CN115589180B - Quadrature error compensation method based on sine and cosine position encoder - Google Patents
Quadrature error compensation method based on sine and cosine position encoder Download PDFInfo
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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
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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
- H02P21/06—Rotor flux based control involving the use of rotor position or rotor speed sensors
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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
- H02P21/18—Estimation of position or speed
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Abstract
The invention discloses an orthogonal error compensation method based on a sine and cosine position encoder in the technical field of motor control, which comprises the following steps: detecting and sampling a sine and cosine encoder voltage signal; performing amplitude scaling and zero point offset of sine and cosine digital variables; performing quadrature error calculation of sine and cosine variables; calculating an ideal cosine variable; and (5) performing position angle calculation after quadrature error compensation. According to the invention, an ideal cosine waveform is fitted according to the sampled sine and cosine waveform with the orthogonal error by a curve fitting method, so that the problem of overlarge position error caused by the orthogonal error is solved, and the stability of a control system is improved while the cost is reduced by adopting a low-cost sine and cosine encoder; the method is free from motor parameters, can be realized only by voltage sampling values of the original sine and cosine encoder, and has higher precision, better effect and easier realization method; the excessive computing power of the MCU is not required, and the number of required instruction cycles is less.
Description
Technical Field
The invention belongs to the technical field of motor control, and particularly relates to an orthogonal error compensation method based on a sine and cosine position encoder.
Background
The permanent magnet motor has simple structure, high efficiency and wide application range. Permanent magnet motors require position feedback for effective control, however, the use of high precision position sensors is too costly and therefore lower cost encoder schemes are often used in practical products. Often high precision position sensors, such as photoelectric encoders, rotary transformers, etc., can be several hundred in price, and the cost in mass production is almost unacceptable. In contrast, the low-cost sine and cosine encoder has a simple structure, and can be realized by only matching one Hall sensor with a related conditioning circuit, and the cost can reach tens of times or even lower. The sine and cosine encoder can output absolute positions, is more convenient to use even than an incremental photoelectric encoder with higher cost, and can only realize partition judgment accuracy greatly improved compared with a common Hall sensor, so that the incremental photoelectric encoder is often used on enterprise products requiring sine wave control of permanent magnet motors.
The sine and cosine position encoder usually generates two mutually orthogonal sine and cosine voltage waveforms, the MCU scales and shifts the amplitude of the sine and cosine voltage to be between minus pi and pi after AD sampling, and the current mechanical position angle can be obtained through atan2 operation. However, in practical applications, the sine and cosine waveforms generated by the low-cost sine and cosine encoder are generally inaccurate, and the main errors include unequal sine and cosine amplitudes, middle shift, harmonic waves, non-orthogonality, and the like. The amplitude inequality and the median offset can basically eliminate the influence through scaling and offset after sampling, and the harmonic problem can be reduced by adding a follower circuit, software and hardware filtering and other methods through a sampling circuit, but the problem caused by the non-orthogonality of sine and cosine waveforms is relatively difficult to eliminate. The phase difference between sine and cosine voltage waveforms of the high-precision sine and cosine encoder is basically pi/2, the error is generally smaller than +/-0.5 degrees, but the phase difference between sine and cosine voltage waveforms of the low-cost sine and cosine encoder is larger than pi/2, the error of a practically used low-cost sine and cosine encoder product can even reach 3.77 degrees, and the position angle precision calculated by using the low-cost encoder is greatly reduced.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide an orthogonal error compensation method based on a sine and cosine position encoder so as to solve the problems in the background art.
