CN112003528A - IPMSM rotating speed estimation method based on discrete vector PI sliding mode observer - Google Patents

IPMSM rotating speed estimation method based on discrete vector PI sliding mode observer Download PDF

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CN112003528A
CN112003528A CN202010742246.1A CN202010742246A CN112003528A CN 112003528 A CN112003528 A CN 112003528A CN 202010742246 A CN202010742246 A CN 202010742246A CN 112003528 A CN112003528 A CN 112003528A
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vector
ipmsm
discrete
sliding mode
formula
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尹忠刚
曹新平
张彦平
刘静
李林涛
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Xian University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • 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
    • 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
    • H02P25/024—Synchronous motors controlled by supply frequency
    • H02P25/026—Synchronous motors controlled by supply frequency thereby detecting the rotor position
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters with pulse width modulation
    • 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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/14—Electronic commutators
    • H02P6/16—Circuit arrangements for detecting position
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
    • H02P6/182—Circuit arrangements for detecting position without separate position detecting elements using back-emf in windings
    • 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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/34—Modelling or simulation for control purposes
    • 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
    • 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 an IPMSM rotating speed estimation method based on a discrete vector PI sliding mode observer, which comprises the steps of firstly, establishing a discrete time complex vector IPMSM model; designing an IPMSM discrete vector PI sliding mode observer according to the discrete time complex vector IPMSM model; and (4) carrying out rotating speed estimation on the permanent magnet synchronous motor by adopting an IPMSM discrete vector PI sliding mode observer. The invention discloses an IPMSM rotating speed estimation method based on a discrete vector PI sliding mode observer, which solves the problems of buffeting and phase lag of the traditional sliding mode observer in the prior art.

Description

IPMSM rotating speed estimation method based on discrete vector PI sliding mode observer
Technical Field
The invention belongs to the technical field of high-performance permanent magnet synchronous motor control, and particularly relates to an IPMSM rotating speed estimation method based on a discrete vector PI sliding mode observer.
Background
An Interior Permanent Magnet Synchronous Motor (IPMSM) is widely applied to the transmission fields of rail transit, industrial control, household appliances and the like due to the characteristics of high efficiency, high power density, easiness in flux weakening and speed expansion and the like. The position-sensorless technology can effectively reduce the system cost and improve the system reliability. Inverter switching frequency (f) in medium and high power applications and high speed PMSM drivesPWM) Frequency ratio to fundamental frequency (carrier ratio f)ratio) Very low, sometimes close to or even less than 10; under the condition of low carrier ratio, the dynamic performance of the motor is limited due to the influence of current loop coupling effect. Meanwhile, the design of the rotor position observer needs to consider the influence of a time delay and a discretization mode on the observation precision. The position observer is usually designed in a continuous domain and then discretized, which has good control effect when the carrier ratio is high, but the precision of the position observer depends on a discretization method, and as the carrier ratio is reduced, larger digital control delay and discretization truncation error are generated, thereby reducing the effectiveness of the position observer. Therefore, intensive research on the IPMSM position sensorless control system with low carrier ratio is needed, that is, a proper discrete rotor position estimation method is designed to realize the system stability and dynamic performance with low carrier ratio.
At present, a position-less sensor observes counter electromotive force according to a motor model in a medium-speed and high-speed domain to further obtain the rotating speed of the motor and the position of a rotor, such as a full-order Observer, a model reference adaptive Sliding Mode Observer (SMO), and the like. The SMO has the advantages of strong anti-interference capability, good dynamic performance, low sensitivity to parameter change and the like, and is widely applied to a sensorless driver of a permanent magnet synchronous motor. In addition, the problem of high-frequency buffeting inherent to SMO is always concerned, and buffeting can be weakened to a certain extent by replacing a sign function with a saturation function, a sigmoid function and a supertwist function as a sliding mode switching function at present. In recent years, the sensor-free drive of the permanent magnet synchronous motor based on the SMO is widely applied to high-power and high-speed occasions, but the performance of the sliding mode observer is reduced due to the reduction of the carrier ratio, namely when the carrier ratio is reduced, the equivalent switching frequency of a symbolic function is reduced, and harmonic waves in estimated current and counter electromotive force are increased, so that the buffeting phenomenon is more serious; in addition, the fundamental frequency is close to the switching frequency, reducing the filtering effect of the low-pass filter. In order to improve the position and rotating speed estimation performance of the low carrier ratio gliding model observer, the invention provides a Vector probability-integral (VPI) sliding model observer.
