CN114374351B - Calculation method for analyzing output component characteristics of robot servo driver - Google Patents

Calculation method for analyzing output component characteristics of robot servo driver Download PDF

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CN114374351B
CN114374351B CN202210277200.6A CN202210277200A CN114374351B CN 114374351 B CN114374351 B CN 114374351B CN 202210277200 A CN202210277200 A CN 202210277200A CN 114374351 B CN114374351 B CN 114374351B
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CN114374351A (en
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李珊瑚
鲁紫荆
韩旭
陶友瑞
黄林峰
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Shahe New Materials And Equipment Industrial Technology Research Institute
Hebei University of Technology
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Hebei University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • 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
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/12—Arrangements for reducing harmonics from ac input or output
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/5387—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
    • H02M7/53871—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics

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Abstract

The application provides a calculation method for analyzing the output component characteristics of a robot servo driver, in the traditional modulation method of a two-level servo driver, the influence of zero voltage vector action time on the output component characteristics is considered, a double Fourier transform method is adopted to carry out mathematical modeling on the common-mode component and harmonic component of output phase voltage, the common-mode component amplitude and the harmonic component amplitude corresponding to different frequencies can be accurately calculated, the influence of the zero voltage vector action time on the output common-mode component and the harmonic component is quantized, the influence of the quantitative analysis of the zero voltage vector action time on the common-mode component and the harmonic component of the output phase voltage is realized, and the accuracy of the analysis calculation method is verified through FFT analysis and comparison. The method can also provide a new calculation method and analysis idea for the output component characteristic analysis of other topology converters and other modulation methods.

Description

Calculation method for analyzing output component characteristics of robot servo driver
Technical Field
The application relates to the technical field of servo driver power electronics, in particular to a computing method for analyzing output component characteristics of a robot servo driver.
Background
The output performance and operational reliability of a drive, which is one of the important components of a servo system, affect the output performance and reliability of the servo system. The two-level driver is a simple voltage source type driver, and occupies more than 90% of a servo system of the robot due to simple topological structure, low cost and simple control.
The two-level driver usually adopts a space vector modulation method, but in the operation process, the output phase voltage contains a large amount of common mode components and harmonic components besides fundamental components. When the converter is used as a converter of a servo system and drives the servo system, the high-frequency high-amplitude output common-mode voltage destroys the winding insulation of a servo motor, and the service life of the servo motor is shortened; harmonic components in the output phase voltage can cause torque ripple and affect the reliable operation of a servo motor driving system, so that the performance and reliability of the whole robot are affected.
At present, the effect of inhibiting common mode components or harmonic components is achieved by hardware compensation and an optimized modulation method, compared with the hardware compensation method, the optimized strategy of the modulation method does not increase the weight and the volume of a system and reduce the power density of the system, only a modulation algorithm needs to be changed, and the method is easy to implement, so that the optimized modulation method has more research significance in inhibiting output components. The method for quantitatively analyzing the output component of the two-level driver usually uses FFT (fast fourier transform) analysis, but the FFT analysis needs to sample, window and the like signals in the process of processing waveforms, which can cause problems of spectrum leakage, aliasing and the like, and thus the FFT analysis result is inaccurate. Another more common quantization method is to calculate the output waveform using the fourier transform principle to obtain an accurate harmonic spectrum. In the above analysis method, in the quantitative analysis method for the output component characteristics, the influence of the zero voltage vector acting time on the output common mode component and harmonic component of the two-level driver is not considered.
Disclosure of Invention
In view of the above disadvantages in the prior art, the present application aims to provide a method for calculating output components of a robot servo driver based on a double fourier transform principle, considering different zero voltage vector acting times, so as to obtain more accurate output low-frequency components, high-frequency components and harmonic components.
The application provides a robot servo driver output component characteristic analysis calculation method, which comprises the following steps:
in the two-level driver, three-phase output load symmetry is set;
dividing the output phase voltage into 6 sectors through 6 effective voltage vectors, and constructing an output reference voltage vector relational expression of each sector;
calculating effective voltage vector duty cycled α、d βAnd zero voltage vector duty cycled 0、d 7；
With zero voltage vector duty cycled 0、d 7Calculating the zero voltage vector duty factorλ；
Using effective voltage vector duty cycled α、d βAnd zero voltage vector duty factorλCalculating jump time of different output phase voltage amplitudesm 1,m 2,m 3And output phase voltages corresponding to each vector action time intervalu 1,u 2,u 3,u 4；
Constructing a double Fourier coefficient mathematical model of the output phase voltage;
obtaining output frequencyf outAnd carrier frequencyf cAnd output the frequencyf outCarrier frequency of the carrierf cAnd the jump time of different output phase voltage amplitudesm 1,m 2,m 3And output phase voltages corresponding to each vector action time intervalu 1,u 2,u 3,u 4Introducing a double Fourier coefficient mathematical model, and solving to obtain common-mode components and harmonic components output at different frequencies;
and processing the output common-mode component and harmonic component to obtain a change rule diagram of the common-mode component and the harmonic component.