The aim of the invention can be achieved by the following technical scheme:
A quadrature error compensation method based on a sine and cosine position encoder comprises the following steps:
step 1, detecting and sampling a sine and cosine encoder voltage signal:
Detecting sine and cosine voltage signals u sin5 and u cos5 output by the position encoder, performing amplitude scaling through a level conversion chip or an operational amplifier to obtain sine and cosine voltage signals u sin3 and u cos3 which can be sampled by an MCU, and converting the voltage signals into digital variables D sindata and D cosdata through an AD sampling module of the MCU;
step 2, amplitude scaling and zero point offset of sine and cosine digital variables are carried out:
Taking sine and cosine digital variables D sindata and D cosdata obtained in the step 1, calculating the maximum value, the minimum value and the median of the two variables, and scaling and shifting the amplitude and the midpoint to obtain sine and cosine variables D sincorr and D coscorr with standard amplitude ranges of-pi and median values of 0;
step 3, quadrature error calculation of sine and cosine variables is carried out:
The values of the sine variable D sincorr and the cosine variable D coscorr at each moment when the motor rotates at a constant speed are recorded, and the amplitude A sin,Acos, the frequency f sin,fcos and the initial phase of the two variables corresponding to the current rotating speed are calculated The expressions D sincorr (t) and D coscorr (t) of sine and cosine variables relative to time can be obtained, and the pair is obtained after confirming that the amplitude frequency is consistentAndMaking a difference to obtain a true sine and cosine phase difference
Step 4, calculating ideal cosine variable:
the true sine and cosine phase difference calculated by the step3 Quadrature error obtained by making a difference from the ideal quadrature phase difference pi/2Calculating an ideal cosine variable expression D cosideal (t) orthogonal to the sine variable expression D sincorr (t) based on the sampled cosine variable expression D coscorr (t), wherein the amplitude and the frequency are the same as those of the expression D coscorr (t), and the initial phase is
Step 5, calculating a position angle after quadrature error compensation:
D sincorr (t) and D coscorr (t) obtained in the step 3 are used for fitting the D cosideal (t) obtained in the step 4, relational expressions of D cosideal, D sincorr and D coscorr are obtained, real-time ideal cosine signals are obtained through real-time sampled sine and cosine signals, the real sine variable D sincorr and the calculated D cosideal are subjected to atan2 operation to obtain a compensated position angle, the position angle is used for vector control interruption PARK and IPark conversion, the accuracy and effect of vector control of the permanent magnet motor are improved, and stable operation of the permanent magnet motor is ensured.
Preferably, the sine and cosine voltage signals u sin5 and u cos5 output by the encoder in the step 1 are voltages with sine variation between 0V and 5V, and the amplitude ranges of the sine and cosine voltage signals u sin3 and u cos3 for the MCU to sample are 0V to 3V.
Preferably, the expressions D sincorr (t) and D coscorr (t) of the sine and cosine variables in the step 3 with respect to time are as follows:
Where A sin,Acos is the amplitude of D sincorr (t) and D coscorr (t), respectively, and ideally A sin＝Acos＝π,fsin,fcos is the frequency of D sincorr (t) and D coscorr (t), respectively, and ideally is the same and is the mechanical angular frequency corresponding to the current speed of constant speed operation.
Preferably, in the step 3, when the quadrature error exists in the sine and cosine variable and the quadrature error does not exist in the sine and cosine variable, the relationship between the position angle and the quadrature error exists is as follows:
θerr＝θ-θcomp
where θ err is the theoretical error in the mechanical position angle at the time of uncompensated.
Preferably, the ideal cosine variable expression D cosideal (t) in the step 4 is as follows:
Preferably, the position angle calculation expression after the quadrature error compensation in the step5 is as follows:
θcomp＝atan2(Dsincorr(t),Dcosideal(t))
Wherein, theta comp is the mechanical position angle after compensation;
the position angle calculation expression before quadrature error compensation is as follows:
θ＝atan2(Dsincorr(t),Dcoscorr(t))
Wherein θ is an uncompensated mechanical position angle;
The expression of D cosideal (t) fitted by D sincorr (t) and D coscorr (t) is shown as follows:
Dcosideal(t)＝p00+p10Dsincorr(t)+p01Dcoscorr(t)
where p00, p10 and p01 are coefficients obtained by curve fitting.
