CN114325387A - Method for monitoring state of induction motor based on particle swarm inversion sliding-mode observer - Google Patents

Method for monitoring state of induction motor based on particle swarm inversion sliding-mode observer Download PDF

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CN114325387A
CN114325387A CN202210046768.7A CN202210046768A CN114325387A CN 114325387 A CN114325387 A CN 114325387A CN 202210046768 A CN202210046768 A CN 202210046768A CN 114325387 A CN114325387 A CN 114325387A
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stator
sliding mode
state
induction motor
monitoring
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CN114325387B (en
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于文新
钟广林
王俊年
赵延明
李燕
钟国亮
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Hunan University of Science and Technology
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Abstract

The invention discloses a particle swarm inversion sliding mode observer-based method for monitoring the state of an induction motor, which comprises the following steps of: establishing a state space mathematical model of the induction motor; designing a standard control law by adopting an inversion design method; designing a approximation law, designing a sliding mode control law by combining a standard control law, and constructing a sliding mode observer; designing a fitness function and optimizing parameters of a sliding mode control law by combining a particle swarm optimization algorithm; the state monitoring of the induction motor under the faults of the stator and rotor windings and the faults of the stator current sensor is realized, the actual output value of the system is compared with the observed value through residual errors, and the monitoring precision is displayed. The invention designs a particle swarm-inversion sliding mode observer method, which is used for implementing parameter optimization on a sliding mode control law through an inversion method construction system and an optimization algorithm so as to improve the performance of the observer. When the model is used for monitoring the state of the induction motor, the stability, the response speed and the observation precision of the induction motor can be effectively improved.

Description

Method for monitoring state of induction motor based on particle swarm inversion sliding-mode observer
Technical Field
The invention relates to a method for monitoring the state of an induction motor based on a particle swarm inversion sliding-mode observer, and belongs to the field of electrical control.
Background
The induction motor has the advantages of simple structure, reliable operation, convenient maintenance, low price and the like, and is widely applied to actual industrial production. However, a motor failure inevitably occurs due to a long-term operation of the induction motor outside and an influence of the surrounding environment. The fault characteristics of the early motor are very weak and unstable, and are sensitive to external interference. If the state quantity of the induction motor is not accurately tracked for early fault monitoring, more serious faults are caused once the fault is missed. The stator current sensor is a device for monitoring a motor system and is one of the keys for improving the reliability of the whole system; stator and rotor coil winding faults are one of the major faults that lead to induction motor failure. Therefore, the method has theoretical significance and practical engineering value for researching the problems of monitoring the faults of the stator current sensor of the induction motor and the early faults of the stator and rotor coil windings.
The stator current is one of important characteristics for identifying faults of the induction motor, so the invention takes the stator current as an observation object to monitor the state of the induction motor. The state monitoring method based on the analytical model is firstly used for estimating the state output of the system, and then the actual output quantity of the system is analyzed and compared with the estimated quantity, so that whether the system has better stability, faster convergence speed and higher tracking precision is judged, and therefore the method is widely applied to theoretical research and actual engineering. The method provides an effective method for state monitoring of the induction motor, but the method has the defects that the method is directly applied to the state monitoring of the induction motor, namely, the sliding-mode observer has a space for improving the observation performance, including response speed, stability, tracking precision and disturbance resistance, and the value of sliding-mode control law parameters of a corresponding model is required to be improved.
Disclosure of Invention
The invention aims to solve the problem of state monitoring of an induction motor, and provides a method for monitoring the state of the induction motor based on a particle swarm inversion sliding mode observer.
In order to solve the technical problem, the invention provides a method for monitoring the state of an induction motor based on a particle swarm inversion sliding mode observer, which comprises the following steps.
Step one, based on an induction motor 'T' equivalent model under a stator reference coordinate system, considering uncertainty of external disturbance of the system, and constructing an induction motor state space mathematical model under the conditions of stator winding faults, rotor winding faults and stator current sensor faults by taking stator current, rotor magnetic flux and mechanical rotation angular velocity as state variables under a synchronous rotation coordinate system.
And step two, designing a standard control law by adopting an inversion design method based on the state space mathematical model of the induction motor.
And step three, designing an approach law, designing a sliding mode control law by combining a standard control law, and constructing the sliding mode observer.