According to the technical scheme provided by the embodiment of the application, the duty ratio of the effective voltage vector is calculatedd α、d βAnd zero voltage vector duty cycled 0、d 7The method comprises the following steps:
constructing effective voltage vector duty cycled α、d βAnd zero voltage vector duty cycled 0、d 7Obtaining a first calculation formula;
acquiring a sector number of a sector in which an output reference voltage vector of a switching carrier period falls, an output phase of the output reference voltage vector, an amplitude of the output reference voltage vector and an input side direct current output line voltage;
inputting the sector number of the sector in which the output reference voltage vector falls, the output phase of the output reference voltage vector, the amplitude of the output reference voltage vector and the voltage of the input side direct current output line into the first calculation formula to obtain the effective voltage vector duty ratio of one switching carrier periodd α、d βAnd zero voltage vector duty cycled 0、d 7。
According to the technical scheme provided by the embodiment of the application, the zero-voltage vector duty ratio coefficientλThe calculation formula of (A) is as follows:
Figure 580495DEST_PATH_IMAGE001
in the formula (I), the compound is shown in the specification,λrepresenting a zero voltage vectorV 0The action time of two zero voltage vectorsV 0AndV 7the ratio of the sum of the action times;d 0representing a zero voltage vectorV 0Duty cycle of (d);d 7representing a zero voltage vectorV 7The duty cycle of (c).
In particular, the method comprises the following steps of,λrepresenting the zero voltage vector of the voltageV 0The action time of the two voltage zero voltage vectorsV 0AndV 7ratio of sum of action times, different zero-voltage vector duty ratio coefficientsλShowing different zero voltage vector action times whenλ=0.5, i.e. zero voltage vectorV 0、V 7When the action time is the same, the method is the traditional space vector modulation method. Using zero-voltage vector duty cycle systemNumber ofλEstablishing output reference voltage vector jump time with different sectorsm 1、m 2、m 3The influence rule of the zero voltage vector action time on the common-mode component and harmonic component of the output phase voltage of the robot servo driver is further reflected.
According to the technical scheme provided by the embodiment of the application, the expression of the double Fourier coefficient mathematical model of the output phase voltage is as follows,
Figure 401821DEST_PATH_IMAGE002
in the formula (I), the compound is shown in the specification,k、qrespectively carrier frequencyf cOutput frequency of the power converterf outThe coefficient of (a);A k,q andB k,q respectively representing the real part and the imaginary part of the double Fourier coefficient, and j represents an imaginary unit;k outa sector number for which the output reference voltage vector falls within the sector;uis the output phase voltage;θ crepresenting the carrier phase;θ outwhich is indicative of the phase of the output,θ out=2πf out t+φ 0whereinf outIn order to output the frequency of the radio frequency,tthe time is represented by the time of day,φ 0an initial phase of the output phase voltage is assumed to be 0;
Figure 62478DEST_PATH_IMAGE003
the double fourier coefficients representing the output phase voltages for each sector can be expressed as:
Figure 765992DEST_PATH_IMAGE004
in the formula (I), the compound is shown in the specification,Dis composed ofθ cOutput phase voltages corresponding to respective vector application periodsu 1,u 2,u 3,u 4The specific expression of (a) is as follows:
Figure 655451DEST_PATH_IMAGE005
wherein, it is toθ cMay be defined by the jump timem 1,m 2,m 3And (4) showing.
In particular, under space vector modulation, the output frequency is taken into accountf outAnd carrier frequencyf cIndependent of each other, according to the space vector modulation principle, in 6 sectors of the driver, double Fourier coefficients of output phase voltages of a two-level driver can be establishedF k,q And (4) a mathematical model expression.
According to the technical scheme provided by the embodiment of the application, the processing of the output common-mode component and harmonic component to obtain the change rule diagram of the common-mode component and the harmonic component comprises the following steps:
obtaining a first per-unit value of the common-mode component and a first per-unit value of the harmonic component by per-unit outputting the amplitude of the common-mode component and the amplitude of the harmonic component;
and drawing a three-dimensional graph by using the first per-unit value of the common-mode component and the first per-unit value of the harmonic component to obtain a change rule graph of the common-mode component and the harmonic component output under different voltage transmission ratios and different zero-voltage vector duty ratio coefficients.
Specifically, the per-unit process is to standardize the output common-mode component amplitude and harmonic component amplitude to make the data comparable and facilitate visual analysis, and input the per-unit result into simulation software Matlab for image processing to obtain different voltage transmission ratiosmAnd different zero voltage vector duty cycle coefficientsλThe change rule graphs of the common-mode component and the harmonic component can observe and analyze the change rules of the common-mode component and the harmonic component more vividly and accurately.
According to the technical solution provided by the embodiment of the present application, the first calculation formula is,
Figure 596862DEST_PATH_IMAGE006
in the formula (I), the compound is shown in the specification,k outfor outputting the sector number of the reference voltage vector, andk out=1,2,3,4,5,6；d α、d β、d 0andd 7respectively representing effective voltage vectorsV αAndV βand zero voltage vectorV 0AndV 7a corresponding duty cycle; non-viable cellsV refI is the amplitude of the output reference voltage vector;θ outis the output phase;u dcrepresents the input side dc output line voltage;d 07representing zero voltage vector duty cycled 0、d 7And (4) summing.
According to the technical scheme provided by the embodiment of the application, the calculation formula of the output reference voltage vector is,
Figure 913574DEST_PATH_IMAGE007
in the formula (I), the compound is shown in the specification,V refrepresenting an output reference voltage vector;V αandV βrepresents an effective voltage vector;V 0andV 7represents a zero voltage vector;
d α、d β、d 0andd 7respectively representing effective voltage vectorsV αAndV βand zero voltage vectorV 0AndV 7the corresponding duty cycle.
