CN115664283A - Sliding mode control method and system based on generalized parameter estimation observer - Google Patents

Sliding mode control method and system based on generalized parameter estimation observer Download PDF

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CN115664283A
CN115664283A CN202211444912.9A CN202211444912A CN115664283A CN 115664283 A CN115664283 A CN 115664283A CN 202211444912 A CN202211444912 A CN 202211444912A CN 115664283 A CN115664283 A CN 115664283A
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parameter estimation
sliding mode
generalized
axis current
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CN115664283B (en
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贺伟
王想
李涛
宋公飞
郑柏超
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Nanjing University of Information Science and Technology
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Abstract

The invention discloses a sliding mode control method and a system based on a generalized parameter estimation observer; converting a mathematical model under a natural coordinate system into a mathematical model under a d-q axis synchronous rotation coordinate system of the three-phase permanent magnet synchronous motor; converting state observation into parameter estimation based on a generalized parameter estimation observation theory, and determining a linear regression equation for estimating q-axis current and load torque; processing the linear regression equation to determine an estimated value of the q-axis current and an estimated value of the load torque; designing a sliding mode controller according to the estimation information of the generalized parameter estimation observer, obtaining a controlled variable according to the sliding mode controller, carrying out inverse Park coordinate transformation on the controlled variable, obtaining a driving signal of the three-phase inverter through an SVPWM module, and adjusting the output of the three-phase inverter according to the driving signal. The advantages are that: the anti-interference capability and robustness of the system are improved, the structure is simple, and on the premise of system stability, the use of the current sensor is reduced, so that the cost is saved.

Description

Sliding mode control method and system based on generalized parameter estimation observer
Technical Field
The invention relates to a sliding mode control method and system based on a generalized parameter estimation observer, and belongs to the technical field of permanent magnet synchronous motor stability control.
Background
In recent years, a permanent magnet synchronous motor has been widely used in various industrial fields such as robots, computer numerical control machines, aviation and the like due to its excellent characteristics such as high power density, high dynamic performance, high efficiency, low inertia, low noise and the like. The traditional PID control has good stability, simple structure and easy adjustment, and the error is reflected by a proportion link according to a certain proportion so as to be convenient for quick adjustment; the integration link is mainly used for eliminating the static error of the system; the differentiation link can foresee the change trend of the system deviation, so that the dynamic performance of the system can be well improved. But for complex systems there can be large errors resulting in overshoot. Since the permanent magnet synchronous motor is nonlinear and there are modeling errors, unavoidable disturbances and variations of parameters, satisfactory performance has not been obtained by PID control alone.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a sliding mode control method and a sliding mode control system based on a generalized parameter estimation observer.
In order to solve the technical problem, the invention provides a sliding mode control method based on a generalized parameter estimation observer, which comprises the following steps:
obtaining a mathematical model of the three-phase permanent magnet synchronous motor under a natural coordinate system, and selecting a q-axis current of the permanent magnet synchronous motor as a state variable and a mechanical angular velocity through Clark coordinate transformation and Park coordinate transformationω r As output and state variables, converting a mathematical model under a natural coordinate system into a mathematical model under a d-q axis synchronous rotation coordinate system of the three-phase permanent magnet synchronous motor;
according to the d-q axis being identicalA mathematical model under a step rotation coordinate system, which is used for converting state observation into parameter estimation based on a generalized parameter estimation observation theory and determining the current for estimating the q axisi q And load torqueT L A linear regression equation of (c);
processing the linear regression equation to make it accord with the excitation condition, estimating the observer according to the preset generalized parameters, and determining the estimated value of the q-axis current
Figure 669418DEST_PATH_IMAGE001
And load torqueT L Is estimated by
Figure 146666DEST_PATH_IMAGE002
；
Designing a sliding mode controller according to the estimation information of the generalized parameter estimation observer, and obtaining a control quantity according to the sliding mode controlleru q To the control quantityu q And after carrying out inverse Park coordinate transformation, obtaining a driving signal of the three-phase inverter through the SVPWM module, and adjusting the output of the three-phase inverter according to the driving signal.
Further, the mathematical model under the d-q axis synchronous rotation coordinate system is represented as:
Figure 731231DEST_PATH_IMAGE003
wherein ,
Figure 226804DEST_PATH_IMAGE004
is composed ofqThe derivative of the shaft current with respect to time,i q is composed ofqThe current of the shaft is measured by the current sensor,R s as the resistance of the stator,Lin order to be an inductor, the inductor,φ f is a magnetic linkage of the permanent magnet and the stator,u q for the q-axis voltage to be also the control input,ω r is the mechanical angular velocity of the rotor and,
Figure 707464DEST_PATH_IMAGE005
is the derivative of the mechanical angular velocity of the rotor with respect to time,Pis the number of the pole pairs of the motor,Jin order to be the moment of inertia,Bin order to obtain a coefficient of viscous friction,T L is the load torque.
