CN113644852A - Robust three-vector model prediction flux linkage control method for permanent magnet synchronous motor - Google Patents

Robust three-vector model prediction flux linkage control method for permanent magnet synchronous motor Download PDF

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CN113644852A
CN113644852A CN202110565963.6A CN202110565963A CN113644852A CN 113644852 A CN113644852 A CN 113644852A CN 202110565963 A CN202110565963 A CN 202110565963A CN 113644852 A CN113644852 A CN 113644852A
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flux linkage
permanent magnet
magnet synchronous
synchronous motor
psi
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CN113644852B (en
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徐艳平
张雁萍
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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
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/06—Rotor flux based control involving the use of rotor position or rotor speed sensors
    • 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
    • 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
    • H02P6/34—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 a robust three-vector model prediction flux linkage control method for a permanent magnet synchronous motor, which is implemented according to the following steps: step 1, establishing a mathematical model of a permanent magnet synchronous motor; step 2, selecting a new flux linkage control variable under one-beat delay compensation control, and calculating a flux linkage prediction equation of the permanent magnet synchronous motor under the control condition of the new flux linkage control variable; step 3, analyzing the influence of the parameter disturbance and unmodeled dynamic disturbance on the accuracy of a flux linkage prediction equation of the permanent magnet synchronous motor; step 4, designing a Longbeige disturbance observer and a stable condition of the Longbeige disturbance observer according to the accuracy influence obtained in the step 3; step 5, compensating the lumped disturbance observed by the Roeberg into a flux linkage prediction equation of the permanent magnet synchronous motor to realize accurate control on the permanent magnet synchronous motor; the problem of robustness brought by sensitivity of model prediction flux linkage control to parameter change and non-consideration of unmodeled dynamic disturbance is solved.

Description

Robust three-vector model prediction flux linkage control method for permanent magnet synchronous motor
Technical Field
The invention belongs to the technical field of motor control, and particularly relates to a robust three-vector model prediction flux linkage control method for a permanent magnet synchronous motor.
Background
Permanent Magnet Synchronous Motors (PMSM) utilize rare earth Permanent magnets for excitation, have the advantages of simple structure, high reliability, high efficiency, high power factor and the like, and are widely applied to the field of transmission of alternating current motors, such as industrial robots, aerospace, electric automobiles and the like. With the continuous development of the above fields, there is also a higher demand for the control of the permanent magnet synchronous motor.
The model predictive control is a new control strategy applied to power converters and transmission devices for the first time in the 80 th century, and has the advantages of simple concept, consideration of multivariable, easiness in inclusion of constraint conditions and nonlinear factors and the like. The method has the main idea that the state of the system at the next moment is predicted according to the state value of the system at the current moment and a mathematical model of a controlled object, online optimization is carried out through a constructed value function, the optimal control sequence is determined, and the control sequence is applied to a control system. The model predictive control can be classified into model predictive current control, model predictive speed control, and model predictive torque control according to the control target. The model prediction flux linkage control is an improved method aiming at the difficulty in setting the weight coefficient in the model prediction torque, an equivalent stator flux linkage vector is obtained through derivation according to the relation among the torque, the flux linkage and the load angle, and the equivalent stator flux linkage vector is used as a control target, so that the weight coefficient is not needed. However, in the model prediction flux linkage control method, the given value of the equivalent stator flux linkage is the permanent magnet flux linkage value, the calculation of the load angle contains motor parameters, and the prediction equation is also based on a system model, so that the dependence on the motor parameters is large. In practical application, the actual value of the motor parameter is inconsistent with the motor nameplate value due to factors such as temperature change, magnetic circuit saturation and inaccurate system measurement, and unmodeled dynamic disturbance of the system is not considered in model prediction flux linkage control, so that a steady-state error between a flux linkage set value and the actual value is caused, the performance of the system is influenced finally, and the system is low in robustness.
At present, methods for improving the robustness of predictive control mainly include: the method comprises the steps of parameter identification, addition of a prediction error correction term, adoption of a controller with strong robustness, super-local model-free prediction control, adoption of an observer to observe lumped disturbance for compensation and the like. The observer is adopted to observe the lumped disturbance, so that the lumped compensation of the parameter disturbance and the unmodeled dynamic disturbance can be realized, and the method has the advantages of simple principle realization and the like, thereby being widely applied.
The model prediction flux linkage control not only contains motor parameters in a prediction model, but also contains the motor parameters in the calculation of a given value and a load angle of the prediction model, and unmodeled dynamic disturbance is not considered in the prediction process, so that the research of improving the robustness of the model prediction flux linkage control is necessary.
Disclosure of Invention
The invention aims to provide a robust three-vector model prediction flux linkage control method for a permanent magnet synchronous motor, which solves the problem of robustness brought by sensitivity of model prediction flux linkage control to parameter change and unconsidered unmodeled dynamic disturbance.
