A constant-temperature hot-wire anemometer stability measurement method based on equivalent pure delay element parameter identification

Abstract

This invention relates to a stability measurement method for a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay element parameters, belonging to the field of fluid measurement and automatic control technology. The method disclosed in this invention includes the following steps: S1. Connecting an ultra-low frequency low-pass filter to the closed-loop circuit of the system to form an in-situ open-loop system with a DC closed loop and an AC open loop; S2. Injecting a sweep frequency excitation signal E at the bias circuit. stimu And measure the output response E of the amplifier circuit. a By comparing the amplitude ratio and phase difference of the two, the open-loop frequency response G of the system under actual operating conditions of the hot wire is obtained. open (jω); S3. Using the preset transfer function model G * open (s) Fit the measured frequency response to identify the pure delay element G introduced by non-ideal factors such as circuit distributed parameters and device hysteresis. delay (s), and uses its parameter b to quantify the non-ideal factors of the system. This invention realizes in-situ measurement of system stability, quantifies non-ideal factors into measurable parameters, and provides a reliable basis for system stability analysis and circuit design.

Description

Technical Field

[0001] This invention relates to a method for measuring the stability of a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay element parameters, belonging to the field of fluid measurement and automatic control technology. Background Technology

[0002] The constant-temperature hot-wire anemometer is a core tool for measuring flow velocity and turbulence in fluid mechanics experiments, with a history dating back to the early 20th century. Its basic principle is based on the hot-wire convection heat transfer theory proposed by King et al.: a thin metal filament (hot wire) heated by electricity is placed in a flow field. When the flow velocity changes, the convective heat transfer between the wire and the fluid changes, resulting in changes in the temperature and resistance of the hot wire.

[0003] A typical isothermal hot-wire anemometer system constitutes a high-gain closed-loop negative feedback circuit, the core of which usually includes a Wheatstone bridge and an operational amplifier. This circuit dynamically adjusts the heating power across the hot wire to counteract the cooling effect caused by changes in flow velocity, thus maintaining the hot wire temperature (i.e., resistance) at a constant set value. In this operating mode, instantaneous changes in flow velocity are rapidly converted into fluctuations in the bridge-top voltage signal output. Compared to constant-current or constant-voltage anemometers, the isothermal hot-wire anemometer, with its unique feedback mechanism, can automatically compensate for the thermal inertia of the hot wire itself, thereby achieving an extremely high frequency response. Its bandwidth typically reaches tens to hundreds of kilohertz, making it an ideal choice for measuring high-frequency turbulent fluctuations.

[0004] Despite the maturity of its theoretical model, significant discrepancies often exist between system performance and theoretical predictions in complex engineering implementations. This gap primarily stems from various non-ideal factors in actual circuits, such as the distributed capacitance and parasitic inductance of the PCB board, the response delay of active devices like operational amplifiers and digitally controlled resistors, and the parasitic parameters of electronic switches. These factors have negligible impact on the low-frequency characteristics of the system, but introduce significant phase delays at high frequencies that affect system stability. In traditional design and debugging, these effects are difficult to accurately model, isolate, or measure.

[0005] Therefore, a core problem in current engineering practice is the difficulty in accurately and quantitatively characterizing the phase delay introduced by these non-ideal factors, and the lack of effective indicators to compare the merits of different circuit designs and layouts. This results in a lack of clear objective criteria in the circuit design process, heavily relying on trial and error and observation of macroscopic waveforms, which is not only inefficient but also makes it difficult to achieve optimal performance.

[0006] While existing research has explored the performance optimization of hot-wire anemometer systems, it largely focuses on parameter adjustment or macroscopic performance verification, lacking precise quantification methods for phase lag introduced by non-ideal factors. For example:

[0007] Du Hai et al. ("Prototype and Experimental Verification of Constant Temperature Hot-Wire Anemometer", Journal of Xihua University (Natural Science Edition), 2023) developed a low-cost constant temperature hot-wire anemometer, achieving high dynamic response and measurement accuracy. However, their research focused on the realization and verification of the overall system performance, without conducting in-depth analysis and quantitative characterization of non-ideal factors such as distributed parameters and device delays in the circuit.