Further, the linear regression equation is:
Figure 327801DEST_PATH_IMAGE006
q e to add a measure of the linear regression equation of the filter,m e to add the regression factors of the filter linear regression equation,
Figure 919319DEST_PATH_IMAGE007
is an intermediate variable of the linear regression equation,
Figure 410343DEST_PATH_IMAGE008
，i q0 error of an initial value of the q-axis current;
Figure 717697DEST_PATH_IMAGE009
Figure 497434DEST_PATH_IMAGE010
Figure 689381DEST_PATH_IMAGE011
s1 is a differential operator, and the differential operator,α 1 、α 2 、β 1 、β 2 as a filter parameter, satisfyα 1 ，α 2 ≠0，β 1 ，β 2 ＞0，q1 is a measurable quantity of a linear regression equation without the addition of a filter,λ 1 in order to gain the observer,λ 1 ＞0，m、ωis an intermediate variable.
Further, solving the intermediate variable m,ωThe method comprises the following steps:
reconstructing q-axis current based on theory of generalized parameter estimation observeri q To obtain the following formula:
Figure 644699DEST_PATH_IMAGE012
wherein ,
Figure 263899DEST_PATH_IMAGE013
representing the q-axis currenti q The derivative of the reconstructed state of (a),ξ y is q-axis currenti q The reconfiguration state of (a);
obtaining a reconstruction state based on a linear system theoryξ y State transition matrix ofX Ax ：
Figure 265353DEST_PATH_IMAGE014
wherein ,
Figure 120045DEST_PATH_IMAGE015
the derivative of the state transition matrix with respect to time,X Ax (0) Is the initial value of the state transition matrix;
the true value of the q-axis current is then expressed as:
Figure 523345DEST_PATH_IMAGE016
wherein ,
Figure 579025DEST_PATH_IMAGE017
for the error of the initial value, it is,i q (0) Represents the initial value of the q-axis current,ξ y (0) Representing the q-axis currenti q The initial value of the reconstruction state of (1);
Figure 474300DEST_PATH_IMAGE018
reconstruction
Figure 211312DEST_PATH_IMAGE005
Expressed as:
Figure 531435DEST_PATH_IMAGE019
Figure 430121DEST_PATH_IMAGE020
Figure 593118DEST_PATH_IMAGE021
then will bemAndωis converted into the form of a differential equation, expressed as:
Figure 868241DEST_PATH_IMAGE022
Figure 777291DEST_PATH_IMAGE023
wherein ,
Figure 50141DEST_PATH_IMAGE024
is a transpose of the state transition matrix,m(0) Is composed ofmAn initial value of (1);
solving the differential equation to obtain an intermediate variable m,ω。
Further, the estimated value of the q-axis current is determined by combining a dynamic regression expansion method based on a generalized observation theory
Figure 44642DEST_PATH_IMAGE001
And load torqueT L Is estimated value of
Figure 123456DEST_PATH_IMAGE002
。
Further, the process of determining the sliding mode controller includes:
the difference between the given mechanical angular velocity and the mechanical angular velocity measured by the sensor is used as an input of the sliding mode controller,
expressed as:
Figure 542805DEST_PATH_IMAGE025
wherein ,eis an input to the sliding mode controller,
Figure 783294DEST_PATH_IMAGE026
is a reference value of the mechanical angular velocity of the rotor;
designing the slip form surfacesExpressed as:
Figure 999511DEST_PATH_IMAGE027
wherein ,cis a parameter of the sliding mode surface and meets the requirementsc＞0，
Figure 678754DEST_PATH_IMAGE028
Representing the derivative of the input error with respect to time;
combining the generalized parameter estimation observer to obtain the control lawu q Comprises the following steps:
Figure 437763DEST_PATH_IMAGE029
wherein ,sgn(s) is a function of the sign,
Figure 849153DEST_PATH_IMAGE001
is q-axis currenti q Is determined by the estimated value of (c),
Figure 83825DEST_PATH_IMAGE002
as a load torqueT L Is determined by the estimated value of (c),ais an intermediate parameter that is a function of,
Figure 504442DEST_PATH_IMAGE030
，kin order to control the rate parameter(s),k＞0。
a sliding mode control system based on a generalized parameter estimation observer comprises:
the transformation module is used for acquiring a mathematical model of the three-phase permanent magnet synchronous motor in a natural coordinate system, and selecting the q-axis current of the permanent magnet synchronous motor as a state variable and a mechanical angular velocity through Clark coordinate transformation and Park coordinate transformationω r As output and state variables, converting a mathematical model under a natural coordinate system into a mathematical model under a d-q axis synchronous rotation coordinate system of the three-phase permanent magnet synchronous motor;
a first determining module, which is used for converting state observation into parameter estimation based on a generalized parameter estimation observation theory according to the mathematical model under the d-q axis synchronous rotation coordinate system, and determining the current for estimating the q axisi q And load torqueT L The linear regression equation of (1);
a second determining module for processing the linear regression equation to make it conform to the excitation condition, and determining the estimated value of the q-axis current according to a preset generalized parameter estimation observer
Figure 644523DEST_PATH_IMAGE001
And load torqueT L Is estimated value of
Figure 492393DEST_PATH_IMAGE002
；
An output module for designing a sliding mode controller according to the estimation information of the generalized parameter estimation observer and obtaining a control quantity according to the sliding mode controlleru q To the control quantityu q And after carrying out inverse Park coordinate transformation, obtaining a driving signal of the three-phase inverter through the SVPWM module, and adjusting the output of the three-phase inverter according to the driving signal.