The technical scheme adopted by the invention is that the robust three-vector model prediction magnetic linkage control method for the permanent magnet synchronous motor is implemented according to the following steps:
step 1, establishing a mathematical model of a permanent magnet synchronous motor;
step 2, selecting a new flux linkage control variable under one-beat delay compensation control, and calculating a flux linkage prediction equation of the permanent magnet synchronous motor under the control condition of the new flux linkage control variable;
step 3, analyzing the influence of the parameter disturbance and unmodeled dynamic disturbance on the accuracy of a flux linkage prediction equation of the permanent magnet synchronous motor;
step 4, designing a Longbeige disturbance observer and a stable condition of the Longbeige disturbance observer according to the accuracy influence obtained in the step 3;
and 5, compensating the lumped disturbance observed by the Roeberg to a flux linkage prediction equation of the permanent magnet synchronous motor, and realizing accurate control on the permanent magnet synchronous motor.
The invention is also characterized in that:
the mathematical model of the permanent magnet synchronous motor in the step 1 is as follows:
Figure BDA0003080681040000031
Figure BDA0003080681040000032
Figure BDA0003080681040000033
Figure BDA0003080681040000034
ψd＝Ldid+ψf (5)
ψq＝Lqiq (6)
in formulae (1) to (6), udIs the direct component of the stator voltage, uqIs the quadrature component of the stator voltage; rsIs a stator resistor; i.e. idIs the direct component of the stator current, iqIs the quadrature component of the stator current; omegareIs the rotor electrical angular velocity; psidIs the direct component of the stator flux linkage, #qIs the quadrature component of the stator flux linkage; l isdIs the direct component of the stator inductance, LqIs the quadrature component of the stator inductance; psifIs a permanent magnet flux linkage; t iseIs an electromagnetic torque; p is a radical ofnThe number of pole pairs of the motor is; j is moment of inertia; b is friction viscosity coefficient; t isLIs the load torque; t is time; wherein, L in the surface-mounted permanent magnet synchronous motord＝Lq＝Ls。
The specific process of the step 2 is as follows:
let psi be based on the mathematical model of the permanent magnet synchronous motords(k)＝Ldid(k) And discretizing by adopting a backward Euler method to obtain:
Figure BDA0003080681040000041
in the formula: psid(k +1) is the predicted value of the direct axis flux linkage at the moment of (k + 1); psiq(k) The predicted value of the quadrature axis flux linkage at the moment k is obtained; u. ofd(k) Is the direct component of the stator voltage at time k;
the straight axis flux linkage psi in the formula (7)dIs equivalent to a pair variable psidsBy using a new control variable psids、ψqAnd (3) carrying out model prediction flux linkage control on the permanent magnet synchronous motor, and reconstructing a value function as follows:
C＝|ψds *-ψds(k+1)|2+|ψq *-ψq(k+1)|2 (8)
in the formula: psids *As a variable psidsA given value of (d);
psi in equation (8) by using one beat delay compensation for PMSM controlds(k +1) and ψq(k +1) is replaced by the quadrature-axis component ψ of the stator flux linkage at time (k +2)ds(k +2) and the quadrature component ψq(k +2), the modified cost function is expressed as:
C＝|ψds *-ψds(k+2)|2+|ψq *-ψq(k+2)|2 (9)
the flux linkage prediction equation of the permanent magnet synchronous motor under the new flux linkage control variable control condition is as follows:
Figure BDA0003080681040000042
Figure BDA0003080681040000043
in the formula: u. ofd(k +1) is the direct component of the stator voltage at time (k +1), uq(k +1) is the intersection of the stator voltage at the time (k +1)An axial component.
The specific process of the step 3 is as follows:
the predicted flux linkage when the actual value of the motor parameter is not deviated from the nominal value of the motor nameplate is expressed as psi'ds、 ψ′qThe predicted flux linkage when the actual value of the motor parameter deviates from the nominal value of the nameplate is expressed as psids、ψqBy delta phifRepresenting the error, Δ L, between the actual value of the permanent magnet flux linkage and the nominal value of the nameplatesRepresenting the error, Δ R, between the actual value of the inductance of the stator and the nominal value of the name platesRepresenting the error between the actual value of the stator resistance and the nominal value of the nameplate, and representing the uncertain disturbance of unmodeled dynamics by using epsilon;
considering the deviation between the actual value of the motor parameter and the nominal value of the nameplate and the unmodeled disturbance, the prediction flux linkage is expressed as:
Figure BDA0003080681040000051
and obtaining the influence of the parameter disturbance and the unmodeled dynamic state on the accuracy of the flux linkage prediction equation of the permanent magnet synchronous motor according to the formula (13).
