CN114006557A - Permanent magnet synchronous motor mechanical parameter identification method based on extended sliding-mode observer - Google Patents
Permanent magnet synchronous motor mechanical parameter identification method based on extended sliding-mode observer Download PDFInfo
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Abstract
The invention discloses a permanent magnet synchronous motor mechanical parameter identification method based on an extended sliding-mode observer, which comprises the following steps: establishing a mathematical model of the surface-mounted permanent magnet synchronous motor and adopting vector control through coordinate transformation; designing an extended sliding mode mechanical parameter view and determining related parameters of the observer; and observing system disturbance information by using the proposed extended sliding-mode observer, and extracting a damping coefficient, a rotational inertia and a load torque from the system disturbance information. Firstly, taking a friction coefficient parameter error, a rotational inertia parameter error and a load torque system disturbance as an extended system state, establishing an extended state equation for designing an extended sliding mode observer, wherein the extended sliding mode observer can track the system state in real time and soften a sliding mode variable structure control signal; therefore, the output of the extended sliding mode observer can be directly used for mechanical parameter estimation without generating phase lag, and the self-tuning control of the permanent magnet synchronous motor system is realized by correctly estimating the mechanical parameters in real time, so that the optimal control is realized.
Description
Technical Field
The invention relates to the field of motor control, in particular to a permanent magnet synchronous motor mechanical parameter identification method based on an extended sliding-mode observer.
Background
The permanent magnet synchronous motor has the advantages of simple structure, small volume, high efficiency, high torque current ratio, high power density and the like, and compared with a speed regulating system formed by other motors, the alternating current permanent magnet speed regulating system formed by the permanent magnet synchronous motor has more excellent performance. The vector control technology is a control method commonly used by a permanent magnet synchronous motor system, and can realize the decoupling of the electromagnetic torque and the magnetic flux of the system through vector control, thereby avoiding the influence caused by the characteristics of nonlinearity and strong coupling of an alternating current motor, and enabling the system to have higher tracking capability, higher tracking precision and good robustness. However, for more complex working conditions, parameter changes of the system and external unknown disturbances, the dynamic performance of the system is reduced, and at the moment, the parameters of the controller should be adjusted in time to suppress the system disturbances caused by the parameter changes, so that the good dynamic performance and the steady-state performance of the system are ensured. The adjustment of the parameters of the controller can come from practical experience, but the adjustment method has no real-time property and cannot be applied to the working condition with frequent parameter change. Compared with the prior art, the parameter self-tuning technology of the controller can adjust the parameters on line, has high real-time performance, and the adjusting effect of the method depends on the accuracy of mechanical parameters such as load torque, rotational inertia and the like. Therefore, the system needs to include a mechanism for accurately identifying system parameters, and the controller parameters are adjusted in time according to the identification values, so that the influence of the disturbance on the system can be reduced or even eliminated.
The mechanical parameters of the permanent magnet synchronous motor system mainly refer to load torque, rotational inertia, damping coefficient and the like, wherein the identification method of the rotational inertia can be generally divided into two categories: an off-line identification method and an on-line identification method.
The off-line identification method comprises a power-off deceleration method, an orthogonal integration method, a single-wire torsional oscillation method and the like, but the methods cannot consider the parameter change of the motor in the actual engineering, are generally only used for initial value setting of motor control, and have the main defect of non-real-time property. The online identification eliminates the defect of offline identification by monitoring parameters in real time, and better meets the actual control requirement, and the negative influence is that a large amount of data needs to be stored and calculated in the working process, so that the requirement on a computer is higher and higher, and the identification accuracy is also influenced to a certain extent.