Disclosure of Invention
The invention aims to provide an IPMSM rotating speed estimation method based on a discrete vector PI sliding mode observer, which solves the problems of buffeting and phase lag of the traditional sliding mode observer in the prior art.
The technical scheme adopted by the invention is that the IPMSM rotating speed estimation method based on the discrete vector PI sliding mode observer is implemented according to the following steps:
step 1, establishing a discrete time complex vector IPMSM model;
step 2, designing an IPMSM discrete vector PI sliding mode observer according to a discrete time complex vector IPMSM model; and (4) carrying out rotating speed estimation on the permanent magnet synchronous motor by adopting an IPMSM discrete vector PI sliding mode observer.
The invention is also characterized in that:
the step 1 specifically comprises the following steps:
step 1.1, establishing a discrete time complex vector IPMSM model based on the extended back electromotive force under a static coordinate system;
the discrete-time complex vector IPMSM model is concretely as follows:
Figure BDA0002607138720000031
in the formula (1), uα、uβ、iα、iβ、eαAnd eβStator voltage, stator current and back electromotive force under an alpha and beta axis coordinate system respectively; rs、Ψf、ωeAnd thetaeRespectively stator resistance, permanent magnet flux linkage, rotorSpeed and rotor position; i.e. id、iq、LdAnd LqRespectively current and inductance under d and q axis coordinate systems; eexIs the extended back emf magnitude; p is a differential operator;
for formula (1), a complex vector form x is adoptedαβ＝xα+jxβAnd (3) representing, wherein the bold is a complex vector, specifically:
Figure BDA0002607138720000032
in the formula (2), uαβ、iαβAnd eαβThe stator voltage, the stator current and the back electromotive force are respectively in complex vector forms under an alpha beta coordinate system, and j is an imaginary unit;
step 1.2, accurately discretizing a discrete time complex vector IPMSM model;
the initial condition being time t0Current response at time iαβ(t0) Solving a differential equation (2) to obtain a current response i at the time tαβ(t), specifically:
Figure BDA0002607138720000033
in the formula (3), R ═ Rs-jωe(Ld-Lq) (ii) a τ is an integral variable; u. ofαβ(t)、eαβ(t) are complex vector forms of stator voltage and back electromotive force at time t, respectively;
the time variable t in the formula (3)0And replacing the sum T with sampling variables kT and (k +1) T to obtain a discrete time difference equation under a static coordinate system, which specifically comprises the following steps:
iαβ[(k+1)T]＝Aiαβ(kT)+Buαβ(kT)-Ceαβ(kT) (4)，
in the formula (4), k is a sampling sequence; t is the sampling time;
Figure BDA0002607138720000041
Figure BDA0002607138720000042
assumed velocity ωe(kT) is equal to ωe[(k-1)T]Then ω iseThe voltage is constant speed, for a non-causal system, the input and output values in the formula (4) need to be delayed by one beat, and in addition, because the control calculation time is limited, the output of the controller is delayed by at least one sampling period T, namely, the voltage in a static coordinate system is delayed by one beat; the discrete time complex vector IPMSM model after accurate discretization is specifically as follows:
iαβ(kT)＝Aiαβ[(k-1)T]+Buαβ[(k-2)T]-Ceαβ[(k-1)T] (5)，
the step 2 specifically comprises the following steps:
step 2.1, discretizing the vector PI controller to obtain a discrete vector PI controller;
step 2.2, constructing an IPMSM discrete vector PI sliding mode observer through the accurately discretized complex vector IPMSM model to obtain a stator current error switching signal;
step 2.3, designing a discrete vector PI sliding mode control law according to the IPMSM discrete vector PI sliding mode observer to obtain estimated back electromotive force;
and 2.4, acquiring the estimated rotor position and the estimated rotating speed of the permanent magnet synchronous motor by using the orthogonal phase-locked loop.
