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CN111293933A - PMSM sensor anti-interference control method based on full-order adaptive observer - Google Patents

PMSM sensor anti-interference control method based on full-order adaptive observer Download PDF

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CN111293933A
CN111293933A CN202010110108.1A CN202010110108A CN111293933A CN 111293933 A CN111293933 A CN 111293933A CN 202010110108 A CN202010110108 A CN 202010110108A CN 111293933 A CN111293933 A CN 111293933A
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徐艳平
王立
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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
    • 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
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/22—Current control, e.g. using a current control loop
    • 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
    • H02P2203/00—Indexing scheme relating to controlling arrangements characterised by the means for detecting the position of the rotor
    • H02P2203/05—Determination of the rotor position by using two different methods and/or motor models
    • 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
    • H02P2205/00—Indexing scheme relating to controlling arrangements characterised by the control loops
    • H02P2205/01—Current loop, i.e. comparison of the motor current with a current reference

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  • Power Engineering (AREA)
  • Control Of Ac Motors In General (AREA)
  • Control Of Motors That Do Not Use Commutators (AREA)

Abstract

The invention discloses a PMSM (permanent magnet synchronous motor) non-speed sensor anti-interference based on a full-order adaptive observer, which specifically comprises the following steps: step 1, sampling voltage and current signals by using a Hall sensor; step 2, Clark and Park conversion is carried out on the current signals collected in the step 1 in sequence; step 3, estimating the rotating speed and the rotor position by adopting a full-order adaptive observer according to the result obtained in the step 2; step 4, carrying out load disturbance estimation and disturbance compensation on the result obtained in the step 3; and 5, constructing a closed-loop control system according to the result obtained in the step 4. According to the invention, the load disturbance observer and the full-order adaptive observer are combined without speed sensor control, so that the sensitivity of the system to load sudden change can be reduced, and the anti-interference capability of the system is improved.

Description

PMSM sensor anti-interference control method based on full-order adaptive observer
Technical Field
The invention belongs to the technical field of permanent magnet synchronous motors, and relates to a PMSM sensor anti-interference control method based on a full-order adaptive observer.
Background
A Permanent Magnet Synchronous Motor (PMSM) is one kind of Synchronous Motor, and compared with an asynchronous Motor, the PMSM has the advantages of high power density, large torque inertia ratio, simple structure, wide speed regulation range, small volume and the like, and in addition, Permanent Magnet materials such as rare earth and the like are gradually improved in performance and continuously reduced in cost, so that the PMSM is widely applied to the field of alternating current speed regulation, such as industrial robots, numerical control machines, electric automobiles, aerospace and the like.
The permanent magnet synchronous motor is a multivariable, nonlinear and strong coupling system, the application environment is generally complex and various uncertain disturbances are often accompanied, and the control system is required to have stronger stability and robustness. In a high-performance permanent magnet synchronous motor control system, accurately acquiring the position and the rotating speed of a motor rotor is a key factor for stable operation of the system. The position and the rotating speed of the rotor are generally obtained by measuring through a mechanical sensor, but the mechanical sensor greatly limits the application occasions due to the defects of high cost, relatively complex installation, difficult maintenance, increased system volume, reduced system reliability and the like. In order to solve the problems, a speed sensor-free control technology is generally adopted to obtain the position and the rotating speed of the motor rotor, and the technology has the advantages of strong adaptability, wide application range, cost saving, easiness in maintenance and the like.
The speed sensorless control technology can be classified into a motor model method and a signal injection method according to whether a motor model is required. The motor model method is to estimate the motor speed and the rotor position by using a mathematical model of the motor without installing a mechanical position sensor on the motor. The motor model method can be classified into a kalman filter method, a model reference adaptive method, an artificial intelligence algorithm, a full-order adaptive observer method and the like, wherein the full-order adaptive observer has the advantages of simple structure, easy realization, convenient calculation, strong universality and the like and is widely concerned. However, the full-order adaptive observer also has the following two disadvantages: firstly, the full-order adaptive observer is sensitive to load sudden change, when the load is suddenly added, the rotating speed drop is obvious, and the recovery time is long; when the load is suddenly reduced, the rotating speed is obviously increased, and the recovery time is longer. Secondly, the selection of the gain matrix in the full-order adaptive observer is difficult, different gain matrices need to be selected to ensure that the system has good dynamic and stable performance at low speed and medium and high speed, and the parameter adjustment of the system is too complex.
Disclosure of Invention
The invention aims to provide a PMSM sensor anti-interference control method based on a full-order adaptive observer, which combines a load disturbance observer and the full-order adaptive observer for speed-sensor-free control, and can reduce the sensitivity of a system to load sudden change and improve the anti-interference capability of the system.
The technical scheme adopted by the invention is that the PMSM non-speed sensor anti-interference control method based on the full-order adaptive observer specifically comprises the following steps:
step 1, sampling voltage and current signals by using a Hall sensor;
step 2, Clark and Park conversion is carried out on the current signals collected in the step 1 in sequence;
step 3, estimating the rotating speed and the rotor position by adopting a full-order adaptive observer according to the result obtained in the step 2;
step 4, carrying out load disturbance estimation and disturbance compensation on the result obtained in the step 3;
and 5, constructing a closed-loop control system according to the result obtained in the step 4.
The present invention is also characterized in that,
the specific process of the step 1 is as follows:
three-phase current i acquired by current Hall sensora、ibAnd icComponent U of stator voltage on d-q axis by Hall voltage sensordAnd UqThe measurement is performed.
The specific process of the step 2 is as follows:
collecting the three-phase current i under the natural coordinate acquired by the current Hall sensor in the step 1a、 ibAnd icConverted into current i under a two-phase static coordinate system through a Clark conversion moduleαAnd iβThen the current is converted into the current i under a two-phase rotating coordinate system through a Park inverse transformation moduledAnd iq。
The specific process of the step 3 is as follows:
the current i under the two-phase rotating coordinate system obtained in the step 2 is measureddAnd iqAnd in step 1 by electricityVoltage U measured by voltage hall sensordAnd UqThese four state variables are used as inputs to reconstruct the current estimate
Figure RE-GDA0002442717480000031
And
Figure RE-GDA0002442717480000032
then measuring the actual current value i of the Hall sensordAnd iqAnd reconstructed current estimate
Figure RE-GDA0002442717480000033
And
Figure RE-GDA0002442717480000034
making a difference to obtain
Figure RE-GDA0002442717480000035
And
Figure RE-GDA0002442717480000036
finally, the obtained current error is sent to a self-adaptive PI regulator, and the estimated rotating speed is obtained by regulating the self-adaptive PI parameter
Figure RE-GDA0002442717480000037
And rotor position
Figure RE-GDA0002442717480000038
The information, adaptive PI regulator is driven by a full-order adaptive observer module.
