CN114465546A - Angular position acquisition method based on signal reconstruction and discrete ESO - Google Patents

Angular position acquisition method based on signal reconstruction and discrete ESO Download PDF

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CN114465546A
CN114465546A CN202111564227.5A CN202111564227A CN114465546A CN 114465546 A CN114465546 A CN 114465546A CN 202111564227 A CN202111564227 A CN 202111564227A CN 114465546 A CN114465546 A CN 114465546A
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angular position
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宋欣达
刘博�
史阳阳
李海涛
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Beihang University
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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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/12—Observer control, e.g. using Luenberger observers or Kalman filters
    • 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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/14—Estimation or adaptation of motor parameters, e.g. rotor time constant, flux, speed, current or voltage
    • 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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/18—Controlling the angular speed together with angular position or phase

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Abstract

An ESO (extended state observer) is used for a low-speed and time-varying speed system for acquiring angular position information based on a linear Hall sensor, firstly, two paths of linear Hall sensor signals are normalized to eliminate the influence of unequal signal amplitudes, and two paths of signals with the amplitude of 1 are obtained; secondly, performing signal reconstruction on the two paths of signals to obtain sine and cosine signals inhibiting most harmonic wave quantity; and finally, aiming at the influence of factors such as residual error, unaccounted system error and the like, a discrete ESO method is adopted to obtain the angular position information meeting the precision requirement.

Description

Angular position acquisition method based on signal reconstruction and discrete ESO
Technical Field
The invention relates to a motor control technology, in particular to an angular position acquisition method based on signal reconstruction and discrete ESO (electronic stability and optimization), wherein ESO (extended state observer) is an extended state observer, aiming at a low-speed and time-varying speed system for acquiring angular position information based on a linear Hall sensor, firstly, two paths of linear Hall sensor signals are subjected to normalization processing to eliminate the influence of unequal signal amplitudes, and two paths of signals with the amplitude of 1 are obtained; secondly, performing signal reconstruction on the two paths of signals to obtain sine and cosine signals with most harmonic quantity suppressed; and finally, aiming at the influence of factors such as residual errors, unaccounted system errors and the like, obtaining the angular position information meeting the precision requirement by adopting a discrete ESO method.
Background
The design of the frame servo motor is limited by the overall size, weight and cost of the spacecraft, and a harmonic reducer is adopted to achieve the purpose of increasing the output torque and reducing the size of the motor. However, due to the nonlinear transmission characteristics of the harmonic reducer, the angular positions of the motor end and the load end cannot be kept in a fixed proportional relationship, and the angular position information of the load end cannot be directly converted and used for the control of the motor end, so that an angular position sensor needs to be installed at the motor end. The linear Hall sensor has small volume, light weight and low cost, and the angular position analysis precision can also meet the requirement on the angular position precision in the frame servo control, so the frame servo motor adopts the linear Hall sensor to acquire the angular position information.
In an ideal state, the motor needs to strictly select a permanent magnet, an ideal structural design, no zero drift of the sensor and other conditions during processing and assembly, so that a relatively ideal signal can be obtained when the linear Hall sensor detects the magnetic field in the motor, and the accuracy of directly analyzed angular position information is relatively high. However, the above operation period is long, and the labor and material resources are also large, so that the ideal conditions are difficult to completely satisfy. In order to meet universality, the motor is a common permanent magnet synchronous servo motor, and the ideal conditions are not achieved completely, so that the linear Hall sensor has a large number of harmonic waves in a magnetic field detected in the motor, and the amplitudes are not equal. At present, the linear Hall sensor is mostly applied to medium and high speed motors to analyze angular positions, and signal extraction is carried out according to fundamental frequency information. Therefore, it is a difficult problem to extract angular position information satisfying the accuracy requirement from the signal detected by the linear hall sensor in the low-speed, time-varying state. The angular position accuracy obtained by direct solution is far from the requirement of a servo motor of a frame system and must be processed. However, most of the research on detecting position information by linear hall is focused on medium and high speed systems, such as a frequency signal extraction method, a quadrature Phase Locked Loop (PLL), etc., which are based on fundamental frequency information of a processed signal during normal operation, while a frame servo system is usually operated in a steady speed and variable speed state, and cannot provide fundamental frequency information when the system is in a time variable speed state, so that the method, such as the frequency signal extraction method, etc., cannot be applied to the frame servo system.