In summary, the present application discloses a method for calculating the output component characteristic analysis of a robot servo driver, which has the beneficial effects that in the conventional modulation method of a two-level servo driver, the influence of the zero-voltage vector action time on the output component characteristic is considered, the double fourier transform method is adopted to perform mathematical modeling on the common-mode component and harmonic component of the output phase voltage, the common-mode component amplitude and harmonic component amplitude corresponding to different frequencies can be accurately calculated, and the zero-voltage vector is used for calculating the common-mode component amplitude and harmonic component amplitude corresponding to different frequenciesThe influence of the quantity action time on the output common-mode component and harmonic component is quantified, and the following conclusion is obtained through analysis: vector duty factor of driver output component with respect to zero voltageλ=0.5 symmetry, selecting only zero voltage vector without changing the selection of active voltage vectorV 0Or zero voltage vectorV 7The effects on the output common mode component and harmonic component are the same; by varying the zero voltage vector duty factorλThe low-frequency common-mode component is not influenced, but the amplitudes of the common-mode component and the harmonic component of partial output phase voltage can be reduced; changing the zero voltage vector duty factorλOn the basis of the voltage transmission ratio of the power supplymThe common mode component and harmonic component of the part output with higher amplitude can be further reduced. The calculation method for analyzing the output component characteristics provides a new calculation method and analysis idea for analyzing the output component characteristics of other topological converters and other modulation methods, and results are analyzed more visually and accurately by using a calculation formula of common-mode components and harmonic components obtained through mathematical modeling.
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Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings.
Fig. 1 is a schematic diagram of a topological structure of a robot servo driver.
Fig. 2 illustrates the space vector modulation principle of the robot servo driver.
Fig. 3 shows the output phase voltage waveform and 6 sector divisions of the robot servo driver.
Fig. 4 is a composite waveform of one switching carrier period of the output phase voltage under space vector modulation.
FIG. 5 shows a frequency of (6 z)1+3)f out (z 1A low-frequency common-mode component of =0,1) is plotted against the voltage transmission ratio and the duty factor of the zero-voltage vector.
FIG. 6 shows a frequency of 2f c、4f cHigh frequency common mode component with voltage transmission ratio and zeroAnd (5) a change rule graph of the voltage vector duty ratio coefficient.
FIG. 7 shows a frequency off c+ (6z1+3)f out (z 1A high-frequency common-mode component of =0,1,2) is plotted against the voltage transfer ratio and the zero-voltage vector duty factor.
FIG. 8 shows a frequency of 3f c+ (6z1+3)f out (z 1The variation law of the high-frequency common-mode component of the =0,1,2) with the voltage transmission ratio and the zero-voltage vector duty ratio coefficient.
FIG. 9 isf c±f out、f c±5f out、f c±7f outThe harmonic component of the output phase voltage of the driver under the frequency is along with the change rule graph of the voltage transmission ratio and the zero voltage vector duty ratio coefficient.
FIG. 10 is 2f c±f out、4f c±f outThe harmonic component of the output phase voltage of the driver under the frequency is along with the change rule graph of the voltage transmission ratio and the zero voltage vector duty ratio coefficient.
FIG. 11 isf c±2z 1 f out (z 1=1,2,4) frequency of the output phase voltage of the driver as a function of the voltage transfer ratio and the duty factor of the zero voltage vector.
FIG. 12 is 2f c±2z 1 f out (z 1=1,2) frequency of the output phase voltage of the driver, as a function of the voltage transfer ratio and the zero-voltage vector duty factor.
FIG. 13 is a graph of driver output phase voltages at different voltage transfer ratios and different zero voltage vector duty cycle coefficientsu agThe simulated FFT analysis spectrogram of (a).
Detailed Description
The present application will be described in further detail with reference to the drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the invention are shown in the drawings, and the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
The present application will now be described in detail with reference to the drawings, in conjunction with the following examples.
Fig. 1 shows a topological structure of a robot servo driver, which is composed of 6 power switching tubes, wherein the voltage on the direct current side is constant, and the reference voltage is output by controlling the turn-off time of the 6 switching tubes.
As shown in fig. 1, the robot servo driver has a topology structure, the two-level driver has three phases a, b, and c, each phase has an upper bridge arm and a lower bridge arm, each bridge arm has a power switch, and the two-level servo driver has six switch tubes. According to the principle that the output cannot be opened, one switch tube of each phase is required to be turned on, and the other switch tube of each phase is required to be turned off. Defining the switch tube to be turned on to 1 and turned off to 0, and according to different states of the switch, 8 switch states can be obtained, namelyS 100 、S 110 、S 010 、S 011 、S 001 、S 101 、S 000 、S 111 (ii) a To be provided withS 100 For example, the two-level driver is shown with the upper bridge arm a-phase switching tube turned on, the b-phase switching tube and the c-phase switching tube turned off, the lower bridge arm a-phase switching tube turned off, and the b-phase switching tube and the c-phase switching tube turned on. The 8 switch states of the two-level driver respectively correspond to 6 effective voltage vectors in 8 voltage vectorsV 1(100)、V 2 (110)、V 3(010)、V 4(011)、V 5(001)、V 6(101) Two zero voltage vectorsV 0(000) AndV 7(111) as shown in fig. 2.
As can be seen from fig. 2, in the conventional modulation method, each sector is divided into two adjacent effective voltage vectorsV α、V βAnd two zero voltage vectorsV 0、V 7Synthesized output reference voltage vectorV refAnd the switching between the vectors is completed by changing the switching state of the switching tube, and the switching principle is that the state of the switching tube changes as little as possible during each switching so as to reduce the switching loss. Under different sectors, two adjacent effective voltage vectorsV αAndV βand zero voltage vectorV 0AndV 7the selection and order of action of (a) are shown in table 1.