The design process of the full-order adaptive observer module in the step 3 is as follows:
step A, constructing a mathematical model of the surface-mounted permanent magnet synchronous motor d-q under a rotating coordinate axis, wherein the mathematical model is shown in the following formula (1):
Figure RE-GDA0002442717480000041
wherein: u. ofdAnd uqAre d and q axis voltages, respectivelyComponent RsIs stator resistance, #dAnd psiqRespectively permanent magnet flux linkage psifD, q axis components of (1);
the state equation under the d-q rotating coordinate axis of the permanent magnet synchronous motor can be obtained by the formula (1):
Figure RE-GDA0002442717480000042
wherein: l issL in surface-mounted permanent-magnet synchronous motors as stator inductances＝Ld＝Lq＝L；
The formula (2) is abbreviated as:
Figure RE-GDA0002442717480000043
wherein: i.e. is＝[idiq]T，us＝[uduq]T，
Figure RE-GDA0002442717480000044
Figure RE-GDA0002442717480000045
Figure RE-GDA0002442717480000046
Step B, establishing a full-order state observer according to a formula (3) in the step A, wherein the following formula (4) shows:
Figure RE-GDA0002442717480000047
in the formula:
Figure RE-GDA0002442717480000051
wherein, the upper mark 'Λ' represents an estimated value; by estimating variables
Figure RE-GDA0002442717480000052
Instead of the actual variable ωr，
Figure RE-GDA0002442717480000053
The matrix contains information on the estimated variables,
Figure RE-GDA0002442717480000054
for reconstructed values of original system variables, i.e. using reconstruction
Figure RE-GDA0002442717480000055
Replacing the A matrix of the original system; the open-loop state observer can be derived from equations (3) and (4) as follows:
Figure RE-GDA0002442717480000056
the open-loop observer shown in (5) cannot be directly used because the initial states of the original system and the reconstructed system may not be identical and other interference exists, so that a current error is introduced
Figure RE-GDA0002442717480000057
Forming a feedback correction term for correcting equation (5) to obtain:
Figure RE-GDA0002442717480000058
Figure RE-GDA0002442717480000059
the feedback correction term is that the difference between the output value of the observed system and the output value of the reconstruction system is used as a correction variable and is fed back to the reconstruction system through a gain matrix G
Figure RE-GDA00024427174800000510
To form a closed loop system; from this, it can be determined that the full-order adaptive observer is:
Figure RE-GDA00024427174800000511
to obtain an estimated rotational speed
Figure RE-GDA00024427174800000512
The permanent magnet synchronous motor is used as a reference model, the full-order adaptive observer shown in the formula (8) is used as an adjustable model, and the output error of the two models is used for driving the adaptive PI regulator, so that the output error of the two models tends to zero.
The adaptive rate selection process of the full-order adaptive observer in the step 3 is as follows:
for obtaining actual current and estimated current error
Figure RE-GDA0002442717480000061
Subtracting equation (6) from equation (3) yields:
Figure RE-GDA0002442717480000062
Figure RE-GDA0002442717480000063
in the formula (10)
Figure RE-GDA0002442717480000064
Equation (9) constitutes a dynamic error feedback system, which must satisfy the following two conditions if this dynamic error feedback system is stable according to the Popov hyperstability theory:
1) transfer function matrix [ SI- (A + G)]-1Must be a strictly positive definite matrix;
2)
Figure RE-GDA0002442717480000065
t1≥0，γ0 2is any finite positive number;
the adaptive rate can be obtained by solving the Popov integral inequality in the condition 2) reversely, and therefore, the formulas (9) and (10) are respectively substituted into the Popov integral inequality to obtain:
Figure RE-GDA0002442717480000066
according to the general structure of model reference adaptive parameters, will
Figure RE-GDA0002442717480000067
Taken as the proportional integral of equation (12), i.e.:
Figure RE-GDA0002442717480000068
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0002442717480000069
in order to estimate the initial value of the rotating speed, the formula represents a universal proportional-integral structure;
when equation (12) is substituted into equation (11), there are:
Figure RE-GDA0002442717480000071
to make η (0, t)1)≥-γ0 2Respectively enable η1(0,t1)≥-γ1 2，η2(0,t1)≥-γ2 2Namely:
Figure RE-GDA0002442717480000072
Figure RE-GDA0002442717480000073
in the formula, gamma1 2And gamma2 2Is any finite positive number;
to prove equation (14), inequality (16) may be utilized, namely:
Figure RE-GDA0002442717480000074
order:
Figure RE-GDA0002442717480000075
Figure RE-GDA0002442717480000076
the derivation of both sides of equation (18) can be found:
Figure RE-GDA0002442717480000077
substituting equation (19) into equation (14) can yield:
Figure RE-GDA0002442717480000078
it can be seen from equation (20) that the inequality satisfies η1(0,t1)≥-γ1 2The conditions of (a);
for equation (15), if the integrand to the left of the inequality is positive, the inequality must satisfy the condition, so it is advisable:
Figure RE-GDA0002442717480000081
substituting equation (21) into equation (15) can yield:
Figure RE-GDA0002442717480000082
it can be seen from equation (22) that the inequality satisfies η2(0,t1)≥-γ2 2The conditions of (a);
in summary, substituting equations (19) and (21) for equation (13) may satisfy the Popov integral inequality, that is:
Figure RE-GDA0002442717480000083
if it is not
Figure RE-GDA0002442717480000084
Taking the form of equation (12), the feedback system formed by equation (9) must be asymptotically stable.
The estimated expression of the rotation speed can be obtained by the following expressions (12), (19) and (21):
Figure RE-GDA0002442717480000085
from equation (24), a rotation speed estimation expression is obtained, namely:
Figure RE-GDA0002442717480000086
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0002442717480000087
generally, 0 is taken; if it will be
Figure RE-GDA0002442717480000088
And
Figure RE-GDA0002442717480000089
substituted type (25), because the surface-mounted permanent magnet synchronous motor generally adopts idAs a result, the rotation speed adaptation law expressed by the stator current can be obtained as follows:
Figure RE-GDA00024427174800000810
the selection process of the gain matrix of the full-order adaptive observer in the step 3 is as follows:
the feedback matrix G is designed as:
Figure RE-GDA0002442717480000091
in the formula:
Figure RE-GDA0002442717480000092
when estimating the rotational speed
Figure RE-GDA0002442717480000093
The dynamic error of the closed-loop observer, when converging on the actual rotational speed ω, can be expressed as:
Figure RE-GDA0002442717480000094
the two diagonal terms in the matrix (A + G) are negative and therefore satisfy [ SI- (A + G)]-1Is a stability condition for strictly positive definite matrix.
The specific process of the step 4 is as follows:
according to the estimated rotating speed obtained in the step 3
Figure RE-GDA0002442717480000095
And rotor position angle
Figure RE-GDA0002442717480000096
Information, estimated rotation speed obtained
Figure RE-GDA0002442717480000097
With the torque current i obtained in step 2qEstimating load disturbance as an input to a load disturbance observer
Figure RE-GDA0002442717480000098
And control the system torque current iqThere is a correspondence relationship and thus can pass
Figure RE-GDA0002442717480000099
The value is used for determining the value of the torque current to be compensated, and then the calculated compensation value is sent to the control system, so that the external disturbance resistance of the control system is improved; the disturbance estimation and compensation are realized by a load disturbance observer module.
