CN115603628B - Sensorless dynamic improvement method for single current regulation of permanent magnet synchronous motor - Google Patents
Sensorless dynamic improvement method for single current regulation of permanent magnet synchronous motor Download PDFInfo
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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- H—ELECTRICITY
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- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0085—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for high speeds, e.g. above nominal speed
- H02P21/0089—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for high speeds, e.g. above nominal speed using field weakening
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/18—Estimation of position or speed
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- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/022—Synchronous motors
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- 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
- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
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Abstract
The invention discloses a sensorless dynamic improving method for single current regulation of a permanent magnet synchronous motor, which comprises the following steps: based on the weak magnetic control of the voltage vector angle under square wave modulation, the corresponding relation between the voltage vector angle and the electromagnetic torque is obtained; calculating the relation between the effective adjusting range of the voltage vector angle under the weak magnetic control and the single current regulator, and removing the uncontrollable section; rotor position estimation value obtained by taking sliding mode observer in rotating coordinate system as position observation modelThereby forming a rotating speed ring; and a single q-axis current regulator field weakening control link is introduced into a closed loop structure of a position-free sensor based on dq-SMO to improve current dynamic response and estimated rotation speed tracking capacity. The method of the invention only adopts one current regulator no matter the traction working condition or the braking working condition, has good dynamic response of current and eliminates the switching between traction/braking control states.
Description
Technical Field
The invention belongs to the technical field of alternating current motor transmission control, and particularly relates to a sensorless dynamic lifting strategy for single current regulation of a permanent magnet synchronous motor.
Background
The motor train unit traction transmission unit has the characteristics of high voltage, large current and wide operation speed range, and meanwhile, the traction motor is required to have the operation capability under the working conditions of low switching frequency and square waves. Along with the rapid development of high-speed rail trains, permanent magnet synchronous motors with wide speed regulation range, high power density and low energy consumption become research hotspots in the current motor train unit traction field, and the existing motor train unit train traction systems all adopt mechanical position/speed sensors to acquire position or rotation speed signals of the motors. In the actual running process of the high-speed train, the electromagnetic environment is complex, the vibration is severe, the mechanical sensor is easy to fail, the traction system is further caused to fail, the large torque impact is caused, and the key components such as a bearing, a gear and a motor are damaged when serious, so that the running safety of the train is endangered. The driving technology without the position sensor can fundamentally eliminate the potential safety hazard, and has the advantages of strong anti-interference capability, high integration level, long service cycle and the like.
In the field of motor train unit traction, the power level of the converter is higher, the switching device is limited by heat dissipation capacity, the highest switching frequency is usually within 500Hz, the fundamental frequency of the permanent magnet synchronous traction motor can often reach more than 300Hz, and the switching frequency during synchronous 3-frequency division modulation can reach 900Hz and is far higher than the limit value of the switching frequency. In order to reduce the switching loss and prolong the service life of the high-power switching tube, single-pulse square wave modulation is generally used when the motor enters a field weakening region, namely, the rotating speed is higher than the rated rotating speed and the terminal voltage amplitude is saturated, so that the bus voltage is fully utilized and the maximum torque output range is reached while the requirements of power devices are met. The amplitude of the voltage vector under square wave modulation is fixed, and only the voltage vector angle can be adjusted.
At present, the method for controlling the field weakening of the permanent magnet synchronous motor mainly comprises double-current regulator control and voltage vector angle control. The dual current regulator still has the characteristic of dual regulation targets during field weakening control, which conflicts with the characteristics of square wave working conditions, and redundant processing is required for the regulator, so that saturation is prevented. The torque output is controlled through the voltage vector angle, so that the square wave modulation characteristic is more accordant, and the dynamic weak-current track is very difficult to plan under the non-position closed loop only by the voltage vector angle adjustable mode, and meanwhile, the dynamic performance of the dynamic weak-current track is relatively poor. Therefore, in the permanent magnet traction system, a single current regulator is introduced by combining the modulation characteristic under the square wave working condition, and the method has important significance for improving the dynamic response capability of the voltage vector angle field weakening control under the operation without a position sensor.