The invention achieves the following beneficial effects:
(1) The sliding mode control method based on the generalized parameter estimation observer is applied to the permanent magnet synchronous motor, the state observation is converted into the parameter estimation, and the q-axis current and the load torque are realized through the dynamic expansion and mixing technology
Figure 214361DEST_PATH_IMAGE031
While simultaneously estimating. On the premise of ensuring the stability of the system, the use of current sensors is reduced, the cost of the system is reduced, and the reliability of the whole system is improved.
(2) The sliding mode control method based on the generalized parameter estimation observer is applied to the permanent magnet synchronous motor, obtains better dynamic performance, improves the anti-interference capability and robustness of a closed-loop system, and can be well applied to engineering.
Drawings
Fig. 1 is a control block diagram of the application of the method of the invention to a permanent magnet synchronous machine;
FIG. 2 is an estimated value and a true value of a q-axis current of a permanent magnet synchronous motor;
FIG. 3 shows the PMSM load torqueT L An estimated value and a true value;
FIG. 4 is an initial value of q-axis current;
fig. 5 shows an output value of the mechanical angular velocity.
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.
Fig. 1 shows a control block diagram of the sliding mode control method based on the generalized parameter estimation observer applied to the permanent magnet synchronous motor, wherein the control block diagram comprises a generalized parameter estimation observer loop, a permanent magnet synchronous motor speed loop, a photoelectric encoder and a sliding mode controller; the photoelectric encoder obtains a rotor position angle, mechanical angular velocity is obtained through calculation and sent to the generalized parameter estimation observer, and the sliding mode controller obtains the rotor position angle according to the given mechanical angular velocity and the real angleThe difference of the actual mechanical angular velocity is used as an input to obtain a q-axis voltage, and a given d-axis current is subtracted from a d-axis current in a feedback circuit to obtain a d-axis voltage.u d Andu q pulse signals are generated through Park and SVPWM and then enter a three-phase inverter to control the permanent magnet synchronous motor. The generalized parameter estimation observer is combined with sliding mode control, so that the system has strong robustness to load disturbance and other uncertain factors. The device comprises the following concrete implementation steps:
step (1):
in order to simplify the establishment of the mathematical model of the permanent magnet synchronous motor, the mathematical model under a natural coordinate system is converted into the mathematical model under a synchronous rotating coordinate system by Park conversion and Clarke conversion, and the state variable isi q ，ω r Both state variables and output models are as follows:
Figure 173090DEST_PATH_IMAGE003
wherein ,
Figure 172270DEST_PATH_IMAGE004
is composed ofqThe derivative of the shaft current with respect to time,i q is composed ofqThe current of the shaft is measured by the current sensor,R s is a resistance of the stator, and is,Lin order to be an inductor, the inductor,φ f is a magnetic linkage of the permanent magnet and the stator,u q is the q-axis voltage and is also the control input,ω r is the mechanical angular velocity of the rotor and,
Figure 191042DEST_PATH_IMAGE005
is the derivative of the mechanical angular velocity of the rotor with respect to time,Pis the number of the pole pairs of the motor,Jin order to be the moment of inertia,Bin order to obtain a coefficient of viscous friction,T L is the load torque.
