CN111431460A - Sensorless model prediction flux linkage control method for permanent magnet synchronous motor - Google Patents

Abstract

The invention belongs to the field of electromechanical control and discloses a sensorless model prediction flux linkage control method for a permanent magnet synchronous motor. Firstly, observing the rotation speed omega and the rotor position angle theta of the motor through a sliding mode observer and a phase-locked loop based on SOGI_e(ii) a Then, the rotation speed ω is given^*And the rotation speed omega is used for obtaining the given torque T through a rotation speed ring SMC controller_e ^*(ii) a Then, the rotational speed ω and the d/q axis current i_d/i_qObserving load disturbancesDynamic value

And perturbing the load by a value

Feed forward compensation to a given torque T_e ^*(ii) a Finally, the observed rotating speed omega and the rotor position angle theta are measured_eGiven torque T_e ^*Load disturbance value

And the three-phase voltage u obtained by sampling_a/u_b/u_cThree-phase current i_a/i_b/i_cAnd substituting the model prediction flux linkage control module for operation. The method adopts a mode of a sliding mode observer and an improved phase-locked loop to improve the estimation precision of the rotor position, simultaneously predicts flux linkage control based on a model, does not need current loop parameter and weight coefficient setting, combines the sliding mode control with a load disturbance observer, and improves the robustness and the anti-interference capability of a system.

Description

Sensorless model prediction flux linkage control method for permanent magnet synchronous motor

Technical Field

The invention relates to the field of electromechanical control, in particular to a sensorless model prediction flux linkage control method for a permanent magnet synchronous motor.

Background

The permanent magnet synchronous motor position sensorless control technology utilizes related electric signals in a winding to estimate the position and the rotating speed of a rotor, thereby omitting a mechanical sensor, reducing the volume and the cost of a motor and increasing the reliability of a system. Current position estimation algorithms can be divided into two categories, signal injection-based and observer-based. The former uses the salient polarity of the motor to estimate the position of the rotor, but the continuous injection of the excitation signal requires complex signal processing, resulting in low utilization rate of the inverter voltage and slow dynamic response. The latter estimates the rotating speed by means of the counter electromotive force in a dynamic model, and is easy to realize in engineering. The sliding mode observer algorithm is one of the latter, has simple structure, strong robustness and fast dynamic response, but also has the problems of difficult filtering, large estimation error of a rotor position angle, delayed estimation value from an actual value, poor low-speed performance and the like.

In addition, for the position sensorless control technology of the permanent magnet synchronous motor, researchers have conducted extensive research based on various control technologies, such as vector control, direct torque control, sliding mode control, fuzzy control and the like, but these control technologies all have certain disadvantages in application, such as large torque ripple, poor robustness, poor dynamic effect, complex algorithm and the like. Therefore, the research on the position-sensor-free control algorithm with accurate rotor position tracking, strong system robustness, small torque pulsation and good dynamic effect has wide development prospect.

Disclosure of Invention

In view of this, the present invention provides a sensorless model predictive flux linkage control method for a permanent magnet synchronous motor, which can accurately track rotor position information, improve system robustness, suppress torque ripple, and improve dynamic operation effect.

The invention provides a sensorless model prediction flux linkage control method for a permanent magnet synchronous motor, which comprises the following steps of:

s1, sampling three-phase current i_a/i_b/i_cAnd voltage u_a/u_b/u_cObtaining αβ axis current i after coordinate transformation of C L ARK and PARK_α/i_βAnd αβ Axis Voltage u_α/u_βAnd dq-axis current i_d/i_qαβ axis current i_α/i_βAnd αβ Axis Voltage u_α/u_βEstimation of extended back electromotive force E by substituting sliding mode observer_αAnd E_β；

S2, expanding the counter electromotive force E_αAnd E_βSubstituting into a phase-locked loop based on SOGI (second-order generalized integrator), and observing the rotation speed omega and the rotor position angle theta_e；