[0008] Wei Qingyan et al. (Stability Study of Constant Temperature Hot-Wire Anemometer System, Journal of Instrumentation, 2015) theoretically analyzed the influence of system parameters on stability and proposed a method based on aKR. a The stability criterion is mainly based on an ideal circuit model and fails to fully consider the phase delay introduced by non-ideal factors in actual circuits. Therefore, it is difficult to use it directly for accurate stability assessment and diagnosis of actual systems.

[0009] Another study by Wei Qingyan et al. ("Dynamic Characteristics Analysis and Experimental Verification of Constant Temperature Hot-Wire Wind Speed ​​Measurement System", Journal of Instrumentation, 2015) proposed a dynamic characteristic adjustment method based on bias voltage. Although this method can improve the system stability to a certain extent, it is essentially a "post-compensation" and does not solve the core problem of accurately measuring and tracing the source of non-ideal factors.

[0010] In summary, current technologies lack a method for accurately and quantitatively characterizing various non-ideal factors in a circuit while it is in actual operating condition. Developing a method capable of accurately measuring the impact of non-ideal factors in a system in situ is of great significance for improving the scientific rigor and reliability of system design and debugging. Summary of the Invention

[0011] The purpose of this invention is to provide a stability measurement method for a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay parameters. This method can accurately identify and quantify the equivalent phase delay introduced by non-ideal factors such as circuit distributed parameters and device hysteresis when the hot wire is in actual working condition, reducing it to a measurable key parameter b, thereby providing a clear quantitative basis for circuit design evaluation and optimization.

[0012] To achieve the above objectives, the present invention provides the following technical solution:

[0013] A method for measuring the stability of a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay element parameters includes the following steps: S1. Connecting an ultra-low frequency low-pass filter into the closed-loop system to form an in-situ open-loop system with a DC closed loop and an AC open loop; S2. Injecting a sweep frequency excitation signal E at the bias circuit. stimu And measure the output response E of the amplifier circuit. aBy comparing the amplitude ratio and phase difference of the two, the open-loop frequency response G of the system under actual operating conditions of the hot wire is obtained. open (jω); S3. Using the preset transfer function model G * open (s) Fit the measured frequency response to identify the pure delay element G introduced by non-ideal factors such as circuit distributed parameters and device hysteresis. delay (s), and use its parameter b to quantify the non-ideal factors of the system.

[0014] The closed-loop transfer function of the constant-temperature hot-wire anemometer during normal operation can be expressed by the following formula:

[0015]

[0016] Where U is the wind speed, E is the output voltage at the top of the Wheatstone bridge, and G is the wind speed. gain (s) is the forward gain transfer function, G open (s) is the open-loop transfer function, which contains the non-ideal characteristics of the system and can be measured by parameter identification.

[0017] Compared to an off-site open-loop system that simply disconnects an electrical connection at a certain point in the system, the in-situ open-loop system can obtain the open-loop frequency characteristic G of the system while the hot wire remains operational. open (jω), also known as the in-situ open-loop frequency response, is tested as follows:

[0018] S41. Inject a sweep frequency excitation signal E into the bias circuit. stimu

[0019] S42. At the output E of the amplifier circuit a Response to the excitation signal at the measurement point;

[0020] S43. Compare E stimu and E a Calculate the open-loop frequency response G based on the amplitude ratio and phase difference of the AC signal. open (jω);

[0021] The ultra-low frequency low-pass filter used to block AC signals should be able to reliably filter out all AC signals within the frequency range of the swept excitation signal. Its specific cutoff frequency and roll-off factor should be determined through the following steps:

[0022] S51. Inject a sweep frequency excitation signal into the bias circuit and set its frequency to the lowest value within the test frequency range;

[0023] S52. Use an oscilloscope to detect the output waveform of the low-pass filter;

[0024] S53. If the detected output waveform has obvious fluctuations, the cutoff frequency of the low-pass filter should be reduced or its roll-off factor should be increased until the output waveform fluctuation is less than 1mV, which can be approximated as DC.