And step four, designing a fitness function and optimizing parameters of the sliding mode control law by combining a particle swarm optimization algorithm.
And fifthly, realizing state monitoring of the induction motor under the faults of the stator and rotor windings and the faults of the stator current sensor, comparing the residual error between the actual output value of the system and the observed value, and displaying the monitoring precision.
The invention has the advantages.
(1) In the second step and the third step of the invention, a standard control law is designed by combining an inversion design method with a mathematical model of the state space of the induction motor, and then a sliding mode control law is designed by introducing an approach law and combining the standard control law to construct a sliding mode observer. The design can make the system sensitively monitor different types of early faults, and the buffeting of the system is smaller, and the robustness is stronger.
(2) In the fourth step of the invention, parameter optimization is implemented on the sliding mode control law by designing a fitness function and combining a particle swarm optimization algorithm. The accuracy of parameter optimization can be effectively improved by designing a fitness function corresponding to the system, and the performance of the observer is improved.
Drawings
FIG. 1 is a block diagram of a sliding mode observer design based on an inversion method.
FIG. 2 is a design block diagram of sliding-mode observer parameter optimization.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The system state output is estimated based on the analytic model, and then the actual output quantity of the system is analyzed and compared with the estimated quantity, so that whether the system has better stability, faster convergence speed and higher tracking precision or not is judged, and therefore the method is widely applied to theoretical research and actual engineering. The method provides an effective method for state monitoring of the induction motor, but the method has the defects that the method is directly applied to the state monitoring of the induction motor, namely, the sliding-mode observer has a space for improving the observation performance, including response speed, stability, tracking precision and disturbance resistance, and the value of sliding-mode control law parameters of a corresponding model is required to be improved. Therefore, the particle swarm-inversion sliding mode observer method is designed, and the performance of the observer is improved by constructing a system through an inversion method and implementing parameter optimization on a sliding mode control law by adopting an optimization algorithm. When the model is used for monitoring the state of the induction motor, the stability, the response speed and the observation precision of the induction motor can be effectively improved.
As shown in fig. 1 to fig. 2, the method for monitoring the state of the induction machine based on the particle swarm inversion sliding mode observer comprises the following steps.
Step one, based on an induction motor 'T' equivalent model under a stator reference coordinate system, considering uncertainty of external disturbance of the system, and constructing an induction motor state space mathematical model under the conditions of stator winding faults, rotor winding faults and stator current sensor faults by taking stator current, rotor magnetic flux and mechanical rotation angular velocity as state variables under a synchronous rotation coordinate system.
The equivalent model of the induction motor T is as follows.
Figure 478832DEST_PATH_IMAGE001
。
In the formula,
Figure 333656DEST_PATH_IMAGE002
is the rotation speed;
Figure 113393DEST_PATH_IMAGE003
is a rotor flux linkage;
Figure 695553DEST_PATH_IMAGE004
the stator current is a state variable;
Figure 509925DEST_PATH_IMAGE005
the stator side voltage is an output vector;
Figure 270071DEST_PATH_IMAGE006
is a stator resistor;
Figure 537104DEST_PATH_IMAGE007
is the rotor resistance;
Figure 922955DEST_PATH_IMAGE008
the self-inductance of the stator is obtained;
Figure 529517DEST_PATH_IMAGE009
self-inductance of the rotor;
Figure 522881DEST_PATH_IMAGE010
mutual inductance between the stator and the rotor;
Figure 467090DEST_PATH_IMAGE011
the number of pole pairs of the motor is;
Figure 204102DEST_PATH_IMAGE012
is the rotational inertia of the motor;
Figure 727488DEST_PATH_IMAGE013
is the load torque.
And combining the induction motor model with unknown load disturbance, a nonlinear function, a stator and rotor winding fault item and a stator current sensor fault item to form a state space mathematical model, and expressing the state space mathematical model in a matrix form.
The state space mathematical model is as follows.
