CN115589180B - A quadrature error compensation method based on sine-cosine position encoder - Google Patents

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

A quadrature error compensation method based on sine-cosine position encoder

Technical Field

The invention belongs to the technical field of motor control, and in particular relates to an orthogonal error compensation method based on a sine-cosine position encoder.

Background Art

Permanent magnet motors have a simple structure, high efficiency and a wide range of applications. Permanent magnet motors require position feedback for effective control. However, the cost of using high-precision position sensors is too high, so lower-cost encoder solutions are often used in actual products. Usually, high-precision position sensors, such as photoelectric encoders and resolvers, can cost hundreds of dollars, and the cost in mass production is almost unacceptable. In contrast, low-cost sine and cosine encoders have a simple structure and usually only require a Hall sensor with related conditioning circuits to achieve a cost of tens or even less. In addition, sine and cosine encoders can output absolute position, and are even more convenient to use than more expensive incremental photoelectric encoders. Compared with ordinary Hall sensors that can only achieve partition judgment accuracy, the accuracy is greatly improved, so they are often used in corporate products that require sine wave control of permanent magnet motors.

The sine and cosine position encoder usually generates two mutually orthogonal sine and cosine voltage waveforms. After AD sampling, the MCU scales and offsets the amplitude of the sine and cosine voltage to between -π and π, and obtains the current mechanical position angle through atan2 operation. However, the sine and cosine waveforms generated by low-cost sine and cosine encoders in actual applications are usually not accurate. The main errors include unequal sine and cosine amplitudes, median offset, harmonics, and non-orthogonality. Among them, the unequal amplitudes and median offset can be basically eliminated by scaling and offsetting after sampling. The harmonic problem can be reduced by adding a follower circuit to the sampling circuit, software and hardware filtering, etc., but the problem caused by the non-orthogonality of the sine and cosine waveforms is relatively difficult to eliminate. The phase difference between the sine and cosine voltage waveforms of high-precision sine and cosine encoders is basically π/2, and the error is generally less than ±0.5°, but the phase difference between the sine and cosine voltage waveforms of low-cost sine and cosine encoders is much different from π/2. The actual low-cost sine and cosine encoder products that have been used can even have an error of 3.77°. The accuracy of the position angle calculated when using such low-cost encoders is greatly reduced.

Summary of the invention

In view of the deficiencies in the prior art, an object of the present invention is to provide an orthogonal error compensation method based on a sine-cosine position encoder to solve the problems raised in the above background technology.

The purpose of the present invention can be achieved through the following technical solutions:

A quadrature error compensation method based on a sine-cosine position encoder comprises the following steps:

Step 1: Detect and sample the sine-cosine encoder voltage signal:

Detect the sine and cosine voltage signals u _sin5 and u _cos5 output by the position encoder, and obtain sine and cosine voltage signals u _sin3 and u _cos3 for MCU sampling through the level conversion chip or operational amplifier, and convert the voltage signals into digital variables D _sindata and D _cosdata through the AD sampling module of the MCU;

Step 2: Perform amplitude scaling and zero point offset of sine and cosine digital variables:

Take the sine and cosine digital variables D _sindata and D _cosdata obtained in step 1, calculate the maximum, minimum and median of the two variables, and obtain the standard sine and cosine variables D _sincorr and D _coscorr with an amplitude range of -π to π and a median of 0 by scaling and offsetting the amplitude and the midpoint;

Step 3: Calculate the orthogonal error of the sine and cosine variables:

Record the values of the sine and cosine variables D _sincorr and D _coscorr at each moment when the motor rotates at a constant speed, and calculate the amplitude A _sin , A _cos , frequency f _sin , f _cos and initial phase of these two variables corresponding to the current speed The expressions of sine and cosine variables with respect to time, D _sincorr (t) and D _coscorr (t), can be obtained. After confirming that the amplitude and frequency are consistent, and Do the difference to get the real sine and cosine phase difference

Step 4: Calculate the ideal cosine variable:

The actual sine and cosine phase difference calculated in step 3 The quadrature error is obtained by subtracting the ideal quadrature phase difference of π/2. Based on the sampled cosine variable expression D _coscorr (t), an ideal cosine variable expression D _cosideal (t) orthogonal to the sine variable expression D _sincorr (t) is calculated. The amplitude and frequency are the same as D _coscorr (t), and the initial phase is

Step 5: Calculate the position angle after orthogonal error compensation:

Use D _sincorr (t) and D _coscorr (t) obtained in step 3 to fit D _cosideal (t) obtained in step 4, and obtain the relationship expression between D _cosideal and D _sincorr and D _coscorr , so as to obtain the real-time ideal cosine signal through the real-time sampled sine and cosine signals, and perform atan2 operation on the real sinusoidal variable D _sincorr and the calculated D _cosideal to obtain the compensated position angle, which is used for vector control interrupt PARK and IPark transformation, thereby improving the accuracy and effect of permanent magnet motor vector control and ensuring the stable operation of the permanent magnet motor.

