CN110212838A - A kind of method for controlling position-less sensor extracting optimal rotor-position - Google Patents

Abstract

The invention discloses a kind of method for controlling position-less sensor for extracting optimal rotor-position, which includes: S1: using traditionalVector control method, in reference input electric currentOn the basis of inject high frequency pulsating signal, obtain superposed signal of the reference input electric current after high frequency signal injection；S2: according to coupled signal of the acquisition containing motor rotor position after superposed signal driving motor；S3: according to coupled signal, the control strategy of Parallel Design is determined；S4: according to control strategy, coupled signal is extracted to the optimal solution of rotor-position reference value after phaselocked loop and extended Kalman filter parallel processing.Control strategy of the invention can transition problem of the effective solution permanent magnet synchronous motor between zero low speed and high speed and the extraction rotor-position reference value optimal solution in full speed segment limit.

Description

Position-sensorless control method for extracting optimal rotor position

Technical Field

The invention belongs to the field of motor control, and particularly relates to a position-sensorless control method for extracting an optimal rotor position.

Background

Permanent magnet synchronous motors are increasingly used due to high efficiency, high power density, high power factor, and the like, such as in electric vehicles or wind power generation pitch variation. In order to realize a high-performance three-phase permanent magnet synchronous motor control system, rotor position information of a motor needs to be acquired, and the acquisition method of the rotor position information includes 2 methods:

one is to mount a position sensor. However, the position sensor is easily damaged or disturbed in a severe environment, and the maintenance cost is increased.

And the other is no position sensor, and the rotor position information is estimated by other physical quantities when the vector control system is designed. Based on the position sensorless control of the permanent magnet synchronous motor, the existing technical scheme is mainly to respectively control the rotor position information under the conditions of low speed and high speed.

The control principle in the high-speed condition is a control mode based on a fundamental wave mathematical model, and the fundamental wave is used for exciting a quantity related to the rotating speed in the mathematical model to carry out rotor position and rotating speed reference, such as counter electromotive force generated by the motor in the high-speed condition, and rotor position information is extracted from the counter electromotive force. However, this method is only suitable for high motor speeds, and fails when the motor speed is zero or at very low motor speeds.

The control principle under the low-speed condition is based on the control mode of high-frequency signal injection, under the condition that the motor rotating speed is low and no back electromotive force can be generated, high-frequency voltage or current signals are superposed on fundamental wave input signals of a control system, synthesized signals are applied to a three-phase winding of the permanent magnet synchronous motor together, and therefore the high-frequency signals are coupled and then have corresponding rotor position information, and the high-frequency signals are extracted through a band-pass filter, so that a rotor position reference value can be obtained.

The method is suitable for the condition that the back electromotive force of the motor is extremely small when the rotating speed of the motor is zero or low. When the motor runs at zero speed and low speed, if a method for extracting the counter electromotive force is adopted to obtain the position information of the rotor of the motor, the signal-to-noise ratio of a useful signal is very low due to the extremely small counter electromotive force, and the rotor position information is usually difficult to extract and obtain.

The above two methods can acquire the rotor position information under two specific conditions, but it cannot be guaranteed whether the rotor position information can be effectively acquired in the transition stage of low speed and high speed, so that the two methods cannot effectively perform the position-sensorless control of the motor in each speed range.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the problems, the invention provides a position-sensorless control method for extracting an optimal rotor position based on parallel design of a phase-locked loop and an extended Kalman filter, which is used for solving the transition problem of a permanent magnet synchronous motor between zero low speed and high speed and extracting an optimal solution of a rotor position reference value in a full-speed range.

The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a position sensorless control method of extracting an optimal rotor position, the method comprising the steps of:

s1, using conventionalReference coordinate system d^*-q^*Lower reference current commandD is obtained after being processed by a current controller^*-q^*Reference voltage command under coordinate systemAt reference voltage commandInjecting a high-frequency pulse vibration signal on the basis of the reference voltage instruction, and acquiring a superposed signal of the reference voltage instruction after high-frequency voltage injection;

s2, outputting a drive coupling signal containing rotor position information after the superposed signal is subjected to coordinate transformation and SVPWM processing, wherein the signal is used for driving a motor PMSM;

s3, according to the coupling signal, designing a parallel control strategy and extracting the optimal rotor positionAnd angular velocity ω^*；

S4, optimizing the angular speed omega^*Feedback to the current controller to optimize the rotor positionAnd (4) replacing the parameters of coordinate transformation to carry out circulation to form a closed-loop system.

