Accuracy analysis of virtual test system

    Abstract: System accuracy is an important indicator that reflects the level of the entire system. How to analyze the accuracy of the virtual test system is a question worth discussing. Combined with the developed permanent magnet DC motor virtual test system, a general method for analyzing accuracy is given, and several errors for measuring system accuracy are specifically calculated.

    Keywords: Virtual test system, motor system accuracy

    Virtual test instruments (systems) are the result of the development of computer test instruments. Generally speaking, it consists of a computer, a modular set of hardware, and software. Users can control the operation of virtual instruments and complete all testing functions by operating the computer graphics panel.

    There is an essential difference between virtual test instruments and general computer test instruments, because the hardware of virtual test instruments only solves the input and output (acquisition and transmission) of signals, and powerful software is the key to the entire instrument system; while general computer test instruments, Hardware is the key to the entire instrument system.

    In the permanent magnet DC motor virtual test system we developed (hereinafter referred to as this test system), the hardware system consists of two parts: power drive and data acquisition based on single-chip microcomputer. Its function is to complete the input of motor voltage and voltage, current and Collection and transmission of rotational speed; in addition to the advanced software environment support, the software system also has multiple advanced professional modules, such as: data processing module, system identification (parameter estimation) module, motor mathematical model module, graphics processing module, characteristics The function of the simulation module is to process, identify, calculate and output the collected data, so that it can replace the hardware to complete many test functions, which is a key part of the entire instrument system. Only in this way can the original computer testing instrument be raised to a new level.

    From the above analysis of the composition of this test system, we can see that its accuracy is mainly determined by the following parts: (1) Hardware system accuracy; (2) Software module accuracy, such as motor modeling accuracy and approximate calculation of applied parameter estimation theory Accuracy of data processing algorithms such as accuracy and filtering. Among them (1) is the premise to ensure high accuracy of the entire system.

    The following takes an aviation permanent magnet DC motor (hereinafter referred to as the motor under test) as the test object, and analyzes its accuracy from four aspects in conjunction with this test system, so as to obtain an overall evaluation of the accuracy of the entire test system.

    1 Accuracy analysis and error compensation of hardware system

    The function of the hardware system is to collect and transmit the relevant state variables of the motor. The accuracy of data collection directly affects subsequent data processing and the accuracy of the virtual test system.

    The following is a specific calculation of the relative voltage error between the motor ground (analog ground) and AD ground (digital ground) in this hardware system to analyze the accuracy of the hardware system.

    First, operate the computer panel of this system and apply two voltage excitations to the motor. Use a RADAL-CANA5001 voltmeter with an accuracy of 5 and a half digits to measure the two voltage values, which are actually 4.2365V and 8.5821V respectively. This is the key factor in the entire hardware system. The voltage of the analog ground; then the hardware system collects these two voltage values, and collects 500 points respectively, and the average values ​​are 4.1040V and 8.4128V, which are the voltages of the system digital ground.

    Calculate the relative errors between the measured and actual input voltages of the two input voltages, which are:

    This value represents the relative error of the entire hardware system. They are generally determined by the system ground potential difference, the accuracy of various components, etc. Therefore, the system ground potential difference can be software compensated here. The compensation value is still measured with the above-mentioned voltmeter. The voltage difference between the motor ground (analog ground) and AD ground (digital ground) in the entire hardware system uΔ=0.1281V, We use the following method to compensate and recalculate:

    After compensation, e11 and e22 are both less than 0.5%, and their accuracy is very high, ensuring the accuracy requirements of the entire test system.

    2 Repeatability accuracy analysis of electric motor virtual test system

    Since the accuracy of this test system in identifying motor electromechanical parameters is very important, the ratio εi of the estimated standard deviation of the static electromechanical parameters of the motor relative to the sample average can be used to measure the repeatability accuracy of the entire system. The specific method is to use this test system to continuously and repeatedly test the motor under test 10 times, and 10 sets of static electromechanical parameters of the motor can be obtained. Taking the four parameters of Ra, Ke, Kt, and J as an example, the obtained values ​​are shown in Table 1.

    Among them, the units of Ra, Ke, Kt and J are respectively: Ω, V/rpmNM/A, N.M. S.