Preferably, the sine and cosine voltage signals u _sin5 and u _cos5 output by the encoder in step 1 are voltages that vary sinusoidally between 0 and 5V, and the amplitude range of the sine and cosine voltage signals u _sin3 and u _cos3 available for sampling by the MCU is 0 to 3V.

Preferably, the expressions of the sine and cosine variables with respect to time in step 3, D _sincorr (t) and D _coscorr (t), are as follows:

Wherein, A _sin , A _cos are the amplitudes of D _sincorr (t) and D _coscorr (t), respectively. Ideally, A _sin =A _cos =π. f _sin , f _cos are the frequencies of D _sincorr (t) and D _coscorr (t), respectively. Ideally, they are equal and are the mechanical angular frequencies corresponding to the current uniform speed.

Preferably, in step 3, when the sine and cosine variables have orthogonal errors and have not been compensated, the relationship between the position angle and the existing orthogonal errors is as follows:

θ _err = θ - θ _comp

Where θ _err is the theoretical error of the uncompensated mechanical position angle.

Preferably, the ideal cosine variable expression D _cosideal (t) in step 4 is as follows:

Preferably, the position angle calculation expression after orthogonal error compensation in step 5 is as follows:

θ _comp =atan2(D _sincorr (t),D _cosional (t))

Where, θ _comp is the mechanical position angle after compensation;

The position angle calculation expression before orthogonal error compensation is as follows:

θ=atan2(D _sincorr (t),D _coscorr (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 as follows:

D _cosideal (t)＝p00+p10D _sincorr (t)+p01D _coscorr (t)

Where p00, p10 and p01 are the coefficients obtained by curve fitting.

Beneficial effects of the present invention:

1. The present invention uses a curve fitting method to fit an ideal cosine waveform according to the sampled sine and cosine waveforms with orthogonal errors, so as to reduce the problem of excessive position error caused by the orthogonal error. While using a low-cost sine and cosine encoder to reduce costs, the stability of the control system is improved;

2. The present invention does not require motor parameters, but only requires the voltage sampling value of the original sine-cosine encoder to be implemented. The correction object only involves the encoder and has nothing to do with the motor. Therefore, the present invention has good versatility and is easy to use. Compared with direct compensation of the position angle error, the present invention has higher accuracy, better effect and easier implementation method.

3. The present invention adopts an offline curve fitting method, which does not need to occupy too much computing power of the MCU. Only two additional trigonometric function operations are required in the MCU. For MCUs with a trigonometric math unit (TMU) (such as DSP 280049C, DSP28075), fewer instruction cycles are required.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

FIG1 is a flow chart of a quadrature error compensation method of the present invention;

FIG2 is a diagram showing theoretical error values of mechanical position angles when orthogonal errors exist in the present invention;

FIG3 is a waveform diagram of the mechanical angle error measured by the low-cost sine-cosine encoder of the present invention;

FIG4 is a comparison diagram of the sampled sine and cosine waveforms and the ideal cosine waveform in the present invention;

FIG. 5 is a schematic diagram of an ideal cosine waveform curve fitting in the present invention.

DETAILED DESCRIPTION

The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Please refer to FIG. 1 , which is a quadrature error compensation method based on a sine-cosine position encoder. The sine-cosine waveform with quadrature error directly generated by the sine-cosine encoder is first sampled through AD, and the sine-cosine waveform is scaled to between -π and π through operations such as amplitude scaling and zero point offset. The motor is rotated at a constant speed to record the values of the sine-cosine variables and calculate the corresponding sine-cosine phases. An ideal cosine waveform function is established and the expression of the ideal cosine waveform is obtained by curve fitting. The compensated position angle is then calculated based on the sampled sine waveform and the ideal cosine waveform to eliminate the position error caused by non-orthogonality.

The orthogonal error compensation method of the present invention comprises the following steps:

Step 1: Detection and sampling of sine-cosine encoder voltage signals:

Detect the sine and cosine voltage signals u _sin5 and u _cos5 (usually a voltage with a sinusoidal variation between 0 and 5 V) output by the position encoder, and obtain sine and cosine voltage signals u _sin3 and u _cos3 with an amplitude range of 0 to 3 V for MCU sampling through a level conversion chip or an operational amplifier. The voltage signals are converted into digital variables D _sindata and D _cosdata with an amplitude range of 0 to 4095 (taking a 12-bit AD sampling port with an AD sampling reference voltage of 3 V as an example) through the AD sampling module of the MCU.