The design process of the load disturbance observer module in the step 4 is as follows:
the dynamic space state equation of the permanent magnet synchronous motor can be expressed as:
Figure RE-GDA00024427174800000910
where x is the state quantity, u is the input, f is the disturbance, y is the output, A, Bu、
BfAnd C is the coefficient matrix, the perturbation term can be expressed as:
Bff＝x-Ax-Buu (30)；
if the rate of change of f is approximately zero, then the estimation of f conforms to the design principle of the disturbance observer, and when the disturbance is estimated
Figure RE-GDA0002442717480000101
When the actual disturbance f is very close, the disturbance observer can be constructed as follows:
Figure RE-GDA0002442717480000102
the disturbance estimation expressions obtained by collating the formulas (30) and (31) are:
Figure RE-GDA0002442717480000103
setting an intermediate variable matrix M, order
Figure RE-GDA0002442717480000104
Equation (32) can be expressed as an equation with intermediate variables:
Figure RE-GDA0002442717480000105
at this time, equation (33) is an equation of the disturbance observer, and since the value of the sampling period in the actual system is very small, the change rate of the load torque in one sampling period is approximately zero, the extended mechanical motion equation of the permanent magnet synchronous motor is as follows:
Figure RE-GDA0002442717480000106
in the formula, TLIs the load torque, B is the viscous friction coefficient, PnFor number of pole pairs, psi, of the motorfIs a permanent magnet flux linkage; j is moment of inertia, iqIs a q-axis current component, ωrIs the mechanical angular velocity;
the PMSM disturbance observation equation obtained by putting the formulas (29) to (34) in order is as follows:
Figure RE-GDA0002442717480000111
the load disturbance observer equation obtained by arranging the formula (35) is as follows:
Figure RE-GDA0002442717480000112
calculated in formula (36)
Figure RE-GDA0002442717480000113
I.e. the load torque
Figure RE-GDA0002442717480000114
Estimated value of k1Must satisfy Lyapunov stability, and k can be obtained according to the stability requirement1Is k1＜0；
Due to load torque
Figure RE-GDA0002442717480000115
Has a certain relation with the q-axis current, so the current can be compensated according to the sudden load disturbance, and the current is compensated
Figure RE-GDA0002442717480000116
Can be expressed as:
Figure RE-GDA0002442717480000117
in summary, the final input i of the quadrature current loop PI regulatorq-inCan be expressed as:
Figure RE-GDA0002442717480000118
the specific process of the step 5 is as follows:
firstly, a given rotation speed omega and the estimated rotation speed obtained in the step 3 are combined
Figure RE-GDA0002442717480000119
Making difference, feeding the rotation speed error into a rotation speed loop PI regulator, and outputting the rotation speed error as a torque current iq *Torque current iq *First with a feedback current iqMaking difference, and then according to load disturbance change value iq *Carrying out torque current compensation with the compensation value of
Figure RE-GDA00024427174800001110
Finally, the final input of the quadrature axis current loop PI regulator is obtained as iq-inAnd the input of the PI regulator which can simultaneously obtain the straight-axis current loop is id *-id(ii) a The output of the current loop PI regulator is the component U of the stator voltage on the d-q axisdAnd UqThen, the voltage U under the two-phase rotating coordinate system is converted into the voltage U under the two-phase rotating coordinate system through a Park inverse transformation moduledAnd UqConversion to voltage U at two-phase stationary coordinateαAnd UβFinally, U is putαAnd UβAnd sending the signals into a space vector pulse width modulation module to obtain six paths of PWM pulse bar driving PMSM to form a closed-loop control system.
The invention has the following beneficial effects:
(1) the full-order adaptive observer is combined with a load disturbance observer without speed sensor control, q-axis compensation current is obtained by the load disturbance observer, the q-axis current output by a speed loop PI regulator is compensated, and then a switching sequence acting on an inverter is obtained, so that the permanent magnet synchronous motor can timely cope with the problem of load sudden change, and the anti-interference capability of the system is remarkably improved.
(2) The full-order adaptive observer estimates the position of a rotor by using a motor model, different gain matrixes need to be set in order to meet the stability requirement of a control system at low speed and medium and high speed, and the selection of the gain matrixes does not have clear theoretical basis at present. The invention adopts a simplified gain matrix, only needs to adjust a gain matrix coefficient, and reduces the complexity of system parameter adjustment.
Drawings
FIG. 1 is a schematic block diagram of a full-order adaptive observer based PMSM sensor disturbance rejection control system of the present invention;
FIG. 2 is a waveform diagram of the rotation speed in a conventional full-order adaptive observer non-speed sensor control method;
FIG. 3 is a waveform diagram of rotor position in a conventional full-order adaptive observer non-speed sensor control method;
FIG. 4 is a waveform diagram of the rotation speed in the PMSM sensor disturbance rejection control method based on the full-order adaptive observer according to the invention;
FIG. 5 is a waveform diagram of rotor position in the PMSM sensor disturbance rejection control method based on the full-order adaptive observer according to the invention.
In the figure, 1, a three-phase inverter, 2, a current detection circuit, 3, a permanent magnet synchronous motor, 4, a Clark conversion module, 5, a Park conversion module, 6, a load disturbance observer, 7, a full-order adaptive observer, 8, a space vector pulse width modulation module and 9, a Park inverse conversion module are adopted.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a PMSM (permanent magnet synchronous motor) disturbance rejection control system based on a full-order adaptive observer, which comprises a rotating speed outer ring and a current inner ring as shown in figure 1, wherein the current inner ring comprises a quadrature-axis (q-axis) current ring and a direct-axis (d-axis) current ring. The working process is as follows: the current detection circuit 2 detects the output current i of the three-phase inverter 1a、ibAnd icThen, the current i in the natural coordinate system is converted by a Clark conversion module 4a、ibAnd icConversion to current i in two-phase stationary frameαAnd iβ. The full-order adaptive observer 7 utilizes the current reference values of the direct axis and the quadrature axis
Figure RE-GDA0002442717480000131
And
Figure RE-GDA0002442717480000132
reference value of voltage
Figure RE-GDA0002442717480000133
And
Figure RE-GDA0002442717480000134
obtaining the estimated rotating speed of the motor
Figure RE-GDA0002442717480000135
And estimating rotor position angle
Figure RE-GDA0002442717480000136
Current i in two-phase stationary coordinateα、iβAnd estimating the rotor position angle
Figure RE-GDA0002442717480000137
Obtaining the direct axis current i and the quadrature axis current i under the two-phase rotating coordinate system through the Park transformation module 5dAnd iq，iqAnd
Figure RE-GDA0002442717480000138
the compensation quantity of quadrature axis current is obtained through a load disturbance observer 6
Figure RE-GDA0002442717480000139
Given value of speed omega*And the resulting estimated rotational speed
Figure RE-GDA00024427174800001310
Obtaining a current reference value through a rotating speed ring PI regulator after difference making
Figure RE-GDA00024427174800001311
And the amount of compensation
Figure RE-GDA00024427174800001312
Summed with quadrature axis current iqMaking a difference, and obtaining a quadrature axis voltage reference value through a q-axis current loop PI regulator
Figure RE-GDA00024427174800001313
Reference value of direct current
Figure RE-GDA00024427174800001314
And the direct axis current idMaking difference, and obtaining a direct axis voltage reference value through a d axis current loop PI regulator
Figure RE-GDA00024427174800001315
And estimating a rotor position angle
Figure RE-GDA00024427174800001316
Obtaining the voltage under the static coordinate system through a Park inverse transformation module 9
Figure RE-GDA00024427174800001317
Figure RE-GDA00024427174800001318
And then the switching sequence of the three-phase inverter 1 is obtained through the space vector pulse width modulation module 8 to control the permanent magnet synchronous motor 3.