Further, the specific method of S1 is as follows:

step S1.1: the current equation under the known d-q coordinate system of the three-phase permanent magnet synchronous motor is as follows:

wherein i_d、i_qIs d-q axis current; u. of_d、u_qIs the d-q axis voltage; l is_d、L_qIs d-q axis inductance component(ii) a R is a stator resistor; psi_fIs a permanent magnet flux linkage; omega_eIs the electrical angular velocity;

if i_d、i_qFully decoupled, the above equation can be changed to:

wherein u is_d0、u_q0D-q axis voltage output after current decoupling; i.e. i_d、i_qIs d-q axis current; l is_d、L_qIs the d-q axis inductance component; r is a stator resistor; psi_fIs a permanent magnet flux linkage; omega_eIs the electrical angular velocity;

to i_d、i_qThe voltage equation after complete decoupling is subjected to Laplace transform to obtain: y is_(s)＝G_(s)U_(s)

Wherein,

wherein u is_d0(s)、u_q0(s) is a complex voltage value after laplace transformation; i.e. i_d(s)、i_q(s) is a complex current value after laplace transform;

adopting PI regulator and carrying out feedforward decoupling to obtain a reference coordinate system d^*-q^*The following output voltages are:

wherein,synchronizing the rotation of the coordinate system d for reference^*-q^*Lower reference current command, i_d、i_qThe current instruction is under a d-q coordinate system of a synchronous rotation coordinate system;is the reference coordinate system d obtained after the processing of the current controller in the step S1^*-q^*A lower voltage; l is_d、L_qIs the d-q axis inductance component; psi_fIs a permanent magnet flux linkage; omega_eIs the electrical angular velocity; k_pd、K_pqTo proportional gain, K_id、K_iqIs the integral gain;

step S1.2: according to step S1.1, d is obtained^*-q^*Coordinate axis output voltageOn the basis of d^*Injecting high frequency sinusoidal voltage signals into the shaft

Wherein:for an injected high-frequency sinusoidal voltage signal u_inIs the amplitude, omega, of a high-frequency sinusoidal voltage signal_inIs the frequency of the high frequency sinusoidal voltage signal, resulting in a superimposed signal.

Further, the specific method of S2 is as follows:

step S2.1: the superposed signals are obtained after 2r/2s coordinate transformationθ_eIs the actual rotor position angle; omega is d-q coordinate axis angular velocity; the 2r/2s coordinate transformation principle is as follows:

transforming the synchronous rotating coordinate system d-q to a stationary coordinate system α - β, T_2r/2sIs a coordinate transformation matrix, which can be expressed as:

step S2.2:after being processed by SVPWM algorithm, the AC side phase voltage u is output_a、u_b、u_cSinusoidal phase current i with mutual difference of 120 DEG electrical angle_a、i_b、i_cDriving a motor PMSM;

in the natural coordinate system ABC, the phase voltage is u_a、u_b、u_cThe sinusoidal phase current with the difference of 120 degrees is i_a、i_b、i_cAfter 3s/2r coordinate transformation, the phase current and the phase voltage are at d^*-q^*Equivalent representation under the coordinate axis asTherefore, the method comprises the following steps:i.e. at d^*-q^*The coupling signal of the motor rotor position is contained under the coordinate axis;

wherein:

solving forThe specific process is as follows:

establishing a reference rotor synchronous coordinate system d^*-q^*Relation to the actual rotor synchronous coordinate system d-q;

wherein α - β is a static coordinate system, omega is d-q axis angular velocity, omega^*Is d^*-q^*The angular speed of the shaft is set to be,for reference rotor position angle, θ_eFor actual rotor position angle, Δ θ_eFor the rotor reference error angle, i.e.:

regarding the permanent magnet synchronous motor as RL circuit, at d^*-q^*D of the coordinate axis^*Injecting a high-frequency voltage signal into the shaft:

wherein: u. of_inFor injecting high-frequency voltage signal amplitude, omega_inIs the frequency of the injected high-frequency voltage signal;

at this time, the voltage equation of the three-phase permanent magnet synchronous motor under the high-frequency excitation in the synchronous rotating coordinate system, namely the voltage equation after coupling, can be simplified as follows:

wherein: i.e. i_din、i_qinIs the current response of the motor under high-frequency excitation; u. of_din、u_qinIs the voltage response of the motor under high-frequency excitation; l is_d、L_qIs the d-q axis inductance component;

in the synchronous rotating coordinate system d-q, the motor stator inductance can be expressed as:

under the stationary coordinate system α - β, the motor stator inductance can be expressed as:

wherein: average inductanceHalf-difference inductor

Then synchronously rotating the coordinate system d on the reference rotor^*-q^*The relationship between the high-frequency voltage and the current is:

wherein:is d^*-q^*A lower current component reference value;is d^*-q^*The lower voltage component reference value.