In step 2.1, the discretization process of the vector PI controller is as follows:
transfer function G of vector PI controllerVPI(s) is specifically:
Figure BDA0002607138720000043
in the formula (6), kPIs the proportionality coefficient, kIIs the integral coefficient, ω0Is the resonance frequency, s is Laplace's calculation
Obtaining a discrete vector PI controller G by pre-twisting Tustin dispersion of the formula (6)VPI(z), specifically:
Figure BDA0002607138720000051
in equation (7), T is the sampling time, and z represents the z transform operator.
In step 2.2, designing an IPMSM discrete vector PI sliding mode observer according to a formula (5), which specifically comprises the following steps:
Figure BDA0002607138720000052
in the formula (8), "[ lambda ]" denotes an estimated value, k is a sample sequence, and u is a sequence of samplesαβ、iαβAnd vαβThe stator voltage, the stator current and the back electromotive force estimation values under the alpha beta coordinate system are in complex vector forms respectively;
and (3) subtracting the formula (8) from the formula (5) to obtain a stator current error switching signal, which specifically comprises:
Figure BDA0002607138720000053
in the formula (9), "-" represents an observation error between the estimated value and the actual value; e.g. of the typeαβIs a complex vector form of the actual back electromotive force in the α β coordinate system.
In step 2.3, the back electromotive force is estimated, specifically:
Figure BDA0002607138720000054
in the formula (10), vαβIs a complex vector form of the back electromotive force estimation value under an alpha beta coordinate system; "to" represents an observation error between the estimated value and the actual value.
In step 2.4, the estimated rotor position and the estimated rotation speed are obtained by utilizing the orthogonal phase-locked loop according to the estimated back electromotive force, and the process is as follows:
Figure BDA0002607138720000055
in the formula (11), the signal is a position error signal; eexIs the extended back emf magnitude; thetaeIs the actual rotor position;
Figure BDA0002607138720000061
is the estimated rotor position;
will get the estimated rotation speed through the quadrature phase-locked loop
Figure BDA0002607138720000062
And obtaining the estimated rotor position by integrating the estimated rotating speed
Figure BDA0002607138720000063
The invention has the beneficial effects that:
compared with the traditional sliding mode observer, the IPMSM rotating speed estimation method based on the discrete vector PI sliding mode observer can eliminate the error between the actual current and the estimated current by utilizing the characteristic of the zero phase shift amplifier under the vector PI resonant frequency, filter the harmonic component of the back electromotive force observed value, and eliminate buffeting and phase lag by replacing a sign function and a low-pass filter of the traditional sliding mode observer; the IPMSM rotating speed estimation method based on the discrete vector PI sliding mode observer establishes an IPMSM complex vector model under a static coordinate system, obtains an accurate discretization form of the IPMSM complex vector model, and directly designs the discrete vector PI sliding mode observer in a discrete domain, so that the stability and the dynamic performance of the IPMSM sensorless position sensor under a low carrier ratio are improved.