The invention provides a PMSM sensor anti-interference control method based on a full-order adaptive observer, which combines a load disturbance observer and the full-order adaptive observer for speed-sensor-free control. The method can reduce the sensitivity of the system to sudden load change and improve the anti-interference capability of the system. Meanwhile, the complexity of parameter adjustment of the system is reduced by adopting a simplified gain matrix in consideration of the complicated parameter selection of the gain matrix of the full-order adaptive observer.
The invention relates to a PMSM (permanent magnet synchronous motor) disturbance rejection control method based on a full-order adaptive observer, which specifically comprises the following steps of:
step 1, sampling current and voltage signals
Three-phase current i acquired by current Hall sensora、ibAnd icComponent U of stator voltage on d-q axis by Hall voltage sensordAnd UqThe measurement is performed.
Step 2, Clark and Park conversion
Collecting the three-phase current i under the natural coordinate acquired by the current Hall sensor in the step 1a、 ibAnd icConverted into current i under a two-phase static coordinate system through Clark conversion module 4(3/2)αAnd iβThen converted into the current i under the two-phase rotating coordinate system through the Park inverse transformation module 9(2/2)dAnd iq。
Step 3, estimating the rotating speed and the rotor position by the full-order adaptive observer
The current i under the two-phase rotating coordinate system obtained in the step 2 is measureddAnd iqAnd the voltage U measured by the voltage Hall sensor in step 1dAnd UqThese 4 state variables are used as inputs to reconstruct the current estimate
Figure RE-GDA0002442717480000141
And
Figure RE-GDA0002442717480000142
then measuring the actual current value i of the Hall sensordAnd iqAnd reconstructed current estimate
Figure RE-GDA0002442717480000143
And
Figure RE-GDA0002442717480000144
making a difference to obtain
Figure RE-GDA0002442717480000145
And
Figure RE-GDA0002442717480000146
finally, the obtained current error is sent to a self-adaptive mechanism (a self-adaptive PI regulator), and the estimated rotating speed is obtained by regulating the self-adaptive PI parameter
Figure RE-GDA0002442717480000151
And rotor position
Figure RE-GDA0002442717480000152
Information, the full-order adaptive observer is specifically designed as follows:
1) full-order adaptive observer module 7 design
A mathematical model of a surface-mounted permanent magnet synchronous motor d-q under a rotating coordinate axis is as follows:
Figure RE-GDA0002442717480000153
wherein: u. ofdAnd uqAre d and q axis voltage components, RsIs stator resistance, #dAnd psiqRespectively permanent magnet flux linkage psifD, q-axis components of (1).
The state equation under the d-q rotating coordinate axis of the permanent magnet synchronous motor can be obtained by the formula (1):
Figure RE-GDA0002442717480000154
wherein: l issL in surface-mounted permanent-magnet synchronous motors as stator inductances＝Ld＝Lq＝L。
It is abbreviated as:
Figure RE-GDA0002442717480000155
wherein: i.e. is＝[idiq]T，us＝[uduq]T，
Figure RE-GDA0002442717480000156
Figure RE-GDA0002442717480000157
Figure RE-GDA0002442717480000158
A full-order state observer is built according to equation (3), then:
Figure RE-GDA0002442717480000161
in the formula:
Figure RE-GDA0002442717480000162
where the upper scale Λ represents the estimated value. By estimating variables
Figure RE-GDA0002442717480000163
Instead of the actual variable ωr，
Figure RE-GDA0002442717480000164
The matrix contains information on the estimated variables,
Figure RE-GDA0002442717480000165
for reconstructed values of original system variables, i.e. using reconstruction
Figure RE-GDA0002442717480000166
Replacing the a matrix of the original system. The open-loop state observer can be derived from equations (3) and (4) as follows:
Figure RE-GDA0002442717480000167
in practice, the initial states of the original system and the reconstructed system may not be identical, and there are other disturbances, and the open-loop observer shown in equation (5) cannot be directly used. Thus introducing a current error
Figure RE-GDA0002442717480000168
Forming a feedback correction term for correcting equation (5) to obtain:
Figure RE-GDA0002442717480000169
Figure RE-GDA00024427174800001610
the feedback correction term is that the difference between the output value of the observed system and the output value of the reconstruction system is used as a correction variable and is fed back to the reconstruction system through a gain matrix G
Figure RE-GDA00024427174800001611
To form a closed loop system. From this, it can be determined that the full-order adaptive observer is:
Figure RE-GDA00024427174800001612
to obtain an estimated rotational speed
Figure RE-GDA00024427174800001613
The permanent magnet synchronous motor is used as a reference model, the full-order adaptive observer shown in the formula (8) is used as an adjustable model, the output error of the two models is used for driving the adaptive mechanism, and the estimation parameters can be continuously corrected under the action of the adaptive rule, so that the output error of the two models tends to zero.
2) Stability certification and adaptive rate selection
In order to obtain the error between the actual current and the estimated current
Figure RE-GDA0002442717480000171
Subtracting equation (6) from equation (3) yields:
Figure RE-GDA0002442717480000172
Figure RE-GDA0002442717480000173
in the formula (10)
Figure RE-GDA0002442717480000174
Equation (9) constitutes a dynamic error feedback system. According to the Popov hyperstability theory, if this dynamic error feedback system is made stable, it must satisfy the following two conditions:
1) transfer function matrix [ SI- (A + G)]-1Must be a strictly positive definite matrix;
2)
Figure RE-GDA0002442717480000175
t1≥0，γ0 2is any finite positive number.
The adaptive rate can be obtained by solving the Popov integral inequality in the condition 2) reversely, and therefore, the formulas (9) and (10) are respectively substituted into the Popov integral inequality to obtain:
Figure RE-GDA0002442717480000176
according to the general structure of model reference adaptive parameters, will
Figure RE-GDA0002442717480000177
Taken as the proportional integral of equation (12), i.e.:
Figure RE-GDA0002442717480000178
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0002442717480000179
to estimate the initial value of the rotation speed, the above equation shows a general proportional-integral structure.