The specific process of the step 4 is as follows:
according to formula (13):
Figure BDA0003080681040000052
Figure RE-GDA0003272680110000053
in the formula: f. ofdTotal perturbation of the direct axis predicted flux linkage, fqIs the total perturbation of the quadrature axis predicted flux linkage;
total disturbance fd、fqIn a steady state, then there are
Figure BDA0003080681040000054
According to equation (14), byds，ψqFor state variables, the Roeberg observer is designed as follows:
Figure BDA0003080681040000055
Figure BDA0003080681040000061
in the formula:
Figure BDA0003080681040000062
is psidsIs determined by the estimated value of (c),
Figure BDA0003080681040000063
is psiqIs determined by the estimated value of (c),
Figure BDA0003080681040000064
is fdIs determined by the estimated value of (c),
Figure BDA0003080681040000065
is fqEstimated value of k1、k2Is the Longbeige observer gain;
the discrete Roeberg observer is:
Figure BDA0003080681040000066
Figure BDA0003080681040000067
in the formula:
Figure BDA0003080681040000068
Figure BDA0003080681040000069
kT1＝k1Ts，kT2＝k2Ts；k1、k2representing observer coefficients, TsRepresents a sampling period;
ignore-omegareTsThe term j, the characteristic equation of the Roeberg observer obtained according to equation (18), is:
Figure BDA00030806810400000610
obtaining the following components:
D(z)＝c0+c1z1+c2z2＝0 (21)
in the formula:
Figure BDA00030806810400000611
c2＝1；
according to the July criterion, the stable essential conditions of the observer are as follows:
Figure BDA0003080681040000071
c in the formula (21)0、c1、c2Substituting formula (22) to obtain:
Figure BDA0003080681040000072
the final condition that the observer needs to be stabilized is obtained according to equation (23):
Figure BDA0003080681040000073
the specific process of the step 5 is as follows:
after the disturbance quantity estimated by the Roeberg observer is added, an expression of a robust three-vector model at the moment of predicting the flux linkage k +2 is obtained according to an expression (14) and by considering one-beat delay compensation:
Figure BDA0003080681040000074
and substituting an expression of the robust three-vector model for predicting the moment of the magnetic linkage k +2 into the modified value function, and when the value of the modified value function is minimum, using a corresponding group of voltage vectors and the action time thereof as an inverter to realize accurate control of the permanent magnet synchronous motor.
The invention has the beneficial effects that:
(1) the control method of the invention abandons a method for obtaining an equivalent reference flux linkage vector by analyzing the mathematical relationship among the reference flux linkage amplitude, the reference torque and the load angle in the model prediction flux linkage control, reselects a flux linkage control variable, realizes the model prediction flux linkage control of the permanent magnet synchronous motor, can ensure that the given value of the flux linkage does not contain motor parameters, and does not need to carry out the conversion of the torque and the flux linkage through the equivalent load angle containing the motor parameters, and has the advantages of simple algorithm and strong parameter robustness.
(2) According to the invention, a Longbeige disturbance observer is constructed by analyzing the influence of parameter change and uncertain dynamic disturbance on a prediction flux linkage equation and according to the prediction flux linkage equation, and is used for observing lumped disturbance including motor parameter change of a system. When the motor parameters change or external disturbance exists, the actual values of the flux linkage and the current can more accurately follow the given values, so that the steady state errors of the flux linkage and the current are reduced, and the robustness of the system is further improved.
Drawings
FIG. 1 is a system schematic diagram of the application of the control method of the present invention;
FIG. 2 is a graph of a rotational speed waveform for the system of FIG. 1 with simultaneous changes in stator resistance, stator flux linkage, and stator inductance;
FIG. 3 is psi for the system of FIG. 1 with simultaneous variation of stator resistance, stator flux linkage and stator inductancedsA waveform diagram;
FIG. 4 is psi for the system of FIG. 1 with simultaneous variation of stator resistance, stator flux linkage and stator inductanceqA waveform diagram;
FIG. 5 is a graph of a-phase current waveforms for the system of FIG. 1 with simultaneous changes in stator resistance, stator flux linkage, and stator inductance;
in the figure, 1, a three-phase inverter, 2, a current detection circuit, 3, a permanent magnet synchronous motor, 4, a rotary encoder, 5, a Clark conversion module, 6, a Park conversion module, 7, k moment flux linkage value estimation module, 8, a Longbeige disturbance observer module, 9, a beat delay compensation module, 10, k +2 moment flux linkage prediction module, 11, an action time calculation module, 12, an expected vector synthesis module and 13, a value function optimization module are included.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The method is mainly used for a permanent magnet synchronous motor, and a control system of the permanent magnet synchronous motor is shown in figure 1 and comprises a signal detection circuit, a main circuit and a control circuit; the main circuit comprises a three-phase inverter 1 which is mainly used for driving a permanent magnet synchronous motor 3; the signal detection circuit comprises a current detection circuit 2 and a rotary encoder 4, and is mainly used for detecting the current of the permanent magnet synchronous motor 3 and a rotor position signal; the control circuit comprises a Clark conversion module 5, a Park conversion module 6, a k moment flux linkage value estimation module 7, a Longbeige disturbance observer module 8, a one-beat delay compensation module 9, a k +2 moment flux linkage prediction module 10, an action time calculation module 11, an expected vector synthesis module 12 and a value function optimization module 13, and is mainly used for processing signals obtained by the signal detection circuit to obtain control signals for controlling the main circuit.