Drawings
FIG. 1 is a block diagram of an IPMSM rotation speed estimation vector system in the IPMSM rotation speed estimation method based on a discrete vector PI sliding mode observer according to the present invention;
FIG. 2 is a block diagram of a vector PI controller employed in the present invention;
FIG. 3 is a block diagram of a discrete vector PI sliding mode observer employed in the present invention;
FIG. 4 is a waveform diagram of a conventional sliding mode observer;
FIG. 4(a) is a waveform diagram of the estimated back EMF, actual rotor position and estimated rotor position of a conventional sliding-mode observer at a carrier ratio of 20
FIG. 4(b) is a waveform diagram of the actual rotation speed, estimated rotation speed, rotation speed error and rotor position error of the conventional sliding mode observer at a carrier ratio of 20
FIG. 5 is a waveform diagram of a discrete vector PI sliding mode observer used in the present invention at a carrier ratio of 20;
FIG. 5(a) is a waveform diagram of the estimated back EMF, actual rotor position and estimated rotor position of a discrete vector PI sliding mode observer employed in the present invention
FIG. 5(b) is a waveform diagram of the actual speed, estimated speed, speed error and rotor position error of the discrete vector PI sliding mode observer employed in the present invention
FIG. 6 is a waveform diagram of a discrete vector PI sliding mode observer employed in the present invention at a carrier ratio of 7.5;
FIG. 6(a) is a waveform diagram of the estimated back EMF, actual rotor position and estimated rotor position of a discrete vector PI sliding mode observer employed in the present invention
FIG. 6(b) is a waveform diagram of the actual speed, estimated speed, speed error and rotor position error of the discrete vector PI sliding mode observer employed in the present invention
Fig. 7 is a diagram of a permanent magnet synchronous motor speed change response dynamic waveform.
FIG. 7(a) is a waveform diagram of the change of the rotating speed of the PMSM (permanent magnet synchronous motor) by using a conventional sliding-mode observer
FIG. 7(b) is a waveform diagram of the change of the rotating speed of the PMSM (permanent magnet synchronous motor) adopting the discrete vector PI sliding mode observer of the invention
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The IPMSM rotating speed estimation method based on the discrete vector PI sliding mode observer adopts an IPMSM rotating speed estimation vector system block diagram based on the discrete vector PI sliding mode observer as shown in figure 1,
the method is implemented according to the following steps:
step 1, establishing a discrete time complex vector IPMSM model; the method specifically comprises the following steps:
step 1.1, establishing a discrete time complex vector IPMSM model based on the extended back electromotive force under a static coordinate system;
the discrete-time complex vector IPMSM model is concretely as follows:
Figure BDA0002607138720000081
in the formula (1), uα、uβ、iα、iβ、eαAnd eβStator voltage, stator current and back electromotive force under an alpha and beta axis coordinate system respectively; rs、Ψf、ωeAnd thetaeRespectively a stator resistor, a permanent magnet flux linkage, a rotating speed and a rotor position; i.e. id、iq、LdAnd LqRespectively current and inductance under d and q axis coordinate systems; eexIs the extended back emf magnitude; p is a differential operator;
for formula (1), a complex vector form x is adoptedαβ＝xα+jxβAnd (3) representing, wherein the bold is a complex vector, specifically:
Figure BDA0002607138720000082
in the formula (2), uαβ、iαβAnd eαβThe stator voltage, the stator current and the back electromotive force are respectively in complex vector forms under an alpha beta coordinate system, and j is an imaginary unit;
step 1.2, accurately discretizing a discrete time complex vector IPMSM model;
the initial condition being time t0Current response at time iαβ(t0) Solving a differential equation (2) to obtain a current response i at the time tαβ(t), specifically:
Figure BDA0002607138720000083
in the formula (3), R ═ Rs-jωe(Ld-Lq) (ii) a τ is an integral variable; u. ofαβ(t)、eαβ(t) are complex vector forms of stator voltage and back electromotive force at time t, respectively;
the time variable t in the formula (3)0And replacing the sum T with sampling variables kT and (k +1) T to obtain a discrete time difference equation under a static coordinate system, which specifically comprises the following steps:
iαβ[(k+1)T]＝Aiαβ(kT)+Buαβ(kT)-Ceαβ(kT) (4)，
in the formula (4), k is a sampling sequence; t is the sampling time;
Figure BDA0002607138720000091
Figure BDA0002607138720000092