The linear hall sensor works by detecting the magnetic field strength, converting the magnetic signal into an electrical signal and sending the electrical signal to a controller to obtain angular position information. However, the magnetic field signal detected by the linear hall sensor is very easily interfered, so that the detection signal is not a standard sine and cosine signal, and the resolution precision of the finally obtained angular position is reduced. The cascaded Kalman filtering method with phase compensation is used for realizing the suppression of signal harmonic waves and improving the angular position precision. Through further deep analysis, the invention provides a method based on signal reconstruction and a discrete Extended State Observer (ESO) for solving the problem that parameters of cascaded Kalman filtering are not easy to adjust, firstly, the influence of unequal signal amplitudes is eliminated by normalizing two signals, and two signals with the amplitude of 1 are obtained; secondly, signal reconstruction is carried out on the signal, most harmonic quantity is suppressed, and a relatively standard sine and cosine signal is obtained; and finally, aiming at the influence of factors such as residual errors, unaccounted system errors and the like, obtaining the angular position information capable of meeting the precision requirement by adopting a discrete extended state observer method.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method comprises the steps that an ESO (extended state observer) is provided, and aiming at a low-speed and time-varying system for acquiring angular position information based on a linear Hall sensor, two paths of linear Hall sensor signals are normalized to eliminate the influence of unequal signal amplitudes, so that two paths of signals with the amplitude of 1 are obtained; secondly, performing signal reconstruction on the two paths of signals to obtain sine and cosine signals with most harmonic quantity suppressed; and finally, aiming at the influence of factors such as residual errors, unaccounted system errors and the like, obtaining the angular position information meeting the precision requirement by adopting a discrete ESO method.
The technical solution of the invention is as follows:
an angular position acquisition method based on signal reconstruction and discrete ESO, characterized by comprising the following steps:
step 1, normalizing two paths of linear Hall sensor signals detected from the angular position of a frame servo motor to eliminate the influence of unequal signal amplitudes and obtain two paths of signals with the amplitude of 1;
step 2, performing signal reconstruction on the two paths of signals to obtain sine and cosine signals with most harmonic quantity suppressed;
and 3, aiming at the influence of residual errors and unaccounted system error factors, obtaining angular position information capable of meeting the precision requirement by adopting a discrete extended state observer method.
The step 1 comprises redefining the information of the two paths of linear hall sensor signals as:
Figure BDA0003421674080000021
in the formula (1), HsIndicating a detected sinusoidal signal, HcShowing the detected cosine signal, alpha and beta showing the amplitude of the output signals of the two linear Hall sensors, alpha is not equal to beta, theta (k) is the electrical angle position of the motor rotor, AiAnd BiRepresenting the amplitude of each harmonic, wherein i is 3,5,7,9, and k represents a discrete time point, although the formula (1) gives the amplitude of each order harmonic relative to the fundamental frequency, the problem of unequal amplitudes still exists, and the execution of the subsequent algorithm is inconvenient, so that the obtained signals are normalized to obtain signals with equal amplitudes;
Figure BDA0003421674080000031
in the formula (2), θdetRepresenting the directly resolved angular position, Hs_1And Hc_1Respectively representing a sine signal and a cosine signal after normalization;
since the coefficients of the original signal can be obtained approximately, the coefficients of the normalized signal can also be obtained, which is expressed as:
Figure BDA0003421674080000032
in the formula (3), CiAnd (3), 5,7 and 9, combining the formula (1) and the formula (2), and obtaining the ideal electrical angle position of the rotor of the motor by theta:
Ci＝0.086 0.084 0.0075 0.014 (4)。
the signal reconstruction in the step 2 comprises: the method comprises the following steps of reconstructing a detection signal on the basis of the property that the relative magnitude relation between each order of harmonic amplitude and fundamental frequency amplitude is basically unchanged at low speed:
according to polynomial equation (5), the harmonics of each order can be expressed as a function of the fundamental frequency as follows:
sinnθ(k)＝fsinθ(k) (5)
in the formula (5), n represents the order of harmonic, n is a positive integer, and f is a function sign;
the signal is reconstructed according to equation (6) as follows:
Figure BDA0003421674080000033
h in the formula (6)s_2Representing the signal obtained after reconstruction, f (-) and f1(. -) shows two functions related to a fundamental frequency signal, the harmonic content of the signal obtained after signal reconstruction processing is greatly reduced, the angular position precision is improved by a lot compared with the initial angular position precision, but the angular position error of 0.04rad still can not meet the requirement, so the sinusoidal signal after signal reconstruction is represented again as:
Hs_2(k)＝sin[θ(k)]+G[θ(k)] (7)
in equation (7), G [ θ (k) ] represents the residual error in the signal.