Wherein, the control circuit detects the three-phase current i obtained after the permanent magnet synchronous motor 3 is detected by the current detection circuit 2a、ibAnd icI is obtained after the treatment of a Clark conversion module 5αAnd iβ(ii) a The rotary encoder 4 detects the rotor position angle theta of the permanent magnet synchronous motor 3, and the angular velocity omega of the motor is obtained by derivationm；iα、iβThe feedback value i of the direct axis current and the quadrature axis current under the two-phase rotating coordinate system is obtained after theta is processed by a Park conversion module 6dAnd iq；idAnd iqThe flux linkage value psi at the moment k is obtained through a flux linkage value estimation module 7 at the moment kds(k)、 ψq(k) (ii) a Flux linkage value psi at time kds(k)、ψq(k) The estimated lumped disturbance is obtained through the Longbeger disturbance observer module 8
Figure BDA0003080681040000091
Mechanical angular velocity omega of motormEstimated lumped perturbation
Figure BDA0003080681040000092
Figure BDA0003080681040000093
And the flux linkage value psi at time kds(k)、ψq(k) The predicted value psi of flux linkage at the moment of k +1 is obtained by a beat delay compensation module 9ds(k+1)、ψq(k + 1); flux linkage prediction value psi at time k +1ds(k+1)、ψq(k +1) and estimated lumped perturbation
Figure BDA0003080681040000094
The flux linkage prediction value psi at the time k +2 is obtained through the flux linkage prediction module 10 at the time k +2ds(k+2)、ψq(k + 2); given value of mechanical angular velocity of motor
Figure BDA0003080681040000095
And the mechanical angular velocity omega of the motormProcessing the difference by a PI controller to obtain a q-axis flux linkage given value
Figure BDA0003080681040000096
By
Figure BDA0003080681040000097
Estimated lumped disturbance
Figure BDA0003080681040000098
And predicted value psi of flux linkage at time k +1ds(k+1)、ψq(k +1) the action time t of two effective vectors and a zero vector is obtained by the action time calculation module 11i,j,z(ii) a Time of vector action ti,j,z6 sets are obtained by the desired vector composition module 12Desired voltage vector uevvⅠ～Ⅵ(ii) a Given value of magnetic flux linkage
Figure BDA0003080681040000101
Desired voltage vector uevvⅠ～ⅥAnd predicted value psi of flux linkage at time k +2ds(k+2)、ψq(k +2) an optimal set of voltage vectors and action time are selected to act on the inverter for controlling the permanent magnet synchronous motor 3 through the cost function optimization module 13.
Therefore, the robustness of the permanent magnet synchronous motor can be improved by obtaining an optimal set of voltage vectors and action time.
The invention discloses a robust three-vector model prediction flux linkage control method for a permanent magnet synchronous motor, which is implemented according to the following steps:
step 1, establishing a mathematical model of a permanent magnet synchronous motor;
the mathematical model of the permanent magnet synchronous motor is as follows:
Figure BDA0003080681040000102
Figure BDA0003080681040000103
Figure BDA0003080681040000104
Figure BDA0003080681040000105
ψd＝Ldid+ψf (5)
ψq＝Lqiq (6)
in formulae (1) to (6), udIs the direct component of the stator voltage, uqIs the quadrature component of the stator voltage; rsFor stator electricityBlocking; i.e. idIs the direct component of the stator current, iqIs the quadrature component of the stator current; omegareIs the rotor electrical angular velocity; psidIs the direct component of the stator flux linkage, #qIs the quadrature component of the stator flux linkage; l isdIs the direct component of the stator inductance, LqIs the quadrature component of the stator inductance; psifIs a permanent magnet flux linkage; t iseIs an electromagnetic torque; p is a radical ofnThe number of pole pairs of the motor is; j is moment of inertia; b is friction viscosity coefficient; t isLIs the load torque; t is time; wherein, L in the surface-mounted permanent magnet synchronous motord＝Lq＝Ls。
Step 2, selecting a new flux linkage control variable under one-beat delay compensation control, and calculating a flux linkage prediction equation of the permanent magnet synchronous motor under the control condition of the new flux linkage control variable;
the specific process of the step 2 is as follows:
selecting a new control variable to perform model prediction flux linkage control according to a mathematical model of the permanent magnet synchronous motor: from equation (3), it can be seen that the quadrature flux linkage is torque dependent and therefore is directly available from the speed loop PI regulator. Let psids(k)＝Ldid(k) And discretizing by adopting a backward Euler method to obtain:
Figure BDA0003080681040000111
in the formula: psid(k +1) is the predicted value of the direct axis flux linkage at the moment of (k + 1); psiq(k) The predicted value of the quadrature axis magnetic chain at the moment k is obtained; u. ofd(k) Is the direct component of the stator voltage at time k;
the straight axis flux linkage psi in the formula (7)dIs equivalent to a pair variable psidsBy using a new control variable psids、ψqAnd (3) carrying out model prediction flux linkage control on the permanent magnet synchronous motor, and reconstructing a value function as follows:
C＝|ψds *-ψds(k+1)|2+|ψq *-ψq(k+1)|2 (8)
in the formula: in the formula: psids *As a variable psidsGiven value of according to idControl 0 psi ds *0. Therefore, the problem that the given value of the direct axis flux linkage is not accurate and the requirement of a control system cannot be met due to the fact that the flux linkage value of the permanent magnet cannot be accurately obtained can be solved.