assumed velocity ωe(kT) is equal to ωe[(k-1)T]Then ω iseThe voltage is constant speed, for a non-causal system, the input and output values in the formula (4) need to be delayed by one beat, and in addition, because the control calculation time is limited, the output of the controller is delayed by at least one sampling period T, namely, the voltage in a static coordinate system is delayed by one beat; the discrete time complex vector IPMSM model after accurate discretization is specifically as follows:
iαβ(kT)＝Aiαβ[(k-1)T]+Buαβ[(k-2)T]-Ceαβ[(k-1)T] (5)，
step 2, designing an IPMSM discrete vector PI sliding mode observer according to a discrete time complex vector IPMSM model; carrying out rotating speed estimation on the permanent magnet synchronous motor by adopting an IPMSM discrete vector PI sliding mode observer; the method specifically comprises the following steps:
step 2.1, discretizing the vector PI controller to obtain a discrete vector PI controller, wherein the block diagram is shown in FIG. 2;
the vector PI controller discretization process is as follows:
transfer function G of vector PI controllerVPI(s) is specifically:
Figure BDA0002607138720000093
in the formula (6), kPIs the proportionality coefficient, kIIs the integral coefficient, ω0Is the resonant frequency, s is the laplace operator;
obtaining a discrete vector PI controller G by pre-twisting Tustin dispersion of the formula (6)VPI(z), specifically:
Figure BDA0002607138720000101
in equation (7), T is the sampling time, z represents the z transform operator;
step 2.2, constructing an IPMSM discrete vector PI sliding mode observer through the accurately discretized complex vector IPMSM model to obtain a stator current error switching signal; the equivalent switching frequency reduction based on the symbolic function in the traditional sliding mode observer under the low carrier ratio is avoided, and the harmonic wave in the estimated back electromotive force is increased, so that the buffeting phenomenon is more serious, and the observation performance is reduced;
designing an IPMSM discrete vector PI sliding mode observer according to a formula (5), which specifically comprises the following steps:
Figure BDA0002607138720000102
in the formula (8), "[ lambda ]" denotes an estimated value, k is a sample sequence, and u is a sequence of samplesαβ、iαβAnd vαβThe stator voltage, the stator current and the back electromotive force estimation values under the alpha beta coordinate system are in complex vector forms respectively;
and (3) subtracting the formula (8) from the formula (5) to obtain a stator current error switching signal, which specifically comprises:
Figure BDA0002607138720000103
in formula (9), "+"represents an observation error between the estimated value and the actual value; e.g. of the typeαβIs a complex vector form of the actual back electromotive force under an alpha beta coordinate system;
step 2.3, designing a discrete vector PI sliding mode control law according to the IPMSM discrete vector PI sliding mode observer to obtain estimated back electromotive force;
estimating the back electromotive force, specifically:
Figure BDA0002607138720000104
in the formula (10), vαβIs a complex vector form of the back electromotive force estimation value under an alpha beta coordinate system; "to" represents an observation error between an estimated value and an actual value;
FIG. 3 is a block diagram of a discrete vector PI sliding-mode observer (i.e., the specific implementation process of equations (8) to (10)), where z is-1Represents a delay unit; obtaining a counter electromotive force estimated value of the permanent magnet synchronous motor through a discrete vector PI controller shown in a formula (7) according to a stator current error switching signal obtained by the formula (9), namely a formula (10);
step 2.4, obtaining the estimated rotor position and the estimated rotating speed of the permanent magnet synchronous motor by utilizing an orthogonal phase-locked loop;
the method comprises the following steps of obtaining an estimated rotor position and an estimated rotating speed by utilizing an orthogonal phase-locked loop according to an estimated back electromotive force, wherein the process comprises the following steps:
Figure BDA0002607138720000111
in the formula (11), the signal is a position error signal; eexIs the extended back emf magnitude; thetaeIs the actual rotor position;
Figure BDA0002607138720000112
is the estimated rotor position;
will get the estimated rotation speed through the quadrature phase-locked loop
Figure BDA0002607138720000113
And obtaining the estimated rotor position by integrating the estimated rotating speed
Figure BDA0002607138720000114
Due to the low carrier ratio, harmonics in the observer's estimated current and back emf increase, thereby degrading the observer's estimation performance. Therefore, the rotational speed will be estimated
Figure BDA0002607138720000115
Resonant frequency omega fed back to IPMSM discrete vector PI sliding mode observer0Is adapted, i.e.