The step 3 comprises the following specific steps:
since the frame servo system usually works in a low-speed and time-varying state, fundamental frequency information cannot be acquired, and therefore processing is performed by adopting a state observation mode based on equation (7), and according to the correlation theory of the extended state observer ESO, the error in equation (7) is regarded as lumped disturbance, and then the state equation is expressed as:
Figure BDA0003421674080000041
in the formula (8), u (k) is a signal H obtained by signal reconstructions_2(k)，x1(k) Denotes sin [ theta (k)]，x2(k) Representing the lumped perturbation, d (k) representing the acceleration of the lumped perturbation, y (k) representing the output signal, expressed as:
Figure BDA0003421674080000042
in the formula (9), θn(k) Representing the resulting angular position, ωn(k) Expressing the finally obtained angular rate, and discretizing the corresponding observer on the basis of the state equation (8) to obtain a discrete extended observer, which is expressed as:
Figure BDA0003421674080000043
in the formula (10), e (k) represents a signal error, z1(k) And z2(k) Are respectively used for estimating x1(k) And x2(k)，h、β1And beta2Is an adjustable parameter of the discrete extended observer;
in order to solve the problem of direct current offset introduced during sine and cosine integration, discrete integration is adopted, only some points are integrated, continuous integration is avoided, and the problem can be well solved, wherein the discrete integration expression is as follows:
z2(k+1)＝z2(k)+h(-β2e(k)-z2(k-m)) (11)
in equation (11), m represents the number of integration points, so equation (10) is rewritten as:
Figure BDA0003421674080000044
harmonic content in sine signals and cosine signals obtained after the discrete ESO processing is obviously reduced, the finally obtained angular position error is about 0.01rad at most, and the angular position error meeting the control requirement of a torque motor of a frame servo system is only 0.013rad at most, so that the finally obtained angular position information can meet the requirement of the angular position precision of the frame system.
The processing mode of cosine signals in the original signals is the same as that of sine signals, and finally the angular position information meeting the precision requirement can be obtained by processing the two obtained signals as follows:
Figure BDA0003421674080000051
in the formula (13), z1sin(k) And z1cos(k) Respectively representing the output quantities of discrete ESO after the sine function signal and the cosine function signal are reconstructed by the signal and processed by adopting a discrete extended state observer method, T represents the sampling period, and thetan(k) Representing the resulting angular position, ωn(k) Representing the resulting angular rate and k the discrete time points.
The invention has the following technical effects: aiming at a low-speed and time-varying speed system for acquiring angular position information based on a linear Hall sensor, firstly, two paths of signals are normalized to eliminate the influence of unequal signal amplitudes and obtain two paths of signals with the amplitude of 1; secondly, signal reconstruction is carried out on the signal, most harmonic quantity is suppressed, and a relatively standard sine and cosine signal is obtained; and finally, aiming at the influence of factors such as residual errors, unaccounted system errors and the like, obtaining the angular position information capable of meeting the precision requirement by adopting a discrete extended state observer method. The method is simple, effective and easy to realize, can obtain the angular position information meeting the precision requirement under the complex working state, and provides the most basic guarantee for the high-precision angular velocity servo control.
