A constant-temperature hot-wire anemometer stability margin measurement method based on in-situ open-loop frequency characteristics

Abstract

This invention relates to a method for measuring the stability margin of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics, 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 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. According to G open (jω) Obtain the phase margin of the system and determine its stability. This invention proposes a new method for measuring the stability margin of a constant-temperature hot-wire anemometer, transforming the complex system stability problem into a measurable and analyzable open-loop frequency characteristic stability margin problem, providing a direct and reliable engineering basis for the circuit design of constant-temperature hot-wire anemometers.

Description

Technical Field

[0001] This invention relates to a method for measuring the stability margin of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics, 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] Although the theoretical model of the constant-temperature hot-wire anemometer is relatively mature, a long-standing and extremely challenging issue in the design and engineering debugging of its actual circuit system is ensuring the stability of the feedback loop and preventing high-frequency oscillations or even complete instability. In practical engineering, especially when integrating components such as electronic switches and digitally controlled resistors to achieve advanced functions such as variable overheat ratio, the system is highly susceptible to self-excited oscillations due to the inherent delays of devices such as the hot wire and operational amplifiers, as well as unavoidable non-ideal factors such as distributed capacitance and parasitic inductance in the circuit layout. This instability manifests as a large-amplitude, high-frequency sinusoidal oscillation in the bridge-top output voltage. The direct consequence is severe distortion of the flow velocity measurement signal, a sharp deterioration in the signal-to-noise ratio, and in extreme cases, burnout of the expensive probe due to uncontrolled hot wire current, posing serious risks to the measurement system and experimental process.

[0005] More importantly, the root causes of such instability problems are highly uncertain and complex. Because the effects of distributed parameters and device switching hysteresis are difficult to model and predict accurately in theoretical design, engineers often face a dilemma during debugging: the system is stable under a certain set of parameters, but suddenly becomes unstable after slight modifications (such as increasing loop gain for a faster response); or a stable parameter combination is found by chance through repeated trial and error, but the stability margin of the current system is unknown, making it impossible to determine whether the system will remain reliable under more stringent operating conditions. This makes the stability design and parameter tuning of CTA systems largely dependent on engineering experience and trial and error, lacking clear theoretical guidance and quantitative basis.

[0006] Existing technologies have made some attempts to solve the stability problem of constant temperature hot-wire anemometers, but all have limitations. For example, authorized invention patents CN 105302187 A and CN 105305368 A focus on the long-term stability of hot-wire temperature and overcurrent hardware protection, respectively, but do not involve the analysis and optimization of closed-loop dynamic stability.

[0007] Wei Qingyan et al. ("Stability Study and Experimental Verification of Constant Temperature Hot-Wire Anemometer System", Journal of Instrumentation, 2015, 36(8): 1802-1809) made contributions to the theoretical analysis, proposing a stability criterion based on aK-Ra and studying in depth the influence of parameters such as amplifier gain and hot-wire overheat ratio on system stability. Through simulation and experiment, they verified the stability of the system under different parameter configurations and proposed a stability control method based on bias voltage. However, this study is mainly based on theoretical models and parameter adjustments, lacking an engineering method that can directly measure the stability margin of the system.

[0008] Traditional off-site open-loop testing methods require completely disconnecting the feedback loop, causing the hot wire to leave its constant-temperature operating state. The measured frequency characteristics do not match the actual operating state of the system, limiting their engineering guidance value. Furthermore, while widely used time-domain methods such as the square wave test can indirectly estimate system bandwidth, they can only be used under conditions of system stability and are difficult to accurately quantify the system's stability margin.

[0009] In conclusion, developing a testing method that can directly characterize the stability of a system under actual working conditions is of vital engineering significance for breaking away from reliance on experience and achieving precise design and performance optimization of hot-wire anemometers. Summary of the Invention

[0010] The purpose of this invention is to provide a new method for measuring the stability margin of a constant-temperature hot-wire anemometer, which transforms the complex system stability problem into a measurable and analyzable open-loop frequency characteristic stability margin problem, providing a direct and reliable engineering basis for the circuit design of the constant-temperature hot-wire anemometer.

[0011] To achieve the above objectives, the present invention provides the following technical solution:

[0012] A method for measuring the stability margin of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics includes the following steps: S1. Connecting an ultra-low frequency low-pass filter to the closed-loop circuit 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. According to G open (jω) is used to obtain the phase margin of the system and determine its stability.