When equation (12) is substituted into equation (11), there are:
Figure RE-GDA0002442717480000181
to make η (0, t)1)≥-γ0 2Respectively enable η1(0,t1)≥-γ1 2，η2(0,t1)≥-γ2 2Namely:
Figure RE-GDA0002442717480000182
Figure RE-GDA0002442717480000183
in the formula, gamma1 2And gamma2 2Is any finite positive number.
To prove equation (14), inequality (16) may be utilized, namely:
Figure RE-GDA0002442717480000184
order:
Figure RE-GDA0002442717480000185
Figure RE-GDA0002442717480000186
the derivation of both sides of equation (18) can be found:
Figure RE-GDA0002442717480000187
substituting equation (19) into equation (14) can yield:
Figure RE-GDA0002442717480000188
it can be seen from equation (20) that the inequality satisfies η1(0,t1)≥-γ1 2The conditions of (1).
For equation (15), if the integrand to the left of the inequality is positive, the inequality must satisfy the condition, so it is advisable:
Figure RE-GDA0002442717480000191
substituting equation (21) into equation (15) can yield:
Figure RE-GDA0002442717480000192
it can be seen from equation (22) that the inequality satisfies η2(0,t1)≥-γ2 2The conditions of (1).
In summary, substituting equations (19) and (21) for equation (13) may satisfy the Popov integral inequality, that is:
Figure RE-GDA0002442717480000193
that is, if
Figure RE-GDA0002442717480000194
Taking the form of equation (12), the feedback system formed by equation (9) must be asymptotically stable.
The estimated expression of the rotation speed can be obtained by the following expressions (12), (19) and (21):
Figure RE-GDA0002442717480000195
according to the formula (24), the invention adopts a PI self-adaptive control mode to obtain a rotating speed estimation expression, namely:
Figure RE-GDA0002442717480000196
in the formula
Figure RE-GDA0002442717480000197
Generally 0 is taken. If it will be
Figure RE-GDA0002442717480000198
And
Figure RE-GDA0002442717480000199
substituted type (25), because the surface-mounted permanent magnet synchronous motor generally adopts idAs a result, the rotation speed adaptation law expressed by the stator current can be obtained as follows:
Figure RE-GDA00024427174800001910
3) selection of gain matrix
In equation (6), a correction term is included in the full-order adaptive observer state estimation equation, and the estimated state is continuously corrected in a feedback correction manner. The state estimation error is multiplied by a feedback gain matrix to optimize the next output of the observer, and the feedback gain matrix is designed to meet the requirement of system stability. The feedback matrix G is designed as:
Figure RE-GDA0002442717480000201
in the formula:
Figure RE-GDA0002442717480000202
when estimating the rotational speed
Figure RE-GDA0002442717480000203
The dynamic error of the closed-loop observer, when converging on the actual rotational speed ω, can be expressed as:
Figure RE-GDA0002442717480000204
the two diagonal terms in the matrix (A + G) are negative and therefore satisfy [ SI- (A + G)]-1Is a stability condition for strictly positive definite matrix. Gain coefficient k selection pair systemThe stable operation is crucial, if the k value is selected too large, the measurement noise is enlarged, and the system is possibly unstable; if the k value is too small, the response speed of the system is reduced, and the convergence of the system is too slow. Therefore, the selection of the k value is crucial to the dynamic steady-state performance of the system.
Step 4, load disturbance estimation and disturbance compensation
From step 3 we obtain the estimated speed
Figure RE-GDA0002442717480000205
And rotor position angle
Figure RE-GDA0002442717480000206
Information, estimated rotation speed obtained
Figure RE-GDA0002442717480000207
With the torque current i obtained in step 2qAs the input quantity of the load disturbance observer, the estimated load disturbance can be obtained by equations (5) to (8)
Figure RE-GDA0002442717480000208
The specific value can be regarded as the variation of the external load disturbance, which is also called disturbance value. Due to the fact that
Figure RE-GDA0002442717480000211
And control the system torque current iqThere is a corresponding relationship as shown in formula (9), then we can pass
Figure RE-GDA0002442717480000212
The value is used for determining the value of the torque current to be compensated, and then the calculated compensation value is sent to the control system, so that the external disturbance resistance of the control system is improved. Since both the disturbance estimation and compensation are realized by the load disturbance observer module 6, the load disturbance observer module 6 is designed as follows:
design and compensation of the load disturbance observer module 6:
the dynamic space state equation of the permanent magnet synchronous motor can be expressed as:
Figure RE-GDA0002442717480000213
where x is the state quantity, u is the input, f is the disturbance, y is the output, A, Bu、BfAnd C is the coefficient matrix, the perturbation term can be expressed as:
Bff＝x-Ax-Buu (30)；
if the rate of change of f is approximately zero, then the estimation of f conforms to the design principle of the disturbance observer, and when the disturbance is estimated
Figure RE-GDA0002442717480000214
When the actual disturbance f is very close, the disturbance observer can be constructed as follows:
Figure RE-GDA0002442717480000215
the disturbance estimation expressions obtained by collating the formulas (30) and (31) are:
Figure RE-GDA0002442717480000216
setting an intermediate variable matrix M, order
Figure RE-GDA0002442717480000217
Equation (32) can be expressed as an equation with intermediate variables:
Figure RE-GDA0002442717480000218
at this time, equation (33) is an equation of the disturbance observer, and since the value of the sampling period in the actual system is very small, the change rate of the load torque in one sampling period is approximately zero, the extended mechanical motion equation of the permanent magnet synchronous motor is as follows:
Figure RE-GDA0002442717480000221
in the formula, TLIs the load torque, B is the viscous friction coefficient, PnFor number of pole pairs, psi, of the motorfIs a permanent magnet flux linkage; j is moment of inertia, iqIs a q-axis current component, ωrIs the mechanical angular velocity.
The PMSM disturbance observation equation obtained by putting the formulas (29) to (34) in order is as follows:
Figure RE-GDA0002442717480000222
the load disturbance observer equation obtained by arranging the formula (35) is as follows:
Figure RE-GDA0002442717480000223
calculated in formula (36)
Figure RE-GDA0002442717480000224
I.e. the load torque
Figure RE-GDA0002442717480000225
Estimated value of k1Must satisfy Lyapunov stability, and k can be obtained according to the stability requirement1Is k1＜0。
Due to load torque
Figure RE-GDA0002442717480000226
Has a certain relation with the q-axis current, so the current can be compensated according to the sudden load disturbance, and the current is compensated
Figure RE-GDA0002442717480000227
Can be expressed as:
Figure RE-GDA0002442717480000228
in summary, the final input i of the quadrature current loop PI regulatorq-inCan be expressed as:
Figure RE-GDA0002442717480000229
in equations (34) - (36), the rotation speed and the current are used simultaneously, since the rotation speed is a mechanical quantity, the current is an electrical quantity, and the mechanical time constant is much larger than the electrical time constant, the speed loop control period T is usually madeωControlling the period T for the current loopi5-20 times of the control period T of the speed loop in the inventionωControlling the period T for the current loopi20 times of the total weight of the powder.