Figure 556913DEST_PATH_IMAGE008
As shown in FIG. 1, under the action of different vectors, the output phase voltage with the load midpoint n as the reference pointu xn(x = a, b, c), output phase voltage with reference to the supply midpoint gu xg(x= a, b, c) and output line voltageu dcThe amplitudes are different from each other, and the corresponding relationship is shown in table 2.
Figure 46801DEST_PATH_IMAGE009
Common mode voltage generated by robot servo driveru ngThe voltage between the load midpoint n and the power reference ground g is the common mode voltage output when the two-level driver drives the three-phase symmetrical loadu ngIn order to realize the purpose,
u ng=(u ag+u bg+u cg)/3 (1)
in the formula (I), the compound is shown in the specification,u ag、u bg、u cgrespectively representing the output phase voltages of three phases a, b and c with the power supply midpoint g as a reference point.
The common mode voltage peak values corresponding to different voltage vectors can be calculated according to table 2 and equation (1), as shown in table 3.
Figure 780401DEST_PATH_IMAGE010
As can be seen from tables 2 and 3, the output phase voltages generated by the two zero voltage vectors and the six effective voltage vectors correspond to each otheru agAmplitude and output common mode voltageu ngThe amplitudes are different, and because the output phase voltage is closely related to the duty ratio of each voltage vector, the duty ratio coefficient of the zero-voltage vector is setλEstablishing a zero voltage vector duty factorλThe relation with the vector jump time of the output reference voltage to realize analysisλThe influence of the continuous variation of (c) on the output common mode component and harmonic component characteristics.
Defining zero voltage vector duty cycle coefficientsλIn order to realize the purpose,
λ=d 0/(d 0+d 7) (2)
in the formula (I), the compound is shown in the specification,λrepresenting a zero voltage vectorV 0The action time is the ratio of the action time of two voltage zero voltage vectors,d 0representing a zero voltage vectorV 0Duty cycle of (d);d 7representing a zero voltage vectorV 7The duty cycle of (c).
When the temperature is higher than the set temperatureλ=0.5, i.e. zero voltage vectorV 0、V 7When the action time is the same, the method is the traditional space vector modulation method.
In a preferred embodiment, the topology of the robot servo drive is shown in fig. 1, the operating conditions are shown in table 4, the output phase voltages are shown in fig. 3,u a、u b、u cthe output phase voltages of the three phases a, b and c are respectively shown.
Figure 533594DEST_PATH_IMAGE011
Using triangular wave as carrier wave of space vector modulation, its carrier functionc(θc) In order to realize the purpose,
c(θ c)=arccos[cos(θ c)]/π (3)
in the formula, carrier phaseθ c=2πf c tAnd is andθ c∈[-π，π]，f cis the carrier frequency and is,trepresenting time.
Since the output waveform of the robot servo driver is related to and independent of the output frequency and the carrier frequency, the output waveform can be quantitatively analyzed by using the output frequency and the carrier frequency. The method adopts a double Fourier transform method to carry out mathematical modeling on the common-mode component and harmonic component of the output phase voltage, and analyzes the influence of the zero voltage vector action time on the output common-mode component and harmonic component, and comprises the following steps:
in the two-level driver, three-phase output load symmetry is set;
because three-phase output loads are symmetrical and the output rule of each phase voltage is the same, in order to research the influence of two different zero voltage vector acting times on the output of low-frequency components, high-frequency common-mode components and high-frequency harmonic components, the phase voltage of a is usedu agFor the purpose of example, the analysis was carried out,u agthe specific expression is as follows,
u ag=u an+u ng (4)
in the formula (I), the compound is shown in the specification,u anrepresenting the output phase voltage with the load midpoint n as a reference point;u ngrepresenting the voltage between the load midpoint n and the supply reference ground g.
Dividing an output phase voltage into 6 sectors through 6 effective voltage vectors;
as shown in FIG. 2, 6 different effective voltage vectors divide the space into 6 sectors, and for each sector numberk outThe value is assigned to the value to be assigned,k out=1,2,3,4,5, 6; as shown in FIG. 3, the output phase voltages 0 to π/3 are set as the 1 st sector, π/3 to 2 π/3 as the 2 nd sector, 2 π/3 to π as the 3 rd sector, π to 4 π/3 as the 4 th sector, 4 π/3 to 5 π/3 as the 5 th sector, 5 π/3 to 2 π/as the 6 th sector.
As shown in fig. 2, in the conventional modulation method of the two-level driver, since the three-phase output load is symmetricalThe output reference voltage vector in each sector consists of two adjacent effective voltage vectorsV α、V βAnd two zero voltage vectorsV 0、V 7Synthesizing, wherein the specific relational expression is,
V ref=d α V α+d β V β+d 0 V 0+d 7 V 7 (5)
in the formula (I), the compound is shown in the specification,V refrepresenting an output reference voltage vector;V αandV βrepresents an effective voltage vector;V 0andV 7represents a zero voltage vector;d α、d β、d 0andd 7respectively representing effective voltage vectorsV αAndV βand zero voltage vectorV 0AndV 7the corresponding duty cycle.
As shown in fig. 2, the effective voltage vector corresponding to each sector is shown in table 5.