The invention has the beneficial effects that:
1. According to the invention, an ideal cosine waveform is fitted according to the sampled sine and cosine waveform with the orthogonal error by a curve fitting method, so that the problem of overlarge position error caused by the orthogonal error is solved, and the stability of a control system is improved while the cost is reduced by adopting a low-cost sine and cosine encoder;
2. The correction method can be realized only by the voltage sampling value of the original sine and cosine encoder without motor parameters, and the correction object only relates to the encoder and is irrelevant to the motor, so that the correction method has the advantages of good universality, convenient use, higher direct compensation precision, better effect and easier realization method compared with the direct compensation of the position angle error;
3. According to the invention, by using an off-line calculation curve fitting method, excessive calculation power of the MCU is not required, and only two additional trigonometric function operations are required in the MCU, so that the number of instruction cycles required for the MCU (such as DSP 280049C, DSP and 28075) with a Trigonometric Mathematical Unit (TMU) is less.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described, and it will be obvious to those skilled in the art that other drawings can be obtained according to these drawings without inventive effort.
FIG. 1 is a flow chart of the quadrature error compensation method of the present invention;
FIG. 2 is a graph of theoretical error values of the mechanical position angle in the presence of quadrature errors in the present invention;
FIG. 3 is a waveform diagram of the measured mechanical angle error of the low cost sine and cosine encoder of the present invention;
FIG. 4 is a graph showing the sampled sine and cosine waveforms compared with an ideal cosine waveform in the present invention;
Fig. 5 is a schematic diagram of an ideal cosine waveform curve fitting in accordance with the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, the quadrature error compensation method based on the sine and cosine position encoder of the present invention firstly samples the sine and cosine waveform with quadrature error generated directly by the sine and cosine encoder through AD, scales the sine and cosine waveform to be between-pi and pi through operations such as amplitude scaling, zero point offset, etc., rotates the motor at a constant speed to record the value of the sine and cosine variable and calculate the corresponding sine and cosine phase, establishes an ideal cosine waveform function, obtains an expression of the ideal cosine waveform through curve fitting, and calculates the compensated position angle according to the sampled sine waveform and the ideal cosine waveform, so as to eliminate the position error caused by non-orthogonality.
The quadrature error compensation method of the invention comprises the following steps:
Step 1, detecting and sampling a sine and cosine encoder voltage signal:
Detecting sine and cosine voltage signals u sin5 and u cos5 (generally, sine-changing voltages between 0 and 5V) output by a position encoder, performing amplitude scaling through a level conversion chip or an operational amplifier to obtain sine and cosine voltage signals u sin3 and u cos3 with amplitude ranges of 0 to 3V, which can be sampled by an MCU, and converting the voltage signals into digital variables D sindata and D cosdata (taking a 12-bit AD sampling port with AD sampling reference voltage of 3V as an example) through an AD sampling module of the MCU;
Step 2, amplitude scaling and zero point offset of sine and cosine digital variables:
Taking sine and cosine digital variables D sindata and D cosdata obtained in the step 1, calculating the maximum value, the minimum value and the median of the two variables, and scaling and shifting the amplitude and the midpoint to obtain sine and cosine variables D sincorr and D coscorr with standard amplitude ranges of-pi and median values of 0;
step 3, quadrature error calculation of sine and cosine variables:
The values of the sine variable D sincorr and the cosine variable D coscorr at each moment when the motor rotates at a constant speed are recorded (at least two complete periods are recorded to reduce random errors), and the amplitude A sin,Acos, the frequency f sin,fcos and the initial phase of the two variables corresponding to the current rotating speed are calculated The expressions D sincorr (t) and D coscorr (t) of sine and cosine variables relative to time can be obtained, and the pair is obtained after confirming that the amplitude frequency is consistentAndMaking a difference to obtain a true sine and cosine phase difference
Wherein, the expressions D sincorr (t) and D coscorr (t) of the sine and cosine variables with respect to time are respectively:
Wherein, A sin,Acos is the amplitude of D sincorr (t) and D coscorr (t), and A sin＝Acos＝π,fsin,fcos is the frequency of D sincorr (t) and D coscorr (t), and is the mechanical angular frequency corresponding to the current constant-speed running speed;
when quadrature errors exist in sine and cosine variables and the quadrature errors do not exist in the sine and cosine variables, the relationship between the position angle and the existing quadrature errors is as follows:
θerr＝θ-θcomp
where θ err is the theoretical error in the mechanical position angle at the time of uncompensated.