Step 5, forming a closed loop control system
The control method is improved on the basis of the traditional vector control, so that a double closed-loop control strategy (a rotating speed loop and a current loop) is also adopted, and an external rotating speed loop firstly gives a given rotating speed omega and the estimated rotating speed obtained in the step 3
Figure RE-GDA0002442717480000231
Making difference, feeding the rotation speed error into a rotation speed loop PI regulator, and outputting the rotation speed error as a torque current iq *First with a feedback current iqMaking difference, then according to the load disturbance change value making torque current compensation for it, the compensation value is
Figure RE-GDA0002442717480000232
Finally, the final input of the quadrature axis current loop PI regulator is obtained as iq-inAs shown in equation (10); in the vector control, in order to obtain the maximum torque of the control system as much as possible, a d-axis current input i is adoptedd *Control mode of 0, then id *With direct axis feedback current idMaking a difference, and finally, the input of the direct-axis current loop PI regulator is id *-id. The output of the current loop PI regulator is the component U of the stator voltage on the d-q axisdAnd UqThen the voltage U under the two-phase rotating coordinate system is converted through a Park inverse transformation module 9dAnd UqConversion to voltage U at two-phase stationary coordinateαAnd UβFinally, U is putαAnd UβAnd the PWM signals are sent to a space pulse width modulation module 8 to obtain 6 paths of PWM pulses to drive a PMSM to form a closed-loop control system.
The invention provides a PMSM sensor anti-interference control method based on a full-order adaptive observer, which combines a load disturbance observer and the full-order adaptive observer for speed-sensor-free control. Considering that the full-order adaptive observer is sensitive to load sudden change, the scheme can reduce the sensitivity of the system to the load sudden change and improve the anti-interference capability of the system. Meanwhile, the complexity of parameter adjustment of the system is reduced by adopting a simplified gain matrix in consideration of the complicated parameter selection of the gain matrix of the full-order adaptive observer.
In order to verify the feasibility and the effectiveness of the scheme provided by the PMSM sensorless disturbance rejection control method based on the full-order adaptive observer, MATLAB/SIMULINK simulation software is used for carrying out simulation verification on the method. The motor parameters used herein are as follows: permanent magnet flux linkage psif0.127Wb, stator inductance Ls1.02mH, stator resistance Rs0.18 omega, and a moment of inertia J of 0.000368kg m2Rated voltage UN200V, rated current INIs 10A, rated power PNIs 2kW, rated rotational speed nNIs 3000r/min, rated torque TNIt was 6.37 N.m. In the simulation verification of the scheme, the value of the gain coefficient k is selected to be 1.2.
Fig. 2 and 3 are simulation waveforms of conventional full-order adaptive observer non-velocity-sensor control, which do not have step 4 (load disturbance estimation and compensation) in the implementation steps. Firstly, current and voltage signals under a natural coordinate system are collected through a Hall element, then the current and voltage signals are converted into current and voltage values required by different coordinate systems through Clark conversion, Park conversion and Park inverse conversion, information of the rotating speed and the rotor position angle is obtained through a full-order adaptive observer, and finally the estimated rotating speed and the feedback current are sent to a control system to form double closed loop control. The specific simulation parameters of the waveforms shown in fig. 2 and 3 are: sampling frequency of 10kHz and rotating speed loop PI parameter kp＝0.005，ki0.00012; q axis electricityFlow loop PI parameter kp＝1，ki0.02; d-axis current loop PI parameter kp＝4.8，ki0.008 percent; adaptive PI parameter kp＝10，ki＝1
FIG. 2 shows the response waveforms of the actual speed and the estimated speed of a PMSM controlled by a conventional full-order adaptive observer without a speed sensor when the given speed is 2000r/min, the load is suddenly increased by 5 N.m in 0.3s, and the load is suddenly decreased to zero in 0.7 s. When the load of 5 N.m is suddenly added for 0.3s, the rotating speed falls to 1850r/min, and the rotating speed is recovered to the given rotating speed when the load is about 0.42 s. When the load suddenly decreases to zero in 0.7s, the rotation speed rises to 2130r/min, and the rotation speed is recovered to the given rotation speed in about 0.82 s. FIG. 3 shows the actual rotor position angle θ and the estimated rotor position angle θ of a PMSM controlled by a full-order adaptive observer without a speed sensor
Figure RE-GDA0002442717480000251
And (4) waveform.
Fig. 4 and 5 are simulation waveforms of a PMSM sensorless disturbance rejection control method based on a full-order adaptive observer, which strictly execute the above five steps in specific implementation steps. Firstly, current and voltage signals under a natural coordinate system are collected through a Hall element, then the current and voltage signals are converted into current and voltage values required by different coordinate systems through Clark conversion, Park conversion and Park inverse conversion, secondly, information of a rotating speed and a rotor position angle is obtained through a full-order adaptive observer, and then in order to restrain the influence of external load disturbance on a control system, the obtained estimated rotating speed is used
Figure RE-GDA0002442717480000252
And torque current iqSending the torque current compensation value to a load disturbance observer to calculate a required torque current compensation value
Figure RE-GDA0002442717480000253
Finally, the rotating speed is estimated
Figure RE-GDA0002442717480000254
Feedback current iqSum current compensation value
Figure RE-GDA0002442717480000255
And sending the signals into a control system to form double closed-loop control. The specific simulation parameters of the waveforms shown in fig. 4 and 5 are: sampling frequency of 10kHz and rotating speed loop PI parameter kp＝0.006，ki0.0001,; q-axis current loop PI parameter kp＝1.2， ki0.04; d-axis current loop PI parameter kp＝5，ki0.01; adaptive PI parameter kp＝8，ki＝1。
FIG. 4 shows the response waveforms of the actual rotation speed and the estimated rotation speed when the PMSM of the PMSM no-speed-sensor disturbance rejection control method based on the full-order adaptive observer is at a given rotation speed of 2000r/min, a load of 0.3s plus 5 N.m suddenly, and a load of 0.7s decreasing to zero. When the load of 5 N.m is suddenly added for 0.3s, the rotating speed falls to 1890r/min, and the rotating speed is recovered to the given rotating speed when the load is about 0.36 s. When the load suddenly decreases to zero at 0.7s, the speed rises to 2110r/min, and about 0.76s, the speed returns to the given speed. FIG. 5 shows the actual rotor position angle θ and the estimated rotor position angle of the PMSM in the PMSM no-speed-sensor disturbance rejection control method based on the full-order adaptive observer according to the present invention
Figure RE-GDA0002442717480000256
And (4) waveform.
As can be seen from the figure, the estimated rotating speed can accurately follow the actual rotating speed in the PMSM speed sensorless disturbance rejection control based on the full-order adaptive observer, the estimated rotor position can accurately follow the actual rotor position, and the system can stably run. When the load is suddenly changed, the full-order adaptive observer speed-sensorless control method is sensitive to the sudden change of the load; the invention reduces the sensitivity of the system to load mutation. Compared with a full-order adaptive observer speed sensor-free control method, the method has better anti-interference performance.