The principle of the invention is as follows: firstly, two paths of signals are normalized to eliminate the influence of unequal signal amplitudes, and two paths of signals with the amplitude of 1 are obtained; secondly, signal reconstruction is carried out on the signal, most harmonic quantity is suppressed, and a relatively standard sine and cosine signal is obtained; and finally, aiming at the influence of factors such as residual errors, unaccounted system errors and the like, obtaining the angular position information capable of meeting the precision requirement by adopting a discrete extended state observer method.
Compared with the prior art, the invention has the advantages that: when the frame servo system works at a constant speed stage, the method provided by the section can effectively solve the problem that signals detected by the linear Hall sensor contain a large number of harmonic waves and are unequal in amplitude, and finally obtained angular position information at any rotating speed within a rotating speed allowable range can meet the requirement of the frame servo system on the angular position accuracy. When the frame servo system works in the speed change stage, the processed final angular position error is suppressed to about 0.01rad from the original 0.2rad, and the result shows that the angular position information obtained by the angular position acquisition method based on signal reconstruction and discrete ESO provided by the section can still meet the requirement of the angular position accuracy of the frame servo motor controller when the frame servo system works in the speed change stage.
Drawings
FIG. 1 is a schematic diagram of a signal reconstruction and discrete ESO strategy for implementing a signal reconstruction and discrete ESO based angular position acquisition method of the present invention. Hs in fig. 1 is the detected sinusoidal signal (left side up); hc is the detected cosine signal (left side down); hs_1Is a normalized sinusoidal signal; hc_1Is a normalized cosine signal; hs_2To reconstruct a sinusoidal signal; hc_2To reconstruct the cosine signal; the ESO is an Extended State Observer (ESO); z is a radical of1sinDiscrete ESO sinusoidal output; z is a radical of1cosIs the discrete ESO cosine output quantity; theta is the electrical angle of the motor rotor; thetanIs the electrical angle of the nth harmonic motor rotor, and n is a positive integer.
Detailed Description
The invention is described below with reference to the accompanying drawings (fig. 1) and examples.
FIG. 1 is a schematic diagram of a signal reconstruction and discrete ESO strategy for implementing a signal reconstruction and discrete ESO based angular position acquisition method of the present invention. Referring to fig. 1, an angular position acquisition method based on signal reconstruction and discrete ESO includes the following steps: step 1, normalizing two paths of linear Hall sensor signals detected from the angular position of a frame servo motor to eliminate the influence of unequal signal amplitudes and obtain two paths of signals with the amplitude of 1; step 2, performing signal reconstruction on the two paths of signals to obtain sine and cosine signals with most harmonic quantity suppressed; and 3, aiming at the influence of residual errors and unaccounted system error factors, obtaining angular position information capable of meeting the precision requirement by adopting a discrete extended state observer method.
