CN115514282A - High-precision rotor position obtaining method for full-digital shaft angle conversion system of rotary transformer - Google Patents

High-precision rotor position obtaining method for full-digital shaft angle conversion system of rotary transformer Download PDF

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CN115514282A
CN115514282A CN202211145972.0A CN202211145972A CN115514282A CN 115514282 A CN115514282 A CN 115514282A CN 202211145972 A CN202211145972 A CN 202211145972A CN 115514282 A CN115514282 A CN 115514282A
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rotor position
rotor
sine
rotary
acquisition system
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徐永向
朱鹏程
邹继斌
邹继明
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Harbin Institute of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • 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
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation

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Abstract

The invention discloses a method for acquiring the position of a high-precision rotor of a full-digital shaft angle conversion system of a rotary transformer, which comprises the following steps: step one, generating an excitation signal of a rotary transformer: a digital signal processor generates a sine pulse width modulation waveform, and the sine pulse width modulation waveform is input into a rotary change excitation winding through a conditioning circuit to obtain sine and cosine signals output by the rotary change; step two, demodulation of the rotary transformer output signal: performing phase-sensitive demodulation on sine and cosine signals output by the rotary transformer to obtain low-frequency sine and cosine signals containing rotor position information; step three, obtaining the position of the rotor: and (3) extracting the rotor position information contained in the sine and cosine signals after phase-sensitive demodulation by using a steady-state extended Kalman filter as an observer of the position information of the rotary-change rotor. The method can effectively improve the position detection precision, the calculation efficiency and the response speed of the rotary variable shaft angle conversion system, and has higher application value in the industrial field of the rotary variable rotor position sensor.

