WO2021097888A1 - 一种马达瞬态失真测量方法及系统 - Google Patents
一种马达瞬态失真测量方法及系统 Download PDFInfo
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- WO2021097888A1 WO2021097888A1 PCT/CN2019/121573 CN2019121573W WO2021097888A1 WO 2021097888 A1 WO2021097888 A1 WO 2021097888A1 CN 2019121573 W CN2019121573 W CN 2019121573W WO 2021097888 A1 WO2021097888 A1 WO 2021097888A1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/34—Testing dynamo-electric machines
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/16—Spectrum analysis; Fourier analysis
- G01R23/20—Measurement of non-linear distortion
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- the present invention relates to a technical solution for measuring transient distortion, in particular to a method and system for measuring transient distortion of a motor.
- THD Total Harmonic Distortion
- the purpose of the present invention is to provide a motor transient distortion measurement method and system to solve the technical problem that the prior art can only measure the non-linear distortion signal in the steady state and cannot measure other distortion signals.
- the first aspect of the present invention provides a method for measuring transient distortion of a motor, which includes the following steps:
- the distortion signal is determined according to the output signal and the measurement signal, and the average transient distortion signal is obtained by using the distortion signal.
- the synchronous frequency sweep signal is expressed as:
- x (t) represents a function of the sweep synchronization signal
- f 1 indicates a start frequency
- L represents a change rate of the frequency
- t represents time.
- the step of using the synchronous frequency sweep signal and the acceleration parameter to determine the order impulse response of the system includes:
- the inverse filter Fourier transform is performed by using the synchronous frequency sweep signal, and the formula of the inverse filter Fourier transform is as follows:
- the inverse filter Fourier transform and the acceleration parameter are used to determine the order impulse response of the system, and the formula of the order impulse response is as follows:
- h(t) represents the order impulse response
- a(t) represents the acceleration parameter
- the step of using the order impulse response and the synchronous frequency sweep signal to obtain the output signal of the system includes:
- the group delay parameter is determined by using the impulse response function, and the formula of the group delay parameter is as follows:
- ⁇ t represents the group delay parameter
- L represents the frequency change rate
- n represents the number of different orders
- the output signal of the system is determined according to the synchronous frequency sweep signal, the impulse response function, and the number of orders, and the formula of the output signal is as follows:
- y(t) represents the output signal
- n represents different orders
- x n (t) represents the synchronous frequency sweep signal corresponding to different orders
- h n (t) represents the order corresponding to different orders
- Impulse response * represents the convolution operation
- N represents the highest order of nonlinearity.
- the step of determining a distortion signal according to the output signal and the measurement signal, and using the distortion signal to obtain an average transient distortion signal includes:
- the time-domain distortion signal is determined by using the modeling signal and the measurement signal, and the formula of the time-domain distortion signal is as follows:
- e(t) represents the time-domain distortion signal
- y FIT (t) represents the modeling signal
- y MES (t) represents the measurement signal
- t represents time
- the frequency domain distortion signal is determined by using the time domain distortion signal, and the transient distortion signal of the input voltage is determined according to the frequency domain distortion signal and a preset effective signal, and the transient distortion signal is as follows:
- d IHD (f) represents the transient distortion signal
- e(f) represents the frequency domain distortion signal
- y RMS represents the effective signal
- the formula for the average transient distortion signal is as follows:
- d MHD (f) represents the average transient distortion signal
- e RMS represents the frequency domain distortion effective signal
- y RMS represents the effective signal
- the step of using the time-domain distortion signal to determine the frequency-domain distortion signal includes:
- the time-domain distortion signal is used to determine the frequency-domain distortion signal according to a preset time-frequency mapping relationship, and the formula of the time-frequency mapping relationship is as follows:
- t represents time
- L represents frequency change rate
- f 1 represents the starting frequency
- f(t) represents the frequency corresponding to time t;
- e(t) represents the time-domain distortion signal
- e(f) represents the frequency-domain distortion signal
- the step of generating a modeling signal according to the output signal and the order includes:
- the value of the order is determined, and the output signal is used to generate a modeling signal corresponding to the value of the order.
- a second aspect of the present invention provides a motor transient distortion measurement system, the system includes:
- the input adjustment module is used to set the input voltage of the motor, and use the input voltage to generate a synchronous frequency sweep signal;
- a signal acquisition module configured to use the synchronous frequency sweep signal to excite the motor, and collect the synchronous frequency sweep signal and the acceleration parameter of the motor in the vibration direction;
- the output calculation module is used to determine the order impulse response of the system by using the synchronous frequency sweep signal and the acceleration parameter, and obtain the output signal of the system by using the order impulse response and the synchronous frequency sweep signal;
- the distortion calculation module is configured to determine a distortion signal according to the output signal and the measurement signal, and use the distortion signal to obtain an average transient distortion signal.
- the present invention provides a motor transient distortion measurement method and system, including: setting the input voltage of the motor, using the input voltage to generate a synchronous frequency sweep signal; using the synchronous frequency sweep signal to control the motor Perform excitation, collect the synchronous frequency sweep signal and the acceleration parameter of the motor in the vibration direction; use the synchronous frequency sweep signal and the acceleration parameter to determine the order impulse response of the system, use the order impulse response and
- the synchronous frequency sweep signal obtains the output signal of the system; the distortion signal is determined according to the output signal and the measurement signal, and the average transient distortion signal is obtained by using the distortion signal.