The step 1 comprises redefining the information of the two paths of linear hall sensor signals as:
Figure BDA0003421674080000061
in the formula (1), HsIndicating a detected sinusoidal signal, HcShowing the detected cosine signal, alpha and beta showing the amplitude of the output signals of the two linear Hall sensors, alpha is not equal to beta, theta (k) is the electrical angle position of the motor rotor, AiAnd BiRepresenting the amplitude of each harmonic, wherein i is 3,5,7,9, and k represents a discrete time point, although the formula (1) gives the amplitude of each order harmonic relative to the fundamental frequency, the problem of unequal amplitudes still exists, and the execution of the subsequent algorithm is inconvenient, so that the obtained signals are normalized to obtain signals with equal amplitudes;
Figure BDA0003421674080000062
in the formula (2), θdetRepresenting the directly resolved angular position, Hs_1And Hc_1Respectively representing a sine signal and a cosine signal after normalization;
since the coefficients of the original signal can be obtained approximately, the coefficients of the normalized signal can also be obtained, which is expressed as:
Figure BDA0003421674080000071
in the formula (3), CiAnd (3), 5,7 and 9, combining the formula (1) and the formula (2), and obtaining the ideal electrical angle position of the rotor of the motor by theta:
Ci＝0.086 0.084 0.0075 0.014 (4)。
the signal reconstruction in the step 2 comprises: the method comprises the following steps of reconstructing a detection signal on the basis of the property that the relative magnitude relation between each order of harmonic amplitude and fundamental frequency amplitude is basically unchanged at low speed:
according to polynomial equation (5), the harmonics of each order can be expressed as a function of the fundamental frequency as follows:
sinnθ(k)＝fsinθ(k) (5)
in the formula (5), n represents the order of harmonic, n is a positive integer, and f is a function sign;
the signal is reconstructed according to equation (6) as follows:
Figure BDA0003421674080000072
h in the formula (6)s-2Representing the signal obtained after reconstruction, f (-) and f1(. -) shows two functions related to a fundamental frequency signal, the harmonic content of the signal obtained after signal reconstruction processing is greatly reduced, the angular position precision is improved by a lot compared with the initial angular position precision, but the angular position error of 0.04rad still can not meet the requirement, so the sinusoidal signal after signal reconstruction is represented again as:
Hs_2(k)＝sin[θ(k)]+G[θ(k)] (7)
in equation (7), G [ θ (k) ] represents the residual error in the signal.
The step 3 comprises the following specific steps: since the frame servo system usually works in a low-speed and time-varying state, fundamental frequency information cannot be acquired, and therefore processing is performed by adopting a state observation mode based on equation (7), and according to the correlation theory of the extended state observer ESO, the error in equation (7) is regarded as lumped disturbance, and then the state equation is expressed as:
Figure BDA0003421674080000081
in the formula (8), u (k) is a signal H obtained by signal reconstructions_2(k)，x1(k) Denotes sin [ theta (k)]，x2(k) Representing the lumped perturbation, d (k) representing the acceleration of the lumped perturbation, y (k) representing the output signal, expressed as:
Figure BDA0003421674080000082
in the formula (9), θn(k) Representing the resulting angular position, ωn(k) Expressing the finally obtained angular rate, and discretizing the corresponding observer on the basis of the state equation (8) to obtain a discrete extended observer, which is expressed as:
Figure BDA0003421674080000083
in the formula (10), e (k) represents a signal error, z1(k) And z2(k) Are respectively used for estimating x1(k) And x2(k)，h、β1And beta2Is an adjustable parameter of the discrete extended observer; in order to solve the problem of direct current offset introduced during sine and cosine integration, discrete integration is adopted, only some points are integrated, continuous integration is avoided, and the problem can be well solved, wherein the discrete integration expression is as follows:
z2(k+1)＝z2(k)+h(-β2e(k)-z2(k-m)) (11)
in equation (11), m represents the number of integration points, so equation (10) is rewritten as:
Figure BDA0003421674080000084
harmonic content in sine signals and cosine signals obtained after the discrete ESO processing is obviously reduced, the finally obtained angular position error is about 0.01rad at most, and the angular position error meeting the control requirement of a torque motor of a frame servo system is only 0.013rad at most, so that the finally obtained angular position information can meet the requirement of the angular position precision of the frame system.
The processing mode of cosine signals in the original signals is the same as that of sine signals, and finally the angular position information meeting the precision requirement can be obtained by processing the two obtained signals as follows:
Figure BDA0003421674080000085
in the formula (13), z1sin(k) And z1cos(k) Respectively representing the output quantities of discrete ESO after the sine function signal and the cosine function signal are reconstructed by the signal and processed by adopting a discrete extended state observer method, T represents the sampling period, and thetan(k) Representing the resulting angular position, ωn(k) Representing the resulting angular rate and k the discrete time points.