Figure 95015DEST_PATH_IMAGE014
。
Wherein,
Figure 336640DEST_PATH_IMAGE015
，
Figure 798715DEST_PATH_IMAGE016
，
Figure 442186DEST_PATH_IMAGE017
，
Figure 715035DEST_PATH_IMAGE018
，
Figure 443957DEST_PATH_IMAGE019
，
Figure 522771DEST_PATH_IMAGE020
，
Figure 207699DEST_PATH_IMAGE021
，
Figure 979346DEST_PATH_IMAGE022
，
Figure 867668DEST_PATH_IMAGE023
，
Figure 750173DEST_PATH_IMAGE024
，
Figure 102657DEST_PATH_IMAGE025
，
Figure 232156DEST_PATH_IMAGE026
，
Figure 670090DEST_PATH_IMAGE027
，
Figure 90708DEST_PATH_IMAGE028
，
Figure 500960DEST_PATH_IMAGE029
，
Figure 614410DEST_PATH_IMAGE030
，
Figure 539640DEST_PATH_IMAGE031
，
Figure 947969DEST_PATH_IMAGE032
。
in the formula, the upper label
Figure 9466DEST_PATH_IMAGE033
Representing the derivation of the term;
Figure 293817DEST_PATH_IMAGE034
stator current, rotor flux and mechanical rotation angular velocity of two shafts under a d-q coordinate system respectively;
Figure 644027DEST_PATH_IMAGE035
voltages at the sides of the two shafts of stators are respectively under a d-q coordinate system;
Figure 672026DEST_PATH_IMAGE036
and
Figure 853609DEST_PATH_IMAGE037
respectively the state of the systemVariables, input vectors and output vectors;
Figure 230232DEST_PATH_IMAGE038
the fault distribution matrix is a distribution matrix of stator and rotor windings;
Figure 130055DEST_PATH_IMAGE039
a distribution matrix for unknown load disturbances;
Figure 633849DEST_PATH_IMAGE040
is an unknown load disturbance representative of the system and is a bounded function;
Figure 935517DEST_PATH_IMAGE041
is a fault function of the stator and rotor windings;
Figure 483042DEST_PATH_IMAGE042
is a non-linear function;
Figure 870161DEST_PATH_IMAGE043
a component in the d-q axis for sensor failure;
Figure 239962DEST_PATH_IMAGE044
a distribution matrix for sensor faults;
Figure 68241DEST_PATH_IMAGE045
is a synchronous rotational angular velocity;
Figure 865296DEST_PATH_IMAGE046
is a stator resistor;
Figure 474132DEST_PATH_IMAGE047
is the rotor resistance;
Figure 647624DEST_PATH_IMAGE048
the self-inductance of the stator is obtained;
Figure 845256DEST_PATH_IMAGE049
self-inductance of the rotor;
Figure 813212DEST_PATH_IMAGE050
mutual inductance between the stator and the rotor;
Figure 909344DEST_PATH_IMAGE051
the number of pole pairs of the motor is;
Figure 558631DEST_PATH_IMAGE052
is the rotational inertia of the motor;
Figure 423819DEST_PATH_IMAGE053
is the load torque.
And step two, designing a standard control law by adopting an inversion design method based on the state space mathematical model of the induction motor.
The standard control law is as follows.
Figure 562676DEST_PATH_IMAGE054
。
Upper label
Figure 880525DEST_PATH_IMAGE033
Representing the derivation of the term; upper label
Figure 130241DEST_PATH_IMAGE055
Representing the second derivative of the term; define the actual state as
Figure 115514DEST_PATH_IMAGE056
(ii) a The expected state is
Figure 818416DEST_PATH_IMAGE057
(ii) a The state error is
Figure 889140DEST_PATH_IMAGE058
(ii) a Define the actual output as
Figure 942547DEST_PATH_IMAGE059
(ii) a The expected value is
Figure 969277DEST_PATH_IMAGE060
(ii) a Monitoring error as
Figure 449937DEST_PATH_IMAGE061
；
Figure 742378DEST_PATH_IMAGE062
And
Figure 537159DEST_PATH_IMAGE063
respectively a state variable, an input vector and an output vector of the system;
Figure 231445DEST_PATH_IMAGE064
the fault distribution matrix is a distribution matrix of stator and rotor windings;
Figure 883007DEST_PATH_IMAGE065
a distribution matrix for unknown load disturbances;
Figure 115274DEST_PATH_IMAGE066
is an unknown load disturbance representative of the system and is a bounded function;
Figure 244904DEST_PATH_IMAGE067
is a fault function of the stator and rotor windings;
Figure 793697DEST_PATH_IMAGE068
is a non-linear function;
Figure 271952DEST_PATH_IMAGE069
a sensor fault distribution matrix;
Figure 538985DEST_PATH_IMAGE070
a distribution matrix for sensor faults;
Figure 737885DEST_PATH_IMAGE071
is any positive number;
Figure 78868DEST_PATH_IMAGE072
is a synchronous rotational angular velocity;
Figure 337811DEST_PATH_IMAGE073
is a stator resistor;
Figure 826561DEST_PATH_IMAGE074
is the rotor resistance;
Figure 563573DEST_PATH_IMAGE075
the self-inductance of the stator is obtained;
Figure 86958DEST_PATH_IMAGE076
self-inductance of the rotor;
Figure 516802DEST_PATH_IMAGE077
mutual inductance between the stator and the rotor;
Figure 903569DEST_PATH_IMAGE078
the number of pole pairs of the motor is;
Figure 444272DEST_PATH_IMAGE079
is the rotational inertia of the motor;
Figure 87743DEST_PATH_IMAGE080
is the load torque;
Figure 157330DEST_PATH_IMAGE081
is an identity matrix;
Figure 886252DEST_PATH_IMAGE082
the inverse of the identity matrix.