- the present invention obtains the distortion signal corresponding to the input voltage signal under different input voltage signals, and eliminates linear and nonlinear distortion signals through modeling to calculate the average transient distortion signal, which can improve the accuracy of evaluating motor performance .
- FIG. 1 is a flow chart of the steps of a method for measuring transient distortion of a motor provided by the present invention
- Fig. 2 is a block diagram of a module of a motor transient distortion measurement system provided by the present invention.
- FIG. 1 is a flow chart of the method for measuring transient distortion of a motor provided by the present invention. The method includes the following steps:
- S101 Set the input voltage of the motor, and use the input voltage to generate a synchronous frequency sweep signal
- step S101 is mainly to set the input voltage of the motor to generate a synchronous frequency sweep signal according to the voltage; for the nonlinear model, its magnitude is directly related to the magnitude of the input signal; in this step, For the motor (exciter), the greater the input voltage, the greater the displacement of the mass, and the greater the corresponding nonlinear distortion.
- Different voltage traversal methods are usually used to obtain the nonlinear distortion under different displacement levels, that is, starting from a small voltage and increasing to the rated voltage level in a certain step; therefore, each time the distortion signal is measured, it needs to be based on the preset unit voltage value. Adjust the input voltage of the motor to obtain distorted signal data under various input voltages.
- S102 Use the synchronous frequency sweep signal to excite the motor, and collect the synchronous frequency sweep signal and the acceleration parameter of the motor in the vibration direction;
- step S102 mainly uses the synchronous frequency sweep signal to excite the motor, and collects the synchronous frequency sweep signal and the acceleration parameter of the motor in the vibration direction through a specific data acquisition module; in this step, the computer The digital signal generated by the PC is sent to the acquisition card NI-DAQ for digital-to-analog conversion into an analog signal, and the analog signal is transmitted to the amplifier AMP2 for amplification to obtain a synchronous frequency sweep signal used to excite the motor.
- the main The accelerometer is used to measure the acceleration parameters in the vibration direction of the motor, and the acceleration parameters are transmitted to APM1 for data processing, and fed back to the acquisition card NI-DAQ.
- the acquisition card NI-DAQ is also used to directly acquire the results amplified by the amplifier AMP2 Synchronous sweep signal.
- S103 Use the synchronous frequency sweep signal and the acceleration parameter to determine the order impulse response of the system, and use the order impulse response and the synchronous frequency sweep signal to obtain the output signal of the system;
- step S103 is mainly to perform data processing on the collected synchronous frequency sweep signal and acceleration parameters, for example, use the synchronous frequency sweep signal to obtain the inverse filter Fourier transform of the signal, and use the inverse filter Fourier transform
- the inner transform and acceleration parameters are subjected to the relevant Fourier transform and the inverse Fourier transform to obtain the impulse response of each order of the system; further, the separation is carried out according to the group delay of different orders in the order impulse response to obtain The order of each order, and then get the output signal size of the system.
- S104 Determine the distortion signal according to the output signal and the measurement signal, and use the distortion signal to obtain an average transient distortion signal.
- Step S104 uses the output signal and the measurement signal to calculate to obtain the distortion signal, and then obtain the average transient distortion signal; in this step, since only specific linear distortion and specific nonlinear distortion can be modeled numerically or parametrically through the model
- the modeling signals corresponding to different orders can be obtained through the output signal, and the distortion signal can be determined according to the modeling signal and the measurement signal, and then the relevant time-frequency mapping processing and the local averaging processing in the frequency domain can be performed on the distortion parameters to obtain the average
- the transient distortion signal, the average transient distortion signal can be used to evaluate the motor performance; further, the motor performance is evaluated by combining the average transient distortion signals obtained under a variety of input voltages, with high accuracy.
- x(t) represents the function of the synchronous frequency sweep signal
- f 1 represents the starting frequency
- L represents the frequency change rate
- t represents the time
- round[] is the rounding operation
- f 1 represents the start frequency
- f 2 is the stop frequency (it should be noted that the stop frequency is an integer multiple of the start frequency f 1 )
- the synchronous sweep signal needs to be phased from zero Start and end with zero phase;
- a synchronous sweep signal with logarithmic frequency sliding is usually used as an excitation, which can easily identify the system.
- the group delay of the impulse response of different orders is different, and the impulse response of different orders can be accurately separated, and the synchronous sweep signal can use the mapping relationship between the time t and the frequency f, which can transform the transient time domain distortion Map out the transient frequency domain distortion.
- the step of determining the order impulse response of the system by using the synchronous frequency sweep signal and the acceleration parameter includes:
- the inverse filter Fourier transform and acceleration parameters are used to determine the order impulse response of the system.
- the formula of the order impulse response is as follows:
- h(t) represents the order impulse response
- a(t) represents the acceleration parameter
- the steps of using the order impulse response and the synchronous frequency sweep signal to obtain the output signal of the system include:
- the impulse response function is used to determine the group delay parameter.
- the formula for the group delay parameter is as follows:
- ⁇ t represents the group delay parameter
- L represents the frequency change rate
- n represents the number of different orders
- y(t) represents the output signal
- n represents different orders
- x n (t) represents the synchronous frequency sweep signal corresponding to different orders
- h n (t) represents the order impulse response corresponding to different orders
- N represents the highest order of nonlinearity
- the step of determining the distortion signal according to the output signal and the measurement signal, and using the distortion signal to obtain the average transient distortion signal includes:
- e(t) represents the time-domain distortion signal
- y FIT (t) represents the modeling signal
- y MES (t) represents the measurement signal
- t represents the time
- the time-domain distortion signal is used to determine the frequency-domain distortion signal, and the frequency-domain distortion signal and the preset effective signal are used to determine the transient distortion signal of the input voltage.