Further, the specific method of S3 is as follows:

step S3.1, mixing i_a、i_b、i_cAfter 3s/2s coordinate transformation, the current is converted into current i under α - β coordinate system_α、i_βI is transformed under 2s/2r coordinate_α、i_βConverted into actual current i under d-q coordinate system_d′、i_q', will i_d′、i_qThe signal is input to an LPF for low-pass filtering and then is input to a current controller as a negative feedback signal;

step S3.2, in step S3.1: known as i_a、i_βThe method is used as the input of the following two observer parallel processing links, and the specific process is as follows:

step S3.2.1, PLL link of phase locked loop

Will i_α、i_βFiltering, and extracting i through a band-pass filter BPF_α、i_βHigh-frequency part signal containing rotor position information is converted into reference rotor synchronous rotation coordinate system d after 2s/2r coordinate transformation^*-q^*Is as follows

To obtain the rotor position, q is needed^*Shaft high frequency currentAmplitude modulation is carried out, and modulation current sin omega is injected_int, where ω_inIs the modulation current angular frequency;

the modulation function can be expressed as:

wherein u is_inIs the amplitude of the high frequency sinusoidal voltage signal; omega_inIs the modulation current angular frequency; l is the average inductance, and Delta L is the half-difference inductance; delta theta_eIs a rotor reference error angle;

when rotor reference error angle delta theta_eTowards zero, Δ θ_e＝0，cosΔθ_e＝1，sin2Δθ_e＝2sinΔθ_ecosΔθ_e＝2sinΔθ_eAt this point, the error signal may be linearized:

wherein k is_ε＝u_in(L_q-L_d)/4ω_inL_dL_q；

The modulation signal is input into a phase-locked loop PLL consisting of a low-pass filter LPF and a PI controller, and the reference angular velocity is obtained through the processing of the phase-locked loop PLLAngle with reference rotor positionBy adjusting f (Δ)_e) Is equal to 0, i.e The rotor position reference value can converge to the rotor position actual value;

step S3.2.2, expanding a Kalman filter EKF link;

knowing the voltage response u under high frequency voltage excitation_a、u_b、u_cThe voltage signal u is obtained after the coordinate transformation of 3s/2s_α、u_βWill u_α、u_βWith step S3.1 i_α、i_βThe reference angular velocity is obtained after the common input to the extended Kalman filter EKF and the processing of the extended Kalman filter EKFAnd a reference rotor position angle

Further, the specific method of S4 is as follows:

step S4.1, outputting observer PLLAnd observer EKF outputSending the solution to a least square solver to obtain an optimal solutionOptimal solutionThe 2r/2S coordinate transformation fed back to step S2.1, the 2S/2r coordinate transformation of step S3.1 and step S3.22s/2r coordinate transformation of (a) instead of (theta)_eThe control parameter is used for participating in the calculation in the coordinate transformation process;

step S4.2, by outputting observer PLLAnd observer EKF outputIs fed to a least squares solver atAndfind the best parameter match omega of the data between^*；

Step S4.3, mixing omega^*The reference current command is sent to a speed controller and is output after being processedIn thatUnder the control method of (2), the reference current instruction is set in the current controllerAnd the actual current command i fed back in step S3.1_d′、i_q' A difference operation is carried out to obtain an error value, and the current controller forms a closed loop system by controlling the error value.

Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:

(1) the phase-locked loop PLL and the extended Kalman filter EKF are designed in parallel, and the high-frequency pulse vibration voltage input signal can accurately obtain the rotor position information of the motor under the condition that the motor is at zero speed or low speed; the extended Kalman filter is a self-adaptive system and can work in a large speed range such as high speed; therefore, the parallel design can obtain the position information of the rotor in the range of the full-speed section, and the separate design of a low-speed section system and a high-speed section system is avoided;

(2) due to rotor position angle theta_eIs obtained by serial integration of the angular velocity ω, small changes in the angular velocity ω will result in a rotor position angle θ_eIs amplified, and the rotor position angle theta is calculated separately by parallel design_eWith the angular velocity omega, the error of the closed-loop control quantity can be effectively prevented from being amplified;

(3) for a reference input signal within a sampling period of a certain widthAndperforming least square parameter identification, and selecting the optimal solution omega^*Andthe influence caused by large error amplitude is weakened to the maximum extent;

(4) optimal solution omega^*Andthe method can adapt to the sensorless control of the motor at each speed stage, so that the motor can effectively acquire the rotor position information in the acceleration or deceleration process, and the sensorless control problem of the permanent magnet synchronous motor in good transition between zero low speed and high speed stages and extraction of the optimal rotor position angle is solved.