[0025] The term used for fitting the in-situ open-loop frequency response G open The transfer function model G of (jω) * open (s) has the following form:

[0026]

[0027] Among them, K open G is the open-loop gain, z1 and z2 are the inherent open-loop zeros of the system, p1 is the inherent open-loop pole of the system, and G is the open-loop gain. filter (s) is the transfer function of the high-frequency filter used to filter noise in the feedback loop, with a cutoff frequency of f; G delay (s) is a pure delay element, whose purpose is to correct the phase difference between the transfer function model and the measured data in the high-frequency range. The transfer function expression is:

[0028]

[0029] Where b is a parameter representing the degree of phase delay, which can be used to quantify the non-ideal factors of the system;

[0030] The fitted in-situ open-loop frequency characteristic G open The steps for (jω) are as follows:

[0031] S61. Based on the preset transfer function model G * open The amplitude-frequency response of (s) is combined with the measured data to fit the parameter K. open z1, z2, p1, and f;

[0032] S62. Ignoring pure delay element G delay (s), let b = 0, draw G * open The phase frequency characteristics of (s) are compared with the measured data. At this time, the two are more consistent in the low frequency range, while the phase difference in the high frequency range gradually increases with frequency.

[0033] S63. Fit G using the phase-frequency characteristic of a pure delay element. * open The difference between the phase frequency characteristics of (s) and the measured data is used to obtain the value of its parameter b.

[0034] S64. Introducing a pure delay element G delay (s), then draw G at this time * openThe phase frequency characteristics of (s) are compared with the measured data. At this time, the two are quite consistent in both the low frequency and high frequency ranges.

[0035] Compared with the prior art, the advantages of this invention are: by constructing an in-situ open-loop test system and introducing parameter identification technology of equivalent pure delay element, the accurate measurement of non-ideal factors in the circuit of constant temperature hot wire anemometer is realized. Attached Figure Description

[0036] Figure 1 This is a block diagram of the constant temperature hot wire anemometer system of the present invention.

[0037] Figure 2 This is the in-situ open-loop frequency response diagram of the constant temperature hot-wire anemometer of the present invention.

[0038] Figure 3 This is a fitting diagram of the in-situ open-loop frequency response of the present invention. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] Please see Figure 1 In this embodiment of the invention, the method for measuring the stability of a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay element parameters includes the following steps: S1. Connecting an ultra-low frequency low-pass filter to the closed-loop circuit of the system to form an in-situ open-loop system with a DC closed loop and an AC open loop; S2. Injecting a sweep frequency excitation signal E at the bias circuit. stimu And measure the output response E of the amplifier circuit. a By comparing the amplitude ratio and phase difference of the two, the open-loop frequency response G of the system under actual operating conditions of the hot wire is obtained. open (jω); S3. Using the preset transfer function model G * open (s) Fit the measured frequency response to identify the pure delay element G introduced by non-ideal factors such as circuit distributed parameters and device hysteresis. delay (s), and use its parameter b to quantify the non-ideal factors of the system.

[0041] The closed-loop feedback circuit of the constant-temperature hot-wire anemometer consists of modules such as a Wheatstone bridge, an amplifier circuit, a bias circuit, a filter circuit, and a current-amplifying transistor; the Wheatstone bridge includes constant resistors R1, R2, and R3, as well as a hot-wire resistor R. wThe heating wire is a thin metal filament with a diameter on the order of micrometers, possessing extremely low thermal inertia, and is placed in the flow field as a sensitive component. The amplification circuit is a multi-stage series amplifier circuit composed of operational amplifiers, with a total gain of over 100 to ensure the constant temperature accuracy of the heating wire. The bias circuit is an inverting adder circuit composed of operational amplifiers, with a constant bias voltage E. bias =3V, and has a dedicated excitation signal input port E stimu The frequency sweep excitation signal is injected into the filter circuit. The filter circuit is a second-order Butterworth filter circuit composed of operational amplifiers with a cutoff frequency of f = 239kHz. It is used to filter out loop noise and improve system stability. The base of the current amplification transistor is connected to the output of the filter circuit, the emitter is connected to the top of the Wheatstone bridge, and the collector is connected to the DC power supply VCC = 12V. It is used to drive the amplified feedback signal and apply it to the top of the Wheatstone bridge.

[0042] The closed-loop transfer function of the constant-temperature hot-wire anemometer during normal operation can be expressed by the following formula:

[0043]

[0044] Where U is the wind speed, E is the output voltage at the top of the Wheatstone bridge, and G is the wind speed. gain (s) is the forward gain transfer function, G open (s) is the open-loop transfer function, which contains the non-ideal characteristics of the system and can be measured by parameter identification.