Step (2):
step 21 utilizesω r Andu q information ofReconstructing the state, and deducing the error of the initial value for estimating the q-axis current based on the generalized parameter observation theoryi q0 And load torqueT L Linear regression equation of
Figure 134727DEST_PATH_IMAGE032
, wherein
Figure 897146DEST_PATH_IMAGE008
。
Is unknown in order to obtain a measurementqAccording to the linear regression equation of the shaft current and the load torque, according to the theory of the generalized parameter estimation observer, firstly reconstructing an unknown state:
Figure 101DEST_PATH_IMAGE012
wherein ,
Figure 189773DEST_PATH_IMAGE013
representing the q-axis currenti q The derivative of the reconstructed state of (a),ξ y is q-axis currenti q The reconstructed state of (a).
Then a state transition matrix is obtained:
Figure 886334DEST_PATH_IMAGE014
Figure 452445DEST_PATH_IMAGE015
the derivative of the state transition matrix with respect to time,X Ax in order to be a state transition matrix,
Figure 895058DEST_PATH_IMAGE033
is the initial value of the state transition matrix.
The true value of the current can be expressed as:
Figure 521212DEST_PATH_IMAGE016
wherein the initial value error is:
Figure 377172DEST_PATH_IMAGE018
i q (0) Represents the initial value of the q-axis current,ξ y (0) Representing the q-axis currenti q Is determined.
In order to more easily satisfy the excitable condition and not to use
Figure 543711DEST_PATH_IMAGE034
The derivative information avoids the method of adopting the following filter because the observer performance is influenced by the noise too much:
Figure 434307DEST_PATH_IMAGE035
Figure 152733DEST_PATH_IMAGE020
Figure 495990DEST_PATH_IMAGE021
sorting into the form of differential equations yields:
Figure 200641DEST_PATH_IMAGE022
Figure 945743DEST_PATH_IMAGE023
wherein ,
Figure 913699DEST_PATH_IMAGE024
is a transpose of the state transition matrix,m(0) Is composed ofmIs started.
The desired linear regression equation can then be obtained:
Figure 681935DEST_PATH_IMAGE036
wherein ,
Figure 127959DEST_PATH_IMAGE011
Figure 55464DEST_PATH_IMAGE008
m、ωis the intermediate variable(s) of the variable,λ 1 in order to gain the observer,λ 1 ＞0
Figure 928742DEST_PATH_IMAGE037
step 22:
applying dynamic regression extension and blending techniques, using filters to the linear regression equation obtained in step 21
Figure 167963DEST_PATH_IMAGE036
Is expanded to obtain
Figure 417678DEST_PATH_IMAGE006
(ii) a Then both sides are multiplied by the adjoint matrix simultaneouslyadj｛ΩGet scalar linear regression equation after mixing
Figure 199690DEST_PATH_IMAGE038
And
Figure 243869DEST_PATH_IMAGE039
the specific process comprises the following steps:
Figure 721118DEST_PATH_IMAGE009
Figure 508945DEST_PATH_IMAGE010
obtaining an expanded linear regression equation:
Figure 348725DEST_PATH_IMAGE006
according to the dynamic regression extended mixing technology, the following can be obtained:
Figure 626123DEST_PATH_IMAGE040
then, one can obtain:
Figure 918564DEST_PATH_IMAGE041
wherein , Yin order to be measurable, the measurement is carried out, Y 1 、Y 2 is thatYS1 is a differential operator,
Figure 431454DEST_PATH_IMAGE042
， q e 、m e 、r、Ωand delta is an intermediate variable,α 1 、α 2 、β 1 、β 2 as a filter parameter, satisfyα 1 ，α 2 ≠0，β 1 ，β 2 ＞0，λ 2 Is a gain coefficient, satisfiesλ 2 ＞0。adjIn order to be a companion matrix, the system is,detin the form of a determinant,r(0) Is composed ofrIs set to the initial value of (a),ω(0) Is composed ofωOf the initial value of (a) is,
Figure 125740DEST_PATH_IMAGE043
is composed ofrThe derivative of (a) of (b),
Figure 574039DEST_PATH_IMAGE044
is composed ofΩThe derivative of (c).
And (3):
step 31 of estimating state based on generalized observation theory and dynamic regression extension technology
Figure 88197DEST_PATH_IMAGE045
：
To account for the fact that the estimation of the parameters can still be achieved without sufficient excitation, i.e. (non-uniform observability), the extended linear regression equation obtained based on the above equation derives a new scalar excitation regression equation without the use of filters.