Figure 929809DEST_PATH_IMAGE012
Calculating effective voltage vector duty cycled α、d βAnd zero voltage vector duty cycled 0、d 7The method comprises the following steps:
constructing effective voltage vector duty cycled α、d βAnd zero voltage vector duty cycled 0、d 7Obtaining a first calculation formula;
according to fig. 2 and the vector composition principle, the first calculation formula is,
Figure 426649DEST_PATH_IMAGE013
(6)
in the formula (I), the compound is shown in the specification,k outfor outputting reference voltage vectorsV refThe sector number of the position; non-viable cellsV refI is the output reference voltage vectorV refThe amplitude of (d);θ outwhich is indicative of the phase of the output,θ out=2πf out t+φ 0，f outin order to output the frequency of the radio frequency,tthe time is represented by the time of day,φ 0an initial phase of the output phase voltage is assumed to be 0;d 07representing zero voltage vector duty cycled 0、d 7And (4) summing.
Obtaining sector number of sector in which output reference voltage vector of one switch carrier period fallsk outVector output phase of output reference voltageθ outOutputting the amplitude of the reference voltage vectorV refI, input side DC output line voltageu dc；
The sector number of the sector in which the output reference voltage vector fallsk outThe output reference voltage vector output phaseθ outThe amplitude of the output reference voltage vector is notV refI, the input side DC output line voltageu dcInputting the first calculation formula (6) to obtain the effective voltage vector duty ratio in a switching carrier periodd α、d βAnd zero voltage vector duty cycled 0、d 7。
With zero voltage vector duty cycled 0、d 7Calculating the zero voltage vector duty factorλAccording to the formula (2), the zero-voltage vector duty ratio coefficient in one switching carrier period can be obtainedλ；
Using effective voltage vector duty cycled α、d βAnd zero voltage vector duty factorλCalculating jump time of different output phase voltage amplitudesm 1,m 2,m 3And output phase voltage corresponding to each vector action time intervalu 1,u 2,u 3,u 4；
As shown in fig. 4, which is a synthesized waveform of the output phase voltage in one switching carrier period, it can be known that the jump time of the output phase voltage amplitude change in one carrier period is not only in proportion to the effective voltage vector duty ratiod α、d βRelated to, and also by the zero-voltage vector duty factorλEffects, i.e. two zero voltage vectorsV 0、V 7The amplitude distribution of the output phase voltage at different moments can be changed due to different action times.
Within one switching carrier period, according to the duty ratio coefficient of the zero voltage vectorλAnd effective voltage vector duty cycled α、d βDifferent sectors of a two-level drive can be determinedk outTime of lower jumpm 1、m 2、m 3As shown in table 6.
Figure 77074DEST_PATH_IMAGE014
As will be appreciated by those skilled in the art, the output phase voltages for each vector application periodu 1、u 2、u 3、u 4Can be obtained by an equivalent circuit principle.
Constructing a double Fourier coefficient mathematical model of the output phase voltage;
performing mathematical modeling on common-mode component and harmonic component of output phase voltage by using a double Fourier transform method, wherein the real part of a double Fourier coefficientA k,q And imaginary partB k,q Representing the common mode and harmonic components of the output phase voltages, respectively. Under space vector modulation, the output frequency is taken into accountf outAnd carrier frequencyf cIndependent of each other, the double Fourier coefficient of the phase voltage output by the two-level driver in 6 sectors of the two-level driver according to the space vector modulation principleF k,q The expression of (a) is as follows,
Figure 470009DEST_PATH_IMAGE002
(7)
in the formula (I), the compound is shown in the specification,k、qare respectively carrier frequencyf cOutput frequency of the power converterf outThe coefficient of (a);A k,q andB k,q respectively representing the real part and the imaginary part of the double Fourier coefficient, and j represents an imaginary unit;k outa sector number for which the output reference voltage falls within the sector;uis the output phase voltage;θ outwhich is indicative of the phase of the output,θ out=2πf out t+φ 0whereinf outIn order to output the frequency of the radio frequency,tthe time is represented by the time of day,φ 0an initial phase of the output phase voltage is assumed to be 0;θ crepresenting the carrier phase;
Figure 93800DEST_PATH_IMAGE015
the double fourier coefficients representing the output phase voltages for each sector can be expressed as:
Figure 925490DEST_PATH_IMAGE016
(8)
in the formula (I), the compound is shown in the specification,Dis composed ofθ cOutput phase voltages corresponding to respective vector application periodsu 1,u 2,u 3,u 4The specific expression of (a) is as follows:
Figure 696000DEST_PATH_IMAGE017
(9)
wherein, it is toθ cMay be defined by the jump timem 1,m 2,m 3And (4) showing.
Obtaining output frequencyf outAnd carrier frequencyf cAnd output the frequencyf outCarrier frequency of the carrierf cAnd the jump time of different output phase voltage amplitudesm 1,m 2,m 3And output phase voltages corresponding to each vector action time intervalu 1,u 2,u 3,u 4The equations (8) and (9) are solved to obtain the difference (A)kf c±qf out) The common mode component and harmonic component output at frequency are expressed by the specific expression,
Figure 525416DEST_PATH_IMAGE018
(10)
in the formula (I), the compound is shown in the specification,mis the voltage transfer ratio;F 0,q in order to output the low-frequency component,F com_n(m,λ) AndF har_n(m,λ) Are respectively andmandλthe correlated output high frequency common mode components and high frequency harmonic components.
Wherein, the expression of the voltage transmission ratio is,
Figure 115797DEST_PATH_IMAGE019
(11)
in the formula (I), the compound is shown in the specification,u dcrepresenting input side DC output line voltage,. gamma.,. gamma.V refI is the output reference voltage vectorV refIs known in linear modulationmHas a range of (0, 1).