- the transient distortion signal is as follows:
- d IHD (f) represents the transient distortion signal
- e(f) represents the frequency domain distortion signal
- y RMS represents the effective signal.
- the effective signal is defined as follows:
- y RMS represents the effective signal
- y(t) represents the output signal
- t represents the time
- the transient distortion signal is used to perform local averaging processing to obtain the average transient distortion signal.
- the formula for the average transient distortion signal is as follows:
- d MHD (f) represents the average transient distortion signal
- e RMS represents the frequency domain distortion effective signal
- y RMS represents the effective signal.
- the frequency domain distortion effective signal is defined as follows:
- e RMS represents the frequency domain distortion effective signal
- e(t) represents the time domain distortion signal
- t represents time.
- this step specifically includes the process of modeling using the output signal, calculating the time-domain distortion signal, obtaining the frequency-domain distortion signal, and calculating the average transient distortion signal, wherein the calculated average transient distortion signal can be used
- the performance of the motors in the system improves the accuracy of the evaluation.
- the step of using the time-domain distortion signal to determine the frequency-domain distortion signal includes:
- the time-domain distortion signal is used to determine the frequency-domain distortion signal according to the preset time-frequency mapping relationship.
- the formula of the time-frequency mapping relationship is as follows:
- t represents time
- L represents frequency change rate
- f 1 represents the starting frequency
- f(t) represents the frequency corresponding to time t;
- e(t) represents a time-domain distortion signal
- e(f) represents a frequency-domain distortion signal
- the time-domain distortion signal is mapped to the frequency-domain distortion signal according to the time-frequency domain mapping relationship, and the frequency-domain distortion signal is used to participate in the calculation of the transient distortion, so as to obtain the relevant transient distortion signal.
- the step of generating a modeling signal according to the output signal and the order includes:
- the modeling signals corresponding to different orders can be obtained through the output signal, and based on the modeling signals and measurement signals Determine the distortion signal; specifically, when the order is 0, all the distortion signals or distortion content are calculated by the function corresponding to the output signal; when the order is 1, the specific linear distortion is calculated by the function corresponding to the output signal; When the order is greater than or equal to 2, the specific nonlinear distortion is calculated by the function corresponding to the output signal; transient distortion (trigger distortion and random distortion) cannot be obtained by numerical or numerical parameter modeling, but can be combined with modeling Way to get.
- FIG. 2 is a block diagram of a motor transient distortion measurement system provided by the present invention.
- the system includes:
- the input adjustment module 201 is used to set the input voltage of the motor and use the input voltage to generate a synchronous frequency sweep signal; in this embodiment, for the nonlinear model, its magnitude is directly related to the magnitude of the input voltage signal; for the motor ( For the exciter), the greater the input voltage, the greater the displacement of the mass, and the greater the corresponding nonlinear distortion. Therefore, the input adjustment module 201 adjusts the size of the input voltage signal and uses different voltage traversal methods. Obtain the nonlinear distortion under different displacement levels, that is, start from a small voltage and increase to the rated voltage level in a certain step.
- the signal acquisition module 202 is used to excite the motor with the synchronous frequency sweep signal, collect the synchronous frequency sweep signal and the acceleration parameter of the motor in the vibration direction; in this embodiment, the digital signal generated by the computer PC is sent to the signal acquisition Module 202, the signal acquisition module 202 includes: acquisition card NI-DAQ, amplifier AMP2 and APM1; specifically, acquisition card NI-DAQ performs digital-to-analog conversion into analog signals, and transmits the analog signals to amplifier AMP2 for amplification to obtain The synchronous frequency sweep signal used to excite the motor.
- the accelerometer is mainly used to measure the acceleration parameters in the direction of the motor vibration, and the acceleration parameters are transmitted to APM1 for data processing and fed back to the acquisition card NI-DAQ.
- the acquisition card NI-DAQ is also used to directly acquire the synchronous frequency sweep signal amplified by the amplifier AMP2.
- the output calculation module 203 is used to determine the order impulse response of the system by using the synchronous frequency sweep signal and acceleration parameters, and obtain the output signal of the system by using the order impulse response and the synchronous frequency sweep signal;
- the distortion calculation module 204 is configured to determine the distortion signal according to the output signal and the measurement signal, and obtain the average transient distortion signal by using the distortion signal.
- the output signal can be used by the distortion calculation module 204 to obtain modeling signals corresponding to different orders, and Determine the distortion signal according to the modeling signal and the measurement signal, and then perform related time-frequency mapping processing and frequency-domain local averaging processing on the distortion parameters to obtain an average transient distortion signal, which can be used to evaluate motor performance; Further, the performance of the motor is evaluated by combining the average transient distortion signals obtained under a variety of input voltages, which has high accuracy.
- the system includes an input adjustment module 201, a signal acquisition module 202, an output calculation module 203, and a distortion calculation module 204; different input voltages of the motor are set through the input adjustment module 201, and corresponding excitations are generated.
- the synchronous frequency sweep signal of the motor is amplified or converted by the signal acquisition module 202, and the synchronous frequency sweep signal and the acceleration parameters of the motor in the vibration direction are collected, and the output signal of the system is acquired through the output calculation module 203, and
- the average transient distortion signal is calculated by the distortion calculation module 204; the corresponding distortion signal is obtained under different input voltage signals, and the linear and nonlinear distortion signals are excluded through modeling to calculate the average transient distortion signal, It can improve the accuracy of evaluating motor performance.