Figure BDA0002607138720000116
The current tracking error can be eliminated, and other frequencies except the running frequency can be filtered out, so that the observation performance of the observer is improved.
A block diagram of an IPMSM rotating speed estimation vector system based on a discrete vector PI sliding mode observer is shown in fig. 1, and the system adopts 3 discrete PI regulators to form a double closed-loop alternating current speed regulation system with rotating speed and current feedback control. The output of the rotating speed outer ring discrete PI regulator is used as the input of the current discrete PI regulator, and the output of the current regulator controls the power electronic converter.
The three-phase current of the motor under a three-phase static coordinate system is detected through a current Hall sensor, and is converted into a current value i under a static two-phase coordinate system through Clark conversion (3s/2s)αβ(k) Then the given rotation speed in the speed outer ring is set
Figure BDA0002607138720000121
And the estimated rotating speed obtained by a discrete vector PI sliding mode observer
Figure BDA0002607138720000122
The compared error is regulated by a speed outer loop controller to obtain the electromagnetic torque set value
Figure BDA0002607138720000123
Then distributing the optimal excitation current by the maximum torque current ratio (MTPA)
Figure BDA0002607138720000124
And torque current
Figure BDA0002607138720000125
Current value i under static two-phase coordinate systemαβ(k) And the estimated rotor position obtained by the discrete vector PI sliding mode observer
Figure BDA0002607138720000126
Converting the excitation current into two-phase feedback under a rotor rotating coordinate system through Park conversion (2s/2r)d(k) And torque current iq(k) In that respect Given exciting current
Figure BDA0002607138720000127
And feedback calculating exciting current id(k) Comparing, and obtaining d-axis output voltage u of two-phase rotation coordinate after current discrete PI regulationd(k) (ii) a Given torque current
Figure BDA0002607138720000128
And feedback calculating torque current iq(k) After comparison, the q-axis output voltage u of the two-phase rotating coordinate is obtained after the current discrete PI regulationq(k) In that respect Two-phase voltage u under rotating coordinate systemd(k) And uq(k) Converted into two-phase voltage u under a static two-phase coordinate system through Park inverse transformation (2r/2s)αβ(k) In that respect Due to the limited control calculation time, the output of the controller is delayed by at least one sampling period T, i.e. the voltage u in the stationary frameαβ(k) There is a one-beat delay, i.e. uαβAnd (k-1) generating SVPWM waves through the regulation of the SVPWM generation module, and driving the built-in permanent magnet synchronous motor to work after passing through the three-phase inverter. Current value i under static two-phase coordinate systemαβ(k) With a two-phase voltage value uαβ(k-1) as the input of the discrete vector PI sliding mode observer, and the output is the estimated rotating speed
Figure BDA0002607138720000129
And estimating rotor position
Figure BDA00026071387200001210
According to estimated speed of rotation
Figure BDA00026071387200001211
For the resonant frequency omega in the discrete vector PI sliding-mode observer0And self-adaptation is carried out, so that a good observation effect is obtained.
In order to verify the feasibility of the IPMSM rotating speed estimation method based on the discrete vector PI sliding mode observer, a system simulation model is built in a Matlab2010a/Simulink environment and simulation verification is carried out. FIGS. 4 and 5 show the PMSM operating at 1500r/min (switching frequency f)PWM2kHz, carrier ratio fratio20) the steady state simulation waveforms of the conventional sliding-mode observer and the discrete vector PI sliding-mode observer employed in the present invention.