Because the digital control system has links of keeping, quantifying and the like, and has the problem of digital delay, one-beat delay compensation is adopted for controlling the permanent magnet synchronous motor, namely psi in the value function shown in the formula (8) is subjected to one-beat delay compensationds(k +1) and ψq(k +1) is replaced by the quadrature component ψ of the stator flux linkage at time (k +2)ds(k +2) and ψq(k +2), the modified cost function is expressed as:
C＝|ψds *-ψds(k+2)|2+|ψq *-ψq(k+2)|2 (9)
the flux linkage prediction equation of the permanent magnet synchronous motor under the new flux linkage control variable control condition is as follows:
Figure BDA0003080681040000121
Figure BDA0003080681040000122
in the formula: u. ofd(k +1) is the direct component of the stator voltage at time (k +1), uqAnd (k +1) is a quadrature component of the stator voltage at the time of (k + 1).
Step 3, analyzing the influence of the parameter disturbance and unmodeled dynamic disturbance on the accuracy of a flux linkage prediction equation of the permanent magnet synchronous motor; the specific process of the step 3 is as follows:
in order to facilitate analysis of prediction errors caused by various disturbances such as parameters, the predicted flux linkage when the actual value of the motor parameter is not deviated from the nominal value of the motor nameplate is expressed as psi'ds、ψ′qThe actual value of the motor parameter and the nominal value of the nameplate are providedThe predicted flux linkage at offset is denoted byds、ψqBy delta phifRepresenting the error, Δ L, between the actual value of the permanent magnet flux linkage and the nominal value of the nameplatesRepresenting the error, Δ R, between the actual value of the inductance of the stator and the nominal value of the name platesRepresenting the error between the actual value of the stator resistance and the nominal value of the nameplate, and representing the uncertain disturbance of unmodeled dynamics by using epsilon;
in an ideal state, the actual value of the motor parameter is the nominal value of the nameplate, the predicted flux linkage is shown as the formula (12),
Figure BDA0003080681040000123
considering the deviation between the actual value of the motor parameter and the nominal value of the nameplate and the unmodeled disturbance, the prediction flux linkage is expressed as:
Figure BDA0003080681040000131
due to the fact that factors such as temperature and magnetic saturation can cause parameter mismatching phenomenon in the system, it can be known from the formula (12) and the formula (13) that the inaccuracy of stator resistance, stator inductance and flux linkage and the un-modeled dynamic uncertain disturbance of the system can affect the accuracy of flux linkage prediction.
And obtaining the influence of the parameter disturbance and the unmodeled dynamic state on the accuracy of the flux linkage prediction equation of the permanent magnet synchronous motor according to the formula (13).
Step 4, designing a Longbeige disturbance observer and a stable condition of the Longbeige disturbance observer according to the accuracy influence obtained in the step 3; the specific process of the step 4 is as follows:
disturbance caused by unmatched observation parameters of the Longbeige observer and unmodeled dynamic uncertain disturbance are adopted and compensated in a prediction model, so that steady-state errors of control variables in a three-vector model prediction flux linkage control strategy are reduced. Considering the effect of parameter mismatch and unmodeled dynamic uncertain disturbance epsilon, equation (13) can be written as:
Figure BDA0003080681040000132
Figure RE-GDA0003272680110000133
in the formula: f. ofdTotal perturbation of the direct axis predicted flux linkage, fqIs the total perturbation of the quadrature axis predicted flux linkage; including stator inductance, disturbances caused by permanent magnet flux and stator resistance mismatch, and unmodeled dynamic disturbances.
Total disturbance fd、fqIn a steady state, then there are
Figure BDA0003080681040000134
According to equation (14), byds，ψqFor state variables, the Roeberg observer is designed as follows:
Figure BDA0003080681040000141
Figure BDA0003080681040000142
in the formula:
Figure BDA0003080681040000143
is psidsIs determined by the estimated value of (c),
Figure BDA0003080681040000144
is psiqIs determined by the estimated value of (c),
Figure BDA0003080681040000145
is fdIs determined by the estimated value of (c),
Figure BDA0003080681040000146
is fqEstimated value of k1、k2Is the Longbeige observer gain;
the discrete Roeberg observer is:
Figure BDA0003080681040000147
u(k)＝ud(k)+j(uq(k)-ωreψf) (19)
in the formula:
Figure BDA0003080681040000148
Figure BDA0003080681040000149
kT1＝k1Ts，kT2＝k2Ts；k1、k2representing observer coefficients, TsRepresents a sampling period;
the stability of the Longbeige observer proved as follows: the Zhuli criterion is a stability criterion which can be applied in a Z domain in a modern control system, namely whether the system can be stable or not can be judged according to whether a characteristic value of the system in the Z domain is in a unit circle or not. Therefore, the characteristic value of the formula (18) is obtained first, and in the actual control system, T is usedsSmaller, neglecting-omegareTsThe term j, the characteristic equation of the Roeberg observer obtained according to equation (18), is:
Figure BDA0003080681040000151
obtaining the following components:
D(z)＝c0+c1z1+c2z2＝0 (21)
in the formula:
Figure BDA0003080681040000152
c2＝1；
according to the July criterion, the stable essential conditions of the observer are as follows:
Figure BDA0003080681040000153
c in the formula (21)0、c1、c2Substituting formula (22) to obtain:
Figure BDA0003080681040000154
the final condition that the observer needs to be stabilized is obtained according to equation (23):
Figure BDA0003080681040000155
step 5, compensating the lumped disturbance observed by the Roeberg to a flux linkage prediction equation of the permanent magnet synchronous motor to realize accurate control on the permanent magnet synchronous motor;
the specific process of the step 5 is as follows:
after the disturbance quantity estimated by the Roeberg observer is added, an expression of a robust three-vector model at the moment of predicting the flux linkage k +2 is obtained according to an expression (14) and by considering one-beat delay compensation:
Figure BDA0003080681040000161
and substituting an expression of the robust three-vector model for predicting the moment of the magnetic linkage k +2 into the modified value function, and when the value of the modified value function is minimum, using a corresponding group of voltage vectors and the action time thereof as an inverter to realize accurate control of the permanent magnet synchronous motor.