And step three, designing an approach law, designing a sliding mode control law by combining a standard control law, and constructing the sliding mode observer.
The approach law is.
Figure 965066DEST_PATH_IMAGE083
。
The sliding mode control law is as follows.
Figure 853257DEST_PATH_IMAGE084
。
The stator current observer is.
Figure 359324DEST_PATH_IMAGE085
。
Wherein,
Figure 575542DEST_PATH_IMAGE086
，
Figure 644998DEST_PATH_IMAGE087
，
Figure 997482DEST_PATH_IMAGE088
，
Figure 940030DEST_PATH_IMAGE089
，
Figure 377965DEST_PATH_IMAGE090
，
Figure 533003DEST_PATH_IMAGE091
，
Figure 5572DEST_PATH_IMAGE092
，
Figure 853443DEST_PATH_IMAGE093
，
Figure 168886DEST_PATH_IMAGE094
，
Figure 393194DEST_PATH_IMAGE095
，
Figure 720270DEST_PATH_IMAGE096
，
Figure 739042DEST_PATH_IMAGE097
，
Figure 151569DEST_PATH_IMAGE098
，
Figure 913988DEST_PATH_IMAGE099
，
Figure 33254DEST_PATH_IMAGE100
，
Figure 488506DEST_PATH_IMAGE101
，
Figure 388329DEST_PATH_IMAGE102
，
Figure 347582DEST_PATH_IMAGE103
。
in the formula, L1、L2、L3For the parameter to be optimized, L1>0、L2>0、L3>0; when the system state approaches the sliding form face,
Figure 383671DEST_PATH_IMAGE104
close to the value of 0 (c) and,
Figure 9825DEST_PATH_IMAGE105
the hyperbolic tangent function can ensure that the sliding mode variable approaches zero infinitely instead of zero; index term
Figure 131365DEST_PATH_IMAGE106
Can ensure when
Figure 235587DEST_PATH_IMAGE107
When the system state is larger, the system state can approach to a sliding mode at a larger speed; upper label
Figure 391762DEST_PATH_IMAGE108
Representing the derivation of the term; upper label
Figure 188816DEST_PATH_IMAGE109
Representing the second derivative of the term;
Figure 187865DEST_PATH_IMAGE110
stator current, rotor flux and mechanical rotation angular velocity of two shafts under a d-q coordinate system respectively;
Figure 361358DEST_PATH_IMAGE111
voltages at the sides of the two shafts of stators are respectively under a d-q coordinate system; define the actual state as
Figure 372039DEST_PATH_IMAGE112
(ii) a The expected state is
Figure 74416DEST_PATH_IMAGE113
(ii) a The state error is
Figure 170548DEST_PATH_IMAGE114
(ii) a Define the actual output as
Figure 616573DEST_PATH_IMAGE115
(ii) a The expected value is
Figure 934290DEST_PATH_IMAGE116
(ii) a Monitoring error as
Figure 73148DEST_PATH_IMAGE117
；
Figure 656576DEST_PATH_IMAGE118
And
Figure 296504DEST_PATH_IMAGE119
respectively a state variable, an input vector and an output vector of the system;
Figure 281778DEST_PATH_IMAGE120
the fault distribution matrix is a distribution matrix of stator and rotor windings;
Figure 591537DEST_PATH_IMAGE121
a distribution matrix for unknown load disturbances;
Figure 396682DEST_PATH_IMAGE122
is an unknown load disturbance representative of the system and is a bounded function;
Figure 450088DEST_PATH_IMAGE123
is a fault function of the stator and rotor windings;
Figure 289868DEST_PATH_IMAGE124
is a non-linear function;
Figure 770528DEST_PATH_IMAGE125
a sensor fault distribution matrix;
Figure 652DEST_PATH_IMAGE126
a distribution matrix for sensor faults;
Figure 857750DEST_PATH_IMAGE127