In order to facilitate later verification and visual analysis of a calculation result, the output common-mode component and harmonic component are processed to obtain a change rule diagram of the common-mode component and the harmonic component, and the method comprises the following steps:
the amplitude of the common-mode component and the amplitude of the harmonic component which are output per unit are obtained to obtain a first common-mode component per unit value and a first harmonic component per unit value, and a specific per unit calculation formula is,
Figure 203707DEST_PATH_IMAGE020
(12)
in the formula (I), the compound is shown in the specification,h com_nis a per unit value of the magnitude of the common mode component,h har_nis the per unit value of the amplitude of the harmonic component;u dcis an input side direct current output line voltage; non-viable cellsV refI is the output reference voltage vectorV refThe amplitude of (c).
And drawing a three-dimensional graph by using the first per-unit value of the common-mode component and the first per-unit value of the harmonic component to obtain a change rule graph of the common-mode component and the harmonic component output under different voltage transmission ratios and different zero-voltage vector duty ratio coefficients.
Inputting the result per unit of the formula (12) into simulation software Matlab for image processing to obtain different voltage transmission ratiosmAnd different zero voltage vector duty cycle coefficientsλThe change law of the common mode component and harmonic component of the lower output is shown in fig. 5,6 and 7.
FIG. 5 shows a frequency of (6 z)1+3)f outLow frequency common mode component voltage dependent transmission ratiomAnd zero voltage vector duty factorλFig. 6, 7 and 8 show the variation pattern of (2) frequencykf c、f c+ (6z1+3)f out、3f c+ (6z1+3)f outHigh frequency common mode component with voltage transfer ratiomAnd zero voltage vector duty factorλFig. 9, 10, 11 and 12 show the transmission ratio of harmonic component of the output phase voltage of the driver with voltage according to the voltage transmission ratio under different frequenciesmAnd zero voltage vector duty factorλA change law map of (2).
FIG. 5 shows a frequency of (6 z)1+3)f out (z 1Three-dimensional plot of common-mode component of =0,1), it can be seen that the frequency is (6)z 1+3)f out (z 1Low frequency common mode component of =0,1) is independent of zero voltage vector action time, onlymLinearly varying, the amplitude of the common mode componenth ncom_Ratio of transmission with voltagemAnd increases as it increases.
FIGS. 6, 7 and 8 show the high frequency components of the common mode voltage,it can be seen that the high frequency common mode component amplitudeh ncom_Is based onλ=0.5, the symmetry axis is symmetrical, so that only analysis is made hereλThe law of influence on the main common mode component in the interval (0, 0.5).
As can be seen from FIG. 6, the switching frequency is an integer multiple of 2f c、4f cAt low voltage transmission ratio of the common mode componentmWhen the temperature of the water is higher than the set temperature,h ncom_to be receivedλThe change of (2) has a large influence of 0<m<At 0.6, the frequency is 2f cIs/are as followsh ncom_With the followingλIncrease and decrease of (A) inλ=0.25 takes the maximum value atλ0 =0.5 is 0; when 0 is present<m<At 0.3, the frequency is 4f cIs/are as followsh ncom_Followed byλThe increase is increased first, then decreased, then increased, then decreased;
at voltage transmission ratiom=0.3 andmwhen =0.8, the frequency is 4f cIs/are as followsh ncom_Is not subject toλAll amplitudes are 0; in thatλFrequency of 2 when =0.5f c、4f cThe high-frequency common-mode component of (2) is not affected by the voltage transfer ratio, and the amplitudes are all 0.
FIG. 7 shows a frequency off c±(3+6z 1)f out (z 1Common mode component of =0,1,2)h ncom_Andλthe mixture is in a direct proportion relation,λthe larger the common mode component; when in useλAnd when =0.5, the maximum is reached.
Frequency of 3f c±(3+6z 1)f out (z 1=0,1,2)h ncom_The change rule is shown in FIG. 8, when 0<m<At 0.4 time, followλIncrease increases first, then decreases and then increases, at 0<λ<Within 1, 3 wave peaks will appear, respectivelyλ=0.15、λ=5 andλand = 0.85. Current to voltage transfer ratiomFrequency of 3 when =0.4f c±(3+6z 1)f out (z 1=0,1,2)h ncom_The variation trend is not influencedλWith a minimum value of 0.
Fig. 9, 10, 11, and 12 show harmonic components in space vector linear modulationh nhar_Law of variation, major harmonic components at different frequencies, andλ=0.5 is a change law in which the axis of symmetry is symmetrical, and therefore only analysis is madeλThe law of influence on the high-frequency harmonic components in section (0, 0.5).
In FIG. 9, the frequencies aref c±f out、f c±5f out、f c±7f outHarmonic of (2)h nhar_At the same voltage transmission ratiomLower, receiveλThe influence of the change is very small, no obvious change exists, and the harmonic amplitude is along with the voltage transmission ratiomThe change trend is linear.
FIG. 10 shows a frequency of 2f c±f out、4f c±f outOf harmonicsh nhar_The law of variation, at low voltage transfer ratios,h nhar_to be receivedλHas a greater influence withmThe size of the mixture is increased, and the mixture is,h nhar_to be receivedλThe influence of (b) is gradually reduced. At 0<m<0.5, frequency 2f c±f outIs/are as followsh nhar_Followed byλIs increased after being decreased, in thatλ=0、λ=1、λ=0.5 maximum value; at 0<m<0.25, frequency 4f c±f outIs/are as followsh nhar_Followed byλThe increase is first reduced, then increased, then reduced and then increased;
harmonic frequency off c±2z 1 f out (z 1=1,2,4)h nhar_To be receivedλAndmthe variation law of (2) is shown in FIG. 11, the harmonic amplitudes of which are equal toλIn an inverse relationship to each other,λthe larger the amplitude, the smaller the amplitude isλ=0.5, with a harmonic amplitude of minimum 0; in thatλWhen not changed, the amplitude value thereof followsmIs increased and decreased.