Disclosure of Invention
The invention aims to provide a sensorless dynamic lifting strategy for single current regulation of a permanent magnet synchronous motor, and the lifting of the sensorless flux weakening control dynamic performance under square wave modulation is realized by introducing a single q-axis current regulator in a square wave flux weakening region.
The technical scheme adopted by the invention is that a sensorless dynamic lifting strategy for single current regulation of a permanent magnet synchronous motor is implemented according to the following steps:
step 1, based on weak magnetic control of a voltage vector angle under square wave modulation, obtaining a corresponding relation between the voltage vector angle and electromagnetic torque;
step 2, calculating the relation between the effective adjusting range of the voltage vector angle under the weak magnetic control and the single current regulator, and removing an uncontrollable section;
step 3, obtaining a rotor position estimated value by taking a sliding mode observer in a rotating coordinate system as a position observation modelThereby forming a rotating speed ring;
and 4, introducing a single q-axis current regulator field weakening control link into the closed loop structure of the position-free sensor based on dq-SMO to improve current dynamic response and estimated rotation speed tracking capacity.
The present invention is also characterized in that,
in step 1, specifically:
step 1.1, under the working condition of high-rotation-speed square waves, establishing a permanent magnet synchronous motor steady-state mathematical model based on a synchronous rotation coordinate system, wherein the steady-state mathematical model is shown as (1) and (2);
T e ＝1.5P[ψ f +(L d -L q )i d ]i q (2)；
in the formulas (1) and (2), u d Is the stator voltage direct axis component; u (u) q Is the stator voltage quadrature component; omega e Is the synchronous electrical angular velocity; t (T) e Is electromagnetic torque; p is the pole pair number of the motor; l (L) d Is the direct axis component of the stator inductance; l (L) q Is the stator inductance quadrature axis component; psi phi type f Is the permanent magnet flux linkage of the motor; i.e d Is the stator current direct axis component; i.e q Is the stator current quadrature component;
step 1.2, the corresponding relation between d-axis and q-axis voltages and the voltage vector amplitude is shown as a formula (3);
in the formula (3), θ VVA Is the voltage vector angle; u (u) max Is the magnitude of the voltage vector, u max ＝2u dc /π，u dc Is the DC bus voltage;
step 1.3, the corresponding relation between electromagnetic torque and voltage vector angle is obtained by the combination formula (1), the formula (2) and the formula (3), and is shown as the formula (4);
deriving the formula (4) to obtain the formula (5):
in step 2, specifically:
step 2.1, in the plane of the voltage ud-uq, a voltage vector of 0rad is positioned on a ud positive half shaft, the anticlockwise direction is taken as the rotation direction of the voltage vector, when the angle of the voltage vector is changed from 0 to 2 pi, the endpoints of different voltage vectors are connected into a circle, and a voltage vector angle distribution diagram on the voltage plane can be obtained;
2.2, carrying out coordinate transformation on the voltage vector angle distribution on the voltage plane to obtain a distribution diagram of the voltage vector angle on the current plane, wherein the effective voltage vector angle ranges are all 0, pi, and the equations of the current limit circle and the voltage limit ellipse are shown in a formula (6);
step 2.3, drawing a relation graph of motor torque and a derivative function thereof and a voltage vector angle by the formula (4) and the formula (5), wherein the positive and negative signs of torque values indicate that the ranges of the voltage vector angles in the braking and traction states are respectively as follows: [0, pi/2) and (pi/2, pi ]; when the output torque is 0, the voltage vector angle is pi/2;
step 2.4, combining the formula (1) and the formula (3) to obtain i d And i q The relation with the voltage vector angle is shown in the formula (7);
step 2.5, based on the range [0, pi ] of the voltage vector angle, the derivative function of the formula (7) is shown as a formula (8);
in step 3, specifically:
step 3.1, establishing a dq sliding mode observer model as shown in a formula (9);
wherein,and->Respectively stator d-axis current observation value and q-axis current observation value, omega re The angular velocity of the rotor is represented by D, which is a differential operator;
V d and V q The control inputs of the synovial membrane observers are respectively; the value of the function sgn is +.> Gain for a sliding mode observer;
step 3.2, performing low-pass filtering through the PI module to obtain the estimated angular velocity of the rotorAs shown in formula (10);
wherein K is po Is proportional gain, K io Is the integral gain;
estimating angular velocity for a rotorPerforming integral operation to obtain rotor position estimated value +.>Thereby forming a rotation speed ring.