Step 2: Amplitude scaling and zero offset of sine and cosine digital variables:

Take the sine and cosine digital variables D _sindata and D _cosdata obtained in step 1, calculate the maximum, minimum and median of the two variables, and obtain the standard sine and cosine variables D _sincorr and D _coscorr with an amplitude range of -π to π and a median of 0 by scaling and offsetting the amplitude and the midpoint;

Step 3: Calculation of orthogonal errors of sine and cosine variables:

Record the values of the sine and cosine variables D _sincorr and D _coscorr at each moment when the motor rotates at a constant speed (record at least two complete cycles to reduce random errors), and calculate the amplitude A _sin , A _cos , frequency f _sin , f _cos and initial phase of these two variables corresponding to the current speed. The expressions of sine and cosine variables with respect to time, D _sincorr (t) and D _coscorr (t), can be obtained. After confirming that the amplitude and frequency are consistent, and Do the difference to get the real sine and cosine phase difference

Among them, the expressions of sine and cosine variables with respect to time are D _sincorr (t) and D _coscorr (t), respectively:

Wherein, A _sin , A _cos are the amplitudes of D _sincorr (t) and D _coscorr (t), respectively. Ideally, A _sin = A _cos = π. f _sin , f _cos are the frequencies of D _sincorr (t) and D _coscorr (t), respectively. Ideally, they are equal and are the mechanical angular frequencies corresponding to the current uniform speed.

When there is an orthogonal error in the sine and cosine variables and they are not compensated, the relationship between the position angle and the existing orthogonal error is:

θ _err = θ - θ _comp

Where θ _err is the theoretical error of the uncompensated mechanical position angle.

Step 4: Calculation of ideal cosine variables:

Take the actual sine and cosine phase difference calculated in step 3 The quadrature error is obtained by subtracting the ideal quadrature phase difference of π/2. Based on the sampled cosine variable expression D _coscorr (t), an ideal cosine variable expression D _cosideal (t) orthogonal to the sine variable expression D _sincorr (t) is calculated. The amplitude and frequency are the same as D _coscorr (t), and the initial phase is

Among them, the ideal cosine variable expression D _cosideal (t) can be expressed as:

Step 5: Position angle calculation after orthogonal error compensation:

Use D _sincorr (t) and D _coscorr (t) obtained in step 3 to fit D _cosideal (t) obtained in step 4, and obtain the relationship expression between D _cosideal and D _sincorr and D _coscorr , so as to obtain the real-time ideal cosine signal through the real-time sampled sine and cosine signals, and perform atan2 operation on the real sinusoidal variable D _sincorr and the calculated D _cosideal to obtain the compensated position angle, which is used for vector control interrupt PARK and IPark transformation, so as to improve the accuracy and effect of permanent magnet motor vector control and ensure the stable operation of the permanent magnet motor;

Among them, the calculation expression of the position angle after orthogonal error compensation is:

θ _comp =atan2(D _sincorr (t),D _cosional (t))

Where θ _comp is the compensated mechanical position angle.

The position angle calculation expression before orthogonal error compensation is:

θ=atan2(D _sincorr (t),D _coscorr (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:

D _cosideal (t)＝p00+p10D _sincorr (t)+p01D _coscorr (t)

Where p00, p10 and p01 are the coefficients obtained by curve fitting.

It can be seen that when there is an uncompensated orthogonal error, the position angle error is not a constant value, but changes with twice the mechanical angular frequency, which also makes it difficult to directly compensate the position angle error. Therefore, compensating the error before atan2 calculation is a better solution.

An ideal cosine waveform is fitted based on the sampled sine-cosine waveform with orthogonal error, and then an atan2 operation is performed, which can significantly reduce the mechanical position angle error. When a low-cost sine-cosine encoder is used, a good permanent magnet motor vector control effect can be achieved. The present invention is also applicable to other sine-cosine functions with orthogonal errors for error correction.

Figure 2 shows the mechanical position angle error when the theoretical quadrature error is 3.77°. At this time, the maximum mechanical position angle error is about 0.065rad, or 3.724°. Taking a 5-pole permanent magnet motor as an example, the maximum electrical angle error can reach about 18.6°, which seriously affects the normal vector control operation of the motor.

Figure 3 is a waveform diagram of the measured mechanical angle error of a low-cost sine-cosine encoder with a measured quadrature error of approximately 3.77°. The dynamic position angle error range caused by the quadrature error is approximately 0.065 rad (the remaining errors are static errors caused by other reasons), which is basically consistent with the theoretical value. This figure verifies the source of the dynamic position error of the low-cost sine-cosine encoder.

FIG4 is a comparison diagram of the sine and cosine waveforms sampled when the motor runs at a constant speed of 240 rpm and the fitted ideal cosine waveforms.

FIG. 5 is a schematic diagram of curve fitting of fitting an ideal cosine waveform by fitting the sampled sine and cosine waveforms.

In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

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,A_cos, the frequency f _sin,f_cos 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,A_cos is the amplitude of D _sincorr (t) and D _coscorr (t), respectively, and ideally A _sin＝A_cos＝π,f_sin,f_cos 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:

θ_err＝θ-θ_comp

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:

θ_comp＝atan2(D_sincorr(t),D_cosideal(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(D_sincorr(t),D_coscorr(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:

D_cosideal(t)＝p00+p10D_sincorr(t)+p01D_coscorr(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.