The action time calculation adopts the existing method, which specifically comprises the following steps:
the action time of three voltage vectors in the three-vector model prediction flux linkage control strategy is calculated according to the quadrature axis flux linkage dead beat principle. Direct-quadrature axis flux linkage slope s during flux linkage control zero vector action prediction of derived robust three-vector modeld0And sq0As shown in equations (26) and (27):
Figure BDA0003080681040000162
Figure BDA0003080681040000163
so that two adjacent effective voltage vectors ui、ujSlope s of quadrature axis flux linkage in operationdi、sqi、sdjAnd sqjThe formulas are respectively as follows:
Figure BDA0003080681040000164
Figure BDA0003080681040000165
Figure BDA0003080681040000166
Figure BDA0003080681040000167
in the formula: u. ofdi、uqiRepresenting a valid vector uiVoltage components at the direct and quadrature axes;
udj、uqjrepresenting a valid vector ujVoltage components on the direct and quadrature axes.
The predicted value of the stator flux linkage is equal to the equivalent reference stator flux linkage vector at the end of a control period, so that the direct-axis and alternating-axis stator flux linkage prediction formula can be rewritten as follows:
ψds(k+2)＝ψds(k+1)+sditi+sdjtj+sd0tz＝ψds * (32)
ψq(k+2)＝ψq(k+1)+sqiti+sqjtj+sq0tz＝ψq * (33)
in the formula: t is tiRepresenting a valid vector uiThe action time of (c);
tjrepresenting a valid vector ujThe action time of (c);
tzrepresenting the action time of the zero vector.
The sum of the action times of the three voltage vectors is exactly equal to one control period TsI.e. by
Ts＝ti+tj+tz (34)
The following equations (26) to (34) are obtained in combination:
Figure BDA0003080681040000171
Figure BDA0003080681040000172
tz＝Ts-ti-tj (37)
because the two-level voltage source inverter has 6 effective voltage vectors and 2 zero vectors in total, 6 effective vectors with variable amplitudes and directions can be synthesized by two adjacent basic voltage vectors and zero vectors according to the vector action time calculated in the step 6, as shown in formulas (38) and (39):
Figure BDA0003080681040000173
Figure BDA0003080681040000174
the voltage vectors synthesized by the equations (38) and (39) are applied to the modified cost function (11), and a group of voltage vectors having the smallest value of the cost function is selected to be applied to the inverter, thereby controlling the permanent magnet synchronous motor.
Examples
The invention provides a robust three-vector model prediction flux linkage control method for a permanent magnet synchronous motor, which comprises the steps of firstly, reselecting a flux linkage variable controlled by a model prediction flux linkage, so that a given value of the flux linkage is not influenced by a flux linkage value of a permanent magnet, and the load angle calculation of motor parameters is not needed, therefore, the robust three-vector model prediction flux linkage control method has the advantages of simple calculation and strong robustness; meanwhile, the prediction error of the model prediction flux linkage control caused by parameter disturbance and unmodeled dynamic disturbance is analyzed, the lumped disturbance existing in the observation of the three-vector model prediction flux linkage control by the Longbeger disturbance observer is researched, and the robustness of the system is improved. To verify the effectiveness of the method of the invention, simulation verification was performed using MATLAB/SIMULINK.