S3, mixing the dq axis current i_d/i_qSubstituting the sum of the rotation speed omega into a load disturbance observer to obtain a load disturbance value

S4, setting the rotating speed omega^*And the rotating speed omega obtains the given torque T through a rotating speed ring SMC (sliding mode control) controller_e ^*Given a torque T_e ^*Obtaining a given flux linkage psi via MTPA_s ^*；

S5, disturbing the load

Feed forward compensation to a given torque T_e ^*And with torque T_eObtaining a torque error Te 'by subtracting, and obtaining a load angle deviation delta through the torque error Te' by a PI controller_sfCalculated value of angle of lift and load_sfObtaining the load angle reference value by difference_sf ^*；

S6, enabling the voltage vector u of the three-phase inverter to be_sSubstituting the rotation speed omega and the dq axis current id/iq into a flux linkage prediction module to predict and obtain a flux linkage psi at the moment of k +1_d(k+1)/ψ_q(k+1)；

S7, giving a magnetic linkage psi_s ^*Reference value of load angle_sf ^*Magnetic linkage psi at time k +1_d(k+1)/ψ_q(k +1), rotor position angle θ_eSubstituting the sum of the rotation speed omega into a minimum cost function module to output a duty ratio signal S_a、S_b、S_cThen the duty ratio signal S_a、S_b、S_cAnd the input three-phase inverter controls the on and off of the three-phase inverter, so that the permanent magnet synchronous motor is driven.

Further, the extended back electromotive force E is generated in step S1_αAnd E_βThe estimation formula of (c) is:

wherein sat(s) is a sliding mode surface control function,

in the formula: z is a radical of_α、z_βControlling a function component for the sliding mode surface;

to estimate the current component; Δ is the boundary layer thickness; k is a radical of_satAdaptive rate, k, of sinusoidal saturation function of varying boundary layer_sat＝k_l·ω，k_lIs a positive real number, and ω is the rotational speed.

Further, the rotation speed ω and the rotor position angle θ are set in step S2_eThe calculation formula of (2) is as follows:

θ_e＝∫ωdt,

wherein λ ═ L_d-L_q)(ωi_d-pi_q)+ωψ_f；K_p/K_iRespectively, proportional/integral coefficients;

is the transfer function of the SOGI;_θ(s) is the amount of positional angle error; '_θ(s) is the filtered position angle error amount; k is a radical of_θIs an error amplification factor.

Further, the load disturbance value in step S3

The calculation formula of (2) is as follows:

in the formula: u is a sliding mode surface control function; g is a feedback gain;

is an electrical angular velocity estimate.

Further, in step S4, a torque T is given_e ^*The calculation formula of (2) is as follows:

in the formula:

c is the sliding mode surface coefficient, α and k_nAll the coefficients are exponential approach rate coefficients and satisfy the following conditions:>0，α≥2，k_n>0。

compared with the prior art, the invention has the advantages and effects that:

the method comprises the steps of applying a model prediction flux linkage control algorithm to control of a position-free sensor, designing a sliding mode observer, a rotating speed loop SMC controller and a load disturbance observer by adopting a boundary layer variable sine type saturated function to reduce system buffeting, adding an SOGI into a phase-locked loop and introducing real-time rotating speed to achieve self-adaptive filtering regulation, wherein the rotating speed and the rotor position angle obtained by the phase-locked loop based on the SOGI are more accurate and are further input or fed back to the rotating speed loop SMC controller and the load disturbance observer to optimize deviation regulation and disturbance compensation, so that the dynamic effect and robustness of a control system are improved, and torque pulsation is restrained. Meanwhile, the salient-polarity permanent magnet synchronous motor is used as a research object, and the application range of the control method is widened.