Drawings

FIG. 1 is a schematic diagram of the structure of the transformation between coordinate systems;

FIG. 2 isReference rotor synchronous coordinate system d^*-q^*D-q relation graph of the coordinate system synchronous with the actual rotor;

FIG. 3 is a diagram of an improved PLL in parallel with an EKF to obtain an optimal solution ω^*Andthe structure block diagram of the permanent magnet synchronous motor position sensorless control system.

Detailed Description

The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.

The technical scheme of the invention is a control scheme which is designed based on the parallel connection of a phase-locked loop and an extended Kalman filter to reduce the amplification of the error of a closed-loop feedback control quantity and simultaneously can obtain the optimal motor rotor position angle within the range of a full-speed section, and the control scheme can be divided into the following steps:

step S1: as shown in fig. 3, using conventionalReference coordinate system d^*-q^*Lower reference current commandD is obtained after being processed by a current controller^*-q^*Reference voltage command under coordinate systemAt reference voltage commandAnd injecting a high-frequency pulse vibration signal on the basis to obtain a superposed signal of the reference voltage instruction after the high-frequency voltage is injected. The method specifically comprises the following steps:

step S1.1: the current equation under the known d-q coordinate system of the three-phase permanent magnet synchronous motor is as follows:

wherein i_d、i_qIs d-q axis current; u. of_d、u_qIs the d-q axis voltage; l is_d、L_qIs the d-q axis inductance component; r is a stator resistor; psi_fIs a permanent magnet flux linkage; omega_eIs the electrical angular velocity.

If i_d、i_qFully decoupled, the above equation can be changed to:

wherein u is_d0、u_q0D-q axis voltage output after current decoupling; i.e. i_d、i_qIs d-q axis current; l is_d、L_qIs the d-q axis inductance component; r is a stator resistor; psi_fIs a permanent magnet flux linkage; omega_eIs the electrical angular velocity.

To i_d、i_qThe voltage equation after complete decoupling is subjected to Laplace transform to obtain: y is_(s)＝G_(s)U_(s)

Wherein:

wherein: u. of_d0(s)、u_q0(s) is a complex voltage value after laplace transformation; i.e. i_d(s)、i_q(s) is a complex current value after laplace transform.

Adopting PI regulator and carrying out feedforward decoupling to obtain a reference coordinate system d^*-q^*The following output voltages are:

wherein,synchronizing the rotation of the coordinate system d for reference^*-q^*Lower reference current command, i_d、i_qThe current instruction is under a d-q coordinate system of a synchronous rotation coordinate system;is the reference coordinate system d obtained after the processing of the current controller in the step S1^*-q^*A lower voltage; l is_d、L_qIs the d-q axis inductance component; psi_fIs a permanent magnet flux linkage; omega_eIs the electrical angular velocity; k_pd、K_pqTo proportional gain, K_id、K_iqIs the integral gain.

Step S1.2: according to step S1.1, d is obtained^*-q^*Coordinate axis output voltageFoundation of (2)Above, at d^*Injecting high frequency sinusoidal voltage signals into the shaft

Wherein:for an injected high-frequency sinusoidal voltage signal u_inIs the amplitude, omega, of a high-frequency sinusoidal voltage signal_inIs the frequency of the high frequency sinusoidal voltage signal, resulting in a superimposed signal.

Step S2: and (3) outputting a drive coupling signal containing rotor position information after the 2r/2s coordinate transformation and SVPWM processing of the superposed signal, wherein the signal is used for driving a motor PMSM. The method specifically comprises the following steps:

step S2.1: the superposed signals are obtained after 2r/2s coordinate transformation

As shown in fig. 1: theta_eIs the actual rotor position angle; omega is d-q coordinate axis angular velocity; the 2r/2s coordinate transformation principle is as follows:

transforming the synchronous rotating coordinate system d-q to a stationary coordinate system α - β, T_2r/2sIs a coordinate transformation matrix, which can be expressed as:

step S2.2:after being processed by SVPWM algorithm, the AC side phase voltage u is output_a、u_b、u_cSinusoidal phase current i with mutual difference of 120 DEG electrical angle_a、i_b、i_cThe motor PMSM is driven.

In the natural coordinate system ABC, the phase voltage is u_a、u_b、u_cThe sinusoidal phase current with the difference of 120 degrees is i_a、i_b、i_cAfter 3s/2r coordinate transformation, the phase current and the phase voltage are at d^*-q^*Equivalent representation under the coordinate axis asTherefore, the method comprises the following steps:i.e. at d^*-q^*And the coordinate axis contains coupling signals of the position of the motor rotor.

Wherein:

solving forThe specific process is as follows:

as shown in fig. 2: establishing a reference rotor synchronous coordinate system d^*-q^*Relation to the actual rotor synchronization coordinate system d-q.