    Assume that the identified values ​​of each electromechanical parameter are pijaverage value pi, then:   

    Among them, j=1． ． ． m is the number of measurements, where m=10

    i represents the subscript corresponding to the average value of the four parameters Ra, Ke, Kt, and J.

    The average value i is also called the sample mean, which is the best estimate of the true value pi0 of the identified quantity pi. The following are the average values ​​of each static electromechanical parameter:

    Suppose the standard deviation of each static electromechanical parameter is σi, which represents the degree of dispersion of each identification result relative to the sample mean, then:

    When n is a finite number of times, the estimated value i of the standard deviation obtained from Bessel’s formula is:

    The estimated standard deviation of each static electromechanical parameter is calculated as follows:

    The ratio εi of the standard deviation estimate relative to the sample mean is used to measure the repeatability accuracy of the entire system, as follows:

    The details of each calculated value are as follows:

εRa＝5.16% εKe＝0.91% εKt＝0.91% εJ＝3.37%

    It can be seen that the ratio of the standard deviation to the average value is mostly less than 5%, and only εRa is 5.16%, so the repeatability accuracy of this system is high.

    3 Use different methods for comparative testing to analyze system accuracy

    The motor current and speed dynamic response characteristicsOutput dynamic response characteristics can be obtained by two methods: one method is to use the hardware system to directly collect, and the curve is called the acquisition curve; the other method is to reconstruct from the identified parameters The mathematical model of the DC motor uses the experimental input voltage as the input excitation of the mathematical model, and then obtains the dynamic characteristics of the motor current and speed through simulation. The curve is called the test curve. Comparing the degree of approximation of the above acquisition and test dynamic characteristics can measure the accuracy of the entire virtual test system.

    Figure 1 is a comparison chart of the measured motor current and speed acquisition curves and test curves. It can be seen intuitively and qualitatively that the test curve is close to the average value of the acquisition curve, and the two agree well.

    The following is a quantitative analysis of the degree of approximation of the two curves. After the two curves enter the steady state, find the average of their 300th to 400th points respectively, and then calculate the relative error of the two averages to characterize the degree of approximation of the two curves.

    Assume that the collected and system measured values ​​of current and speed are respectively: im, nm and is, ns, and the average values ​​are respectively, then there are:



    Among them, p = i, n; k = m, s; N1 represents the starting point of the value; N2 represents the end point of the value; N1 = 300; N2 = 400.

    Due to the large amount of data, the specific data will not be listed here. The average values ​​calculated according to the above formula are as follows:

    The relative error of the mean is calculated as follows:

    It can be seen from the above calculation results that the relative error of the two average values ​​is very small, indicating that the two curves are very close, and the accuracy of the entire system is relatively high.

    4 Comparative testing with different testing instruments for accuracy analysis

    Various static and dynamic characteristics of the motor, such as mechanical characteristics, working characteristics, etc., can be tested with this test system and with general test instruments. Then comparing the approximation of the test results of the two test instruments is also a measure of the entire virtual test system. A very important method to test the accuracy of the system.

    The mechanical characteristics of a DC motor represent the relationship between its electromagnetic torque Tem and speed n under certain conditions of the motor terminal voltage U. This relationship for permanent magnet DC motors can be expressed as follows:

    Substitute the electromechanical parameters Ra, Ce>Φ=Ke, CTΦ=Kt of the tested motor measured by this test system into the above formula, and take a Tem sequence, and simulate the corresponding n to make the mechanical characteristic curve of the motor as shown in the figure. As shown in Curve 2 in 2 (this is the biggest feature of the “virtual” test system - the mechanical characteristic curve of the motor can be measured without using torque equipment). Curve 1 is the mechanical characteristic curve measured by a general torque bench tester (imported torque bench, accuracy 0.5%). It can be seen from Figure 2 that the two curves are basically consistent.

    Next, calculate the relative errors of the test data of the above two test instruments, and quantitatively analyze the approximation of the two characteristic curves.

    Assume that the relative error of the rotational speed is εn, the actual measured value is nreal, and the system simulation value is n simulated, then:

    Table 2 is the test mechanical characteristic data and relative error table of the torque table instrument and this test system. It can be seen from the table that the maximum relative error of the two test data is 1.45%, indicating that the accuracy of this test system is relatively high.