Claims (10)

1. The PMSM no-speed sensor disturbance rejection control method based on the full-order adaptive observer is characterized by comprising the following steps: the method specifically comprises the following steps:
step 1, sampling voltage and current signals by using a Hall sensor;
step 2, Clark and Park conversion is carried out on the current signals collected in the step 1 in sequence;
step 3, estimating the rotating speed and the rotor position by adopting a full-order adaptive observer according to the result obtained in the step 2;
step 4, carrying out load disturbance estimation and disturbance compensation on the result obtained in the step 3;
and 5, constructing a closed-loop control system according to the result obtained in the step 4.
2. The full-order adaptive observer-based PMSM disturbance rejection control method according to claim 1, characterized in that: the specific process of the step 1 is as follows:
three-phase current i acquired by current Hall sensora、ibAnd icComponent U of stator voltage on d-q axis by Hall voltage sensordAnd UqThe measurement is performed.
3. The full-order adaptive observer-based PMSM disturbance rejection control method according to claim 2, characterized in that: the specific process of the step 2 is as follows:
collecting the three-phase current i under the natural coordinate acquired by the current Hall sensor in the step 1a、ibAnd icConverted into current i under a two-phase static coordinate system through a Clark conversion moduleαAnd iβThen the current is converted into the current i under a two-phase rotating coordinate system through a Park inverse transformation moduledAnd iq。
4. The full-order adaptive observer-based PMSM disturbance rejection control method according to claim 3, characterized in that: the specific process of the step 3 is as follows:
the current i under the two-phase rotating coordinate system obtained in the step 2 is measureddAnd iqAnd the voltage U measured by the voltage Hall sensor in step 1dAnd UqThese four state variables are used as inputs to reconstruct the current estimate
Figure RE-FDA0002442717470000021
And
Figure RE-FDA0002442717470000022
then measuring the actual current value i of the Hall sensordAnd iqAnd reconstructed current estimate
Figure RE-FDA0002442717470000023
And
Figure RE-FDA0002442717470000024
making a difference to obtain
Figure RE-FDA0002442717470000025
And
Figure RE-FDA0002442717470000026
finally, the obtained current error is sent to a self-adaptive PI regulator, and the estimated rotating speed is obtained by regulating the self-adaptive PI parameter
Figure RE-FDA0002442717470000027
And rotor position
Figure RE-FDA0002442717470000028
The information, adaptive PI regulator is driven by a full-order adaptive observer module.
5. The full-order adaptive observer-based PMSM disturbance rejection control method according to claim 4, characterized in that: the design process of the full-order adaptive observer module in the step 3 is as follows:
step A, constructing a mathematical model of the surface-mounted permanent magnet synchronous motor d-q under a rotating coordinate axis, wherein the mathematical model is shown in the following formula (1):
Figure RE-FDA0002442717470000029
wherein: u. ofdAnd uqAre d and q axis voltage components, RsIs stator resistance, #dAnd psiqRespectively permanent magnet flux linkage psifD, q axis components of (1);
the state equation under the d-q rotating coordinate axis of the permanent magnet synchronous motor can be obtained by the formula (1):
Figure RE-FDA00024427174700000210
wherein: l issL in surface-mounted permanent-magnet synchronous motors as stator inductances＝Ld＝Lq＝L；
The formula (2) is abbreviated as:
Figure RE-FDA0002442717470000031
wherein: i.e. is＝[idiq]T，us＝[uduq]T，
Figure RE-FDA0002442717470000032
Figure RE-FDA0002442717470000033
Figure RE-FDA0002442717470000034
Step B, establishing a full-order state observer according to a formula (3) in the step A, wherein the following formula (4) shows:
Figure RE-FDA0002442717470000035
in the formula:
Figure RE-FDA0002442717470000036
wherein the upper mark 'Λ' represents an estimated value; by estimating variables
Figure RE-FDA0002442717470000037
Instead of the actual variable ωr，
Figure RE-FDA0002442717470000038
The matrix contains information on the estimated variables,
Figure RE-FDA0002442717470000039
for reconstructed values of original system variables, i.e. using reconstruction
Figure RE-FDA00024427174700000310
Replacing the A matrix of the original system; the open-loop state observer can be derived from equations (3) and (4) as follows:
Figure RE-FDA00024427174700000311
the open-loop observer shown in (5) cannot be directly used because the initial states of the original system and the reconstructed system may not be identical and other interference exists, so that a current error is introduced
Figure RE-FDA00024427174700000312
Forming a feedback correction term for correcting equation (5) to obtain:
Figure RE-FDA0002442717470000041
Figure RE-FDA0002442717470000042
the feedback correction term is that the difference between the output value of the observed system and the output value of the reconstruction system is used as a correction variable and is fed back to the reconstruction system through a gain matrix G
Figure RE-FDA0002442717470000043
To form a closed loop system; from this, it can be determined that the full-order adaptive observer is:
Figure RE-FDA0002442717470000044
to obtain an estimated rotational speed
Figure RE-FDA0002442717470000045
The permanent magnet synchronous motor is used as a reference model, the full-order adaptive observer shown in the formula (8) is used as an adjustable model, and the output error of the two models is used for driving the adaptive PI regulator, so that the output error of the two models tends to zero.
6. The full-order adaptive observer-based PMSM disturbance rejection control method according to claim 5, characterized in that: the adaptive rate selection process of the full-order adaptive observer in the step 3 is as follows:
for obtaining actual current and estimated current error
Figure RE-FDA0002442717470000046
Subtracting equation (6) from equation (3) yields:
Figure RE-FDA0002442717470000047
Figure RE-FDA0002442717470000048
in the formula (10)
Figure RE-FDA0002442717470000049
Equation (9) constitutes a dynamic error feedback system, which must satisfy the following two conditions if this dynamic error feedback system is stable according to the Popov hyperstability theory:
1) transfer function matrix [ SI- (A + G)]-1Must be a strictly positive definite matrix;
2)
Figure RE-FDA0002442717470000051
γ0 2is any finite positive number;
the adaptive rate can be obtained by solving the Popov integral inequality in the condition 2) reversely, and therefore, the formulas (9) and (10) are respectively substituted into the Popov integral inequality to obtain:
Figure RE-FDA0002442717470000052
according to the general structure of model reference adaptive parameters, will
Figure RE-FDA0002442717470000053
Taken as the proportional integral of equation (12), i.e.:
Figure RE-FDA0002442717470000054
in the formula (I), the compound is shown in the specification,
Figure RE-FDA0002442717470000055
in order to estimate the initial value of the rotating speed, the formula represents a universal proportional-integral structure;
when equation (12) is substituted into equation (11), there are:
Figure RE-FDA0002442717470000056
to make η (0, t)1)≥-γ0 2Respectively enable η1(0,t1)≥-γ1 2，η2(0,t1)≥-γ2 2Namely:
Figure RE-FDA0002442717470000057
Figure RE-FDA0002442717470000058
in the formula, gamma1 2And gamma2 2Is any finite positive number;
to prove equation (14), inequality (16) may be utilized, namely:
Figure RE-FDA0002442717470000059
order:
Figure RE-FDA0002442717470000061
Figure RE-FDA0002442717470000062
the derivation of both sides of equation (18) can be found:
Figure RE-FDA0002442717470000063
substituting equation (19) into equation (14) can yield:
Figure RE-FDA0002442717470000064
it can be seen from equation (20) that the inequality satisfies η1(0,t1)≥-γ1 2The conditions of (a);
for equation (15), if the integrand to the left of the inequality is positive, the inequality must satisfy the condition, so it is advisable:
Figure RE-FDA0002442717470000065
substituting equation (21) into equation (15) can yield:
Figure RE-FDA0002442717470000066
it can be seen from equation (22) that the inequality satisfies η2(0,t1)≥-γ2 2The conditions of (a);
in summary, substituting equations (19) and (21) for equation (13) may satisfy the Popov integral inequality, that is:
Figure RE-FDA0002442717470000067
if it is not
Figure RE-FDA0002442717470000068
Taking the form of equation (12), the feedback system formed by equation (9) must be asymptotically stable.