Drawings

Fig. 1 is a control block diagram of a sensorless model predictive flux linkage control method for a permanent magnet synchronous motor according to an embodiment of the present invention;

FIG. 2 is a schematic block diagram of an SOGI-based phase-locked loop according to an embodiment of the present invention;

FIG. 3 is a schematic block diagram of a load disturbance observer provided by an embodiment of the present invention;

FIG. 4 is a functional block diagram of a speed loop SMC controller provided by an embodiment of the present invention;

FIG. 5 is a diagram of simulation results of the PMSM speed without the position sensor control algorithm provided by the embodiment of the present invention;

FIG. 6 is a comparison graph of simulation results of rotor position angle errors of a PMSM between a position sensorless control algorithm and a conventional position sensorless control algorithm according to an embodiment of the present invention;

FIG. 7 is a comparison graph of simulation results of PMSM torque for a position sensorless control algorithm and a conventional position sensorless control algorithm provided in an embodiment of the present invention;

fig. 8 is a control block diagram of a conventional sensorless control method of a permanent magnet synchronous motor.

Detailed Description

The present invention will be described in further detail below by way of examples with reference to the accompanying drawings, which are illustrative of the present invention and are not to be construed as limiting the present invention.

As shown in fig. 1, the present invention provides a sensorless model predictive flux linkage control method for a permanent magnet synchronous motor, comprising the following steps:

s1, sampling three-phase current i_a/i_b/i_cAnd voltage u_a/u_b/u_cObtaining αβ axis current i after coordinate transformation of C L ARK and PARK_α/i_βAnd αβ Axis Voltage u_α/u_βAnd dq-axis current i_d/i_qαβ axis current i_α/i_βAnd αβ Axis Voltage u_α/u_βEstimation of extended back electromotive force E by substituting sliding mode observer_αAnd E_β；

Specifically, the invention extends the back electromotive force E_αAnd E_βThe estimation process of (2) is illustrated as follows:

αβ the stator voltage equation for the coordinate system is:

in the formula u_α、u_βRespectively αβ axis voltage i_α、i_βαβ axis currents, L_d、L_qDq-axis inductances, respectively; r is a stator resistor; ω is the rotational speed; p is a differential operator; e_α、E_βTo extend the back emf; psi_fIs a permanent magnet flux linkage; theta_eIs the rotor position angle.

The equation (1) is rewritten as a current state equation with the stator current as a state variable:

selecting a sliding mode surface s (x) as 0 on a stator current track as follows:

in the formula:

to estimate the current component;

to estimate the current error component.

To obtain extended back emf, the sliding mode observer is designed as:

in the formula: z is a radical of_α、z_βIs a sliding mode surface control function component.

And (3) subtracting the equations (6) and (3) to obtain an error equation of the stator current as follows:

the sliding mode surface control function in the formulas (5) and (6) is shown as a formula (7).

In the formula: Δ is the boundary layer thickness, k_satAdaptive rate, k, of sinusoidal saturation function of varying boundary layer_sat＝k_l·ω，k_lIs a positive real number, and ω is the rotational speed. The sliding mode surface control function can effectively reduce the buffeting of the system and has the capability of real-time adjustment along with the change of the rotating speed.

When the state variable reaches the sliding mode surface, i.e., s (x) is 0, the observer state will be maintained. According to the equivalent control principle of the sliding mode variable structure control, the following can be obtained:

s2, expanding the counter electromotive force E_αAnd E_βSubstituting the phase-locked loop based on the SOGI to observe and obtain the rotating speed omega and the rotor position angle theta through the phase-locked loop based on the SOGI_e；

Specifically, the rotational speed ω and the rotor position angle θ in the present invention_eThe calculation process of (a) is illustrated as follows:

the transfer function of the SOGI is:

wherein λ ═ L_d-L_q)(ωi_d-pi_q)+ωψ_f，_θ(s) is a position angle error amount'_θ(s) is the amount of position angle error after filtering, k_θIs an error amplification factor.