Description

High-precision rotor position obtaining method for full-digital shaft angle conversion system of rotary transformer
Technical Field
The invention relates to a high-precision rotor position acquisition method for a full-digital shaft angle conversion (RDC) system of a rotary transformer, in particular to a rotor position acquisition method based on a steady-state extended Kalman filter (SSEKF), which can be used for improving the position detection precision, the calculation efficiency and the response speed of the full-digital shaft angle conversion system of the rotary transformer.
Background
In a full-digital shaft-angle conversion system of a rotary transformer, a rotor position acquisition method can influence the comprehensive performance of rotary position detection. The arctangent method and the angle tracking observer method are two commonly used rotor position acquisition methods, the code amount of the arctangent method is small, but the arctangent method is easily influenced by noise due to an open-loop system; the angle tracking observer method has strong noise resistance and higher precision, can directly obtain rotating speed information from the rotating speed information, and is widely applied to various special rotating and decoding chips, but the method has more integral operations and lower calculation efficiency, and has certain phase lag to influence the precision of rotating position detection, and if the angle tracking observer is second-order, when the tracking acceleration is input, certain steady-state error also exists to influence the tracking performance of the RDC system.
In summary, it is necessary to design a resolver rotor position obtaining method with strong noise immunity, high calculation efficiency, high position detection precision and good dynamic performance to improve the overall performance of the RDC system.
Disclosure of Invention
The invention provides a high-precision rotor position acquisition method for a fully digital shaft-to-angle conversion system of a rotary transformer, which takes the defects of phase lag, low calculation efficiency and the like existing in the process of acquiring rotor position information by using a traditional Angle Tracking Observer (ATO) method into consideration. The method can effectively improve the position detection precision, the calculation efficiency and the response speed of the rotary-transformer shaft angle conversion system, and has higher application value in the industrial field of converting the rotary-transformer shaft angle into the rotor position sensor.
The purpose of the invention is realized by the following technical scheme:
a method for acquiring the position of a high-precision rotor of a full-digital shaft-to-angle conversion system of a rotary transformer comprises the following steps:
step one, generating an excitation signal of a rotary transformer: a Digital Signal Processor (DSP) generates a Sine Pulse Width Modulation (SPWM) waveform, and the waveform is input into a rotary change excitation winding through a conditioning circuit to obtain sine and cosine signals output by the rotary change;
step two, demodulation of the rotary transformer output signal: performing phase-sensitive demodulation on sine and cosine signals output by the rotary transformer to obtain low-frequency sine and cosine signals containing rotor position information;
step three, obtaining the position of the rotor: the method comprises the following steps of using a Steady State Extended Kalman Filter (SSEKF) as an observer of the position information of a rotary-variable rotor to extract the position information of the rotor contained in sine and cosine signals after phase-sensitive demodulation, and specifically comprising the following steps of:
step three, modeling of an SSEKF rotor position acquisition system:
selecting the position theta and the rotation speed omega of the rotary transformer rotor r And the acceleration a is a state variable, the discrete process equation of the rotation-variable rotor position acquisition system is as follows:
Figure BDA0003855257900000021
in the formula, x (k + 1) is a state variable of the SSEKF rotor position acquisition system at the k +1 th moment; θ (k) is the rotor position (rad) at the k-th time of the rotation; omega r (k) Is the angular velocity (rad/s) at the k-th moment of the revolution; a (k) is the angular acceleration (rad/s) at the k-th time of the rotation 2 ) (ii) a T is a sampling period(s); ω (k) is the process noise at time k;
the rotation transformation rotor position acquisition system matrix F is recorded as:
Figure BDA0003855257900000031
the measurement equation of the rotary transformer rotor position acquisition system is given by the demodulated rotary transformer sine and cosine winding output signals:
Figure BDA0003855257900000032
in the formula, y (k) is an output variable of the SSEKF rotor position acquisition system at the k moment; y is 1 (k) And y 2 (k) Respectively, the demodulated rotary sine and cosine output signals; v (k) is the measurement noise at the k-th moment of the system;
the output matrix h (x (k)) of the measurement equation of the resolver position acquisition system is recorded as:
Figure BDA0003855257900000033
the state space expression of the rotation transformer position acquisition system is as follows:
Figure BDA0003855257900000034
step two, simplification of the SSEKF rotor position acquisition system:
introducing a Park transformation matrix T (theta):
Figure BDA0003855257900000035
the linearization expression of the measurement equation output matrix h (x (k)) of the resolver position acquisition system is as follows:
Figure BDA0003855257900000041
Figure BDA0003855257900000042
in the formula (I), the compound is shown in the specification,
Figure BDA0003855257900000043
obtaining estimated state variables of the system at the kth time for the SSEKF rotor position, wherein
Figure BDA0003855257900000044
Figure BDA0003855257900000045
A predicted value (rad) of rotor position for the k-th instant;
Figure BDA0003855257900000046
a pre-estimated value (rad/s) of the rotational angular velocity for the k-th time;
Figure BDA0003855257900000047
for the pre-estimation of the rotational angular acceleration (rad/s) at the k-th instant 2 )；
Updating error covariance matrix P by reference Kalman filter k The updating expression of the error covariance matrix of the rotation rotor position acquisition system is as follows:
P k+1 ＝FP k F T +Q-K k H k P k F T ；
further simplification:
Figure BDA0003855257900000048
let prior error covariance matrix
Figure BDA0003855257900000049
K can be simplified by the following steps k ：
Figure BDA00038552579000000410
In the formula, T k To represent
Figure BDA00038552579000000411
Order to
Figure BDA00038552579000000412
Then kalman gain K k The method is divided into two parts: time invariant part
Figure BDA00038552579000000413
And a time-varying part T k ；
Since the first row of the matrix H is all 0, let
Figure BDA00038552579000000414
Comprises the following steps:
Figure BDA0003855257900000051
in the formula, k 1 ,k 2 And k 3 Are all preset constants, and the following expression is given:
Figure BDA0003855257900000052
defining a deviation
Figure BDA0003855257900000053
Then:
Figure BDA0003855257900000054
step three, obtaining an optimal estimation value updating expression of the steady state extended Kalman filter according to the step three:
Figure BDA0003855257900000055
Figure BDA0003855257900000056
in the formula, the optimal state estimation value at the k +1 th time (i.e. the latest time)
Figure BDA0003855257900000057
Figure BDA0003855257900000058
An optimal estimate of the rotor position for the latest instant,
Figure BDA0003855257900000059
for the optimum estimated value of the rotational angular velocity at the latest moment,
Figure BDA00038552579000000510
and (4) performing optimal estimation on the rotation angular acceleration at the latest moment.
Compared with the prior art, the invention has the following advantages:
the method provided by the invention only needs to write a software program on the basis of the original full digital shaft angle conversion system hardware circuit, does not need to add any additional hardware, and does not cause any additional cost and energy loss; the operation, control, use and the like are kept unchanged, and only the program of the rotor position acquisition module needs to be changed; the method is applied to the rotary variable shaft angle conversion system, so that the precision, the dynamic performance and the calculation efficiency of the position detection of the rotary variable shaft angle conversion system can be effectively improved.
Drawings
FIG. 1 is a schematic diagram of an RDC system;
FIG. 2 is a block diagram of the SSEKF structure;
FIG. 3 is a unit step response for a four angle observer system and an SSEKF.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a method for acquiring the position of a high-precision rotor of a full-digital shaft angle conversion system of a rotary transformer, which is shown in figure 1 and needs to complete the following three steps through a hardware circuit and a software algorithm in order to realize the full-digital shaft angle conversion of the rotary transformer:
(1) Generation of resolver excitation signals: a Sine Pulse Width Modulation (SPWM) waveform is generated by a Digital Signal Processor (DSP) and is input into the rotary change excitation winding through a conditioning circuit to obtain sine and cosine signals output by the rotary change.
(2) Demodulation of the resolver output signal: in order to remove the high-frequency excitation signal in the resolver output signal, the sine and cosine signal output by the resolver is subjected to phase-sensitive demodulation (also called frequency shift technology) to obtain a low-frequency sine and cosine signal containing rotor position information.
(3) Acquiring the position of the rotary transformer rotor: in order to extract the rotor position information contained in the sine and cosine signals after phase-sensitive demodulation, the invention provides an observer using a Steady State Extended Kalman Filter (SSEKF) as the position information of a rotary-variable rotor, the basic structure block diagram is shown in FIG. 2, and y in the figure 1 (k) And y 2 (k) The output values of the cosine signal and the sine signal obtained by the phase-sensitive demodulation method at the k-th moment are respectively. The method for acquiring the position of the rotary variable rotor is the research focus of the invention.
The method comprises the following specific steps:
1. modeling of the SSEKF rotor position acquisition system:
selecting the position theta and the rotation speed omega of the rotary transformer rotor r And the acceleration a is a state variable, the discrete process equation of the rotation rotor position acquisition system is as follows:
Figure BDA0003855257900000071
in the formula, x (k + 1) is a state variable of the SSEKF rotor position acquisition system at the k +1 th moment; θ (k) is the rotor position (rad) at the k-th time of the rotation; omega r (k) Is the angular velocity (rad/s) at the k-th moment of the revolution; a (k) is the angular acceleration (rad/s) at the k-th time of the rotation 2 ) (ii) a T is a sampling period(s); ω (k) is the process noise at time k.