In step 4, specifically:
step 4.1, calculating a preliminary d-axis current instruction through the MTPA control relationAs shown in formula (11);
step 4.2, adjusting a current instruction according to the weak magnetic control target; the method comprises the following steps:
step 4.2.1 d-and q-axis feed-forward voltages provided by the feed-forward linkAnd->Calculating feedback voltage amplitude +.>As shown in formula (12);
step 4.2.2, the voltage vector magnitude u max PI adjustment is carried out on the error of the feedback voltage amplitude value to obtain weak magnetic compensation current delta i d，wkfd ；
Step 4.2.3, the weak magnetic compensation current delta i is output through the voltage closed loop d，wkfd Correcting the d-axis current instruction to an optimal current track as shown in a formula (13);
step 4.2.4, calculating the q-axis current instruction under the weak magnetic control constraint through a torque formulaAs shown in formula (14);
step 4.3, obtaining a final voltage output instruction based on voltage vector angle control of the single q-axis current regulator; the method comprises the following steps:
step 4.3.1 for three-phase current i A 、i B 、i C Sampling, clark conversion and rotor position estimation value obtained in the step 3Performing Park conversion to obtain stator currentQuadrature component i q ；
Step 4.3.2, q-axis current instruction under weak magnetic control constraint obtained in step 4.2And the stator current quadrature component i obtained in step 4.3.1 q The voltage vector angle θ can be obtained from equation (15) VVA ；
Wherein K is p Is proportional gain, K i Is the integral gain;
and 4.3.3, calculating d-axis and q-axis command voltages output under the voltage vector angle field weakening control of the single q-axis current regulator according to the formula (3), and improving the current dynamic response and estimated rotating speed tracking capacity.
The beneficial effects of the invention are as follows:
1) The sensorless dynamic improvement of the motor train unit permanent magnet synchronous motor single-current regulator under the square wave modulation under the weak magnetic control is realized;
2) Essentially eliminating the problems of regulator adjustment conflict and saturation existing in the double-current regulator flux weakening control method;
3) Only one current regulator is adopted, so that the dynamic response of the current is good, and the switching between traction/braking control states is eliminated;
drawings
FIG. 1 is a functional block diagram of a sensorless dynamic boost strategy for single current regulation of a permanent magnet synchronous motor of the present invention;
FIG. 2 is a block diagram of the experimental system hardware circuit used in the sensorless dynamic boost strategy of the single current regulation of the permanent magnet synchronous motor of the present invention;
FIG. 3 is a block diagram of a flux weakening control strategy under single q-axis current regulation of the permanent magnet synchronous motor of the invention;
FIG. 4 is a diagram of the voltage vector angle definition in the method of the present invention;
FIG. 5 is a graph of voltage vector angle distribution on a voltage plane in the method of the present invention;
FIG. 6 is a graph of voltage vector angle distribution in the current plane in the method of the present invention;
FIG. 7 is a graph of the relationship between the transfer function and the voltage vector in the present invention;
FIG. 8 is a PI module in a sensorless dynamics boost strategy for single current regulation of a permanent magnet synchronous motor according to the present invention;
FIG. 9 is a graph of experimental waveform of current response of the alternating and direct axes under constant speed load torque variation without position sensor according to the present invention;
FIG. 10 is a waveform diagram of the voltage vector angle range and the speed tracking performance experiment of the invention under constant speed load torque variation without a position sensor;
FIG. 11 is a waveform diagram of the speed tracking performance experiment of the present invention under constant load torque without position sensor speed variation.