To obtain new regression variables, the error is initialized with unknown quantities
Figure 155510DEST_PATH_IMAGE017
A new kinetic equation is defined for one of the states:
Figure 969882DEST_PATH_IMAGE046
z 1 is the state of the new kinetic equation,
Figure 526766DEST_PATH_IMAGE047
to representz 1 The derivative with respect to time is that of,
Figure 590537DEST_PATH_IMAGE048
to represent
Figure 523858DEST_PATH_IMAGE017
The derivative with respect to time is that of, u 1 、u 2 、u 3 are the system parameters of the kinetic model and,Y 1 is the first element of the known quantity of the linear regression equation finally obtained in the step (2),z 1 (0) Indicating a statez 1 The initial value of (1);
the above dynamic equation is then reconstructed:
Figure 114108DEST_PATH_IMAGE049
wherein ,ξ 1 is composed of
Figure 841892DEST_PATH_IMAGE017
The reconstructed state of,ξ 2 Is composed ofz 1 The state of the reconstruction of (a) is,ξ 1 (0) To representξ 1 Is set to the initial value of (a),ξ 2 (0) To representξ 2 Is the parameter of the linear regression equation finally obtained in the step (2),
Figure 392959DEST_PATH_IMAGE050
to representξ 1 The derivative of (a) of (b),
Figure 129971DEST_PATH_IMAGE051
to representξ 2 A derivative of (a);
the state transition matrix after the dynamic equation is reconstructed is recorded as
Figure 325460DEST_PATH_IMAGE052
，Φ 11 、Φ 21 、Φ 12 、Φ 22 The elements in the state transition matrix can be obtained by the following differential equations;
Figure 224146DEST_PATH_IMAGE053
by expanding the above equation, the equation for phi is obtained 11 、Φ 21 The differential equation of (a) is as follows:
Figure 465772DEST_PATH_IMAGE054
Figure 803212DEST_PATH_IMAGE055
is phi 11 The derivative of (a) of (b),
Figure 915525DEST_PATH_IMAGE056
is phi 21 A derivative of (d); selecting system parametersu 1 、u 2 、u 3 Comprises the following steps:
Figure 437642DEST_PATH_IMAGE057
phi can be obtained by solving the differential equation 11 、Φ 21 。
Defining new known quantities
Figure 635405DEST_PATH_IMAGE058
Then, a new regression equation is obtained as:
Figure 776536DEST_PATH_IMAGE059
a new regression equation is used to estimate the parameters and the above equation is substituted:
Figure 743355DEST_PATH_IMAGE060
Figure 187106DEST_PATH_IMAGE061
is composed of
Figure 137744DEST_PATH_IMAGE017
Is determined by the estimated value of (c),
Figure 754671DEST_PATH_IMAGE062
is composed of
Figure 903892DEST_PATH_IMAGE061
The derivative of (a) of (b),γ 1 in order to gain the observer,γ 1 ＞0；
an estimate of the q-axis current may then be obtained
Figure 580861DEST_PATH_IMAGE001
：
Figure 940167DEST_PATH_IMAGE063
。
Step 32 of estimating the load torque based on the generalized observation theory and the dynamic regression extension technologyT L ：
As above, with the newly defined unknown quantity
Figure 360784DEST_PATH_IMAGE064
A new kinetic equation is defined for one of the states:
Figure 364512DEST_PATH_IMAGE065
z 2 is the state of the new kinetic equation,
Figure 212383DEST_PATH_IMAGE066
to representz 2 The derivative with respect to time is that of,
Figure 809717DEST_PATH_IMAGE067
to represent
Figure 34025DEST_PATH_IMAGE064
The derivative with respect to time is that of,u 12 、u 22 、u 32 are the system parameters of the kinetic model and,Y 2 is the second element of the known vector of the linear regression equation finally obtained in the step (2),z 2 (0) Indicating a statez 2 An initial value of (1);
then, reconstructing the dynamic equation to obtain:
Figure 95522DEST_PATH_IMAGE068
wherein ,ξ 12 is composed of
Figure 911031DEST_PATH_IMAGE064
The state of the reconstruction of (a) is,ξ 22 is composed ofz 2 The state of the reconstruction of (a) is,ξ 12 (0) Representξ 12 Is set to the initial value of (a),ξ 22 (0) Representξ 22 Is set to the initial value of (a),
Figure 57979DEST_PATH_IMAGE069
to representξ 12 The derivative of (a) of (b),
Figure 7349DEST_PATH_IMAGE070
to representξ 22 A derivative of (a);
the state transition matrix of the above system is noted as
Figure 923353DEST_PATH_IMAGE071
，φ 112 、φ 212 、φ 122 、φ 222 The elements in the state transition matrix can be obtained by the following differential equations;
Figure 175342DEST_PATH_IMAGE072
by developing the above equation, the equation is obtained for phi 112 、φ 212 The differential equation of (a) is as follows:
Figure 809586DEST_PATH_IMAGE073
Figure 110117DEST_PATH_IMAGE074
is phi 112 The derivative of (a) of (b),
Figure 83890DEST_PATH_IMAGE075
is phi 212 A derivative of (a); selecting system parametersu 12 、u 22 、u 32 Comprises the following steps:
Figure 444464DEST_PATH_IMAGE076
phi can be obtained by solving the above differential equation 112 、φ 212 。
Defining new known quantities
Figure 362741DEST_PATH_IMAGE077
Then, a new regression equation is obtained as:
Figure 466964DEST_PATH_IMAGE078
obtaining the estimated value of the load torque according to the regression equation
Figure 544510DEST_PATH_IMAGE002
：
Figure 75985DEST_PATH_IMAGE079
wherein ,
Figure 684821DEST_PATH_IMAGE002
as a load torqueT L Is determined by the estimated value of (c),
Figure 389472DEST_PATH_IMAGE080
is composed of
Figure 134574DEST_PATH_IMAGE002
The derivative of (a) of (b),γ 2 ＞0，γ 2 is the observer gain.
