N+1 points. It requires: 1 ) equal sampling intervals; 2) the sampling interval multiplied by N (where N is the number of sampling points per period) should be strictly equal to the period of the signal being measured, i.e., Ts×N＝T. If it is exactly equal to one period of the signal being measured, it is idealized synchronous sampling. When the number of sampling points conforms to the sampling theorem, there is no synchronous sampling error [4-5] . However, in actual microcomputer testing, the period of the signal being measured and the sampling interval are generally represented by the microprocessor's count value, which is a positive integer. Rounding errors occur during division operations, resulting in a sampling interval Ts ≠ T/N, thus causing a synchronization error (called period error), the magnitude of which is:
△T=N×T s -TAs shown in Figure 2, the first sampling point of the test system is at point α[sub]1[/sub] of the fundamental frequency, and the Nth sampling point is at point α. Due to the existence of synchronization error ΔT, α 1 ≠ α 2. At this time, the actual sampling interval is: It can be seen that the synchronization error is caused by factors such as the system frequency of the microprocessor used in the test system not being infinitely high, its counting period not being infinitely small, and fluctuations in the mains voltage.
In practice, synchronous sampling is impossible, which introduces asynchronous sampling errors. When synchronization errors exist, the sampling start point position is related to the errors in the RMS and active power measurement methods. Choosing an appropriate sampling start point position can reduce or even eliminate the impact of synchronization errors on the signal's RMS and active power. Sampling near the "optimal sampling start point" results in very small errors and is convenient for engineering implementation. The traditional "zero-crossing sampling" method is not conducive to suppressing the effects of synchronization errors.
Simulation experiments using the arbitrary waveform generator in HP VEE to generate standard waveforms show that the optimal sampling starting point for measuring the effective value of a sine wave signal is around 0°; and the optimal sampling starting point for measuring the harmonic content of a sine wave is around 60°. Table 2 shows the relationship between synchronization error, effective value error, and active power measurement error at different sampling starting points.
When calculating power, the simultaneity of voltage and current sampling is critical. If the voltage and current samples are not taken simultaneously, with a time difference of t, the measured power will contain non-simultaneous sampling errors.
δ=|wttanρ|×100%In the formula, ρ is the power factor angle and w is the angular frequency of the sampled signal [6] .
As shown in equation (5), the non-simultaneous sampling error will increase sharply as the power factor decreases. Therefore, the system should fully consider this error. Since it is impossible to complete the task of simultaneously sampling voltage and current signals using only one A/D converter, this system starts three A/D converters simultaneously during sampling, allowing the analog voltage and analog current signals to enter the A/D converters respectively, thereby minimizing the impact of non-simultaneous sampling error on the system accuracy.
5. Conclusion
Equipment selection is crucial, and error handling is also important. Through the above error handling, the measurement accuracy of this testing system is as follows.
Steady-state voltage: ±1.0% Transient voltage: ±0.5% Steady-state frequency: ±0.4% Current: ±1.0% Phase shift: ±0.5° Power: ±1.5% Practice has proven that this system can provide a strong basis for the design and finalization of the power supply system for domestically produced aircraft.
References:
[1] Yan Yangguang. Power Supply Systems for Aerospace Vehicles [M]. Beijing: Aviation Industry Press, 1994.
[2] Xiao Zhongxiang. Principles of Data Acquisition [M]. Xi'an: Northwestern Polytechnical University Press, 2000.
[3] Li Songlun. Electrical Testing Technology [M]. Xi'an: Northwestern Polytechnical University Press, 1992.
[4] Ma Hongzhong, Hu Qiansheng. Error analysis of software synchronous sampling [J]. Journal of Electrical Engineering, 1996, 11(2): 25-28.
[5] Cao Lingzhi. Error analysis and processing of automatic transformer testing system [J]. Journal of Zhengzhou University of Light Industry, 1997(3): 24-27.
[6] Fang Hui. Analysis of uncertainty of error, relative error, reference error and relative uncertainty of error [J]. Metrology and Testing Technology, 2006(5):30-33.
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