Detailed Description
The invention relates to a sensorless dynamic lifting strategy for single current regulation of a permanent magnet synchronous motor, which is shown in a schematic block diagram in fig. 1, is based on a dq-SMO sensorless closed-loop structure, and is used for designing a single q-axis current regulator flux weakening control link, as shown in fig. 3, and improving current dynamic response and estimated rotation speed tracking capacity; the method is implemented according to the following steps:
step 1, based on weak magnetic control of a voltage vector angle under square wave modulation, obtaining a corresponding relation between the voltage vector angle and electromagnetic torque; the method comprises the following steps:
step 1.1, under the working condition of high-rotation-speed square waves, establishing a permanent magnet synchronous motor steady-state mathematical model based on a synchronous rotation coordinate system, wherein the steady-state mathematical model is shown as (1) and (2);
T e ＝1.5P[ψ f +(L d -L q )i d ]i q (2)；
in the formulas (1) and (2), u d Is fixed toA sub-voltage direct axis component; u (u) q Is the stator voltage quadrature component; omega e Is the synchronous electrical angular velocity; t (T) e Is electromagnetic torque; p is the pole pair number of the motor; l (L) d Is the direct axis component of the stator inductance; l (L) q Is the stator inductance quadrature axis component; psi phi type f Is the permanent magnet flux linkage of the motor; i.e d Is the stator current direct axis component; i.e q Is the stator current quadrature component;
step 1.2, as shown in fig. 4, the correspondence between d-axis and q-axis voltages and the voltage vector magnitude is shown in formula (3);
in the formula (3), θ VVA Is the voltage vector angle; u (u) max Is the amplitude of the voltage vector, u under the square wave working condition max ＝2u dc /π，u dc Is the DC bus voltage;
step 1.3, the corresponding relation between electromagnetic torque and voltage vector angle is obtained by the combination formula (1), the formula (2) and the formula (3), and the magnitude of output torque can be controlled by adjusting the voltage vector angle, as shown in the formula (4);
deriving the formula (4) to obtain the formula (5):
step 2, calculating the relation between the effective adjusting range of the voltage vector angle under the weak magnetic control and the single current regulator, and removing an uncontrollable section; the method comprises the following steps:
step 2.1, in the plane of the voltage ud-uq, a voltage vector of 0rad is positioned on a ud positive half shaft, the anticlockwise direction is taken as the rotation direction of the voltage vector, when the angle of the voltage vector is changed from 0 to 2 pi, the endpoints of different voltage vectors are connected into a circle, and a voltage vector angle distribution diagram on the voltage plane can be obtained, as shown in fig. 5;
step 2.2, performing coordinate transformation on the voltage vector angle distribution on the voltage plane to obtain a distribution diagram of the voltage vector angle on the current plane, as shown in fig. 6, wherein the effective voltage vector angle ranges are all in [0, pi ], and the equations of the current limit circle and the voltage limit ellipse are shown in formula (6);
step 2.3, the relation graph between the motor torque and the derivative thereof and the voltage vector angle can be drawn according to the formulas (4) and (5), as shown in fig. 7, the ranges of the voltage vector angle in the braking and traction states are respectively as follows: [0, pi/2) and (pi/2, pi ]; when the output torque is 0, the voltage vector angle is pi/2, which can correspond to the formula (4);
step 2.4, combining the formula (1) and the formula (3) to obtain i d And i q The relation with the voltage vector angle is shown in the formula (7);
step 2.5, according to the range of voltage vector angles [0, pi ]]The derivative of formula (7) is represented by formula (8) and is represented by di q /dθ VVA The characteristic that the current and the voltage vector angle of the q-axis are kept in monotonically increasing relation, only one group of adjusting parameters is needed for traction/braking working conditions, and the voltage vector angle control based on the single q-axis current regulator can be used for traction and braking working conditions in flux weakening control.