Wherein α - β is a static coordinate system, omega is d-q axis angular velocity, omega^*Is d^*-q^*The angular speed of the shaft is set to be,for reference rotor position angle, θ_eFor actual rotor position angle, Δ θ_eFor the rotor reference error angle, i.e.:

high frequency in normal conditionsThe frequency of the injection signal is 0.5-2 kHz and is far higher than the fundamental frequency of the motor, at this time, the permanent magnet synchronous motor can be regarded as an RL circuit, and d^*-q^*D of the coordinate axis^*Injecting a high-frequency voltage signal into the shaft:

wherein: u. of_inFor injecting high-frequency voltage signal amplitude, omega_inIs the frequency of the injected high frequency voltage signal.

At this time, the voltage equation of the three-phase permanent magnet synchronous motor under the high-frequency excitation in the synchronous rotating coordinate system, namely the voltage equation after coupling, can be simplified as follows:

wherein: i.e. i_din、i_qinIs the current response of the motor under high-frequency excitation; u. of_din、u_qinIs the voltage response of the motor under high-frequency excitation; l is_d、L_qIs the d-q axis inductance component.

In the synchronous rotating coordinate system d-q, the motor stator inductance can be expressed as:

under the stationary coordinate system α - β, the motor stator inductance can be expressed as:

wherein: average inductanceHalf-difference inductor

Then synchronously rotating the coordinate system d on the reference rotor^*-q^*The relationship between the high-frequency voltage and the current is:

wherein:is d^*-q^*A lower current component reference value;is d^*-q^*The lower voltage component reference value.

Step S3: and according to the coupling signals, designing a parallel control strategy and extracting the optimal rotor position.

According to step S2.2, reference is made to the rotor synchronous rotation coordinate system d^*-q^*Reference value of lower current componentCan be expressed as:

wherein:is d^*-q^*A lower current component reference value; u. of_inFor injecting high-frequency voltage signal amplitude, omega_inIs the frequency of the injected high-frequency voltage signal; l is the average inductance, and Delta L is the half-difference inductance; delta theta_eIs the rotor reference error angle.

It can be seen that when there is a difference in inductance between the d-axis and the q-axis, i.e., Δ L ≠ 0, the reference rotor synchronous rotation coordinate system d^*-q^*Reference value of lower current componentAre all aligned with the rotor position reference error angle delta theta_eIt is related. When Δ θ_eWhen q is 0^*High frequency current component of referenceEqual to zero.

By making a pair q^*The method for obtaining the position of the rotor by processing the shaft high-frequency current specifically comprises the following steps:

step S3.1: in step S2.2, the current response i under high-frequency voltage excitation is known_a、i_b、i_c。

i_a、i_b、i_cAfter 3s/2s coordinate transformation, the current is converted into current i under α - β coordinate system_α、i_βIn aI is converted under the coordinate of 2s/2r_α、i_βConverted into actual current i under d-q coordinate system_d′、i_q', will i_d′、i_q' input to LPF for low pass filtering and then input to current controller as negative feedback signal.

Step S3.2: in step S3.1: known as i_α、i_βIt is now used as input for the following two observer parallel processing links. The specific process is as follows:

step S3.2.1: and a phase-locked loop PLL (phase-locked loop) link.

Will now i_α、i_βFiltering, and extracting i through a band-pass filter BPF_α、i_βHigh-frequency part signal containing rotor position information is converted into reference rotor synchronous rotation coordinate system d after 2s/2r coordinate transformation^*-q^*Is as follows

To obtain the rotor position, q is needed^*Shaft high frequency currentAmplitude modulation is carried out, and modulation current sin omega is injected_int, where ω_inTo modulate the current angular frequency.

The modulation function can be expressed as:

wherein u is_inIs the amplitude of the high frequency sinusoidal voltage signal; omega_inIs the modulation current angular frequency; l is the average inductance, and Delta L is the half-difference inductance; delta theta_eIs the rotor reference error angle.

When rotor reference error angleΔθ_eTowards zero, Δ θ_e＝0，cosΔθ_e＝1，sin2Δθ_e＝2sinΔθ_ecosΔθ_e＝2sinΔθ_eAt this point, the error signal may be linearized:

wherein k is_ε＝u_in(L_q-L_d)/4ω_inL_dL_q；

The modulation signal is input into a phase-locked loop PLL consisting of a low-pass filter LPF and a PI controller, and the reference angular velocity is obtained through the processing of the phase-locked loop PLLAngle with reference rotor position

By adjusting f (Δ)_e) Is equal to 0, i.eThe rotor position reference value can converge to the rotor position actual value.

Step S3.2.2: and an EKF link of an extended Kalman filter.