In FIG. 12, the frequency is 2f c±2z 1 f out (z 1=1,2)h nhar_At the same timeλIs increased and decreased, inλ=0.5 minimum value of 0 is obtained in the same wayλIts amplitude variation trend ismThe increase in (c) increases first and then decreases.
To verify the above zero voltage vector duty cycle coefficient λ and voltage transfer ratio under double Fourier modelingmAnd (3) establishing simulation for the correctness of the rule of analyzing the phase voltage common-mode component and the harmonic component of the output phase of the robot servo driver based on Matlab/Simulink, wherein the topological structure of the robot servo driver is shown in figure 1, and the simulation parameters are shown in table 4.
When the output phase voltage is analyzed by adopting FFT, when the carrier frequency and the output frequency are both integers, and the time corresponding to the waveform intercepted by the FFT analysis is just an integral multiple of the carrier period and the output period, the result obtained by the FFT analysis is basically the same as the result obtained based on the double Fourier transform. Based on the conditions, FFT analysis is carried out on the simulated output phase voltage, comparison is carried out on the output phase voltage and the output component obtained through double Fourier series calculation, and the analysis result is verified.
Fig. 13 is a spectrum diagram of output phase voltages under different conditions, which are subjected to FFT analysis. Wherein FIG. 13(a) shows the transmission ratio at lowm=0.2，λ=0.2、λ=0.5、λOutput phase voltage spectrogram of =0.8, wherein fig. 13(b) shows the output phase voltage spectrogram at the transmission ratiom=0.5，λ=0.2、λ=0.5、λOutput phase voltage spectrogram of =0.8, wherein fig. 13(c) shows the spectrum at a high transmission ratiom=0.8，λ=0.2、λ=0.5、λOutput phase voltage spectrogram of = 0.8. The three graphs from top to bottom of each group are respectively an output component spectrogram, a common mode component spectrogram and a harmonic component spectrogram.
The output component amplitude is the amplitude synthesis result of the amplitude of the common mode component and the amplitude of the harmonic component, and a calculation formula for obtaining the sum of the amplitude of the common mode component and the amplitude of the harmonic component is shown as formula (7) to formula (10)
Figure 563145DEST_PATH_IMAGE021
（13）
In the formula (I), the compound is shown in the specification,V k,q the sum of the amplitude of the common mode component and the amplitude of the harmonic component;F k,q outputting a double Fourier coefficient of the phase voltage for the two-level driver;A k,q andB k,q representing the real and imaginary parts of the doublet fourier coefficients, respectively.
Extracting the main common-mode component and harmonic component from the spectrogram shown in fig. 13, and performing per unit on them, where table 7 shows that the common-mode component is not presentmAnd is different fromλPer unit value of, Table 8 shows the harmonic components are differentmAnd is different fromλPer unit value of.
Figure 829041DEST_PATH_IMAGE022
Figure 906718DEST_PATH_IMAGE023
As can be seen from tables 7 and 8, whenmAt a certain time, different zero voltage vector duty ratio coefficientsλThe amplitude of the common mode component and the harmonic component in the output phase voltage is changed and the amplitude is changedλ=0.5 is a symmetric axis, and the symmetric change rule is presented; at a frequency off c±3f outThe peak value of the common-mode component is larger than the peak values of other common-mode components; at a frequency ofkf c±f out (kThe harmonic component of = 2,4) is a major harmonic component, and its peak value is larger than the peak values of the other harmonic components. In thatm=0.2, the maximum amplitude of the output phase voltage component is 54% atm=0.5, the maximum amplitude of the output phase voltage component is 38% atm=0.8, the maximum amplitude of the output phase voltage component is 21%. Compared with the change rule graphs (figure 5, figure 6, figure 7, figure 8, figure 9, figure 10, figure 11 and figure 12) of the output common-mode component and harmonic component, the change rule is the same as the rule of the double Fourier modeling analysis, and the positive of the double Fourier theory analysis is provedAnd (5) determining.
In conclusion, according to the space vector modulation principle of the robot servo driver, the influence of the zero voltage vector acting time on the output common-mode component and harmonic component of the robot servo driver is quantitatively calculated and analyzed by using a double Fourier transform method. The following conclusions can be drawn by analysis:
1) vector duty ratio coefficient of output component of robot servo driver relative to zero voltageλ=0.5 symmetry, zero voltage vector without changing the selection of the effective voltage vectorV 0Or zero voltage vectorV 7The effects on the output common mode component and harmonic component are the same;
2) by varying the zero voltage vector duty factorλThe low-frequency common-mode component is not influenced, but the common-mode component and the amplitude of harmonic component of partial output phase voltage can be reduced;
3) in changingλOn the basis of the voltage transmission ratio of the power supplymThe amplitudes of the part of the common mode component and the harmonic component with higher amplitudes can be further reduced;
the conclusion can provide theoretical basis and theoretical basis for the modulation strategy for improving the output performance of the robot servo driver.