is any positive number;
Figure 552036DEST_PATH_IMAGE128
is a synchronous rotational angular velocity;
Figure 387619DEST_PATH_IMAGE129
is a stator resistor;
Figure 432935DEST_PATH_IMAGE130
is the rotor resistance;
Figure 828144DEST_PATH_IMAGE131
the self-inductance of the stator is obtained;
Figure 314620DEST_PATH_IMAGE132
self-inductance of the rotor;
Figure 402662DEST_PATH_IMAGE133
mutual inductance between the stator and the rotor;
Figure 669695DEST_PATH_IMAGE134
the number of pole pairs of the motor is;
Figure 603016DEST_PATH_IMAGE135
is the rotational inertia of the motor;
Figure 662108DEST_PATH_IMAGE136
is the load torque;
Figure 921051DEST_PATH_IMAGE137
is an identity matrix;
Figure 409801DEST_PATH_IMAGE138
the inverse of the identity matrix.
And step four, designing a fitness function and optimizing parameters of the sliding mode control law by combining a particle swarm optimization algorithm.
The fitness function is as follows.
Figure 146813DEST_PATH_IMAGE139
。
Figure 670198DEST_PATH_IMAGE140
。
In the formula,
Figure 834463DEST_PATH_IMAGE141
the amplification factor can be adjusted according to the actual condition of the system; t is the adjustment time;
Figure 263040DEST_PATH_IMAGE142
is the convergence time interval of the sliding mode observer;
Figure 803742DEST_PATH_IMAGE143
is a sliding mode surface of two axes under a d-q coordinate system,
Figure 181634DEST_PATH_IMAGE144
the actual output values of the stator currents of the two shafts under the d-q coordinate system,
Figure 720063DEST_PATH_IMAGE145
and the observed values of the stator currents of the two shafts under the d-q coordinate system are obtained.
The specific process of optimizing the parameters of the sliding mode control law is as follows.
Including the population size n, performing particle swarm initialization, and randomly generating the position of each particle
Figure 183405DEST_PATH_IMAGE146
And velocity
Figure 527799DEST_PATH_IMAGE147
。
Assigning the randomly generated correlation value of each particle to a sliding mode control law
Figure 25776DEST_PATH_IMAGE148
According to the fitness function designed by the invention, the fitness value of each particle is calculated
Figure 718795DEST_PATH_IMAGE149
。
For each particle
Figure 935012DEST_PATH_IMAGE150
To adjust its fitness value
Figure 817518DEST_PATH_IMAGE151
And individual extremum
Figure 107685DEST_PATH_IMAGE152
Fitness value of
Figure 784654DEST_PATH_IMAGE153
And (5) comparing the sizes. If it is
Figure 222588DEST_PATH_IMAGE154
Then use
Figure 908785DEST_PATH_IMAGE155
Substitution
Figure 305655DEST_PATH_IMAGE156
。
For each particle
Figure 419105DEST_PATH_IMAGE157
To adjust its fitness value
Figure 344336DEST_PATH_IMAGE158
And global extremum
Figure 506327DEST_PATH_IMAGE159
Fitness value of
Figure 833403DEST_PATH_IMAGE160
And (5) comparing the sizes. If it is
Figure 117754DEST_PATH_IMAGE161
Then use
Figure 264701DEST_PATH_IMAGE158
Substitution
Figure 479651DEST_PATH_IMAGE160
。
And (3) the particles iteratively update the speed and the position of the particles through the two extreme values, wherein the updating formulas are respectively.