In the above process equation, the rotational speed ω of the rotation transformer r Is a double integral of the process noise ω (k), so theoretically it tracks the uniform acceleration inputNo steady state error exists; if the spin rate is only a double integral of the process noise ω (k), it will have steady state errors in tracking the input of the uniform acceleration.
The system matrix F is recorded as:
Figure BDA0003855257900000072
the measurement equation of the system is given by the demodulated output signals of the rotary sine and cosine windings:
Figure BDA0003855257900000081
in the formula, y (k) is an output variable of the SSEKF rotor position acquisition system at the kth moment; y is 1 (k) And y 2 (k) Respectively, the demodulated rotary sine and cosine output signals; v (k) is the measurement noise at the k-th moment of the system.
Let h (x (k)) be:
Figure BDA0003855257900000082
the state space expression of the rotation transformer position acquisition system is as follows:
Figure BDA0003855257900000083
let the system process noise ω (k) follow a Gaussian distribution with variance 1, and its error covariance matrix Q is given by:
Figure BDA0003855257900000084
let the measurement noise v (k) follow the gaussian distribution of the error covariance matrix R as shown below:
Figure BDA0003855257900000085
in the formula, λ is an adjustment factor, and the noise suppression capability of the system can be obtained by adjusting the position of the rotary transformer rotor through λ.
2. Simplification of the SSEKF rotor position acquisition system:
introducing a Park transformation matrix T (theta):
Figure BDA0003855257900000086
the measurement equation output matrix h (x (k)) linearization expression of the system is as follows:
Figure BDA0003855257900000091
Figure BDA0003855257900000092
in the formula (I), the compound is shown in the specification,
Figure BDA0003855257900000093
obtaining estimated state variables of the system at the kth time for the SSEKF rotor position, wherein
Figure BDA0003855257900000094
Figure BDA0003855257900000095
A predicted value (rad) of rotor position for the k-th instant;
Figure BDA0003855257900000096
a pre-estimated value (rad/s) of the rotational angular velocity for the k-th time;
Figure BDA0003855257900000097
for the pre-estimation of the rotational angular acceleration (rad/s) at the k-th instant 2 )。
By T k To represent
Figure BDA0003855257900000098
Updating error covariance matrix P by reference Kalman filter k The updating expression of the error covariance matrix of the rotation rotor position acquisition system is as follows:
P k+1 ＝FP k F T +Q-K k H k P k F T ；
further simplification:
Figure BDA0003855257900000099
as can be seen from the above equation, all the Park transformation matrices T (θ) can be eliminated, P k+1 No longer changing with time, i.e. as the rotating rotor position acquisition system gradually converges to a steady state, P k+1 Will also converge to the steady state solution
Figure BDA00038552579000000910
Kalman gain K at this time k While still time-varying, let the a priori error covariance matrix
Figure BDA00038552579000000911
K can be simplified by the following steps k ：
Figure BDA00038552579000000912
Order to
Figure BDA00038552579000000913
Kalman gain K k Then divided into two parts, the time-invariant part
Figure BDA0003855257900000101
And a time-varying part T k . Since all the first rows of the matrix H are 0, it is possible to set
Figure BDA0003855257900000102
Comprises the following steps:
Figure BDA0003855257900000103
in the formula, k 1 ,k 2 And k 3 Are constants that can be set in advance, and the following expression can be given:
Figure BDA0003855257900000104
defining a deviation
Figure BDA0003855257900000105
Then:
Figure BDA0003855257900000106
3. according to the simplified steps, the optimal estimation value updating expression of the steady-state extended Kalman filter can be obtained:
Figure BDA0003855257900000107
Figure BDA0003855257900000108
Figure BDA0003855257900000109
namely, the rotor position optimal estimated value obtained by the SSEKF is input into the DSP for application.
The closed-loop transfer function Φ(s) of the conventional angle observer method is expressed as follows:
Figure BDA00038552579000001010
essentially a low pass filter, there is some phase lag. And can calculate when tracking the uniform acceleration input theta = kt according to the theorem of final value 2 (R(s)＝2/s 3 ) Presence of steady state error:
Figure BDA0003855257900000111
the method for acquiring the SSEKF rotor position can ensure that steady-state errors do not exist when SSEKF tracks and accelerates uniformly through a reasonable modeling method; meanwhile, the Kalman filter is an optimal state estimation algorithm, and if the system model and the observation model are correct, the Kalman filter is estimated in real time, so that theoretically, a high-precision and quick-response rotary variable shaft angle conversion effect can be achieved. FIG. 3 shows unit step responses of the SSEKF and four systems (System 1 to System 4) of the conventional angle observer method, which shows that the SSEKF has the fastest response speed, i.e. the amplitude value is converged to 1 quickly, and overshoot and steady-state errors basically do not exist; because the calculation of the Kalman filter is quite efficient, the calculation efficiency of the SSEKF can be greatly improved through reasonable simplification. In conclusion, the rotor position acquisition method based on the SSEKF can improve the comprehensive performance of the rotation position detection system.