And (4):
a photoelectric encoder obtains a rotor position angle, mechanical angular velocity is obtained through calculation and is sent to a generalized parameter estimation observer, a sliding mode controller obtains q-axis voltage according to the difference between the given mechanical angular velocity and the actual mechanical angular velocity as input, and given d-axis current and current in a feedback circuit
Figure 774634DEST_PATH_IMAGE081
Subtracting the shaft currents to obtain
Figure 605187DEST_PATH_IMAGE081
The shaft voltage.u d Andu q pulse signals are generated through Park and SVPWM and then enter a three-phase inverter to control the permanent magnet synchronous motor.
Step 41 takes the difference between the given mechanical angular velocity and the mechanical angular velocity measured by the sensor as input to the sliding mode controller:
Figure 113528DEST_PATH_IMAGE025
wherein ,
Figure 713137DEST_PATH_IMAGE026
is a reference value for the mechanical angular velocity of the rotor.
Step 42 design slip form face:
Figure 851994DEST_PATH_IMAGE027
wherein ,cis a parameter of the sliding mode surface and meets the requirementsc＞0，
Figure 356794DEST_PATH_IMAGE028
Representing the derivative of the input of the sliding mode controller with respect to time;
step 43 combines the generalized parameter estimation observer to obtain the control law ofu q ：
Figure 606510DEST_PATH_IMAGE082
wherein ,sgn(s) is a function of the sign,
Figure 122942DEST_PATH_IMAGE001
is q-axis currenti q Is determined by the estimated value of (c),
Figure 167121DEST_PATH_IMAGE002
as a load torqueT L Is determined by the estimated value of (c),aas an intermediate parameter, the parameter is,
Figure 909949DEST_PATH_IMAGE030
，kin order to control the rate parameter(s),k＞0。
correspondingly, the invention also provides a sliding mode control system based on the generalized parameter estimation observer, which is characterized by comprising the following steps:
the transformation module is used for acquiring a mathematical model of the three-phase permanent magnet synchronous motor in a natural coordinate system, and selecting the q-axis current of the permanent magnet synchronous motor as a state variable and a mechanical angular velocity through Clark coordinate transformation and Park coordinate transformationω r As output and state variables, converting a mathematical model under a natural coordinate system into a mathematical model under a d-q axis synchronous rotation coordinate system of the three-phase permanent magnet synchronous motor;
a first determining module, which is used for converting state observation into parameter estimation based on a generalized parameter estimation observation theory according to the mathematical model under the d-q axis synchronous rotation coordinate system, and determining the current for estimating the q axisi q And load torqueT L The linear regression equation of (1);
a second determining module for processing the linear regression equation to make it conform to the excitation condition, and determining the estimated value of the q-axis current according to a preset generalized parameter estimation observer
Figure 697777DEST_PATH_IMAGE001
And load torqueT L Is estimated value of
Figure 334294DEST_PATH_IMAGE002
；
An output module for designing a sliding mode controller according to the estimation information of the generalized parameter estimation observer and obtaining a control quantity according to the sliding mode controlleru q To the control quantityu q To carry outAnd after the inverse Park coordinate transformation, obtaining a driving signal of the three-phase inverter through the SVPWM module, and adjusting the output of the three-phase inverter according to the driving signal.
The generalized parameter estimation observer is combined with a dynamic hybrid expansion technology to convert state observation into parameter estimation, so that q-axis current can be realizedi q And load torqueT L Meanwhile, the use of the sensor is reduced, so that the stability of the whole system can be improved. And designing a sliding mode controller based on the estimated information to improve the anti-interference capability and robustness of the system.