- the present invention provides a motor transient distortion measurement method and system, including: setting the input voltage of the motor, using the input voltage to generate a synchronous frequency sweep signal; using the synchronous frequency sweep signal to excite the motor and collecting Synchronous frequency sweep signal and the acceleration parameters of the motor in the vibration direction; use the synchronous frequency sweep signal and acceleration parameters to determine the order impulse response of the system, and use the order impulse response and synchronous frequency sweep signal to obtain the output signal of the system; according to the output signal and Measure the signal to determine the distorted signal, and use the distorted signal to obtain the average transient distortion signal.
- the present invention obtains the distortion signal corresponding to the input voltage signal under different input voltage signals, and eliminates linear and nonlinear distortion signals through modeling to calculate the average transient distortion signal, which can improve the accuracy of evaluating motor performance .
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Abstract
一种马达瞬态失真测量方法及系统，方法包括：设定马达的输入电压，利用输入电压生成同步扫频信号（S101）；利用同步扫频信号对马达进行激励，采集同步扫频信号及马达在振动方向上的加速度参数（S102）；利用同步扫频信号及加速度参数确定系统的阶次脉冲响应，利用阶次脉冲响应及同步扫频信号得到系统的输出信号（S103）；根据输出信号及测量信号确定失真信号，利用失真信号得到平均瞬态失真信号（S104）。相应的，系统包括：输入调节模块（201）、信号采集模块（202）、输出计算模块（203）、失真计算模块（204）。通过在不同输入电压信号的情况下获取输入电压信号对应的失真信号，并通过建模的方式排除线性及非线性失真信号，以计算平均瞬态失真信号，可提高评估马达性能的准确度。
Description
本发明涉及瞬态失真测量的技术方案，尤其涉及一种马达瞬态失真测量方法及系统。
随着智能手机、平板电脑等便携设备应用的越来越普及，为这些便携设备提供触觉反馈变得越来越重要，这成为了提升用户体验的一种有效方式。通常会在这些便携设备中放置激励器(简称马达)来实现振动功能，以提醒用户或者进行效果反馈。
对于单纯的线性系统控制是比较容易的，它可以通过类似传递函数的形式进行；但是由于受到磁路、结构和工艺等方面的影响，激励器或多或少会呈现出一定的非线性，这使得输出较输入产生了额外的频率分量；同时，由于音圈工艺、质量块行程等方面的影响，激励器也会概率性的产生一些输出噪声。所有这些不希望输出的分量都可以统称为失真，有必要研究不同激励器的失真情况，以便对其性能进行评估。
现有技术中，通常采用的方法是测量激励器的总稳态谐波失真，即THD(Total Harmonic Distortion，总谐波失真)测量。该方法只能测量到激励器在稳态下的非线性失真，对其评估具有一定的局限性。
因此，有必要提供一种新的马达瞬态失真测量方法及系统。
【发明内容】
本发明的目的在于提供一种马达瞬态失真测量方法及系统，以解决现有技术中只能测量稳态下的非线性失真信号，无法测量其他失真信号的技术问题。
本发明的技术方案如下：
本发明的第一方面提供一种马达瞬态失真测量方法，包括以下步骤：
设定马达的输入电压，利用所述输入电压生成同步扫频信号；
利用所述同步扫频信号对马达进行激励，采集所述同步扫频信号及所述马达在振动方向上的加速度参数；
利用所述同步扫频信号及所述加速度参数确定系统的阶次脉冲响应，利用所述阶次脉冲响应及所述同步扫频信号得到所述系统的输出信号；
根据所述输出信号及测量信号确定失真信号，利用所述失真信号得到平均瞬态失真信号。
可选的，所述同步扫频信号表示为：
其中，x(t)表示所述同步扫频信号的函数，f
1表示起始频率，L表示频率变化率，t表示时间。