The technical problem to be solved by the invention is as follows: the invention aims to overcome the defects of the prior art and solve the problem that the methods such as direct calculation, common-frequency signal extraction, orthogonal PLL (phase locked loop) and the like cannot be applied to a frame servo system. The method can effectively solve the problem that signals detected by a linear Hall sensor contain a large number of harmonics and different amplitudes, and angular position information finally obtained at any rotating speed within a rotating speed allowable range can meet the requirement of a frame servo system on angular position accuracy. The technical scheme adopted by the invention for solving the technical problems is as follows: an angular position acquisition method based on signal reconstruction and discrete ESO. In the specific implementation process, the specific implementation steps of the invention are as follows:
(1) firstly, normalizing the obtained signals to obtain signals with equal amplitude, wherein the method comprises the following specific steps:
redefining the information of the two paths of signals as:
Figure BDA0003421674080000091
in the formula, HsRepresenting the detected sinusoidal signal, HcRepresenting the detected cosine signal. Although the formula (1) gives the magnitude of each order harmonic relative to the fundamental frequency, the problem of unequal magnitudes still exists and causes inconvenience to the execution of the subsequent algorithm, so that the obtained signals are normalized to obtain signals with equal magnitudes.
Figure BDA0003421674080000092
In the formula, thetadetRepresenting the directly resolved angular position, Hs_1And Hc_1Respectively representing the normalized sine and cosine signals.
Since the coefficients of the original signal can be obtained approximately, the coefficients of the normalized signal can also be obtained, which is expressed as:
Figure BDA0003421674080000093
in the formula, CiThe magnitude of each harmonic is shown, and i is 3,5,7, 9. Combining (1) and (2) to obtain
Ci＝0.086 0.084 0.0075 0.014 (4)
(2) The method comprises the following steps of:
the order harmonics can be expressed as a function of the fundamental frequency according to polynomial equation (5).
sinnθ(k)＝fsinθ(k) (5)
In the formula, n represents the order of harmonics.
The signal is reconstructed according to the following formula.
Figure BDA0003421674080000101
In the formula Hs_2Representing the signal obtained after reconstruction, f (-)&And f1(. cndot.) represents two functions with respect to a fundamental frequency signal.
The harmonic content of the signal obtained after the signal reconstruction processing is greatly reduced, the angular position precision is improved by a lot compared with the initial angular position precision, but the angular position error of 0.04rad still cannot meet the requirement, so the sinusoidal signal after the signal reconstruction can be represented as follows:
Hs_2(k)＝sin[θ(k)]+G[θ(k)] (7)
in the formula, G [ theta (k) ] represents the residual error in the signal.
(3) A method for using a discrete extended state observer for the effects of residual errors and unaccounted for systematic errors, characterized in that: the method comprises the following specific steps:
since the frame servo system is usually operated in a low-speed, time-varying state, and thus cannot acquire fundamental frequency information, the processing is performed by using a state observation method based on equation (7). According to the correlation theory of the Extended State Observer (ESO), considering the error in equation (7) as a lumped disturbance, the state equation is expressed as:
Figure BDA0003421674080000102
wherein u (k) is a signal H obtained by signal reconstructions_2(k),x1(k) Denotes sin [ theta (k)]，x2(k) Representing lumped disturbances, d (k) representing accelerations of lumped disturbances, y (k)Representing the output signal, expressed as:
Figure BDA0003421674080000103
in the formula, thetan(k) Representing the resulting angular position, ωn(k) Indicating the resulting angular rate, both of which are calculated in a manner to be given later. Discretizing the corresponding observer on the basis of the state equation (8) to obtain a discrete extended observer, which is expressed as:
Figure BDA0003421674080000111
wherein e (k) represents a signal error, z1(k) And z2(k) Are respectively used for estimating x1(k) And x2(k)。
In order to solve the problem of direct current offset introduced during sine and cosine integration, discrete integration is adopted in the method, only some points are integrated, continuous integration is avoided, the problem can be well solved, and the discrete integration expression is as follows:
z2(k+1)＝z2(k)+h(-β2e(k)-z2(k-m)) (11)
in the equation, m represents the number of integration points, so equation (10) can be rewritten as:
Figure BDA0003421674080000112
harmonic content in sine signals and cosine signals obtained after the discrete ESO processing is obviously reduced, the error of the finally obtained angular position is about 0.01rad at most, and the error of the angular position meeting the control requirement of a torque motor of a frame servo system is about 0.013rad at most, so that the finally obtained angular position information can meet the requirement of the frame system on the accuracy of the diagonal position.