In order to verify the effectiveness of the sliding mode control method based on the generalized parameter estimation observer, the control performance of the controller designed by the invention on the permanent magnet synchronous single machine is tested on a Matlab/simulink simulation platform. And verifying whether the designed observer can accurately and quickly estimate the q-axis current of the motor system. The parameters used in the simulation experiments of the permanent magnet synchronous motor are shown in table 1. It can be seen from fig. 2 that the observer can immediately track the current that observes the system. FIG. 3 is a graph of a tracking estimate for load torque givenT L At 1N · m, the observer can estimate the value of the load torque within 0.05s, the output mechanical angular velocity of fig. 4 can be stabilized and coincide with the desired output value within 0.05s, and the output mechanical angular velocity of fig. 5 can be stabilized and coincide with the desired output value within 0.05 s.
Simulation results show that the control method can realize the control of the angular speed of the permanent magnet synchronous motor. Under the condition that the load torque is unknown, the stability of a closed-loop system can still be ensured, the use of current sensors is reduced, the cost is reduced, the reliability is improved, and the method has good application value in engineering.
TABLE 1
Figure 814954DEST_PATH_IMAGE083
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, it is possible to make various improvements and modifications without departing from the technical principle of the present invention, and those improvements and modifications should be considered as the protection scope of the present invention.

Claims (7)

1. A sliding mode control method based on a generalized parameter estimation observer is characterized by comprising the following steps:
obtaining a mathematical model of the three-phase permanent magnet synchronous motor under a natural coordinate system, and selecting a q-axis current of the permanent magnet synchronous motor as a state variable and a mechanical angular velocity through Clark coordinate transformation and Park coordinate transformationω r As output and state variables, converting a mathematical model under a natural coordinate system into a mathematical model under a d-q axis synchronous rotation coordinate system of the three-phase permanent magnet synchronous motor;
according to the mathematical model under the d-q axis synchronous rotation coordinate system, converting state observation into parameter estimation based on the generalized parameter estimation observation theory, and determining the current for estimating the q axisi q And load torqueT L The linear regression equation of (1);
processing the linear regression equation to make it accord with the excitation condition, estimating the observer according to the preset generalized parameters, and determining the estimated value of the q-axis current
Figure 259197DEST_PATH_IMAGE001
And load torqueT L Is estimated value of
Figure 775629DEST_PATH_IMAGE002
；
Designing a sliding mode controller according to the estimation information of the generalized parameter estimation observer, and obtaining a control quantity according to the sliding mode controlleru q To the control quantityu q And after carrying out inverse Park coordinate transformation, obtaining a driving signal of the three-phase inverter through the SVPWM module, and adjusting the output of the three-phase inverter according to the driving signal.
2. The sliding-mode control method based on the generalized parameter estimation observer according to claim 1, wherein the mathematical model under the d-q axis synchronous rotation coordinate system is represented as:
Figure 491912DEST_PATH_IMAGE003
wherein ,
Figure 93795DEST_PATH_IMAGE004
is composed ofqThe derivative of the shaft current with respect to time,i q is composed ofqThe current of the shaft is measured by the current sensor,R s as the resistance of the stator,Lin order to be an inductor, the inductor,φ f is a magnetic linkage of the permanent magnet and the stator,u q for the q-axis voltage to be also the control input,ω r is the mechanical angular velocity of the rotor and,
Figure 802994DEST_PATH_IMAGE005
is the derivative of the mechanical angular velocity of the rotor with respect to time,Pis the number of the pole pairs of the motor,Jin order to be the moment of inertia,Bin order to obtain a coefficient of viscous friction,T L is the load torque.
3. The sliding-mode control method based on the generalized parameter estimation observer according to claim 2, wherein the linear regression equation is:
Figure 173932DEST_PATH_IMAGE006
q e for adding linear regression equations of filtersThe measurement is carried out by measuring the temperature of the sample,m e to add the regression factors of the filter linear regression equation,
Figure 61117DEST_PATH_IMAGE007
is an intermediate variable of the linear regression equation,
Figure 884716DEST_PATH_IMAGE008
，i q0 error of an initial value of the q-axis current;
Figure 397606DEST_PATH_IMAGE009
Figure 623051DEST_PATH_IMAGE010
Figure 681137DEST_PATH_IMAGE011
s1 is a differential operator, and the differential operator,α 1 、α 2 、β 1 、β 2 as a filter parameter, satisfyα 1 ，α 2 ≠0，β 1 ，β 2 ＞0，q1 is a measurable quantity of a linear regression equation without the addition of a filter,λ 1 in order to gain the observer,λ 1 ＞0，m、ωis an intermediate variable.