可选的，所述利用所述同步扫频信号及所述加速度参数确定系统的阶次脉冲响应的步骤包括：
利用所述同步扫频信号进行逆滤波傅里叶变换，所述逆滤波傅里叶变换的公式如下：
其中，
表示所述同步扫频信号的逆滤波傅里叶变换，f
1表示起始频率，L表示频率变化率，t表示时间，f表示与时间对应的频率；
利用所述逆滤波傅里叶变换及所述加速度参数确定系统的阶次脉冲响，所述阶次脉冲响应的公式如下：
其中，h(t)表示所述阶次脉冲响应，a(t)表示所述加速度参数，
表示所述同步扫频信号的逆滤波傅里叶变换。
可选的，所述利用所述阶次脉冲响应及所述同步扫频信号得到所述系 统的输出信号的步骤包括：
利用所述脉冲响应函数确定群延时参数，所述群延时参数的公式如下：
Δt＝L·ln(n)
其中，Δt表示所述群延时参数，L表示频率变化率，n表示不同的阶次数；
根据所述群延时函数确定所述脉冲响应函数包含的阶次数；
根据所述同步扫频信号、所述脉冲响应函数及所述阶次数确定所述系统的输出信号，所述输出信号的公式如下：
其中，y(t)表示所述输出信号，n表示不同的阶次数，x
n(t)表示不同阶次对应的所述同步扫频信号，h
n(t)表示不同阶次数对应的阶次脉冲响应，*表示卷积操作，N表示非线性的最高阶次数。
可选的，所述根据所述输出信号及测量信号确定失真信号，利用所述失真信号得到平均瞬态失真信号的步骤包括：
根据所述输出信号及所述阶次数生成建模信号；
利用所述建模信号及所述测量信号确定时域失真信号，所述时域失真信号的公式如下：
e(t)＝y
FIT(t)-y
MES(t)
其中，e(t)表示所述时域失真信号，y
FIT(t)表示所述建模信号，y
MES(t)表示所述测量信号，t表示时间；
利用所述时域失真信号确定频域失真信号，根据所述频域失真信号及预设的有效信号确定所述输入电压的瞬态失真信号，所述瞬态失真信号如下：
其中，d
IHD(f)表示所述瞬态失真信号，e(f)表示所述频域失真信号，y
RMS表示有效信号；
利用所述瞬态失真信号进行局部平均处理，得到平均瞬态失真信号，所述平均瞬态失真信号的公式如下：
其中，d
MHD(f)表示所述平均瞬态失真信号，e
RMS表示频域失真有效信号，y
RMS表示有效信号。
可选的，所述利用所述时域失真信号确定频域失真信号的步骤包括：
利用所述时域失真信号根据预设的时间频率映射关系确定所述频域失真信号，所述时间频率映射关系的公式如下：
其中，t表示时间，L表示频率变化率，f
1表示起始频率，f(t)表示与时间t对应的频率；
所述时域失真信号与所述频域失真信号之间的关系表示如下：
其中，e(t)表示所述时域失真信号，e(f)表示所述频域失真信号。
可选的，所述根据所述输出信号及所述阶次数生成建模信号的步骤包括：
确定所述阶次数的值，利用所述输出信号生成与所述阶次数的值对应建模信号。
本发明的第二方面提供一种马达瞬态失真测量系统，所述系统包括：
输入调节模块，用于设定马达的输入电压，利用所述输入电压生成同步扫频信号；
信号采集模块，用于利用所述同步扫频信号对马达进行激励，采集所 述同步扫频信号及所述马达在振动方向上的加速度参数；
输出计算模块，用于利用所述同步扫频信号及所述加速度参数确定系统的阶次脉冲响应，利用所述阶次脉冲响应及所述同步扫频信号得到所述系统的输出信号；
失真计算模块，用于根据所述输出信号及测量信号确定失真信号，利用所述失真信号得到平均瞬态失真信号。
本发明的有益效果在于：本发明提供一种马达瞬态失真测量方法及系统，包括：设定马达的输入电压，利用所述输入电压生成同步扫频信号；利用所述同步扫频信号对马达进行激励，采集所述同步扫频信号及所述马达在振动方向上的加速度参数；利用所述同步扫频信号及所述加速度参数确定系统的阶次脉冲响应，利用所述阶次脉冲响应及所述同步扫频信号得到所述系统的输出信号；根据所述输出信号及测量信号确定失真信号，利用所述失真信号得到平均瞬态失真信号。本发明通过在不同输入电压信号的情况下获取输入电压信号对应的失真信号，并通过建模的方式排除线性及非线性失真信号，以计算平均瞬态失真信号，可提高评估马达性能的准确度。
图1为本发明提供的一种马达瞬态失真测量方法的步骤流程图；
图2为本发明提供的一种马达瞬态失真测量系统的模块方框图。
下面结合附图和实施方式对本发明作进一步说明。
本发明的第一方面提供一种马达瞬态失真测量方法，请参阅图1，图1为本发明提供的一种马达瞬态失真测量方法的步骤流程图，该方法包括以下步骤：
S101：设定马达的输入电压，利用输入电压生成同步扫频信号；
在本发明的实施例中，步骤S101主要是设定马达的输入电压，以根据该电压生成同步扫频信号；对于非线性模型，其大小于输入信号的大小有 直接的关系；本步骤中，对于马达(激励器)而言，输入电压越大，造成的质量块位移越大，相应的非线性失真也就越大。通常采用不同电压遍历的方法来获取不同位移水平下的非线性失真，即从小电压开始，以一定的步长增加到额定电压水平；因此，每次测量失真信号前需要根据预设的单位电压值调整马达的输入电压，以得到多种输入电压下的失真信号数据。
S102：利用同步扫频信号对马达进行激励，采集同步扫频信号及马达在振动方向上的加速度参数；
在本发明的实施例中，步骤S102主要利用同步扫频信号对马达进行激励，并通过特定的数据采集模块采集同步扫频信号及马达在振动方向上的加速度参数；在本步骤中，通过电脑PC生成的数字信号送入到采集卡NI-DAQ进行数模转换成模拟信号，并将模拟信号传输至放大器AMP2进行放大，以得到用于激励马达的同步扫频信号，在马达被激励后主要采用加速度计测量马达振动方向上的加速度参数，将该加速度参数传输至APM1进行数据处理，以及反馈至采集卡NI-DAQ，同时，采集卡NI-DAQ还用于直接采集放大器AMP2放大后得到的同步扫频信号。
