CN115664283A - Sliding mode control method and system based on generalized parameter estimation observer - Google Patents
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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
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
And load torqueT L Is estimated by
；
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:
wherein ,
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,
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:
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,
is an intermediate variable of the linear regression equation,
，i q0 error of an initial value of the q-axis current;
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:
wherein ,
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 ：
wherein ,
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:
wherein ,
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);
reconstruction
Expressed as:
then will bemAndωis converted into the form of a differential equation, expressed as:
wherein ,
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
And load torqueT L Is estimated value of
。
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:
wherein ,eis an input to the sliding mode controller,
is a reference value of the mechanical angular velocity of the rotor;
designing the slip form surfacesExpressed as:
wherein ,cis a parameter of the sliding mode surface and meets the requirementsc＞0，
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:
wherein ,sgn(s) is a function of the sign,
is q-axis currenti q Is determined by the estimated value of (c),
as a load torqueT L Is determined by the estimated value of (c),ais an intermediate parameter that is a function of,
，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
And load torqueT L Is estimated value of
；
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
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:
wherein ,
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,
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
, wherein 
。
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:
wherein ,
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:
The true value of the current can be expressed as:
wherein the initial value error is:
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
The derivative information avoids the method of adopting the following filter because the observer performance is influenced by the noise too much:
sorting into the form of differential equations yields:
wherein ,
is a transpose of the state transition matrix,m(0) Is composed ofmIs started.
The desired linear regression equation can then be obtained:
wherein ,
m、ωis the intermediate variable(s) of the variable,λ 1 in order to gain the observer,λ 1 ＞0
step 22:
applying dynamic regression extension and blending techniques, using filters to the linear regression equation obtained in step 21
Is expanded to obtain
(ii) a Then both sides are multiplied by the adjoint matrix simultaneouslyadj｛ΩGet scalar linear regression equation after mixing
And
the specific process comprises the following steps:
obtaining an expanded linear regression equation:
according to the dynamic regression extended mixing technology, the following can be obtained:
then, one can obtain:
wherein , Yin order to be measurable, the measurement is carried out, Y 1 、Y 2 is thatYS1 is a differential operator,
， 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,
is composed ofrThe derivative of (a) of (b),
is composed ofΩThe derivative of (c).
And (3):
step 31 of estimating state based on generalized observation theory and dynamic regression extension technology
：
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
A new kinetic equation is defined for one of the states:
z 1 is the state of the new kinetic equation,
to representz 1 The derivative with respect to time is that of,
to represent
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:
wherein ,ξ 1 is composed of
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),
to representξ 1 The derivative of (a) of (b),
to representξ 2 A derivative of (a);
the state transition matrix after the dynamic equation is reconstructed is recorded as
，Φ 11 、Φ 21 、Φ 12 、Φ 22 The elements in the state transition matrix can be obtained by the following differential equations;
by expanding the above equation, the equation for phi is obtained 11 、Φ 21 The differential equation of (a) is as follows:
phi can be obtained by solving the differential equation 11 、Φ 21 。
Defining new known quantities
Then, a new regression equation is obtained as:
a new regression equation is used to estimate the parameters and the above equation is substituted:
an estimate of the q-axis current may then be obtained
：
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
A new kinetic equation is defined for one of the states:
z 2 is the state of the new kinetic equation,
to representz 2 The derivative with respect to time is that of,
to represent
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:
wherein ,ξ 12 is composed of
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),
to representξ 12 The derivative of (a) of (b),
to representξ 22 A derivative of (a);
the state transition matrix of the above system is noted as
，φ 112 、φ 212 、φ 122 、φ 222 The elements in the state transition matrix can be obtained by the following differential equations;
by developing the above equation, the equation is obtained for phi 112 、φ 212 The differential equation of (a) is as follows:
phi can be obtained by solving the above differential equation 112 、φ 212 。
Defining new known quantities
Then, a new regression equation is obtained as:
obtaining the estimated value of the load torque according to the regression equation
：
wherein ,
as a load torqueT L Is determined by the estimated value of (c),
is composed of
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
Subtracting the shaft currents to obtain
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:
wherein ,
is a reference value for the mechanical angular velocity of the rotor.
Step 42 design slip form face:
wherein ,cis a parameter of the sliding mode surface and meets the requirementsc＞0，
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 ：
wherein ,sgn(s) is a function of the sign,
is q-axis currenti q Is determined by the estimated value of (c),
as a load torqueT L Is determined by the estimated value of (c),aas an intermediate parameter, the parameter is,
，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
And load torqueT L Is estimated value of
；
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
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
And load torqueT L Is estimated value of
；
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:
wherein ,
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,
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:
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,
is an intermediate variable of the linear regression equation,
，i q0 error of an initial value of the q-axis current;
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:
wherein ,
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 ：
wherein ,
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:
wherein ,
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);
reconstruction
Expressed as:
then will bemAndωis converted into the form of a differential equation, expressed as:
wherein ,
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
And load torqueT L Is estimated value of
。
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:
wherein ,eis an input to the sliding mode controller,
is a reference value of the mechanical angular velocity of the rotor;
designing the slip form surfacesExpressed as:
wherein ,cis a parameter of the sliding mode surface and meets the requirementsc＞0，
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:
wherein ,sgn(s) isThe function of the sign is that the sign function,
is q-axis currenti q Is determined by the estimated value of (c),
as a load torqueT L Is determined by the estimated value of (c),aas an intermediate parameter, the parameter is,
，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
And load torqueT L Is estimated value of
；
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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| CN116599413A (en) * | 2023-07-17 | 2023-08-15 | 南京信息工程大学 | Position-sensor-free control method and device for permanent magnet synchronous motor |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108923712A (en) * | 2018-08-28 | 2018-11-30 | 青岛大学 | Permanent magnet synchronous motor revolving speed monocycle control method, apparatus and system |
| CN114006557A (en) * | 2021-09-30 | 2022-02-01 | 湖南科技大学 | Permanent magnet synchronous motor mechanical parameter identification method based on extended sliding-mode observer |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108923712A (en) * | 2018-08-28 | 2018-11-30 | 青岛大学 | Permanent magnet synchronous motor revolving speed monocycle control method, apparatus and system |
| CN114006557A (en) * | 2021-09-30 | 2022-02-01 | 湖南科技大学 | Permanent magnet synchronous motor mechanical parameter identification method based on extended sliding-mode observer |
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| 任核权等: "一种电动汽车用PMSM速度电流单环控制方法" * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116599413A (en) * | 2023-07-17 | 2023-08-15 | 南京信息工程大学 | Position-sensor-free control method and device for permanent magnet synchronous motor |
| CN116599413B (en) * | 2023-07-17 | 2023-09-22 | 南京信息工程大学 | Position-sensor-free control method and device for permanent magnet synchronous motor |
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