Step 3, obtaining a rotor position estimated value by taking a sliding mode observer in a rotating coordinate system as a position observation modelThereby forming a rotating speed ring, specifically:
step 3.1, establishing a dq sliding mode observer model as shown in a formula (9);
wherein,and->Respectively stator d-axis current observation value and q-axis current observation value, omega re The angular velocity of the rotor is represented by D, which is a differential operator;
V d and V q The control inputs of the synovial membrane observers are respectively; the value of the function sgn is +.> Gain for a sliding mode observer;
step 3.2, obtaining the estimated angular velocity of the rotor by a PI module, as shown in FIG. 8, and performing low-pass filteringAs shown in formula (10);
wherein K is po Is proportional gain, K io Is the integral gain;
estimating angular velocity for a rotorPerforming integral operation to obtain rotor position estimated value +.>Thereby forming a rotating speed ring;
and 4, introducing a single q-axis current regulator field weakening control link into the closed loop structure of the position-free sensor based on dq-SMO to improve current dynamic response and estimated rotation speed tracking capacity. The method comprises the following steps:
step 4.1, calculating a preliminary d-axis current instruction through the MTPA control relationAs shown in formula (11);
step 4.2, adjusting a current instruction according to the weak magnetic control target; the method comprises the following steps:
step 4.2.1 d-and q-axis feed-forward voltages provided by the feed-forward linkAnd->Calculating feedback voltage amplitude +.>As shown in formula (12);
step 4.2.2, the voltage vector magnitude u max And error in the amplitude of the feedback voltagePI regulation is carried out to obtain weak magnetic compensation current delta i d，wkfd ；
Step 4.2.3, the weak magnetic compensation current delta i is output through the voltage closed loop d，wkfd Correcting the d-axis current instruction to an optimal current track as shown in a formula (13);
step 4.2.4, calculating the q-axis current instruction under the weak magnetic control constraint through a torque formulaAs shown in formula (14);
and 4.3, obtaining a final voltage output instruction based on voltage vector angle control of the single q-axis current regulator. The method comprises the following steps:
step 4.3.1 for three-phase current i A 、i B 、i C Sampling, clark conversion and rotor position estimation value obtained in the step 3Performing Park conversion to obtain a stator current quadrature component i q ；
Step 4.3.2, q-axis current instruction under weak magnetic control constraint obtained in step 4.2And the stator current quadrature component i obtained in step 4.3.1 q The voltage vector angle θ can be obtained from equation (15) VVA ；
Wherein K is p Is proportional gain, K i Is the integral gain;
and 4.3.3, d-axis and q-axis command voltages output under the voltage vector angle field weakening control of the single q-axis current regulator can be calculated according to the formula (3), and the current dynamic response and estimated rotating speed tracking capacity are improved.
When the permanent magnet synchronous motor operates in a high-speed region, the permanent magnet synchronous motor is generally positioned in a square wave working condition, and the amplitude of a voltage vector under square wave modulation is fixed and only the voltage vector angle can be adjusted. The double-current regulator in the square wave field weakening control is extremely easy to saturate under the condition of direct current bus voltage limitation, so that the dynamic response capability of a current loop and a torque loop is reduced, the rotor position estimation error is increased, and the dynamic field weakening current track is extremely difficult to plan under a position-free closed loop only in a mode of voltage vector angle adjustment. Aiming at the field weakening control of the position-free sensor of the built-in permanent magnet synchronous motor under square wave modulation, the invention provides a field weakening control method of a single q-axis current regulator, so as to improve the field weakening control performance of the position-free sensor under square wave working conditions and improve the current dynamic response and estimated rotating speed tracking capacity.