S103：利用同步扫频信号及加速度参数确定系统的阶次脉冲响应，利用阶次脉冲响应及同步扫频信号得到系统的输出信号；
在本发明的实施中，步骤S103主要是对采集后的同步扫频信号及加速度参进行数据处理，比如，利用同步扫频信号获取该信号的逆滤波傅里叶变换，且利用该逆滤波傅里叶变换及加速度参数进行相关傅里叶变换及傅里叶反变换，以得到系统的各阶次脉冲响应；进一步的，根据阶次脉冲响应中不同阶次数的群延时进行分离，以得到各阶次数，进而得到系统的输出信号大小。
S104：根据输出信号及测量信号确定失真信号，利用失真信号得到平均瞬态失真信号。
步骤S104利用输出信号及测量信号进行计算，得到失真信号，进而求取平均瞬态失真信号；在该步骤中，由于只有特定的线性失真及特定的非线性失真可以通过模型进行数值或者参数建模，这样可以通过输出信号获 取不同阶次对应的建模信号，并根据建模信号及测量信号确定失真信号，进而对失真参数进行相关的时间频率映射处理及频域的局部平均处理，以得到平均瞬态失真信号，该平均瞬态失真信号可用于评估马达性能；进一步的，结合多种输入电压下得到的平均瞬态失真信号对马达性能进行评估，具有较高的准确度。
在本发明的实施例中，同步扫频信号的公式表示为：
其中，x(t)表示同步扫频信号的函数，f
1表示起始频率，L表示频率变化率，t表示时间；
进一步的，对于频率变化率L的定义如下：
其中，round[]为取整操作，
为扫频信号的近似时间长度，f
1表示起始频率,f
2为终止频率(应当注意的是，终止频率是起始频率f
1的整数倍)，而且该同步扫频信号需要从零相位开始和零相位结束；在本实施例中，对于线性和非线性系统辨识，通常采用对数频率滑动的同步扫频信号作为激励，可方便地对系统进行辨识，该同步扫频信号对于系统的不同阶次脉冲响应的群延时不相同，而且可以准确分离不同阶次的脉冲响应，及该同步扫频信号可利用时间t和频率f之间存在的映射关系，可以将瞬态时域失真映射出瞬态频域失真。
在本发明的实施例中，利用同步扫频信号及加速度参数确定系统的阶次脉冲响应的步骤包括：
利用同步扫频信号进行逆滤波傅里叶变换，逆滤波傅里叶变换的公式如下：
其中，
表示同步扫频信号的逆滤波傅里叶变换，f
1表示起始频率，L表示频率变化率，t表示时间，f表示与时间对应的频率；
利用逆滤波傅里叶变换及加速度参数确定系统的阶次脉冲响，阶次脉冲响应的公式如下：
其中，h(t)表示阶次脉冲响应，a(t)表示加速度参数，
表示同步扫频信号的逆滤波傅里叶变换。
在本发明的实施例中，利用阶次脉冲响应及同步扫频信号得到系统的输出信号的步骤包括：
利用脉冲响应函数确定群延时参数，群延时参数的公式如下：
Δt＝L·ln(n)
其中，Δt表示群延时参数，L表示频率变化率，n表示不同的阶次数；
根据群延时函数确定脉冲响应函数包含的阶次数；
根据同步扫频信号、脉冲响应函数及阶次数确定系统的输出信号，输出信号的公式如下：
其中，y(t)表示输出信号，n表示不同的阶次数，x
n(t)表示不同阶次对应的同步扫频信号，h
n(t)表示不同阶次数对应的阶次脉冲响应，*表示卷积操作，N表示非线性的最高阶次数；在本实施中，通过输出信号可获取各阶次的失真内容，其中，阶次数n包含0、1及2的阶次数，其中，阶次数n＝1时，可得到对应的特定线性失真；当n≥2的时，可得到对应的特定非线性失真；应当注意的是，瞬态失真无法通过数值或参数建模获取，其中，瞬态失真包括瞬态失真及随机失真。
在本发明的实施例中，根据输出信号及测量信号确定失真信号，利用失真信号得到平均瞬态失真信号的步骤包括：
根据输出信号及阶次数生成建模信号；
利用建模信号及测量信号确定时域失真信号，时域失真信号的公式如下：
e(t)＝y
FIT(t)-y
MES(t)
其中，e(t)表示时域失真信号，y
FIT(t)表示建模信号，y
MES(t)表示测量信号，t表示时间；
利用时域失真信号确定频域失真信号，根据频域失真信号及预设的有效信号确定输入电压的瞬态失真信号，瞬态失真信号如下：
其中，d
IHD(f)表示瞬态失真信号，e(f)表示频域失真信号，y
RMS表示有效信号，该有效信号定义如下：
其中，y
RMS表示有效信号，y(t)表示输出信号，t表示时间；
进一步的，由于瞬态失真IHD在频谱上的波动比较大，利用瞬态失真信号进行局部平均处理，得到平均瞬态失真信号，平均瞬态失真信号的公式如下：
其中，d
MHD(f)表示平均瞬态失真信号，e
RMS表示频域失真有效信号，y
RMS表示有效信号，其中，频域失真有效信号定义如下：
其中，e
RMS表示频域失真有效信号，e(t)表示时域失真信号，t表示时间。在本实施例中，该步骤具体包括：利用输出信号进行建模、计算时域失真信号、获取频域失真信号及计算平均瞬态失真信号的过程，其中，计算得到的平均瞬态失真信号可用于系统内马达的性能，提高在评估上的准确性。
在本发明的实施中，利用时域失真信号确定频域失真信号的步骤包括：
利用时域失真信号根据预设的时间频率映射关系确定频域失真信号，时间频率映射关系的公式如下：
其中，t表示时间，L表示频率变化率，f
1表示起始频率，f(t)表示与时间t对应的频率；
时域失真信号与频域失真信号之间的关系表示如下：
其中，e(t)表示时域失真信号，e(f)表示频域失真信号。在本实施中，根据时间频域映射关系将时域失真信号映射出频域失真信号，该频域失真信号用于参与瞬态失真的计算，从而得到相关的瞬态失真信号。