The processing method of the cosine signal in the original signal is the same as the processing method of the sine signal. And finally, processing the two obtained signals as follows to obtain the angular position information meeting the precision requirement.
Figure BDA0003421674080000113
In the formula, z1sin(k) And z1cos(k) The output quantities of the discrete ESO processed by the sine function and the cosine function by the method are respectively shown, and T represents a sampling period.
The method can be used as a new angular position acquisition method based on signal reconstruction and discrete ESO, firstly, the influence of unequal signal amplitudes is eliminated by normalizing two signals, and two signals with the amplitude of 1 are obtained; secondly, signal reconstruction is carried out on the signal, most harmonic quantity is suppressed, and a relatively standard sine and cosine signal is obtained; and finally, aiming at the influence of factors such as residual errors, unaccounted system errors and the like, obtaining the angular position information capable of meeting the precision requirement by adopting a discrete extended state observer method. When the frame servo system works at a constant speed stage, the method provided by the section can effectively solve the problem that signals detected by the linear Hall sensor contain a large number of harmonic waves and are unequal in amplitude, and finally obtained angular position information at any rotating speed within a rotating speed allowable range can meet the requirement of the frame servo system on the angular position accuracy. When the frame servo system works in the speed change stage, the processed final angular position error is suppressed to about 0.01rad from the original 0.2rad, and the result shows that the angular position information obtained by the angular position acquisition method based on signal reconstruction and discrete ESO provided by the section can still meet the requirement of the angular position accuracy of the frame servo motor controller when the frame servo system works in the speed change stage. The method is simple, effective and easy to implement, and experiments in the SGMSCMG low-speed frame servo system prove that the method can obtain the angular position information meeting the precision requirement under the complex working state.
Those skilled in the art will appreciate that the invention may be practiced without these specific details. It is pointed out here that the above description is helpful for the person skilled in the art to understand the invention, but does not limit the scope of protection of the invention. Any such equivalents, modifications and/or omissions as may be made without departing from the spirit and scope of the invention may be resorted to.

Claims (5)

1. An angular position acquisition method based on signal reconstruction and discrete ESO, characterized by comprising the following steps:
step 1, normalizing two paths of linear Hall sensor signals detected from the angular position of a frame servo motor to eliminate the influence of unequal signal amplitudes and obtain two paths of signals with the amplitude of 1;
step 2, performing signal reconstruction on the two paths of signals to obtain sine and cosine signals with most harmonic quantity suppressed;
and 3, aiming at the influence of residual errors and unaccounted system error factors, obtaining angular position information capable of meeting the precision requirement by adopting a discrete extended state observer method.
2. The method of signal reconstruction and discrete ESO based angular position acquisition as claimed in claim 1, wherein said step 1 comprises redefining the information of two linear Hall sensor signals as:
Figure FDA0003421674070000011
in the formula (1), HsIndicating a detected sinusoidal signal, HcShowing the detected cosine signal, alpha and beta showing the amplitude of the output signals of the two linear Hall sensors, alpha is not equal to beta, theta (k) is the electrical angle position of the motor rotor, AiAnd BiThe amplitude of each harmonic is expressed, and i is 3,5,7,9, k represents a discrete time point, although the formula (1) gives the amplitude of each order harmonic relative to the fundamental frequency, the problem of unequal amplitudes still exists and causes inconvenience to the execution of the subsequent algorithm, so that the amplitude of each order harmonic is obtained firstCarrying out normalization processing on the obtained signals to obtain signals with equal amplitude;
Figure FDA0003421674070000012
in the formula (2), θdetRepresenting the directly resolved angular position, Hs_1And Hc_1Respectively representing a sine signal and a cosine signal after normalization;
since the coefficients of the original signal can be obtained approximately, the coefficients of the normalized signal can also be obtained, which is expressed as:
Figure FDA0003421674070000013
in the formula (3), CiAnd (3), 5,7 and 9, combining the formula (1) and the formula (2), and obtaining the ideal electrical angle position of the rotor of the motor by theta:
Ci＝0.086 0.084 0.0075 0.014 (4)。
3. the method of signal reconstruction and discrete ESO based angular position acquisition as claimed in claim 1, wherein said signal reconstruction in step 2 comprises: the method comprises the following steps of reconstructing a detection signal on the basis of the property that the relative magnitude relation between each order of harmonic amplitude and fundamental frequency amplitude is basically unchanged at low speed:
according to polynomial equation (5), the harmonics of each order can be expressed as a function of the fundamental frequency as follows:
sin nθ(k)＝f sinθ(k) (5)
in the formula (5), n represents the order of harmonic, n is a positive integer, and f is a function sign;
the signal is reconstructed according to equation (6) as follows:
Figure FDA0003421674070000021
h in the formula (6)s_2Representing the signal obtained after reconstruction, f (-) and f1(. cndot.) represents two functions related to fundamental frequency signals, the harmonic content of the signals obtained after signal reconstruction processing is greatly reduced, the angular position accuracy is improved by a lot compared with the initial angular position accuracy, but the angular position error of 0.04rad still can not meet the requirement, so the sinusoidal signals after signal reconstruction are represented again as:
Hs_2(k)＝sin[θ(k)]+G[θ(k)] (7)
in equation (7), G [ θ (k) ] represents the residual error in the signal.
4. The method for angular position acquisition based on signal reconstruction and discrete ESO as claimed in claim 1, wherein said step 3 comprises the following specific steps:
since the frame servo system usually works in a low-speed and time-varying state, fundamental frequency information cannot be acquired, and therefore processing is performed by adopting a state observation mode based on equation (7), and according to the correlation theory of the extended state observer ESO, the error in equation (7) is regarded as lumped disturbance, and then the state equation is expressed as:
Figure FDA0003421674070000022
in the formula (8), u (k) is a signal H obtained by signal reconstructions_2(k)，x1(k) Denotes sin [ theta (k)]，x2(k) Representing the lumped perturbation, d (k) representing the acceleration of the lumped perturbation, y (k) representing the output signal, expressed as:
Figure FDA0003421674070000023
in the formula (9), θn(k) Representing the resulting angular position, ωn(k) Expressing the finally obtained angular velocity, and discretizing the corresponding observer on the basis of the state equation (8) to obtain a discretized extended observer which expresses the discrete extended observerComprises the following steps:
Figure FDA0003421674070000031
in the formula (10), e (k) represents a signal error, z1(k) And z2(k) Are respectively used for estimating x1(k) And x2(k)，h、β1And beta2Is an adjustable parameter of the discrete extended observer;
in order to solve the problem of direct current offset introduced during sine and cosine integration, discrete integration is adopted, only some points are integrated, continuous integration is avoided, and the problem can be well solved, wherein the discrete integration expression is as follows:
z2(k+1)＝z2(k)+h(-β2e(k)-z2(k-m)) (11)
in equation (11), m represents the number of integration points, so equation (10) is rewritten as:
Figure FDA0003421674070000032
harmonic content in sine signals and cosine signals obtained after the discrete ESO processing is obviously reduced, the finally obtained angular position error is about 0.01rad at most, and the angular position error meeting the control requirement of a torque motor of a frame servo system is only 0.013rad at most, so that the finally obtained angular position information can meet the requirement of the angular position precision of the frame system.
5. The method for acquiring the angular position based on the signal reconstruction and the discrete ESO as claimed in claim 1, wherein the cosine signal in the original signal is processed in the same way as the sine signal, and the angular position information meeting the accuracy requirement can be obtained by finally processing the two obtained signals as follows:
Figure FDA0003421674070000033
in formula (13), z1sin(k) And z1cos(k) Respectively representing the output quantities of discrete ESO after the sine function signal and the cosine function signal are reconstructed by the signal and processed by adopting a discrete extended state observer method, T represents the sampling period, and thetan(k) Representing the resulting angular position, ωn(k) Representing the resulting angular rate and k the discrete time points.
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