FIG. 4 adopts a traditional sliding mode observer, and the carrier ratio is 20, because the observation performance of the traditional sliding mode observer is influenced by the reduction of the equivalent switching frequency of the sign function, the estimated back electromotive force waveform of the traditional sliding mode observer is distorted, the buffeting is intensified, the rotating speed error is 15r/min, and the rotor position error is 12 degrees, so the observation precision is reduced; FIG. 5 is a discrete vector PI sliding mode observer of the present invention with a carrier ratio of 20; the rotating speed error and the rotor position error are respectively reduced to 6r/min and 4 degrees, which shows that the observation precision of the discrete vector PI sliding mode observer is higher than that of the traditional sliding mode observer.
Fig. 6 is a steady state simulation waveform of the discrete vector PI sliding mode observer using the present invention at a carrier ratio of 7.5. As can be seen from fig. 6, when the carrier ratio is 7.5, the discrete vector PI sliding mode observer adopted in the present invention still has good position observation performance at a low carrier ratio.
Fig. 7(a) and 7(b) are dynamic waveform diagrams of the rotating speed change response of the conventional sliding-mode observer and the discrete vector PI sliding-mode observer, respectively. As can be seen from the figure, the rotating speed of the discrete vector PI sliding-mode observer can reach 2400rpm, which shows that the method can be operated under the operating condition that the carrier ratio is 6.25. And when the rotating speed of the traditional sliding mode observer is 1000rpm and the carrier ratio is 15, the position of the rotor cannot be observed correctly, and the system is unstable.
Therefore, the discrete vector PI sliding mode observer has better rotor position observation performance under a low carrier ratio.
The invention relates to an IPMSM rotating speed estimation method based on a discrete vector PI sliding mode observer, which utilizes the estimated back electromotive force containing rotor position information to obtain the IPMSM estimated rotating speed and the estimated rotor position through an orthogonal phase-locked loop, and finally realizes the velocity-sensor-free vector control of the IPMSM.

Claims (7)

1. The IPMSM rotating speed estimation method based on the discrete vector PI sliding mode observer is characterized by comprising the following steps:
step 1, establishing a discrete time complex vector IPMSM model;
step 2, designing an IPMSM discrete vector PI sliding mode observer according to the discrete time complex vector IPMSM model; and estimating the rotating speed of the permanent magnet synchronous motor by adopting the IPMSM discrete vector PI sliding mode observer.
2. The IPMSM rotating speed estimation method based on the discrete vector PI sliding mode observer according to claim 1, wherein the step 1 specifically comprises the following steps:
step 1.1, establishing a discrete time complex vector IPMSM model based on the extended back electromotive force under a static coordinate system;
the discrete-time complex vector IPMSM model is concretely as follows:
Figure FDA0002607138710000011
in the formula (1), uα、uβ、iα、iβ、eαAnd eβStator voltage, stator current and back electromotive force under an alpha and beta axis coordinate system respectively; rs、Ψf、ωeAnd thetaeRespectively a stator resistor, a permanent magnet flux linkage, a rotating speed and a rotor position; i.e. id、iq、LdAnd LqRespectively current and inductance under d and q axis coordinate systems; eexIs the extended back emf magnitude; p is a differential operator;
for formula (1), a complex vector form x is adoptedαβ＝xα+jxβAnd (3) representing, wherein the bold is a complex vector, specifically:
Figure FDA0002607138710000021
in the formula (2), uαβ、iαβAnd eαβThe stator voltage, the stator current and the back electromotive force are respectively in complex vector forms under an alpha beta coordinate system, and j is an imaginary unit;
step 1.2, accurately discretizing the discrete time complex vector IPMSM model;
the initial condition being time t0Current response at time iαβ(t0) Solving a differential equation (2) to obtain a current response i at the time tαβ(t), specifically:
Figure FDA0002607138710000022
in the formula (3), R ═ Rs-jωe(Ld-Lq) (ii) a τ is an integral variable; u. ofαβ(t)、eαβ(t) are complex vector forms of stator voltage and back electromotive force at time t, respectively;