In the simulation model, a Clark conversion module 5, a Park conversion module 6, a k moment flux value estimation module 7, a Longbeige disturbance observer module 8, a one-beat delay compensation module 9, a k +2 moment flux prediction module 10, an action time calculation module 11, an expected vector synthesis module 12 and a value function optimization module 13 are all realized by adopting an S-function Builder functional module and C language programming, and the sampling frequency is 10 kHz. In the simulation model, the parameters of the permanent magnet synchronous motor are set as follows: the permanent magnet flux linkage is 0.303Wb, the stator inductance is 11.57mH, the rated voltage is 380V, the rated current is 4.4A, the stator resistance is 1.64 omega, the rated rotating speed is 2430(r/min), the number of pole pairs is 4, and the rotor inertia is 0.0011 (kg.m)2) A damping coefficient of 0.001 and a rated load torque of 9.6 (N.m); the parameters of the simulation model are set as follows: PI coefficient of 0.001, integral coefficient of 0.00003, and Lorberg disturbance observer coefficient kT1＝0.286、 kT2＝-58.6。
FIG. 2 shows the permanent magnet flux linkage of the motor changed to 120% phifStator resistance becomes 120% RsThe stator inductance becomes 80% LsStarting to 1000r/min in no-load; the rotation speed of 0.1s is set to be changed from 1000r/min to 1500r/min in a sudden change manner; the load of 9.6 N.m is suddenly added for 0.2 s; a 0.3s load torque is suddenly reduced from 9.6 N.m to no-load speed response waveform diagram, and figure 3 shows psidsA waveform diagram; figure 4 is psiqA waveform diagram; FIG. 5 is a phase current waveform of phase a;
as can be seen from FIG. 2, in the control system for controlling the permanent magnet synchronous motor by the control method, when the actual values of the flux linkage, the stator resistance and the stator inductance of the motor are inconsistent with the nameplate value, the rotating speed can accurately follow the given value, and the rotating speed is not influenced by the parameter change of the motor and the unmodeled dynamic state.
As can be seen from FIGS. 3 and 4, the method controls psi when the actual values of the flux linkage, the stator resistance and the stator inductance of the motor are inconsistent with the nameplate valuedsAnd psiqThe actual value can still accurately follow the given value, steady-state errors caused by parameter changes and unmodeled dynamics do not exist, more accurate control can be realized, and the robustness of the system is improved.
It can be seen from fig. 5 that the robust three-vector model predictive flux linkage control of the permanent magnet synchronous motor can still keep better sine degree when the parameters are changed.
The above embodiment further illustrates the effectiveness of the robust three-vector model prediction flux linkage control method of the permanent magnet synchronous motor according to the present invention. Therefore, the robust three-vector model prediction flux linkage control method for the permanent magnet synchronous motor can ensure that the motor still has accurate control when the parameters are not matched and dynamic disturbance exists for modeling, and improves the robustness of model prediction flux linkage.

Claims (6)

1. The robust three-vector model prediction flux linkage control method for the permanent magnet synchronous motor is characterized by comprising the following steps of:
step 1, establishing a mathematical model of a permanent magnet synchronous motor;
step 2, selecting a new flux linkage control variable under one-beat delay compensation control, and calculating a flux linkage prediction equation of the permanent magnet synchronous motor under the control condition of the new flux linkage control variable;
step 3, analyzing the influence of the parameter disturbance and unmodeled dynamic disturbance on the accuracy of a flux linkage prediction equation of the permanent magnet synchronous motor;
step 4, designing a Longbeige disturbance observer and a stable condition of the Longbeige disturbance observer according to the accuracy influence obtained in the step 3;
and 5, compensating the lumped disturbance observed by the Roeberg into a flux linkage prediction equation of the permanent magnet synchronous motor, and realizing accurate control on the permanent magnet synchronous motor.
2. The robust three-vector model predictive flux linkage control method for the permanent magnet synchronous motor according to claim 1, wherein the mathematical model of the permanent magnet synchronous motor in step 1 is as follows:
Figure FDA0003080681030000011
Figure FDA0003080681030000012
Figure FDA0003080681030000013
Figure FDA0003080681030000014
ψd＝Ldid+ψf (5)
ψq＝Lqiq (6)
in formulae (1) to (6), udIs the direct component of the stator voltage, uqIs the quadrature component of the stator voltage; rsIs a stator resistor; i.e. idIs the direct component of the stator current, iqIs the quadrature component of the stator current; omegareIs the rotor electrical angular velocity; psidIs the direct component of the stator flux linkage, #qIs the quadrature component of the stator flux linkage; l isdIs the direct-axis component of the stator inductance,Lqis the quadrature component of the stator inductance; psifIs a permanent magnet flux linkage; t iseIs an electromagnetic torque; p is a radical ofnThe number of pole pairs of the motor is; j is moment of inertia; b is friction viscosity coefficient; t isLIs the load torque; t is time; wherein, L in the surface-mounted permanent magnet synchronous motord＝Lq＝Ls。
3. The robust three-vector model predictive flux linkage control method for the permanent magnet synchronous motor according to claim 2 is characterized in that the specific process of the step 2 is as follows:
let psi be based on the mathematical model of the permanent magnet synchronous motords(k)＝Ldid(k) And discretizing by adopting a backward Euler method to obtain:
Figure FDA0003080681030000021
in the formula: psid(k +1) is the predicted value of the direct axis flux linkage at the moment of (k + 1); psiq(k) The predicted value of the quadrature axis flux linkage at the moment k is obtained; u. ofd(k) Is the direct component of the stator voltage at time k;
the straight axis flux linkage psi in the formula (7)dIs equivalent to a pair variable psidsBy using a new control variable psids、ψqAnd (3) carrying out model prediction flux linkage control on the permanent magnet synchronous motor, and reconstructing a value function as follows:
C＝|ψds *-ψds(k+1)|2+|ψq *-ψq(k+1)|2 (8)
in the formula: psids *As a variable psidsA given value of (d);
psi in equation (8) by using one beat delay compensation for PMSM controlds(k +1) and ψq(k +1) is replaced by the quadrature-axis component ψ of the stator flux linkage at time (k +2)ds(k +2) and the quadrature component ψq(k +2), the modified cost function is expressed as:
C＝|ψds *-ψds(k+2)|2+|ψq *-ψq(k+2)|2 (9)
the flux linkage prediction equation of the permanent magnet synchronous motor under the new flux linkage control variable control condition is as follows:
Figure FDA0003080681030000031
Figure FDA0003080681030000032
in the formula: u. ofd(k +1) is the direct component of the stator voltage at time (k +1), uqAnd (k +1) is a quadrature component of the stator voltage at the time of (k + 1).