The system hardware structure of the invention is shown in fig. 2, and comprises: the device comprises a rectification circuit, a filter circuit, a three-phase full-bridge inverter, an IPSM (interior permanent magnet synchronous motor), an FPGA controller, an isolation driving circuit, a rotary transformer and a current acquisition circuit; the system adopts a rotary transformer to collect real position signals. Fig. 9 to 11 are waveform diagrams of current dynamic response and estimated rotation speed tracking capability experiment of the motor in the square wave field weakening mode without position sensor control after using the single q-axis current regulator under the control of the hardware system shown in fig. 2. FIG. 9 is a graph of the AC-DC axis current response under single q-axis current regulation without position sensor: the rotation speed is constant at 1980r/min, the q-axis current actual value can well follow the instruction value to change when the torque step rises and falls, and the q-axis current can finish instruction tracking in 75ms (5 fundamental wave periods) and 60ms (4 fundamental wave periods) respectively in two dynamic processes of 5 Nm-15 Nm and 15 Nm-5 Nm, and at the moment, the rotation speed is close to the rated rotation speed, and the dynamic response is good. Fig. 10 is a waveform diagram of the voltage vector angle change range and the feedback estimated rotation speed when the constant speed load changes: the change of the load torque can change the voltage vector angle during the field weakening, and the estimated rotating speed keeps better tracking on the rotating speed given value. Fig. 11 is a waveform diagram of the rotational speed tracking at the time of a load torque constant rotational speed change: under the regulation of single q-axis current, the fluctuation of the estimated rotating speed reaches 25r/min, when the given rotating speed value is suddenly increased, the fed-back estimated rotating speed can reach a new steady-state value within about 100ms, and the whole process keeps good tracking performance for the given rotating speed.
Claims (1)
1. A sensorless dynamic improving method for single current regulation of a permanent magnet synchronous motor is characterized by comprising the following steps:
step 1, based on weak magnetic control of a voltage vector angle under square wave modulation, obtaining a corresponding relation between the voltage vector angle and electromagnetic torque; the method comprises the following steps:
step 1.1, under the working condition of high-rotation-speed square waves, establishing a permanent magnet synchronous motor steady-state mathematical model based on a synchronous rotation coordinate system, wherein the steady-state mathematical model is shown as (1) and (2);
T e ＝1.5P[ψ f +(L d -L q )i d ]i q (2)；
in the formulas (1) and (2), u d Is the stator voltage direct axis component; u (u) q Is the stator voltage quadrature component; omega e Is the synchronous electrical angular velocity; t (T) e Is electromagnetic torque; p is the pole pair number of the motor; l (L) d Is the direct axis component of the stator inductance; l (L) q Is the stator inductance quadrature axis component; psi phi type f Is the permanent magnet flux linkage of the motor; i.e d Is the stator current direct axis component; i.e q Is the stator current quadrature component;
step 1.2, the corresponding relation between d-axis and q-axis voltages and the voltage vector amplitude is shown as a formula (3);
in the formula (3), θ VVA Is the voltage vector angle; u (u) max Is the magnitude of the voltage vector, u max ＝2u dc /π，u dc Is the DC bus voltage;
step 1.3, the corresponding relation between electromagnetic torque and voltage vector angle is obtained by the combination formula (1), the formula (2) and the formula (3), and is shown as the formula (4);
deriving the formula (4) to obtain the formula (5):
step 2, calculating the relation between the effective adjusting range of the voltage vector angle under the weak magnetic control and the single current regulator, and removing an uncontrollable section; the method comprises the following steps:
step 2.1, in the plane of the voltage ud-uq, a voltage vector of 0rad is positioned on a ud positive half shaft, the anticlockwise direction is taken as the rotation direction of the voltage vector, when the angle of the voltage vector is changed from 0 to 2 pi, the endpoints of different voltage vectors are connected into a circle, and a voltage vector angle distribution diagram on the voltage plane can be obtained;