the time variable t in the formula (3)0And replacing the sum T with sampling variables kT and (k +1) T to obtain a discrete time difference equation under a static coordinate system, which specifically comprises the following steps:
iαβ[(k+1)T]＝Aiαβ(kT)+Buαβ(kT)-Ceαβ(kT) (4)，
in the formula (4), k is a sampling sequence; t is the sampling time;
Figure FDA0002607138710000023
Figure FDA0002607138710000024
assumed velocity ωe(kT) is equal to ωe[(k-1)T]Then ω iseThe voltage is constant speed, for a non-causal system, the input and output values in the formula (4) need to be delayed by one beat, and in addition, because the control calculation time is limited, the output of the controller is delayed by at least one sampling period T, namely, the voltage in a static coordinate system is delayed by one beat; the discrete time complex vector IPMSM model after accurate discretization is specifically as follows:
iαβ(kT)＝Aiαβ[(k-1)T]+Buαβ[(k-2)T]-Ceαβ[(k-1)T] (5)。
3. the IPMSM rotating speed estimation method based on the discrete vector PI sliding mode observer according to claim 2, wherein the step 2 specifically comprises the following steps:
step 2.1, discretizing the vector PI controller to obtain a discrete vector PI controller;
step 2.2, constructing an IPMSM discrete vector PI sliding mode observer through the accurately discretized complex vector IPMSM model to obtain a stator current error switching signal;
step 2.3, designing a discrete vector PI sliding mode control law according to the IPMSM discrete vector PI sliding mode observer to obtain estimated back electromotive force;
and 2.4, acquiring the estimated rotor position and the estimated rotating speed of the permanent magnet synchronous motor by using the orthogonal phase-locked loop.
4. The IPMSM rotation speed estimation method based on the discrete vector PI sliding mode observer as claimed in claim 3, wherein in step 2.1, the discretization process of the vector PI controller is as follows:
transfer function G of the vector PI controllerVPI(s) is specifically:
Figure FDA0002607138710000031
in the formula (6), kPIs the proportionality coefficient, kIIs the integral coefficient, ω0Is the resonant frequency, s is the laplace operator;
obtaining a discrete vector PI controller G by pre-twisting Tustin dispersion of the formula (6)VPI(z), specifically:
Figure FDA0002607138710000032
in equation (7), T is the sampling time, and z represents the z transform operator.
5. The IPMSM rotation speed estimation method based on the discrete vector PI sliding mode observer according to claim 4, characterized in that in step 2.2, the IPMSM discrete vector PI sliding mode observer is designed according to formula (5), specifically:
Figure FDA0002607138710000033
in the formula (8), "[ lambda ]" denotes an estimated value, k is a sample sequence, and u is a sequence of samplesαβ、iαβAnd vαβThe stator voltage, the stator current and the back electromotive force estimation values under the alpha beta coordinate system are in complex vector forms respectively;
and (3) subtracting the formula (8) from the formula (5) to obtain a stator current error switching signal, which specifically comprises:
Figure FDA0002607138710000041
in the formula (9), "-" represents an observation error between the estimated value and the actual value; e.g. of the typeαβIs a complex vector form of the actual back electromotive force in the α β coordinate system.
6. The IPMSM rotation speed estimation method based on the discrete vector PI sliding-mode observer according to claim 5, characterized in that in step 2.3, the estimated back electromotive force is specifically:
Figure FDA0002607138710000042
in the formula (10), vαβIs a complex vector form of the back electromotive force estimation value under an alpha beta coordinate system; "to" represents an observation error between the estimated value and the actual value.
7. The IPMSM speed estimation method based on the discrete vector PI sliding mode observer according to claim 6, characterized in that in step 2.4, the estimated rotor position and the estimated speed are obtained by a quadrature phase-locked loop according to the estimated back electromotive force, and the process is as follows:
Figure FDA0002607138710000043
in the formula (11), the signal is a position error signal; eexIs the extended back emf magnitude; thetaeIs the actual rotor position;
Figure FDA0002607138710000044
is the estimated rotor position;
obtaining the estimated rotating speed through an orthogonal phase-locked loop
Figure FDA0002607138710000045
And obtaining the estimated rotor position by integrating the estimated rotating speed
Figure FDA0002607138710000046
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