Knowing the voltage response u under high frequency voltage excitation_a、u_b、u_cThe voltage signal u is obtained after the coordinate transformation of 3s/2s_α、u_βWill u_α、u_βI with step S3.2_α、i_βThe reference angular velocity is obtained after the common input to the extended Kalman filter EKF and the processing of the extended Kalman filter EKFAnd a reference rotor position angle

Step S3.3: and extracting the optimal rotor position to form a closed-loop control system.

Step S3.3.1: at the point in time of step S3.2.1PLL, the process,obtaining the reference angular velocity after the PLL processingAngle with reference rotor positionIn step S3.2.2EKF, u_α、u_βAnd i_α、i_βObtaining a reference angular velocity after EKF treatmentAnd a reference rotor position angle

Step S3.3.2: the least square method is adopted in a sampling period with a certain width, and the least square method refers to a mathematical optimization technology which is used for finding the optimal function matching of data by minimizing the square sum of errors.

Outputting observer PLLAnd observer EKF outputSending the solution to a least square solver to obtain an optimal solution

Assuming that within a set of sample periodsAndeach obtaining n sets of sample values, for several sets of data input to a least squares solver2n discrete points can be regarded in a plane rectangular coordinate system to obtain 2n discrete data sequences

The 2n discrete points are described by a best-fit curve L such that the 2n discrete points are all well above or below the curve. The fitting curve L can reflect the overall distribution of data, can not generate local larger fluctuation, and can reflect the characteristics of approximated discrete data points.

Let 2n discrete point coordinates be (x)_i，y_i) (i ═ 1, 2, … 2n), function f (x)_i) Fitting a curve to the functional expression through the 2n discrete pointsThe most appropriate function model is obtained from a discrete large amount of data without passing through all known points but reflecting the fundamental relationship of the data.

When the fitting function does not require strict passing through all discrete data points (x)_i，y_i) (i ═ 1, 2, … 2n), that is, the fitting functionAnd f (x)_i) At x_iWhere there is a residual error(i ═ 1, 2, … 2n), and δ (x)_i) Not necessarily all zero, but δ (x) is required to reflect the variation trend of all discrete data as much as possible in order to make the fitted curve_i) Taking the minimum value. Notation vector e ═ delta₁，δ₂…δ_2n]According to the 2-norm theory, when the minimum is found, a least squares solution can be found.

Setting fitting function

The residual function should be made by 2-norm theory:

the function S is subjected to partial derivatives and made zero, i.e.

It is written in matrix form as:

when in useWhen the linear independence exists, the equation set has a unique solution which is the optimal solution, namely a fitting functionFitting a functionI.e. the found optimal solution omega^*Is used for the functional expression of (1).

Because the observer PLL is mainly used for observing and outputting the state of the motor in a low-speed stateThe extended Kalman filter EKF has a large speed observation range, and is usually used for state observation and output in medium and high speed statesObtaining groups within a certain sampling widthReference value and input to least square solver atFind the best parameter match of data betweenThe motor can complete good transition between zero low speed and medium high speed.

Optimal solutionThe 2r/2S coordinate transformation fed back to step S2.1, the 2S/2r coordinate transformation of step S3.1 and the 2S/2r coordinate transformation of step S3.2s/2r coordinate transformation instead of theta_eThe control parameter is used for participating in the calculation in the coordinate transformation process;

by outputting observer PLL at the same speed backgroundAnd observer EKF outputIs fed to a least squares solver atAndfind the best parameter match omega of the data between^*The greatest reduction is due toAndthe influence caused by larger amplitude error exists between the two phases, so that the motor can complete good transition between zero low speed and medium high speed, and the optimal rotor position information can be effectively obtained in the acceleration or deceleration process.

Will omega^*The reference current command is sent to a speed controller and is output after being processedIn thatUnder the control method, the current controller is internally provided with a reference current instructionAnd the actual current command i fed back in step S3.1_d′、i_qThe current controller forms a closed loop system by controlling the error value, and reduces the error value to gradually stabilize the system.

In summary, the following steps: designing a phase-locked loop PLL and an extended Kalman filter EKF in parallel, and separately calculating a rotor position angle theta by adopting a method of inputting a high-frequency pulse vibration voltage signal_eAnd the angular speed omega effectively avoids the error of the closed-loop control quantity from being amplified. At the same time, in a sampling period with a certain width, the reference input signal is subjected toAndperforming least square parameter identification, and selecting the optimal solution omega^*Andand the influence caused by large error amplitude is weakened to the maximum extent.

Optimal solution omega^*Andthe method can adapt to the sensorless control of the motor at each speed stage, so that the motor can effectively acquire the rotor position information in the acceleration or deceleration process, and the sensorless control problem of the permanent magnet synchronous motor in good transition between zero low speed and high speed stages and extraction of the optimal rotor position angle is solved.