[0013] The closed-loop transfer function of the constant-temperature hot-wire anemometer during normal operation can be expressed by the following formula:

[0014]

[0015] 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, and its phase margin is the key to judging the stability of the system;

[0016] 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:

[0017] S41. Inject a sweep frequency excitation signal E into the bias circuit. stimu

[0018] S42. At the output E of the amplifier circuit a Response to the excitation signal at the measurement point:

[0019] S43. Compare E stimu Calculate the open-loop frequency response G based on the amplitude ratio and phase difference of the AC signal Ea. open (jω);

[0020] 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:

[0021] S51. Inject a sweep frequency excitation signal into the bias circuit and set its frequency to the lowest value within the test frequency range;

[0022] S52. Use an oscilloscope to detect the output waveform of the low-pass filter;

[0023] 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.

[0024] Compared with existing technologies, the advantages of this invention are: by introducing an ultra-low frequency low-pass filter to construct an in-situ testing system with "DC closed loop and AC open loop", the stability margin of the system can be accurately measured under the premise that the hot wire always maintains an actual constant temperature working state; this method provides a direct and reliable engineering basis for the circuit design of constant temperature hot wire anemometers, and effectively solves the long-standing engineering problem that the stability design of constant temperature hot wire anemometers relies on experience trial and error and lacks quantitative basis. Attached Figure Description

[0025] Figure 1 This is a block diagram of the constant temperature hot wire anemometer system of the present invention.

[0026] Figure 2 This is a closed-loop response waveform diagram of the constant temperature hot-wire anemometer of the present invention.

[0027] Figure 3 This is the in-situ open-loop frequency response diagram of the constant temperature hot-wire anemometer of the present invention. Detailed Implementation

[0028] 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.

[0029] Please see Figure 1 In this embodiment of the invention, the method for measuring the stability margin of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics includes the following steps: S1. Connecting an ultra-low frequency low-pass filter to the closed-loop circuit 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. stimuThe output response Ea of the amplifier circuit was measured, and the amplitude ratio and phase difference of the two were compared to obtain the open-loop frequency characteristic G of the system under actual operating conditions of the hot wire. open (jω); S3. According to G open (jω) is used to obtain the phase margin of the system and determine its stability.

[0030] 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. w The 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.

[0031] The closed-loop transfer function of the constant-temperature hot-wire anemometer during normal operation can be expressed by the following formula:

[0032]

[0033] 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, and its phase margin is the key to judging the stability of the system;

[0034] 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:

[0035] S41. Inject a sweep frequency excitation signal E into the bias circuit. stimu ;

[0036] S42. At the output E of the amplifier circuit a Response to the excitation signal at the measurement point;

[0037] 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);

[0038] 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:

[0039] S51. Inject a sweep frequency excitation signal into the bias circuit and set its frequency to the lowest value within the test frequency range;

[0040] S52. Use an oscilloscope to detect the output waveform of the low-pass filter;

[0041] 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.

[0042] Please see Figure 2 In this embodiment of the invention, the closed-loop response waveform of the constant-temperature hot-wire anemometer gradually changes from stable to oscillating as the gain K of the amplifier circuit increases. Specifically, when K = 120 and K = 200, the system is stable, and the waveform is a smooth straight line since the wind speed is 0. When K = 300, the system exhibits a small sinusoidal oscillation with an amplitude of 492.1mV and a frequency of 1.3MHz. At this time, if a certain disturbance is applied to the hot wire, the signal will still fluctuate. When K = 400, the system begins to oscillate significantly with an amplitude of 832.8mV and a frequency of 1.2MHz. At this time, if the hot wire is disturbed, the signal will not respond at all, indicating that the system has become completely unstable.

[0043] Please see Figure 3 In this embodiment of the invention, the in-situ open-loop frequency characteristic of the constant-temperature hot-wire anemometer varies with the phase margin γ as the gain K of the amplifier circuit increases, as follows:

[0044] K = 120: γ = +71.2°

[0045] K = 200: γ = +24.5°

[0046] K = 300: γ = -11.5°

[0047] K = 400: γ = -32.1°

[0048] Therefore, it can be inferred that the system is stable when K=120 and K=200; while it is unstable when K=300 and K=400, and the phase margin is smaller when K=400, which means that the oscillation of the system will be more violent when K=400. This inference is consistent with... Figure 2 The closed-loop response stability of the constant-temperature hot-wire anemometer shown is completely consistent with the actual situation, which proves the predictive role of the in-situ open-loop frequency characteristics on system stability.

[0049] 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 margin of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics, comprising the following steps: S1. Connecting an ultra-low frequency low-pass filter into the closed-loop circuit 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 into 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. According to G open (jω) is used to obtain the phase margin of the system and determine its stability.

2. The method for measuring the stability margin of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics 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, and its phase margin is the key to judging the stability of the system.

3. The method for stability margin analysis of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics 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. oppen (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. At the output E of the amplifier circuit a Response to the excitation signal at the measurement point; 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 margin of a constant-temperature hot-wire anemometer based on in-situ open-loop frequency characteristics 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.

Images