Expanding the counter electromotive force E in the formula (9)_αAnd E_βInputting a phase-locked loop based on the SOGI to obtain the rotation speed omega and the rotor position angle theta_eThe schematic block diagram is shown in fig. 2. The SOGI is added into a phase-locked loop and the real-time rotating speed is introduced to adjust the bandwidth and the error so as to improve the self-adaptive filtering effect of the phase-locked loop, thereby reducing the harmonic interference caused by the buffeting of the system and improving the estimation precision of the rotor position angle.

In the formula: k_pIs a proportionality coefficient, K_iIs an integral coefficient.

S3, mixing the dq axis current i_d/i_qSubstituting the sum of the rotation speed omega into a load disturbance observer to obtain a load disturbance value

Specifically, the load disturbance value in the present invention

The calculation process of (a) is illustrated as follows:

the voltage equation in dq coordinate system is:

the torque equation:

equation of motion:

in the formula, T_lIs the load torque; b is friction torque viscosity coefficient; j is moment of inertia.

According to PMSM torque and motion equations shown in equations (13) and (14), and taking the load torque as an extended state variable, constructing an extended state equation as follows:

in the formula: since the electrical time constant is much smaller than the mechanical time constant, the load torque can be considered constant during the control period, i.e. the load torque is constant

Based on the equation (15), the load torque and the rotor electrical angular velocity are used as state variables, the velocity estimation error is used as a sliding mode switching surface, and a sliding mode plane is defined as

An extended sliding-mode observer is established as

In the formula:

g is a feedback gain;

respectively an electrical angular velocity estimate and a load disturbance estimate.

According to the equivalent control principle of sliding mode variable structure control, the load disturbance estimation value can be obtained

The functional block diagram is shown in fig. 3:

according to the formula (17), the load disturbance observer also adopts a sliding mode surface control function with the real-time adjustment capability along with the change of the rotating speed, so that the obtained load disturbance estimation value is more real-time and accurate.

S4, setting the rotating speed omega^*And the rotation speed omega obtains the given torque T through a rotation speed ring SMC controller_e ^*Given a torque T_e ^*Obtaining a given flux linkage psi via MTPA_s ^*；

Specifically, the predetermined torque T is set in the present invention_e ^*And a given flux linkage psi_s ^*The calculation process of (a) is illustrated as follows:

the rotating speed state equation is constructed as follows:

from formulae (14) and (18):

selecting a linear sliding mode surface function as follows: s ═ cx₁+x₂(20)

The following is derived from equation (20):

substituting (21) for formula (20) to obtain:

the design index approach rate is: s ═ x |₁|αsat(s)-k_ns，>0，α≥2，k_n>0 (23)

The exponential approximation rate is substituted into formula (22) to obtain the given torque T_e ^*The schematic block diagram is shown in fig. 4:

as can be seen from formula (24), in-x₁|^αs and-k_ns, the state variable can rapidly approach the sliding mode surface to be stable, and sat(s) can further reduce the buffeting of the system.

Will be provided with

And (3) as a system disturbance feedforward compensation to load torque input, obtaining a torque error as follows:

the stability of the approach rate proves that:

the reference value of the flux linkage amplitude is calculated by an MTPA algorithm, the method considers the influence of weak magnetism and efficiency when the motor runs, and the calculation formula is as follows:

s5, disturbing the load

Feed forward compensation toConstant torque T_e ^*And with torque T_eMaking a difference to obtain a torque error T_e', torque error T_e' obtaining the load angular deviation Delta through a PI controller_sfCalculated value of angle of lift and load_sfObtaining the load angle reference value by difference_sf ^*；

In step S5, the load angle reference value in the present invention_sf ^*The calculation process of (a) is illustrated as follows:

the mathematical model of the permanent magnet synchronous motor under dq coordinates is as follows:

equation (27) is substituted for equation (12) to derive the current differential equation:

discretization of equation (29) yields:

in the formula: t is_sIs a control cycle.