4. The sliding-mode control method based on the generalized parameter estimation observer of claim 3, wherein solving the intermediate variable m,ωThe method comprises the following steps:
reconstructing q-axis current based on theory of generalized parameter estimation observeri q To obtain the following formula:
Figure 257612DEST_PATH_IMAGE012
wherein ,
Figure 311543DEST_PATH_IMAGE013
representing the q-axis currenti q The derivative of the reconstructed state of (a),ξ y is q-axis currenti q The reconfiguration state of (a);
obtaining a reconstruction state based on a linear system theoryξ y State transition matrix ofX Ax ：
Figure 391494DEST_PATH_IMAGE014
wherein ,
Figure 886061DEST_PATH_IMAGE015
the derivative of the state transition matrix with respect to time,X Ax (0) Is the initial value of the state transition matrix;
the true value of the q-axis current is then expressed as:
Figure 418673DEST_PATH_IMAGE016
wherein ,
Figure 7786DEST_PATH_IMAGE017
for the error of the initial value, it is,i q (0) Represents the initial value of the q-axis current,ξ y (0) Representing the q-axis currenti q The initial value of the reconstruction state of (1);
Figure 207823DEST_PATH_IMAGE018
reconstruction
Figure 873291DEST_PATH_IMAGE005
Expressed as:
Figure 893200DEST_PATH_IMAGE019
Figure 551583DEST_PATH_IMAGE020
Figure 606127DEST_PATH_IMAGE021
then will bemAndωis converted into the form of a differential equation, expressed as:
Figure 176916DEST_PATH_IMAGE022
Figure 949700DEST_PATH_IMAGE023
wherein ,
Figure 146195DEST_PATH_IMAGE024
is a transpose of the state transition matrix,m(0) Is composed ofmAn initial value of (1);
solving the differential equation to obtain an intermediate variable m,ω。
5. The sliding-mode control method based on the generalized parameter estimation observer according to claim 4, wherein the estimated value of the q-axis current is determined by combining a dynamic regression expansion method based on the generalized observation theory
Figure 55246DEST_PATH_IMAGE001
And load torqueT L Is estimated value of
Figure 62516DEST_PATH_IMAGE002
。
6. The sliding-mode control method based on the generalized parameter estimation observer according to claim 4, wherein the process of determining the sliding-mode controller comprises:
the difference between the given mechanical angular velocity and the mechanical angular velocity measured by the sensor is used as an input of the sliding mode controller,
expressed as:
Figure 57017DEST_PATH_IMAGE025
wherein ,eis an input to the sliding mode controller,
Figure 60132DEST_PATH_IMAGE026
is a reference value of the mechanical angular velocity of the rotor;
designing the slip form surfacesExpressed as:
Figure 89268DEST_PATH_IMAGE027
wherein ,cis a parameter of the sliding mode surface and meets the requirementsc＞0，
Figure 1860DEST_PATH_IMAGE028
Representing the derivative of the input error with respect to time;
combining the generalized parameter estimation observer to obtain the control lawu q Comprises the following steps:
Figure 483657DEST_PATH_IMAGE029
wherein ,sgn(s) isThe function of the sign is that the sign function,
Figure 897321DEST_PATH_IMAGE001
is q-axis currenti q Is determined by the estimated value of (c),
Figure 905597DEST_PATH_IMAGE002
as a load torqueT L Is determined by the estimated value of (c),aas an intermediate parameter, the parameter is,
Figure 113725DEST_PATH_IMAGE030
，kin order to control the rate parameter(s),k＞0。
7. a sliding mode control system based on a generalized parameter estimation observer is characterized by comprising:
the transformation module is used for acquiring a mathematical model of the three-phase permanent magnet synchronous motor in a natural coordinate system, and selecting the q-axis current of the permanent magnet synchronous motor as a state variable and a mechanical angular velocity through Clark coordinate transformation and Park coordinate transformationω r As output and state variables, converting a mathematical model under a natural coordinate system into a mathematical model under a d-q axis synchronous rotation coordinate system of the three-phase permanent magnet synchronous motor;
a first determining module, which is used for converting state observation into parameter estimation based on a generalized parameter estimation observation theory according to the mathematical model under the d-q axis synchronous rotation coordinate system, and determining the current for estimating the q axisi q And load torqueT L The linear regression equation of (1);
a second determining module for processing the linear regression equation to make it conform to the excitation condition, and determining the estimated value of the q-axis current according to a preset generalized parameter estimation observer
Figure 958184DEST_PATH_IMAGE001
And load torqueT L Is estimated value of
Figure 175539DEST_PATH_IMAGE002
；
An output module for designing a sliding mode controller according to the estimation information of the generalized parameter estimation observer and obtaining a control quantity according to the sliding mode controlleru q To the control quantityu q And after carrying out inverse Park coordinate transformation, obtaining a driving signal of the three-phase inverter through the SVPWM module, and adjusting the output of the three-phase inverter according to the driving signal.
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