[0045] Compared to an off-site open-loop system that simply disconnects an electrical connection at a certain point in the system, the in-situ open-loop system can obtain the open-loop frequency characteristic G of the system while the hot wire remains operational. open (jω), also known as the in-situ open-loop frequency response, is tested as follows:

[0046] S41. Inject a sweep frequency excitation signal E into the bias circuit. stimu ;

[0047] S42. At the output E of the amplifier circuit a Response to the excitation signal at the measurement point;

[0048] S43. Compare E stimu and E a Calculate the open-loop frequency response G based on the amplitude ratio and phase difference of the AC signal. open (jω);

[0049] The ultra-low frequency low-pass filter used to block AC signals has a cutoff frequency of 10Hz and a roll-off factor of -40dB / dec. It was determined through the following steps that it can reliably filter out all AC signals within the frequency range of the sweep excitation signal:

[0050] S51. Inject a sweep frequency excitation signal into the bias circuit and set its frequency to the lowest value within the test frequency range;

[0051] S52. Use an oscilloscope to detect the output waveform of the low-pass filter;

[0052] S53. If the detected output waveform has obvious fluctuations, the cutoff frequency of the low-pass filter should be reduced or its roll-off factor should be increased until the output waveform fluctuation is less than 1mV, which can be approximated as DC.

[0053] Please see Figure 2 In this embodiment of the invention, the method for fitting the in-situ open-loop frequency response G... open The transfer function model G of (jω) * open (s) has the following form:

[0054]

[0055] Among them, K open G is the open-loop gain, z1 and z2 are the inherent open-loop zeros of the system, p1 is the inherent open-loop pole of the system, and G is the open-loop gain. filter (s) is the transfer function of the high-frequency filter used to filter noise in the feedback loop, with a cutoff frequency of f; G delay (s) is a pure delay element, whose purpose is to correct the phase difference between the transfer function model and the measured data in the high-frequency range. The transfer function expression is:

[0056]

[0057] Where b is a parameter representing the degree of phase delay, which can be used to quantify the non-ideal factors of the system;

[0058] Depend on Figure 2 It can be seen that the overall trend of the in-situ open-loop amplitude-frequency characteristic of the constant-temperature hot-wire anemometer is first decreasing, then increasing, and then decreasing again, while the trend of its roll-off coefficient is -20dB / dec, 0dB / dec, 20dB / dec to -20dB / dec; among them, the transition of the roll-off coefficient from 20dB / dec to -20dB / dec occurs around 230kHz, which corresponds to the parameter configuration of the filter circuit, while the changes before 230kHz can be correlated with the zero point z1 of the preset transfer function model and z 2 and corresponding to the pole p1, which means that the preset transfer function model can be used to fit the in-situ open-loop frequency characteristics of the constant temperature hot wire anemometer.

[0059] Please see Figure 3 In this embodiment of the invention, the fitted in-situ open-loop frequency response G openThe steps for (jω) are as follows:

[0060] S61. According to the preset transfer function G * open (s), combined with the measured amplitude-frequency response data, and using the five-parameter least squares method for fitting, K can be obtained. open =6.676, z1=249128, z2=6396, p1=1318.2 and f=238206;

[0061] S62. Ignoring pure delay element G delay (s), let b = 0, draw G * open The phase frequency characteristics of (s) are compared with the measured data, such as Figure 3 (a) It can be seen that the two are more consistent in the low frequency range, while the phase difference in the high frequency range gradually increases with frequency;

[0062] S63. Because a pure delay element only delays the phase and does not change the gain, it can be used to fit G. * open The difference between the phase frequency characteristic of (s) and the measured data is used to obtain its parameter b = 5.737;

[0063] S64. Introducing a pure delay element G delay (s), then draw G at this time * open The phase frequency characteristics of (s) are compared with the measured data, such as Figure 3 (b) It can be seen that the two are quite consistent in both the low-frequency and high-frequency ranges at this time. G delay (s) is introduced by non-ideal factors such as circuit distributed parameters and device hysteresis, and its parameter b = 5.737 can quantify the non-ideal factors of the system.

[0064] This invention is not limited to the above embodiments. Based on the technical solutions disclosed in this invention, those skilled in the art can make some simple modifications, equivalent changes and alterations to some of the technical features without creative effort, all of which fall within the scope of the technical solutions of this invention.