Step 4, calculating an ideal cosine variable:
taking the true sine and cosine phase difference calculated in the step3 Quadrature error obtained by making a difference from the ideal quadrature phase difference pi/2Calculating an ideal cosine variable expression D cosideal (t) orthogonal to the sine variable expression D sincorr (t) based on the sampled cosine variable expression D coscorr (t), wherein the amplitude and the frequency are the same as those of the expression D coscorr (t), and the initial phase is
Wherein the ideal cosine variable expression D cosideal (t) can be expressed as:
step 5, calculating a position angle after quadrature error compensation:
D sincorr (t) and D coscorr (t) obtained in the step 3 are used for fitting the D cosideal (t) obtained in the step 4, relational expressions of D cosideal, D sincorr and D coscorr are obtained, real-time ideal cosine signals are obtained through real-time sampled sine and cosine signals, the real sine variable D sincorr and the calculated D cosideal are subjected to atan2 operation to obtain a compensated position angle, the position angle is used for vector control interruption PARK and IPark conversion, the accuracy and effect of vector control of the permanent magnet motor are improved, and stable operation of the permanent magnet motor is ensured;
the position angle calculation expression after the quadrature error compensation is as follows:
θcomp＝atan2(Dsincorr(t),Dcosideal(t))
Where θ comp is the compensated mechanical position angle.
The position angle calculation expression before quadrature error compensation is:
θ＝atan2(Dsincorr(t),Dcoscorr(t))
Where θ is the uncompensated mechanical position angle.
The expression of D cosideal (t) fitted by D sincorr (t) and D coscorr (t) is:
Dcosideal(t)＝p00+p10Dsincorr(t)+p01Dcoscorr(t)
where p00, p10 and p01 are coefficients obtained by curve fitting.
It is obtained that when there is an uncompensated quadrature error, the error of the position angle is not a constant value but varies with twice the mechanical angular frequency, which also results in that the position angle error is difficult to be directly compensated. Compensating for errors before atan2 computation is therefore a better solution.
The ideal cosine waveform is fitted according to the sampled sine and cosine waveform with the quadrature error, and then atan2 operation is carried out, so that the mechanical position angle error can be obviously reduced, a good permanent magnet motor vector control effect can be obtained when a low-cost sine and cosine encoder is adopted, and the method is also suitable for error correction of other sine and cosine functions with the quadrature error.
Fig. 2 is a graph of mechanical position angle error for a theoretical quadrature error of 3.77 °. The maximum mechanical position angle error is now about 0.065rad, i.e. 3.724 °. Taking a permanent magnet motor with 5 pairs of poles as an example, the maximum electrical angle error can reach about 18.6 degrees, and the normal vector control operation of the motor is seriously affected.
Fig. 3 is a waveform diagram of a measured mechanical angle error of a low cost sine and cosine encoder with a measured quadrature error of about 3.77 °. Wherein the dynamically changing position angle error caused by the quadrature error ranges from about 0.065rad (the remaining error being the static error caused by other reasons) substantially coincides with the theoretical value. This figure verifies the source of dynamic position error for low cost sine and cosine encoders.
Fig. 4 is a graph comparing a sampled sine and cosine waveform with a fitted ideal cosine waveform when the motor is running at a constant speed of 240 rpm.
Fig. 5 is a schematic diagram of curve fitting of an ideal cosine waveform by fitting a sampled sine and cosine waveform.
In the description of the present specification, the descriptions of the terms "one embodiment," "example," "specific example," and the like, mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims.