4. The robust three-vector model predictive flux linkage control method for the permanent magnet synchronous motor according to claim 3 is characterized in that the specific process of the step 3 is as follows:
the predicted flux linkage when the actual value of the motor parameter is not deviated from the nominal value of the motor nameplate is expressed as psi'ds、ψ′qThe predicted flux linkage when the actual value of the motor parameter deviates from the nominal value of the nameplate is expressed as psids、ψqBy delta phifRepresenting the error, Δ L, between the actual value of the permanent magnet flux linkage and the nominal value of the nameplatesRepresenting the error, Δ R, between the actual value of the inductance of the stator and the nominal value of the name platesRepresenting the error between the actual value of the stator resistance and the nominal value of the nameplate, and representing the uncertain disturbance of unmodeled dynamics by using epsilon;
considering the deviation between the actual value of the motor parameter and the nominal value of the nameplate and the unmodeled disturbance, the prediction flux linkage is expressed as:
Figure FDA0003080681030000033
and obtaining the influence of the parameter disturbance and the unmodeled dynamic state on the accuracy of the flux linkage prediction equation of the permanent magnet synchronous motor according to the formula (13).
5. The robust three-vector model predictive flux linkage control method for the permanent magnet synchronous motor according to claim 4 is characterized in that the specific process of the step 4 is as follows:
according to formula (13):
Figure RE-FDA0003229328410000041
Figure RE-FDA0003229328410000042
in the formula: f. ofdTotal perturbation of the direct axis predicted flux linkage, fqIs the total perturbation of the quadrature axis predicted flux linkage;
total disturbance fd、fqIn a steady state, then there are
Figure RE-FDA0003229328410000043
According to equation (14), byds，ψqFor state variables, the Roeberg observer is designed as follows:
Figure RE-FDA0003229328410000044
Figure RE-FDA0003229328410000045
in the formula:
Figure RE-FDA0003229328410000048
is psidsIs determined by the estimated value of (c),
Figure RE-FDA0003229328410000049
is psiqIs determined by the estimated value of (c),
Figure RE-FDA00032293284100000410
is fdIs determined by the estimated value of (c),
Figure RE-FDA00032293284100000411
is fqEstimated value of k1、k2Is the Longbeige observer gain;
the discrete Roeberg observer is:
Figure RE-FDA0003229328410000046
u(k)＝ud(k)+j(uq(k)-ωreψf) (19)
in the formula:
Figure RE-FDA0003229328410000047
Figure RE-FDA0003229328410000051
kT1＝k1Ts，kT2＝k2Ts；k1、k2representing observer coefficients, TsRepresents a sampling period;
ignore-omegareTsThe term j, the characteristic equation of the Roeberg observer obtained according to equation (18), is:
Figure RE-FDA0003229328410000052
obtaining the following components:
D(z)＝c0+c1z1+c2z2＝0 (21)
in the formula:
Figure RE-FDA0003229328410000053
c2＝1；
according to the July criterion, the stable essential conditions of the observer are as follows:
Figure RE-FDA0003229328410000054
c in the formula (21)0、c1、c2Substituting formula (22) to obtain:
Figure RE-FDA0003229328410000055
the final condition that the observer needs to be stabilized is obtained according to equation (23):
Figure RE-FDA0003229328410000056
6. the robust three-vector model predictive flux linkage control method for the permanent magnet synchronous motor according to claim 5 is characterized in that the specific process of the step 5 is as follows:
after the disturbance quantity estimated by the Roeberg observer is added, an expression of a robust three-vector model at the moment of predicting the flux linkage k +2 is obtained according to an expression (14) and by considering one-beat delay compensation:
Figure FDA0003080681030000061
and substituting an expression of the robust three-vector model for predicting the moment of the magnetic linkage k +2 into the modified value function, and when the value of the modified value function is minimum, acting a corresponding group of voltage vectors and action time thereof on the inverter to realize accurate control of the permanent magnet synchronous motor.
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