在本发明的实施例中，根据输出信号及阶次数生成建模信号的步骤包括：
确定阶次数的值，利用输出信号生成与阶次数的值对应建模信号。在该步骤中，由于只有特定的线性失真及特定的非线性失真可以通过模型进行数值或者参数建模，这样可以通过输出信号获取不同阶次对应的建模信号，并根据建模信号及测量信号确定失真信号；具体的，当阶次数为0时，通过输出信号对应的函数计算得到所有的失真信号或失真内容；当阶次数为1时，通过输出信号对应的函数计算得到特定的线性失真；当阶次数大于或等于2时，通过输出信号对应的函数计算得到特定的非线性失真；瞬态失真(触发失真及随机失真)无法通过数值或数值参数建模的方式得到，可通过结合建模的方式获取。
本发明的第二方面提供一种马达瞬态失真测量系统，请参阅图2，图2为本发明提供的一种马达瞬态失真测量系统的模块方框图，该系统包括：
输入调节模块201，用于设定马达的输入电压，利用输入电压生成同步扫频信号；在本实施例中，对于非线性模型，其大小于输入电压信号的大小有直接的关系；对于马达(激励器)而言，输入电压越大，造成的质量块位移越大，相应的非线性失真也就越大，因此，通过输入调节模块201调节输入电压信号的大小，以不同电压遍历的方法来获取不同位移水平下的非线性失真，即从小电压开始，以一定的步长增加到额定电压水平。
信号采集模块202，用于利用同步扫频信号对马达进行激励，采集同步扫频信号及马达在振动方向上的加速度参数；在本实施例中，通过电脑PC生成的数字信号送入到信号采集模块202，该信号采集模块202包括：采集卡NI-DAQ、放大器AMP2及APM1；具体的，采集卡NI-DAQ进行数模转换成模拟信号，并将模拟信号传输至放大器AMP2进行放大，以得到用于激励马达的同步扫频信号，在马达被激励后主要采用加速度计测量马达振动方向上的加速度参数，将该加速度参数传输至APM1进行数据处理，以及反馈至采集卡NI-DAQ，同时，采集卡NI-DAQ还用于直接采集放大器AMP2放大后得到的同步扫频信号。
输出计算模块203，用于利用同步扫频信号及加速度参数确定系统的阶次脉冲响应，利用阶次脉冲响应及同步扫频信号得到系统的输出信号；
失真计算模块204，用于根据输出信号及测量信号确定失真信号，利用失真信号得到平均瞬态失真信号。在本实施例中，由于只有特定的线性失真及特定的非线性失真可以通过模型进行数值或者参数建模，因此，可以通过失真计算模块204利用输出信号获取不同阶次对应的建模信号，并根据建模信号及测量信号确定失真信号，进而对失真参数进行相关的时间频率映射处理及频域的局部平均处理，以得到平均瞬态失真信号，该平均瞬态失真信号可用于评估马达性能；进一步的，结合多种输入电压下得到的平均瞬态失真信号对马达性能进行评估，具有较高的准确度。
在本发明的实施中，该系统包含输入调节模块201、信号采集模块202、 输出计算模块203及失真计算模块204；通过输入调节模块201设定马达的不同输入电压，并生成对应的用于激励马达的同步扫频信号，通过信号采集模块202对同步扫频信号进行放大或转换处理及采集同步扫频信号及马达在振动方向上的加速度参数，通过输出计算模块203获取系统的输出信号，及通过失真计算模块204进行计算得到平均瞬态失真信号；通过在不同输入电压信号的情况下获取对应的失真信号，通过建模的方式排除线性及非线性失真信号，以计算平均瞬态失真信号，可提高评估马达性能的准确度。
本发明的有益效果在于：本发明提供一种马达瞬态失真测量方法及系统，包括：设定马达的输入电压，利用输入电压生成同步扫频信号；利用同步扫频信号对马达进行激励，采集同步扫频信号及马达在振动方向上的加速度参数；利用同步扫频信号及加速度参数确定系统的阶次脉冲响应，利用阶次脉冲响应及同步扫频信号得到系统的输出信号；根据输出信号及测量信号确定失真信号，利用失真信号得到平均瞬态失真信号。本发明通过在不同输入电压信号的情况下获取输入电压信号对应的失真信号，并通过建模的方式排除线性及非线性失真信号，以计算平均瞬态失真信号，可提高评估马达性能的准确度。
以上所述的仅是本发明的实施方式，在此应当指出，对于本领域的普通技术人员来说，在不脱离本发明创造构思的前提下，还可以做出改进，但这些均属于本发明的保护范围。
Claims (8)
- 一种马达瞬态失真测量方法，其特征在于，包括以下步骤：设定马达的输入电压，利用所述输入电压生成同步扫频信号；利用所述同步扫频信号对马达进行激励，采集所述同步扫频信号及所述马达在振动方向上的加速度参数；利用所述同步扫频信号及所述加速度参数确定系统的阶次脉冲响应，利用所述阶次脉冲响应及所述同步扫频信号得到所述系统的输出信号；根据所述输出信号及测量信号确定失真信号，利用所述失真信号得到平均瞬态失真信号。
- 根据权利要求1所述的马达瞬态失真测量方法，其特征在于，所述同步扫频信号表示为：
其中，x(t)表示所述同步扫频信号的函数，f 1表示起始频率，L表示频率变化率，t表示时间。 - 根据权利要求1所述的马达瞬态失真测量方法，其特征在于，所述利用所述同步扫频信号及所述加速度参数确定系统的阶次脉冲响应的步骤包括：利用所述同步扫频信号进行逆滤波傅里叶变换，所述逆滤波傅里叶变换的公式如下：
其中，表示所述同步扫频信号的逆滤波傅里叶变换，f 1表示起始频率，L表示频率变化率，t表示时间，f表示与时间对应的频率；
利用所述逆滤波傅里叶变换及所述加速度参数确定系统的阶次脉冲响，所述阶次脉冲响应的公式如下：
其中，h(t)表示所述阶次脉冲响应，a(t)表示所述加速度参数，表示所述同步扫频信号的逆滤波傅里叶变换。