The estimated expression of the rotation speed can be obtained by the following expressions (12), (19) and (21):
Figure RE-FDA0002442717470000071
from equation (24), a rotation speed estimation expression is obtained, namely:
Figure RE-FDA0002442717470000072
in the formula (I), the compound is shown in the specification,
Figure RE-FDA0002442717470000073
generally, 0 is taken; if it will be
Figure RE-FDA0002442717470000074
And
Figure RE-FDA0002442717470000075
substituted type (25), because the surface-mounted permanent magnet synchronous motor generally adopts idAs a result, the rotation speed adaptation law expressed by the stator current can be obtained as follows:
Figure RE-FDA0002442717470000076
7. the full-order adaptive observer-based PMSM disturbance rejection control method according to claim 6, characterized in that: the selection process of the gain matrix of the full-order adaptive observer in the step 3 is as follows:
the feedback matrix G is designed as:
Figure RE-FDA0002442717470000077
in the formula:
Figure RE-FDA0002442717470000078
when estimating the rotational speed
Figure RE-FDA0002442717470000079
The dynamic error of the closed-loop observer, when converging on the actual rotational speed ω, can be expressed as:
Figure RE-FDA00024427174700000710
the two diagonal terms in the matrix (A + G) are negative and therefore satisfy [ SI- (A + G)]-1Is a stability condition for strictly positive definite matrix.
8. The full-order adaptive observer-based PMSM disturbance rejection control method according to claim 7, characterized in that: the specific process of the step 4 is as follows:
according to the estimated rotating speed obtained in the step 3
Figure RE-FDA0002442717470000081
And rotor position angle
Figure RE-FDA0002442717470000082
Information, estimated rotation speed obtained
Figure RE-FDA0002442717470000083
With the torque current i obtained in step 2qEstimating load disturbance as an input to a load disturbance observer
Figure RE-FDA0002442717470000084
And control the system torque current iqThere is a correspondence relationship and thus can pass
Figure RE-FDA0002442717470000085
The value is used for determining the value of the torque current to be compensated, and then the calculated compensation value is sent to the control system, so that the external disturbance resistance of the control system is improved; the disturbance estimation and compensation are realized by a load disturbance observer module.
9. The full-order adaptive observer-based PMSM disturbance rejection control method according to claim 8, characterized in that: the design process of the load disturbance observer module in the step 4 is as follows:
the dynamic space state equation of the permanent magnet synchronous motor can be expressed as:
Figure RE-FDA0002442717470000086
where x is the state quantity, u is the input, f is the disturbance, y is the output, A, Bu、BfAnd C is the coefficient matrix, the perturbation term can be expressed as:
Bff＝x-Ax-Buu (30)；
if the rate of change of f is approximately zeroThen the estimation of f follows the design principle of the disturbance observer when estimating the disturbance
Figure RE-FDA0002442717470000087
When the actual disturbance f is very close, the disturbance observer can be constructed as follows:
Figure RE-FDA0002442717470000091
the disturbance estimation expressions obtained by collating the formulas (30) and (31) are:
Figure RE-FDA0002442717470000092
setting an intermediate variable matrix M, order
Figure RE-FDA0002442717470000093
Equation (32) can be expressed as an equation with intermediate variables:
Figure RE-FDA0002442717470000094
at this time, equation (33) is an equation of the disturbance observer, and since the value of the sampling period in the actual system is very small, the change rate of the load torque in one sampling period is approximately zero, the extended mechanical motion equation of the permanent magnet synchronous motor is as follows:
Figure RE-FDA0002442717470000095
in the formula, TLIs the load torque, B is the viscous friction coefficient, PnFor number of pole pairs, psi, of the motorfIs a permanent magnet flux linkage; j is moment of inertia, iqIs a q-axis current component, ωrIs the mechanical angular velocity;
the PMSM disturbance observation equation obtained by putting the formulas (29) to (34) in order is as follows:
Figure RE-FDA0002442717470000096
the load disturbance observer equation obtained by arranging the formula (35) is as follows:
Figure RE-FDA0002442717470000097
calculated in formula (36)
Figure RE-FDA0002442717470000101
I.e. the load torque
Figure RE-FDA0002442717470000102
Estimated value of k1Must satisfy Lyapunov stability, and k can be obtained according to the stability requirement1Is k1＜0；
Due to load torque
Figure RE-FDA0002442717470000103
Has a certain relation with the q-axis current, so the current can be compensated according to the sudden load disturbance, and the current is compensated
Figure RE-FDA0002442717470000104
Can be expressed as:
Figure RE-FDA0002442717470000105
in summary, the final input of the quadrature current loop PI regulator
Figure RE-FDA0002442717470000106
Can be expressed as:
Figure RE-FDA0002442717470000107
10. the full-order adaptive observer-based PMSM sensorless disturbance rejection control method according to claim 9, wherein: the specific process of the step 5 is as follows:
firstly, a given rotation speed omega and the estimated rotation speed obtained in the step 3 are combined
Figure RE-FDA0002442717470000108
Making difference, feeding the rotation speed error into a rotation speed loop PI regulator, and outputting the rotation speed error as a torque current iq *Torque current iq *First with a feedback current iqMaking difference, and then according to load disturbance change value iq *Carrying out torque current compensation with the compensation value of
Figure RE-FDA0002442717470000109
Finally, the final input of the quadrature axis current loop PI regulator is obtained as iq-inAnd the input of the PI regulator which can simultaneously obtain the straight-axis current loop is id *-id(ii) a The output of the current loop PI regulator is the component U of the stator voltage on the d-q axisdAnd UqThen, the voltage U under the two-phase rotating coordinate system is converted into the voltage U under the two-phase rotating coordinate system through a Park inverse transformation moduledAnd UqConversion to voltage U at two-phase stationary coordinateαAnd UβFinally, U is putαAnd UβAnd sending the signals into a space vector pulse width modulation module to obtain six paths of PWM pulse bar driving PMSM to form a closed-loop control system.
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