Claims (5)

1. A position-sensorless control method of extracting an optimal rotor position, the method comprising the steps of:

s1, using conventionalReference coordinate system d^*-q^*Lower reference current commandD is obtained after being processed by a current controller^*-q^*Reference voltage command under coordinate systemAt reference voltage commandInjecting a high-frequency pulse vibration signal on the basis of the reference voltage instruction, and acquiring a superposed signal of the reference voltage instruction after high-frequency voltage injection;

s2, outputting a drive coupling signal containing rotor position information after the superposed signal is subjected to coordinate transformation and SVPWM processing, wherein the signal is used for driving a motor PMSM;

s3, according to the coupling signal, designing a parallel control strategy and extracting the optimal rotor positionAnd angular velocity ω^*；

S4, optimizing the angular speed omega^*Feedback to the current controller to optimize the rotor positionAnd (4) replacing the parameters of coordinate transformation to carry out circulation to form a closed-loop system.

2. The position sensorless control method for extracting an optimal rotor position according to claim 1, wherein the specific method of S1 is as follows:

step S1.1: the current equation under the known d-q coordinate system of the three-phase permanent magnet synchronous motor is as follows:

wherein i_d、i_qIs d-q axis current; u. of_d、u_qIs the d-q axis voltage; l is_d、L_qIs the d-q axis inductance component; r is a stator resistor; psi_fIs a permanent magnet flux linkage; omega_eIs the electrical angular velocity;

if i_d、i_qFully decoupled, the above equation can be changed to:

wherein u is_d0、u_q0D-q axis voltage output after current decoupling; i.e. i_d、i_qIs d-q axis current; l is_d、L_qIs the d-q axis inductance component; r is a stator resistor; psi_fIs a permanent magnet flux linkage; omega_eIs the electrical angular velocity;

to i_d、i_qThe voltage equation after complete decoupling is subjected to Laplace transform to obtain: y is_(s)＝G_(s)U_(s)

Wherein:

wherein: u. of_d0(s)、u_q0(s) is a complex voltage value after laplace transformation; i.e. i_d(s)、i_q(s) is a complex current value after laplace transform;

adopting PI regulator and carrying out feedforward decoupling to obtain a reference coordinate system d^*-q^*The following output voltages are:

wherein,synchronizing the rotation of the coordinate system d for reference^*-q^*Lower reference current command, i_d、i_qThe current instruction is under a d-q coordinate system of a synchronous rotation coordinate system;is the reference coordinate system d obtained after the processing of the current controller in the step S1^*-q^*A lower voltage; l is_d、L_qIs the d-q axis inductance component; psi_fIs a permanent magnet flux linkage; omega_eIs the electrical angular velocity; k_pd、K_pqTo proportional gain, K_id、K_iqIs the integral gain;

step S1.2: according to step S1.1, d is obtained^*-q^*Coordinate axis output voltageOn the basis of d^*Injecting high frequency sinusoidal voltage signals into the shaft

Wherein:for an injected high-frequency sinusoidal voltage signal u_inIs the amplitude, omega, of a high-frequency sinusoidal voltage signal_inIs the frequency of the high frequency sinusoidal voltage signal, resulting in a superimposed signal.

3. The position sensorless control method for extracting the optimal rotor position according to claim 2, wherein the specific method of S2 is as follows:

step S2.1: the superposed signals are obtained after 2r/2s coordinate transformationθ_eIs the actual rotor position angle; omega is d-q coordinate axis angular velocity; the 2r/2s coordinate transformation principle is as follows:

transforming the synchronous rotating coordinate system d-q to a stationary coordinate system α - β, T_2r/2sIs a coordinate transformation matrix, which can be expressed as:

step S2.2:after being processed by SVPWM algorithm, the AC side phase voltage u is output_a、u_b、u_cSinusoidal phase current i with mutual difference of 120 DEG electrical angle_a、i_b、i_cDriving a motor PMSM;

in the natural coordinate system ABC, the phase voltage is u_a、u_b、u_cThe sinusoidal phase current with the difference of 120 degrees is i_a、i_b、i_cAfter 3s/2r coordinate transformation, the phase current and the phase voltage are at d^*-q^*Equivalent representation under the coordinate axis asTherefore, the method comprises the following steps:i.e. at d^*-q^*The coupling signal of the motor rotor position is contained under the coordinate axis;

wherein:

solving forThe specific process is as follows:

establishing a reference rotor synchronous coordinate system d^*-q^*Relation to the actual rotor synchronous coordinate system d-q;

wherein α - β is a static coordinate system, omega is d-q axis angular velocity, omega^*Is d^*-q^*The angular speed of the shaft is set to be,for reference rotor position angle, θ_eFor actual rotor position angle, Δ θ_eFor the rotor reference error angle, i.e.:

regarding the permanent magnet synchronous motor as RL circuit, at d^*-q^*D of the coordinate axis^*Injecting a high-frequency voltage signal into the shaft:

wherein: u. of_inFor injecting high-frequency voltage signal amplitude, omega_inIs the frequency of the injected high-frequency voltage signal;

at this time, the voltage equation of the three-phase permanent magnet synchronous motor under the high-frequency excitation in the synchronous rotating coordinate system, namely the voltage equation after coupling, can be simplified as follows:

wherein: i.e. i_din、i_qinIs the current response of the motor under high-frequency excitation; u. of_din、u_qinIs the voltage response of the motor under high-frequency excitation; l is_d、L_qIs the d-q axis inductance component;

in the synchronous rotating coordinate system d-q, the motor stator inductance can be expressed as:

under the stationary coordinate system α - β, the motor stator inductance can be expressed as:

wherein: average inductanceHalf-difference inductor

Then synchronously rotating the coordinate system d on the reference rotor^*-q^*The relationship between the high-frequency voltage and the current is:

wherein:is d^*-q^*A lower current component reference value;is d^*-q^*The lower voltage component reference value.

4. The position sensorless control method for extracting the optimal rotor position according to claim 3, wherein the specific method of S3 is as follows:

step S3.1, mixing i_a、i_b、i_cAfter 3s/2s coordinate transformation, the current is converted into current i under α - β coordinate system_α、i_βI is transformed under 2s/2r coordinate_α、i_βConverted into actual current i under d-q coordinate system_d′、i_q', will i_d′、i_qThe signal is input to an LPF for low-pass filtering and then is input to a current controller as a negative feedback signal;

step S3.2, in step S3.1: known as i_α、i_βThe method is used as the input of the following two observer parallel processing links, and the specific process is as follows:

step S3.2.1, PLL link of phase locked loop

Will i_α、i_βFiltering, and extracting i through a band-pass filter BPF_a、i_βHigh-frequency part signal containing rotor position information is converted into reference rotor synchronous rotation coordinate system d after 2s/2r coordinate transformation^*-q^*Is as follows

To obtain the rotor position, q is needed^*Shaft high frequency currentAmplitude modulation is carried out, and modulation current sin omega is injected_int, where ω_inIs the modulation current angular frequency;

the modulation function can be expressed as:

wherein u is_inIs the amplitude of the high frequency sinusoidal voltage signal; omega_inIs the modulation current angular frequency; l is the average inductance, and Delta L is the half-difference inductance; delta theta_eIs a rotor reference error angle;

when rotor reference error angle delta theta_eTowards zero, Δ θ_e＝0，cosΔθ_e＝1，sin2Δθ_e＝2sinΔθ_ecosΔθ_e＝2sinΔθ_eAt this point, the error signal may be linearized:

wherein k is_ε＝u_in(L_q-L_d)/4ω_inL_dL_q；

The modulation signal is input into a phase-locked loop PLL consisting of a low-pass filter LPF and a PI controller, and the reference angular velocity is obtained through the processing of the phase-locked loop PLLAngle with reference rotor positionBy adjusting f (Δ)_e) Is equal to 0, i.e The rotor position reference value can converge to the rotor position actual value;

step S3.2.2, expanding a Kalman filter EKF link;

knowing the voltage response u under high frequency voltage excitation_a、u_b、u_cThe voltage signal u is obtained after the coordinate transformation of 3s/2s_a、u_βWill u_α、u_βWith step S3.1 i_α、i_βThe reference angular velocity is obtained after the common input to the extended Kalman filter EKF and the processing of the extended Kalman filter EKFAnd a reference rotor position angle

5. The position sensorless control method for extracting the optimal rotor position according to claim 4, wherein the specific method of S4 is as follows:

step S4.1, outputting observer PLLAnd observer EKF outputSending the solution to a least square solver to obtain an optimal solutionOptimal solutionThe 2r/2S coordinate transformation fed back to step S2.1, the 2S/2r coordinate transformation of step S3.1 and the 2S/2r coordinate transformation of step S3.2, instead of θ_eParticipating in a coordinate transformation process as a control parameterThe calculation of (1);

step S4.2, by outputting observer PLLAnd observer EKF outputIs fed to a least squares solver atAndfind the best parameter match omega of the data between^*，

Step S4.3, mixing omega^*The reference current command is sent to a speed controller and is output after being processedIn thatUnder the control method of (2), the reference current instruction is set in the current controllerAnd the actual current command i fed back in step S3.1_d′、i_q' A difference operation is carried out to obtain an error value, and the current controller forms a closed loop system by controlling the error value.