- 根据权利要求1所述的马达瞬态失真测量方法，其特征在于，所述利用所述阶次脉冲响应及所述同步扫频信号得到所述系统的输出信号的步骤包括：利用所述脉冲响应函数确定群延时参数，所述群延时参数的公式如下：Δt＝L·ln(n)其中，Δt表示所述群延时参数，L表示频率变化率，n表示不同的阶次数；根据所述群延时函数确定所述脉冲响应函数包含的阶次数；根据所述同步扫频信号、所述脉冲响应函数及所述阶次数确定所述系统的输出信号，所述输出信号的公式如下：
其中，y(t)表示所述输出信号，n表示不同的阶次数，x n(t)表示不同阶次对应的所述同步扫频信号，h n(t)表示不同阶次数对应的阶次脉冲响应，*表示卷积操作，N表示非线性的最高阶次数。 - 根据权利要求4所述的马达瞬态失真测量方法，其特征在于，所述根据所述输出信号及测量信号确定失真信号，利用所述失真信号得到平均瞬态失真信号的步骤包括：根据所述输出信号及所述阶次数生成建模信号；利用所述建模信号及所述测量信号确定时域失真信号，所述时域失真信号的公式如下：e(t)＝y FIT(t)-y MES(t)其中，e(t)表示所述时域失真信号，y FIT(t)表示所述建模信号，y MES(t)表示所述测量信号，t表示时间；利用所述时域失真信号确定频域失真信号，根据所述频域失真信号及预设的有效信号确定所述输入电压的瞬态失真信号，所述瞬态失真信号如下：
其中，d IHD(f)表示所述瞬态失真信号，e(f)表示所述频域失真信号，y RMS表示有效信号；利用所述瞬态失真信号进行局部平均处理，得到平均瞬态失真信号，所述平均瞬态失真信号的公式如下：
其中，d MHD(f)表示所述平均瞬态失真信号，e RMS表示频域失真有效信号，y RMS表示有效信号。 - 根据权利要求5所述的马达瞬态失真测量方法，其特征在于，所述利用所述失真信号确定频域失真信号的步骤包括：利用所述时域失真信号根据预设的时间频率映射关系确定所述频域失真信号，所述时间频率映射关系的公式如下：
其中，t表示时间，L表示频率变化率，f 1表示起始频率，f(t)表示与时间t对应的频率；所述时域失真信号与所述频域失真信号之间的关系表示如下：
其中，e(t)表示所述时域失真信号，e(f)表示所述频域失真信号。 - 根据权利要求5所述的马达瞬态失真测量方法，其特征在于，所述根据所述输出信号及所述阶次数生成建模信号的步骤包括：确定所述阶次数的值，利用所述输出信号生成与所述阶次数的值对应建模信号。
- 一种马达瞬态失真测量系统，其特征在于，所述系统包括：输入调节模块，用于设定马达的输入电压，利用所述输入电压生成同步扫频信号；信号采集模块，用于利用所述同步扫频信号对马达进行激励，采集所述同步扫频信号及所述马达在振动方向上的加速度参数；输出计算模块，用于利用所述同步扫频信号及所述加速度参数确定系统的阶次脉冲响应，利用所述阶次脉冲响应及所述同步扫频信号得到所述系统的输出信号；失真计算模块，用于根据所述输出信号及测量信号确定失真信号，利用所述失真信号得到平均瞬态失真信号。
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103323195A (zh) * | 2013-07-06 | 2013-09-25 | 北京航空航天大学 | 一种旋转振动激励与动态测量装置 |
| US9628002B2 (en) * | 2013-03-13 | 2017-04-18 | Cirrus Logic, Inc. | Circuit and method for detecting missed commutation of a brushless DC motor |
| CN109901066A (zh) * | 2018-12-31 | 2019-06-18 | 瑞声科技(新加坡)有限公司 | 马达系统辨识方法 |
| CN110162171A (zh) * | 2019-04-18 | 2019-08-23 | 瑞声科技(新加坡)有限公司 | 一种马达驱动信号设置方法、电子设备及存储介质 |
| CN110247631A (zh) * | 2019-04-12 | 2019-09-17 | 瑞声科技(新加坡)有限公司 | 一种马达非线性失真补偿方法及装置 |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9628002B2 (en) * | 2013-03-13 | 2017-04-18 | Cirrus Logic, Inc. | Circuit and method for detecting missed commutation of a brushless DC motor |
| CN103323195A (zh) * | 2013-07-06 | 2013-09-25 | 北京航空航天大学 | 一种旋转振动激励与动态测量装置 |
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| CN110247631A (zh) * | 2019-04-12 | 2019-09-17 | 瑞声科技(新加坡)有限公司 | 一种马达非线性失真补偿方法及装置 |
| CN110162171A (zh) * | 2019-04-18 | 2019-08-23 | 瑞声科技(新加坡)有限公司 | 一种马达驱动信号设置方法、电子设备及存储介质 |
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