Claims (2)

1. A method for acquiring the position of a high-precision rotor of a full-digital shaft angle conversion system of a rotary transformer is characterized by comprising the following steps:
step one, generating an excitation signal of a rotary transformer: a digital signal processor generates a sine pulse width modulation waveform, and the sine pulse width modulation waveform is input into a rotary change excitation winding through a conditioning circuit to obtain sine and cosine signals output by the rotary change;
step two, demodulation of the rotary transformer output signal: performing phase-sensitive demodulation on sine and cosine signals output by the rotary transformer to obtain low-frequency sine and cosine signals containing rotor position information;
step three, obtaining the position of the rotor: and (3) using a steady-state extended Kalman filter as an observer of the rotational-variation rotor position information to extract the rotor position information contained in the sine and cosine signals after phase-sensitive demodulation.
2. The method for acquiring the high-precision rotor position of the fully digital shaft-to-angle conversion system of the resolver according to claim 1, wherein the third step is as follows:
step three, modeling of an SSEKF rotor position acquisition system:
selecting the position theta and the rotation speed omega of the rotation transformer rotor r And the acceleration a is a state variable, the discrete process equation of the rotation-variable rotor position acquisition system is as follows:
Figure FDA0003855257890000011
in the formula, x (k + 1) is a state variable of the SSEKF rotor position acquisition system at the k +1 th moment; θ (k) is a rotor position at the k-th time of the rotation; omega r (k) The angular velocity at the k-th moment of the rotation; a (k) is the angular acceleration at the k-th moment of the rotation; t is a sampling period; ω (k) is the process noise at time k;
the rotation transformation rotor position acquisition system matrix F is recorded as:
Figure FDA0003855257890000021
the measurement equation of the rotary transformer rotor position acquisition system is given by the demodulated rotary transformer sine and cosine winding output signals:
Figure FDA0003855257890000022
in the formula, y (k) is an output variable of the SSEKF rotor position acquisition system at the k moment; y is 1 (k) And y 2 (k) Respectively, the demodulated rotary sine and cosine output signals; v (k) is the measurement noise at the k-th moment of the system;
the output matrix h (x (k)) of the measurement equation of the resolver position acquisition system is recorded as:
Figure FDA0003855257890000023
the state space expression of the rotation transformer position acquisition system is as follows:
Figure FDA0003855257890000024
step two, the simplification of the SSEKF rotor position acquisition system:
introducing a Park transformation matrix T (theta):
Figure FDA0003855257890000025
the linearization expression of the measurement equation output matrix h (x (k)) of the resolver position acquisition system is as follows:
Figure FDA0003855257890000026
Figure FDA0003855257890000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003855257890000032
obtaining estimated state variables for the SSEKF rotor position at time k of the system,
Figure FDA0003855257890000033
estimating the position of a rotor of the resolver at the kth moment;
updating error covariance matrix P by reference Kalman filter k The step of rotating the rotorThe updating expression of the error covariance matrix of the position acquisition system is as follows:
P k+1 ＝FP k F T +Q-K k H k P k F T ；
further simplification:
Figure FDA0003855257890000034
let prior error covariance matrix
Figure FDA0003855257890000035
K can be simplified by the following steps k ：
Figure FDA0003855257890000036
In the formula, T k To represent
Figure FDA0003855257890000037
Order to
Figure FDA0003855257890000038
Then kalman gain K k The method is divided into two parts: time invariant part
Figure FDA0003855257890000039
And a time-varying part T k ；
Since the first row of the matrix H is all 0, let
Figure FDA00038552578900000310
Comprises the following steps:
Figure FDA00038552578900000311
in the formula, k 1 ,k 2 And k 3 Are all preset constants, and the following expression is given:
Figure FDA00038552578900000312
defining a deviation
Figure FDA0003855257890000041
Then:
Figure FDA0003855257890000042
step three, obtaining an optimal estimation value updating expression of the steady state extended Kalman filter according to the step three:
Figure FDA0003855257890000043
Figure FDA0003855257890000044
in the formula, the optimal state estimation value at the k +1 th time, namely the latest time
Figure FDA0003855257890000045
Figure FDA0003855257890000046
An optimal estimate of the rotor position for the latest instant,
Figure FDA0003855257890000047
for the optimum estimated value of the rotational angular velocity at the latest moment,
Figure FDA0003855257890000048
is a rotation of the latest momentAnd (4) optimal estimation value of variable angular acceleration.
CN202211145972.0A 2022-09-20 2022-09-20 High-precision rotor position obtaining method for full-digital shaft angle conversion system of rotary transformer Pending CN115514282A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116070066A (en) * 2023-02-20 2023-05-05 北京自动化控制设备研究所 Method for calculating rolling angle of guided projectile

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116070066A (en) * 2023-02-20 2023-05-05 北京自动化控制设备研究所 Method for calculating rolling angle of guided projectile
CN116070066B (en) * 2023-02-20 2024-03-15 北京自动化控制设备研究所 Method for calculating rolling angle of guided projectile

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