Substituting equation (30) into (29) yields the predicted stator flux linkage at time (k +1) as:

the sampled stator current i at the current moment_s(k) Applied to equations (27) - (29), the stator flux linkage vector ψ at time k_s(k) And torque T_e(k) Can be calculated. According to the definition of the load angle, the load angle at the moment k_sf(k) Can be calculated as:

will give a given torque T_e ^*Torque T at time k_e(k) The difference value is input into a PI controller, and the load angle deviation is obtained as follows:

load angle at time k_sf(k) Deviation from load angle Δ_sf(k) The reference load angle at the (k +1) time is obtained by addition_sf ^*(k +1) is:

in the formula, K_PTAnd K_ITRespectively, a proportional gain and an integral gain of the rotating speed PI controller.

S6, converting the voltage vector u of the two-level voltage source type inverter_sSubstituting the rotation speed omega and the dq axis current id/iq into a flux linkage prediction module to predict and obtain a flux linkage psi at the moment of k +1_d(k+1)/ψ_q(k+1)；

S7, giving a magnetic linkage psi_s ^*Reference value of load angle_sf ^*Magnetic linkage psi at time k +1_d(k+1)/ψ_q(k +1), rotor position angle θ_eSubstituting the sum of the rotation speed omega into a minimum cost function module to output a duty ratio signal S_a、S_b、S_cThen the duty ratio signal S_a、S_b、S_cAnd the input three-phase inverter controls the on and off of the three-phase inverter, so that the permanent magnet synchronous motor is driven.

Step S6, the flux linkage ψ at time k +1 is described in the present invention_d(k+1)/ψ_qThe prediction process of (k +1) is illustrated as follows:

combining equation (33) and equation (34), the reference value of the flux linkage vector at time (k +1) in the dq coordinate system is:

step S7, the operation principle of the minimum cost function module in the present invention is described as follows:

predicting flux linkage vectors under the action of 7 different basic voltage vectors (us is u0 or u7, u1, … and u6), respectively calculating corresponding objective functions of the different flux linkage vectors, and selecting the voltage vector which enables the objective function to be minimum as the optimal output of the converter, wherein the objective function is as follows:

in the formula: psi_d(k+1)/ψ_q(k +1) is the flux linkage vector at time k +1, psi_d ^*(k+1)/ψ_q ^*And (k +1) is a reference value of the flux linkage vector at the time of (k + 1).

According to a control block diagram shown in figure 1, MAT L AB/SIMU L INK software is used for building a permanent magnet synchronous motor sensorless model to predict flux linkage control system simulation, and motor parameters are selected as follows, wherein the motor parameters comprise a rated power of 600W, a rated rotating speed of 750rpm, a rated torque of 7.6 N.m, a pole pair number of 13, a permanent magnet flux linkage amplitude of 0.08Wb, an armature winding resistance of 0.8 omega, quadrature-direct axis inductances of 6.5mH and 6.3mH respectively, and a rotational inertia of 0.004 kg.m²The friction torque viscosity coefficient was 0.0004N · m · s. The simulation gives conditions as follows: the idling speed is initially given at 50rpm, the speed is abruptly changed to 500rpm at 0.2s, and the load is 4 N.m at 0.4 s. Under the above conditions, the simulation results of the rotation speed under the method of the present patent are shown in fig. 5, and the simulation results of the rotor position angle error and the motor torque under the conventional sensorless method and the method of the present patent are shown in fig. 6 and 7. A control block diagram of the conventional sensorless control method is shown in fig. 8. As can be seen from FIG. 5, the method of the invention can effectively track the actual rotating speed, the estimated rotating speed has small pulsation, the overshoot is small when the rotating speed is suddenly changed, the given rotating speed value can be tracked in a short time when the torque is suddenly changed, and the robustness is good; as can be seen from FIGS. 6 and 7, the method of the present invention has the advantages of more accurate tracking of the rotor position angle and stronger suppression capability to the torque ripple.

The above description of the present invention is intended to be illustrative. Various modifications, additions and substitutions for the specific embodiments described may be made by those skilled in the art without departing from the scope of the invention as defined in the accompanying claims.