The above-mentioned embodiments of the present application are merely examples for clearly illustrating the present application, and are not intended to limit the embodiments of the present application, and it will be apparent to those skilled in the art that other variations and modifications can be made on the basis of the above description, and all obvious variations and modifications of the present application are covered by the protection scope of the present application.

Claims (5)

1. A computing method for analyzing output component characteristics of a robot servo driver is characterized by comprising the following steps:
in a two-level driver, three-phase output load symmetry is set;
dividing the output phase voltage into 6 sectors through 6 effective voltage vectors, and constructing a vector relation of output reference voltages of the sectors;
calculating the effective voltage vector duty ratio dα、dβAnd zero voltage vector duty cycle d0、d7；
With zero voltage vector duty cycle d0、d7Calculating a zero-voltage vector duty ratio coefficient lambda;
using effective voltage vector duty cycle dα、dβCalculating jump time m of different output phase voltage amplitudes by using the zero-voltage vector duty ratio coefficient lambda1,m2,m3And the output phase voltage u corresponding to each vector action time interval1,u2,u3,u4；
Constructing a double Fourier coefficient mathematical model of the output phase voltage;
obtaining an output frequency foutAnd carrier frequency fcAnd output the frequency foutCarrier frequency fcAnd jump time m of different output phase voltage amplitudes1,m2,m3And the output phase voltage u corresponding to each vector action time interval1,u2,u3,u4Introducing a double Fourier coefficient mathematical model, and solving to obtain common-mode components and harmonic components output at different frequencies;
processing the output common-mode component and harmonic component to obtain a change rule diagram of the common-mode component and the harmonic component;
the zero-voltage vector duty ratio coefficient lambda is calculated by the following formula:
λ＝d0/(d0+d7)
in the formula, λ represents a zero voltage vector V0The action time of two zero voltage vectors V0And V7The ratio of the sum of the action times; d0Representing a zero voltage vector V0Duty cycle of (d); d7Representing a zero voltage vector V7Duty cycle of (d);
the expression of the double Fourier coefficient mathematical model of the output phase voltage is as follows:
Figure FDA0003636368430000011
wherein k and q are carrier frequencies fcOutput frequency foutThe coefficient of (a); a. thek,qAnd Bk,qRespectively representing the real part and the imaginary part of the double Fourier coefficient, and j represents an imaginary unit; k is a radical ofoutA sector number for which the output reference voltage vector falls within the sector; u is the output phase voltage; theta.theta.cRepresenting the carrier phase; thetaoutWhich is indicative of the phase of the output,
Figure FDA0003636368430000012
wherein f isoutTo output the frequency, t represents time,
Figure FDA0003636368430000013
an initial phase of the output phase voltage is assumed to be 0;
Figure FDA0003636368430000014
the double fourier coefficients representing the output phase voltages for each sector can be expressed as:
Figure FDA0003636368430000021
wherein D is thetacOutput phase voltage u corresponding to each vector action period1,u2,u3,u4The specific expression of (a) is as follows:
Figure FDA0003636368430000022
wherein for thetacCan be defined by the jump time m1,m2,m3And (4) showing.
2. The method of claim 1, wherein the step of calculating the output component characteristic analysis of the robot servo driver comprises the steps of,calculating the effective voltage vector duty ratio dα、dβAnd zero voltage vector duty cycle d0、d7The method comprises the following steps:
construction of effective Voltage vector Duty ratio dα、dβAnd zero voltage vector duty cycle d0、d7Obtaining a first calculation formula;
acquiring a sector number of a sector in which an output reference voltage vector of a switching carrier period falls, an output phase of the output reference voltage vector, an amplitude of the output reference voltage vector and an input side direct current output line voltage;
inputting the sector number of the sector in which the output reference voltage vector falls, the output phase of the output reference voltage vector, the amplitude of the output reference voltage vector and the voltage of the input side direct current output line into the first calculation formula to obtain the effective voltage vector duty ratio d of one switching carrier periodα、dβAnd zero voltage vector duty cycle d0、d7。
3. The method of claim 1, wherein the processing the output common mode component and harmonic component to obtain a variation law map of the common mode component and harmonic component comprises:
obtaining a first per-unit value of the common-mode component and a first per-unit value of the harmonic component by per-unit outputting the amplitude of the common-mode component and the amplitude of the harmonic component;
and drawing a three-dimensional graph by using the first per-unit value of the common-mode component and the first per-unit value of the harmonic component to obtain a change rule graph of the common-mode component and the harmonic component output under different voltage transmission ratios and different zero-voltage vector duty ratio coefficients.
4. The method of claim 2, wherein the first calculation formula is:
Figure FDA0003636368430000031
in the formula, koutIs the sector number where the output reference voltage vector is located, and kout＝1,2,3,4,5,6；dα、dβ、d0And d7Respectively representing effective voltage vectors VαAnd VβAnd zero voltage vector V0And V7A corresponding duty cycle; | VrefI is the amplitude of the output reference voltage vector; thetaoutIs the output phase; u. ofdcRepresents the input side dc output line voltage; d07Representing zero voltage vector duty cycle d0、d7And (4) summing.
5. The method of claim 4, wherein the output reference voltage vector is calculated by the following formula,
Vref＝dαVα+dβVβ+d0V0+d7V7
in the formula, VrefRepresenting an output reference voltage vector; vαAnd VβRepresents an effective voltage vector; v0And V7Represents a zero voltage vector;
dα、dβ、d0and d7Respectively representing effective voltage vectors VαAnd VβAnd zero voltage vector V0And V7The corresponding duty cycle.
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