Figure 661233DEST_PATH_IMAGE162
。
Figure 116485DEST_PATH_IMAGE163
。
Wherein,l 1 in order to be the inertial weight,
Figure 953991DEST_PATH_IMAGE164
，
Figure 520102DEST_PATH_IMAGE165
，
Figure 556191DEST_PATH_IMAGE166
for the current number of iterations,
Figure 182345DEST_PATH_IMAGE167
is the velocity of the particles and is the velocity of the particles,
Figure 490835DEST_PATH_IMAGE168
as a factor of the acceleration, the acceleration is,
Figure 860636DEST_PATH_IMAGE169
is represented by
Figure 16811DEST_PATH_IMAGE170
Second in the second iteration
Figure 751549DEST_PATH_IMAGE171
The particles are in
Figure 360385DEST_PATH_IMAGE172
Individual extrema at dimensional positions, position extrema, and velocity extrema,
Figure 268298DEST_PATH_IMAGE173
is represented by
Figure 465930DEST_PATH_IMAGE174
The population of extreme values at the time of the sub-iteration,
Figure 433886DEST_PATH_IMAGE175
to be distributed in
Figure 530018DEST_PATH_IMAGE176
A random number in between. To prevent blind particle search, the position and velocity limits are
Figure 241622DEST_PATH_IMAGE177
，
Figure 310072DEST_PATH_IMAGE178
。
Updating the particle velocity according to the above updating formula
Figure 448930DEST_PATH_IMAGE179
And position
Figure 766779DEST_PATH_IMAGE180
. If the termination condition is satisfied, the maximum number of iterations is reached or
Figure 466094DEST_PATH_IMAGE181
Then quit the optimization algorithm to obtain the optimal solution
Figure 451368DEST_PATH_IMAGE182
Wherein
Figure 761127DEST_PATH_IMAGE183
Is the minimum adaptation value.
And fifthly, realizing state monitoring of the induction motor under the faults of the stator and rotor windings and the faults of the stator current sensor, comparing the residual error between the actual output value of the system and the observed value, and displaying the monitoring precision.
Figure 566272DEST_PATH_IMAGE184
。
Figure 557361DEST_PATH_IMAGE185
。
In the formula,
Figure 397141DEST_PATH_IMAGE186
the stator current components of two axes under the d-q coordinate system,
Figure 877801DEST_PATH_IMAGE187
the observed values of the stator currents of two axes under the d-q coordinate system are components,
Figure 622772DEST_PATH_IMAGE188
is used for judging the threshold value of the monitoring precision.

Claims (3)

1. A method for monitoring the state of an induction motor based on a particle swarm inversion sliding mode observer is characterized by comprising the following steps:
step one, constructing an induction motor state space mathematical model under the conditions of stator winding faults, rotor winding faults and stator current sensor faults by taking stator current, rotor magnetic flux and mechanical rotation angular velocity as state variables under a synchronous rotation coordinate system based on an induction motor 'T' equivalent model under a stator reference coordinate system and considering uncertainty of system external disturbance;
designing a standard control law by adopting an inversion design method based on a state space mathematical model of the induction motor;
designing an approximation rule, designing a sliding mode control rule by combining a standard control rule, and constructing a sliding mode observer;
designing a fitness function and optimizing parameters of the sliding mode control law by combining a particle swarm optimization algorithm;
and fifthly, realizing state monitoring of the induction motor under the faults of the stator and rotor windings and the faults of the stator current sensor, comparing the residual error between the actual output value of the system and the observed value, and displaying the monitoring precision.