Claims (5)

1. A sensorless model prediction flux linkage control method for a permanent magnet synchronous motor is characterized by comprising the following steps: comprises the following steps:

s1, sampling three-phase current i_a/i_b/i_cAnd voltage u_a/u_b/u_cObtaining αβ axis current i after coordinate transformation of C L ARK and PARK_α/i_βAnd αβ Axis Voltage u_α/u_βAnd dq-axis current i_d/i_qαβ axis current i_α/i_βAnd αβ Axis Voltage u_α/u_βEstimation of extended back electromotive force E by substituting sliding mode observer_αAnd E_β；

S2, expanding the counter electromotive force E_αAnd E_βSubstituting the phase-locked loop based on the SOGI to observe the rotation speed omega and the rotor position angle theta_e；

S3, mixing the dq axis current i_d/i_qSubstituting the sum of the rotation speed omega into a load disturbance observer to obtain a load disturbance value

S4, setting the rotating speed omega^*And the rotation speed omega obtains the given torque T through a rotation speed ring SMC controller_e ^*Given a torque T_e ^*Obtaining a given flux linkage psi via MTPA_s ^*；

S5, disturbing the load

Feed forward compensation to a given torque T_e ^*And with torque T_eMaking difference to obtain a torque error T'_eTorque error T'_eObtaining the load angle deviation delta through a PI controller_sfCalculated value of angle of lift and load_sfObtaining the load angle reference value by difference_sf ^*；

S6, enabling the voltage vector u of the three-phase inverter to be_sSubstituting the rotation speed omega and the dq axis current id/iq into a flux linkage prediction module to predict and obtain a flux linkage psi at the moment of k +1_d(k+1)/ψ_q(k+1)；

S7, giving a magnetic linkage psi_s ^*Reference value of load angle_sf ^*Magnetic linkage psi at time k +1_d(k+1)/ψ_q(k +1), rotor position angle θ_eSubstituting the sum of the rotation speed omega into a minimum cost function module to output a duty ratio signal S_a、S_b、S_cThen the duty ratio signal S_a、S_b、S_cAnd the input three-phase inverter controls the on and off of the three-phase inverter, so that the permanent magnet synchronous motor is driven.

2. The sensorless model predictive flux linkage control method for the permanent magnet synchronous motor according to claim 1, wherein the extended back electromotive force E is used in step S1_αAnd E_βThe estimation formula of (c) is:

wherein sat(s) is a sliding mode surface control function,

z_α、z_βcontrolling a function component for the sliding mode surface;

to estimate the current component; Δ is the boundary layer thickness; k is a radical of_satAdaptive rate, k, of sinusoidal saturation function of varying boundary layer_sat＝k_l·ω，k_lIs a positive real number, and ω is the rotational speed.

3. A pmsm sensorless model predictive magnet in accordance with claim 1Chain control method, characterized in that in step S2, the rotation speed ω and the rotor position angle θ are set_eThe calculation formula of (2) is as follows:

wherein λ ═ L_d-L_q)(ωi_d-pi_q)+ωψ_f；K_p/K_iRespectively, proportional/integral coefficients;

is the transfer function of the SOGI;_θ(s) is the amount of positional angle error; '_θ(s) is the filtered position angle error amount; k is a radical of_θIs an error amplification factor.

4. The sensorless model predictive flux linkage control method for the permanent magnet synchronous motor according to claim 3, wherein the load disturbance value in step S3

The calculation formula of (2) is as follows:

in the formula: u is a sliding mode surface control function; g is a feedback gain;

is an electrical angular velocity estimate.

5. The sensorless model predictive flux linkage control method of the permanent magnet synchronous motor according to claim 3, wherein the torque T is given in step S4_e ^*The calculation formula of (2) is as follows:

in the formula:

c is the sliding mode surface coefficient, α and k_nAll the coefficients are exponential approach rate coefficients and satisfy the following conditions:>0，α≥2，k_n>0。

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