Claims (7)
1. The quadrature error compensation method based on the sine and cosine position encoder is characterized by comprising the following steps:
step 1, detecting and sampling a sine and cosine encoder voltage signal:
Detecting sine and cosine voltage signals u sin5 and u cos5 output by the position encoder, performing amplitude scaling through a level conversion chip or an operational amplifier to obtain sine and cosine voltage signals u sin3 and u cos3 which can be sampled by an MCU, and converting the voltage signals into digital variables D sindata and D cosdata through an AD sampling module of the MCU;
step 2, amplitude scaling and zero point offset of sine and cosine digital variables are carried out:
Taking sine and cosine digital variables D sindata and D cosdata obtained in the step 1, calculating the maximum value, the minimum value and the median of the two variables, and scaling and shifting the amplitude and the midpoint to obtain sine and cosine variables D sincorr and D coscorr with standard amplitude ranges of-pi and median values of 0;
step 3, quadrature error calculation of sine and cosine variables is carried out:
The values of the sine variable D sincorr and the cosine variable D coscorr at each moment when the motor rotates at a constant speed are recorded, and the amplitude A sin,Acos, the frequency f sin,fcos and the initial phase of the two variables corresponding to the current rotating speed are calculated The expressions D sincorr (t) and D coscorr (t) of sine and cosine variables relative to time can be obtained, and the pair is obtained after confirming that the amplitude frequency is consistentAndMaking a difference to obtain a true sine and cosine phase difference
Step 4, calculating ideal cosine variable:
the true sine and cosine phase difference calculated by the step3 Quadrature error obtained by making a difference from the ideal quadrature phase difference pi/2Calculating an ideal cosine variable expression D cosideal (t) orthogonal to the sine variable expression D sincorr (t) based on the sampled cosine variable expression D coscorr (t), wherein the amplitude and the frequency are the same as those of the expression D coscorr (t), and the initial phase is
Step 5, calculating a position angle after quadrature error compensation:
D sincorr (t) and D coscorr (t) obtained in the step 3 are used for fitting the D cosideal (t) obtained in the step 4, relational expressions of D cosideal, D sincorr and D coscorr are obtained, real-time ideal cosine signals are obtained through real-time sampled sine and cosine signals, the real sine variable D sincorr and the calculated D cosideal are subjected to atan2 operation to obtain a compensated position angle, the position angle is used for vector control interruption PARK and IPark conversion, the accuracy and effect of vector control of the permanent magnet motor are improved, and stable operation of the permanent magnet motor is ensured.
2. The quadrature error compensation method based on the sine and cosine position encoder as set forth in claim 1, wherein the sine and cosine voltage signals u sin5 and u cos5 outputted from the encoder in the step 1 are voltages with sine variation between 0 and 5V, and the amplitude ranges of the sine and cosine voltage signals u sin3 and u cos3 for the MCU to sample are 0 to 3V.
3. The quadrature error compensation method of claim 1, wherein the expressions D sincorr (t) and D coscorr (t) of the sine and cosine variable with respect to time in the step 3 are as follows:
Where A sin,Acos is the amplitude of D sincorr (t) and D coscorr (t), respectively, and ideally A sin＝Acos＝π,fsin,fcos is the frequency of D sincorr (t) and D coscorr (t), respectively, and ideally is the same and is the mechanical angular frequency corresponding to the current speed of constant speed operation.
4. The quadrature error compensation method based on the sine and cosine position encoder as set forth in claim 1, wherein, in the step 3, when the sine and cosine variable has a quadrature error and is not compensated, a relationship between a position angle and the quadrature error is as follows:
θerr＝θ-θcomp
where θ err is the theoretical error in the mechanical position angle at the time of uncompensated.
5. The quadrature error compensation method based on the sine and cosine position encoder as set forth in claim 1, wherein the ideal cosine variable expression D cosideal (t) in the step 4 is as follows:
6. the quadrature error compensation method based on the sine and cosine position encoder as set forth in claim 1, wherein the quadrature error compensated position angle calculation expression in the step 5 is as follows:
θcomp＝atan2(Dsincorr(t),Dcosideal(t))
Wherein, theta comp is the mechanical position angle after compensation;
the position angle calculation expression before quadrature error compensation is as follows:
θ＝atan2(Dsincorr(t),Dcoscorr(t))
Wherein θ is an uncompensated mechanical position angle;
The expression of D cosideal (t) fitted by D sincorr (t) and D coscorr (t) is shown as follows:
Dcosideal(t)＝p00+p10Dsincorr(t)+p01Dcoscorr(t)
where p00, p10 and p01 are coefficients obtained by curve fitting.
7. The quadrature error compensation method of claim 1, wherein the quadrature error compensation method is also applicable to other quadrature error-based sine and cosine functions for error correction.
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