2.2, carrying out coordinate transformation on the voltage vector angle distribution on the voltage plane to obtain a distribution diagram of the voltage vector angle on the current plane, wherein the effective voltage vector angle ranges are all 0, pi, and the equations of the current limit circle and the voltage limit ellipse are shown in a formula (6);
step 2.3, drawing a relation graph of motor torque and a derivative function thereof and a voltage vector angle by the formula (4) and the formula (5), wherein the positive and negative signs of torque values indicate that the ranges of the voltage vector angles in the braking and traction states are respectively as follows: [0, pi/2) and (pi/2, pi ]; when the output torque is 0, the voltage vector angle is pi/2;
step 2.4, combining the formula (1) and the formula (3) to obtain i d And i q The relation with the voltage vector angle is shown in the formula (7);
step 2.5, based on the range [0, pi ] of the voltage vector angle, the derivative function of the formula (7) is shown as a formula (8);
step 3, obtaining a rotor position estimated value by taking a sliding mode observer in a rotating coordinate system as a position observation modelThereby forming a rotating speed ring; the method comprises the following steps:
step 3.1, establishing a dq sliding mode observer model as shown in a formula (9);
wherein,and->Respectively observing current values of a stator D axis and a stator q axis, wherein ωre is the angular speed of the rotor, and D is a differential operator;
V d and V q The control inputs of the synovial membrane observers are respectively; the value of the function sgn is +.> Gain for a sliding mode observer;
step 3.2, performing low-pass filtering through the PI module to obtain the estimated angular velocity of the rotorAs shown in formula (10);
wherein K is po Is proportional gain, K io Is the integral gain;
estimating angular velocity for a rotorPerforming integral operation to obtain rotor position estimated value +.>Thereby forming a rotating speed ring;
step 4, introducing a single q-axis current regulator field weakening control link into a dq-SMO-based position-free sensor closed loop structure to improve current dynamic response and estimated rotation speed tracking capacity;
the method comprises the following steps:
step 4.1, calculating a preliminary d-axis current instruction through the MTPA control relationAs shown in formula (11);
step 4.2, adjusting a current instruction according to the weak magnetic control target; the method comprises the following steps:
step 4.2.1 d-and q-axis feed-forward voltages provided by the feed-forward linkAnd->Calculating feedback voltage amplitude +.>As shown in formula (12);
step 4.2.2, the voltage vector magnitude u max PI adjustment is carried out on the error of the feedback voltage amplitude value to obtain weak magnetic compensation current delta i d,wkfd ；
Step 4.2.3, the weak magnetic compensation current delta i is output through the voltage closed loop d,wkfd Correcting the d-axis current instruction to an optimal current track as shown in a formula (13);
step 4.2.4, calculating the q-axis current instruction under the weak magnetic control constraint through a torque formulaAs shown in formula (14);
step 4.3, obtaining a final voltage output instruction based on voltage vector angle control of the single q-axis current regulator; the method comprises the following steps:
step 4.3.1 for three-phase current i A 、i B 、i C Sampling, clark conversion and rotor position estimation value obtained in the step 3Performing Park conversion to obtain a stator current quadrature component iq;
step 4.3.2, q-axis current instruction under weak magnetic control constraint obtained in step 4.2And the stator current quadrature axis component iq obtained in step 4.3.1, the voltage vector angle θ can be obtained from equation (15) VVA ；
Wherein K is p Is proportional gain, K i Is the integral gain;
and 4.3.3, calculating d-axis and q-axis command voltages output under the voltage vector angle field weakening control of the single q-axis current regulator according to the formula (3), and improving the current dynamic response and estimated rotating speed tracking capacity.
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