2. The method for monitoring the state of the induction machine based on the particle swarm inversion sliding mode observer according to claim 1, wherein in the second step and the third step,
the standard control law is as follows:
Figure 31292DEST_PATH_IMAGE001
，
the approach law is as follows:
Figure 948433DEST_PATH_IMAGE002
，
the sliding mode control law is as follows:
Figure 665853DEST_PATH_IMAGE003
，
the stator current observer is:
Figure 61062DEST_PATH_IMAGE004
，
Figure 813117DEST_PATH_IMAGE005
，
Figure 635580DEST_PATH_IMAGE006
，
Figure 902613DEST_PATH_IMAGE007
，
Figure 39196DEST_PATH_IMAGE008
，
Figure 708075DEST_PATH_IMAGE009
，
Figure 639122DEST_PATH_IMAGE010
，
Figure 393452DEST_PATH_IMAGE011
，
Figure 68146DEST_PATH_IMAGE012
，
Figure 591532DEST_PATH_IMAGE013
，
Figure 959059DEST_PATH_IMAGE014
，
Figure 200685DEST_PATH_IMAGE015
，
Figure 413491DEST_PATH_IMAGE016
，
Figure 56962DEST_PATH_IMAGE017
，
Figure 392129DEST_PATH_IMAGE018
，
Figure 58733DEST_PATH_IMAGE019
，
Figure 137548DEST_PATH_IMAGE020
，
Figure 573208DEST_PATH_IMAGE021
，
in the formula, L1、L2、L3For the parameter to be optimized, L1>0、L2>0、L3>0; upper label
Figure 344855DEST_PATH_IMAGE022
Representing the derivation of the term; upper label
Figure 233177DEST_PATH_IMAGE023
Representing the second derivative of the term;
Figure 115682DEST_PATH_IMAGE024
stator current, rotor flux and mechanical rotation angular velocity of two shafts under a d-q coordinate system respectively;
Figure 468166DEST_PATH_IMAGE025
voltages at the sides of the two shafts of stators are respectively under a d-q coordinate system; define the actual state as
Figure 348397DEST_PATH_IMAGE026
(ii) a The expected state is
Figure 786332DEST_PATH_IMAGE027
(ii) a The state error is
Figure 206949DEST_PATH_IMAGE028
(ii) a Define the actual output as
Figure 679519DEST_PATH_IMAGE029
(ii) a The expected value is
Figure 730651DEST_PATH_IMAGE030
(ii) a Monitoring error as
Figure 655882DEST_PATH_IMAGE031
；
Figure 880190DEST_PATH_IMAGE032
And
Figure 879370DEST_PATH_IMAGE033
respectively a state variable, an input vector and an output vector of the system;
Figure 163721DEST_PATH_IMAGE034
the fault distribution matrix is a distribution matrix of stator and rotor windings;
Figure 576248DEST_PATH_IMAGE035
a distribution matrix for unknown load disturbances;
Figure 536070DEST_PATH_IMAGE036
is an unknown load disturbance representative of the system and is a bounded function;
Figure 655336DEST_PATH_IMAGE037
is a fault function of the stator and rotor windings;
Figure 845009DEST_PATH_IMAGE038
is a non-linear function;
Figure 744832DEST_PATH_IMAGE039
a sensor fault distribution matrix;
Figure 248625DEST_PATH_IMAGE040
a distribution matrix for sensor faults;
Figure 550294DEST_PATH_IMAGE041
is any positive number;
Figure 848551DEST_PATH_IMAGE042
is a synchronous rotational angular velocity;
Figure 235670DEST_PATH_IMAGE043
is a stator resistor;
Figure 543154DEST_PATH_IMAGE044
is the rotor resistance;
Figure 371433DEST_PATH_IMAGE045
the self-inductance of the stator is obtained;
Figure 168488DEST_PATH_IMAGE046
self-inductance of the rotor;
Figure 715007DEST_PATH_IMAGE047
mutual inductance between the stator and the rotor;
Figure 888499DEST_PATH_IMAGE048
the number of pole pairs of the motor is;
Figure 836864DEST_PATH_IMAGE049
is the rotational inertia of the motor;
Figure 804820DEST_PATH_IMAGE050
is the load torque;
Figure 838635DEST_PATH_IMAGE051
is an identity matrix;
Figure 550239DEST_PATH_IMAGE052
the inverse of the identity matrix.
3. The method for monitoring the state of the induction machine based on the particle swarm inversion sliding mode observer according to claim 1, wherein in the fourth step,
the fitness function is:
Figure 353110DEST_PATH_IMAGE053
，
Figure 491967DEST_PATH_IMAGE054
，
in the formula,
Figure 13078DEST_PATH_IMAGE055
the amplification factor can be correspondingly adjusted according to the actual condition;
Figure 262794DEST_PATH_IMAGE056
to adjust the time;
Figure 248068DEST_PATH_IMAGE057
is the convergence time interval of the sliding mode observer;
Figure 495509DEST_PATH_IMAGE058
the sliding mode surfaces of two shafts under a d-q coordinate system;
Figure 566233DEST_PATH_IMAGE059
the actual output values of the stator currents of the two shafts under the d-q coordinate system are obtained;
Figure 557323DEST_PATH_IMAGE060
and the observed values of the stator currents of the two shafts under the d-q coordinate system are obtained.
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