Claims

1. A method for measuring the stability of a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay element parameters, comprising the following steps: S1. Connecting an ultra-low frequency low-pass filter into the closed-loop circuit of the system to form an in-situ open-loop system with a DC closed loop and an AC open loop; S2. Injecting a sweep frequency excitation signal E at the bias circuit. stimu And measure the output response E of the amplifier circuit. a By comparing the amplitude ratio and phase difference of the two, the open-loop frequency response G of the system under actual operating conditions of the hot wire is obtained. open (jω); S3. Using the preset transfer function model G * open (s) Fit the measured frequency response to identify the pure delay element G introduced by non-ideal factors such as circuit distributed parameters and device hysteresis. delay (s), and use its parameter b to quantify the non-ideal factors of the system.

2. The method for measuring the stability of a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay parameters as described in claim 1, characterized in that, The closed-loop transfer function of the constant-temperature hot-wire anemometer during normal operation can be expressed by the following formula: Where U is the wind speed, E is the output voltage at the top of the Wheatstone bridge, and G is the wind speed. gain (s) is the forward gain transfer function, G open (s) is the open-loop transfer function, which contains the non-ideal characteristics of the system and can be measured through parameter identification.

3. The method for measuring the stability of a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay parameters as described in claim 1, characterized in that, Compared to an off-site open-loop system that simply disconnects an electrical connection at a certain point in the system, the in-situ open-loop system can obtain the open-loop frequency characteristic G of the system while the hot wire remains operational. open (jω), also known as the in-situ open-loop frequency response, is tested as follows: S41. Inject a sweep frequency excitation signal E into the bias circuit. stimu ; S42. Measure the excitation signal response at the output Ea of the amplifier circuit; S43. Compare E stimu and E a Calculate the open-loop frequency response G based on the amplitude ratio and phase difference of the AC signal. open (jω).

4. The method for measuring the stability of a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay parameters as described in claim 1, characterized in that, The ultra-low frequency low-pass filter used to block AC signals should be able to reliably filter out all AC signals within the frequency range of the swept excitation signal. Its specific cutoff frequency and roll-off factor should be determined through the following steps: S51. Inject a sweep frequency excitation signal into the bias circuit and set its frequency to the lowest value within the test frequency range; S52. Use an oscilloscope to detect the output waveform of the low-pass filter; S53. If the detected output waveform has obvious fluctuations, the cutoff frequency of the low-pass filter should be reduced or its roll-off factor should be increased until the output waveform fluctuation is less than 1mV, which can be approximated as DC.

5. The method for measuring the stability of a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay parameters as described in claim 1, characterized in that, The term used for fitting the in-situ open-loop frequency response G open The transfer function model G of (jω) * open (s) has the following form: Among them, K open G is the open-loop gain, z1 and z2 are the inherent open-loop zeros of the system, p1 is the inherent open-loop pole of the system, and G is the open-loop gain. filter (s) is the transfer function of the high-frequency filter used to filter noise in the feedback loop, with a cutoff frequency of f; G delay (s) is a pure delay element, whose purpose is to correct the phase difference between the transfer function model and the measured data in the high-frequency range. The transfer function expression is: Where b is a parameter representing the degree of phase delay, which can be used to quantify the non-ideal factors of the system.

6. The method for measuring the stability of a constant-temperature hot-wire anemometer based on the identification of equivalent pure delay parameters as described in claim 1, characterized in that, The fitted in-situ open-loop frequency characteristic G open The steps for (jω) are as follows: S61. Based on the preset transfer function model G * open The amplitude-frequency response of (s) is combined with the measured data to fit the parameter K. open z1, z2, p1, and f; S62. Ignoring pure delay element G delay (s), let b = 0, draw G * open The phase frequency characteristics of (s) are compared with the measured data. At this time, the two are more consistent in the low frequency range, while the phase difference in the high frequency range gradually increases with frequency. S63. Fit G using the phase-frequency characteristic of a pure delay element. * open The difference between the phase frequency characteristics of (s) and the measured data is used to obtain the value of its parameter b. S64. Introducing a pure delay element G delay (s), then draw G at this time * open The phase frequency characteristics of (s) are compared with the measured data. At this time, the two are quite consistent in both the low frequency and high frequency ranges.

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