The online identification method comprises a state observer, extended Kalman filtering, model reference adaptive identification, least square identification and the like. The parameter identification method based on the model reference adaptive system is simple and feasible, and is applied to many practical engineering applications, but the method cannot be used for estimating the load torque in real time. The model-referenced adaptive method can estimate parameters by continuously adjusting adaptive law or function cost, but is difficult to be practically applied due to the complexity of practical implementation and the sensitivity of adaptive gain. The extended kalman filter algorithm takes the mechanical parameter as one of the system variables and takes it as a direct output of the extended kalman filter. The recursive least square algorithm iteratively solves the least square estimation when converging, and the dependence of the least square estimation on the initial condition is large. Although the recursive least squares method can be used to estimate the parameters of the permanent magnet synchronous motor control system, a longer estimation time is required in the estimation process. Therefore, this method is limited in scientific practice and practical industrial manufacturing. When load torque identification of the permanent magnet synchronous motor is carried out, the rotational inertia is defined as a known parameter by a disturbance observer, but in actual production practice, the two variables are generally unknown, and a good identification result is difficult to achieve in such a case.
Disclosure of Invention
In order to solve the technical problem, the invention provides a permanent magnet synchronous motor mechanical parameter identification method which can track the system state in real time, can be directly used for mechanical parameter estimation and does not generate phase lag.
The technical scheme for solving the problems is as follows: a permanent magnet synchronous motor mechanical parameter identification method based on an extended sliding-mode observer comprises the following steps:
1) establishing a mathematical model of the surface-mounted permanent magnet synchronous motor, and performing coordinate transformation by adopting vector control: firstly, establishing a mathematical model under an A-B-C three-phase static coordinate system to obtain a phase voltage equation, a flux linkage equation, a torque equation and a mechanical motion equation of each phase, and then obtaining the mathematical model under an alpha-beta two-phase static coordinate system and a d-q axis two-phase rotating coordinate system through Clark conversion and Park conversion in sequence to realize complete decoupling of exciting current and torque current so as to be convenient for control;
2) designing an extended sliding mode observer and determining observer related parameters: according to a mechanical motion equation of the PMSM, taking a damping coefficient parameter error, a rotational inertia parameter error and load torque system disturbance as an extended system state, establishing an extended state equation for designing an extended sliding mode observer, and ensuring the stability of the observer by considering a Lyapunov function;
3) observing system disturbance information by using the proposed extended sliding-mode observer, and extracting a damping coefficient, a rotational inertia and a load torque from the system disturbance information: firstly, the permanent magnet synchronous motor runs at two different steady-state speeds, the damping coefficient is estimated by utilizing the actually measured speed information and the estimated disturbance, then the rotary inertia is estimated by respectively running the permanent magnet synchronous motor at two different constant acceleration or constant deceleration, and finally, the damping coefficient and the rotary inertia are directly used for estimating the load torque.
The permanent magnet synchronous motor mechanical parameter identification method based on the extended sliding mode observer comprises the following specific processes in the step 1):
firstly, establishing a mathematical model under an A-B-C three-phase static coordinate system, wherein a voltage equation of the A-B-C three-phase static coordinate system is as follows:
wherein R issAs stator resistance，UA、UB、UCIs a stator three-phase voltage iA、iB、iCFor stator three-phase currents, ΨsA、ΨsB、ΨsCThe stator is a stator three-phase full magnetic linkage, and the vector form is as follows:
in the formula psisFor stator flux linkage, USIs the stator voltage; i.e. isIs the stator current;
the flux linkage equation is:
in the formula, ΨfA、ΨfB、ΨfCFlux linkage i for three-phase interlinkage of permanent magnet field and statorsA、isB、isCRespectively representing A, B, C three-phase stator currents, LsIn order to realize the synchronous inductance of the stator,
LA＝LB＝LC＝Lsσ+Lmlwherein L isA、LB、LCFor self-induction of each phase, LmlExciting inductance for each phase; l isSσIs the leakage inductance of each phase;
the torque equation:
the electromagnetic torque is considered as a result of the interaction between the stator, rotor and armature, and is expressed as:
wherein p is the number of pole pairs, TeBeing electromagnetic torque, ΨfMagnetic linkage psi linking the permanent magnet field with the statorsA stator flux linkage;
mechanical equation of motion:
ωmas mechanical angular speed of the rotor, TLThe load torque is J, the moment of inertia is J, and the damping coefficient of the motor is B;
and finally obtaining a mathematical model under a d-q axis two-phase rotating coordinate system through Clark transformation and Park transformation to realize complete decoupling of exciting current and torque current so as to perform vector control:
the flux linkage equation:
in the formula, Ψd、ΨqIs the quadrature-direct component of the stator flux linkage, Ld、LqComponent of stator inductance in d, q axes, id、iqD and q axis stator currents;
voltage equation:
in the formula of Ud、UqThe quadrature-direct component, omega, of the stator voltageeRepresenting the rotor angular velocity;
the torque equation:
in the formula, Ld、LqThe inductance values are direct axis and quadrature axis inductance values; therefore, the decoupling of the torque is realized under the d-q axis, and the torque equation is as follows:
in the method for identifying mechanical parameters of the permanent magnet synchronous motor based on the extended sliding mode observer, in the step 2), a kinetic equation of the motor is expressed as follows:
wherein B is0、J0Is a rough estimation of real parameters, Δ B, Δ J are parameter errors between the real system and its rough estimation, and the moment of inertia J ═ J0+ Δ J, damping coefficient B ═ B0+ Δ B, ω is the rotational speed, d represents disturbances including parameter errors and load disturbances;
considering the disturbance d as an extended system state, in order to perform parameter estimation, the extended sliding mode observer is designed as follows:
wherein,
is an estimate of the disturbance,
is an estimate of the velocity, m is a sliding mode parameter, usmoRepresents the sliding mode observer signal and usmoEta, sgn (S), eta is real number, S is sliding mode surface and negative value, and is designed as
The error equation is now obtained as follows:
error of the measurement
Intermediate volume
In order to ensure the occurrence of the sliding mode, the stable condition of the variable structure of the sliding mode must be met; thus, consider the following Lyapunov function: v is 0.5s2V and s represent the speed versus time in a motion system, differentiating V from time t:
namely:
in order to ensure the stability of the extended sliding-mode observer, a stability condition must be satisfied
Eta is<-|e2-B0e1In practical application, the following parameter adaptation law is adopted: eta ═ l | e2-B0e1|,l>1, l is the safety factor of the sliding mode; error e1And derivatives thereof
Can converge to zero along a sliding mode occurring within a limited time, i.e.
Therefore, the error equation is simplified to
Namely, it is
Thus, e2The results of (a) are expressed as: e.g. of the type2＝e-mt[C+∫r·emtdt]Where e is a mathematical constant and C is a constant, in order to ensure a disturbance estimation error e2Converging to zero, and selecting sliding mode parameters as parameters m of disturbance estimation>0; therefore, the sliding-mode observer parameters are extendedThe choice of number is constrained by η and m;
speed after occurrence of sliding mode
Observer equation simplification to
Thus, the equation is obtained:
the observer is equivalent to a low-pass filter after the sliding mode occurs; therefore, the disturbance observation effect of the extended sliding mode observer is equivalent to the output of the actual system disturbance of the filtering.
In the method for identifying mechanical parameters of the permanent magnet synchronous motor based on the extended sliding mode observer, in the step 3), the permanent magnet synchronous motor is enabled to run at two different stable speeds, so as to estimate the damping coefficient B;
when the motor runs at a first steady-state rotating speed omega (t), based on the extended sliding-mode observer and the disturbance d, the following disturbance estimation is obtained:
after a time delay τ of the motor, the disturbance of the second steady speed ω (t + τ) is estimated as follows,
when the permanent magnet synchronous motor control system reaches the steady-state rotating speed, the load torque TLRegarded as a constant, the above two are subtracted：
Therefore, the temperature of the molten metal is controlled,
writing:
thus, an estimated parameter is obtained
Comprises the following steps:
in the above method for identifying mechanical parameters of a permanent magnet synchronous motor based on the extended sliding-mode observer, in step 3), when the motor is in the first constant acceleration state ac1When the method is operated, based on an extended sliding-mode observer and a disturbance equation, the B estimation value obtained in the previous step is substituted, and the following disturbance estimation value can be obtained:
then, by ensuring that the two different constant accelerations correspond exactly to two different time periods, respectively, after a time delay τ, the second constant acceleration state ac2The interference estimate of (c) is given by:
the estimation parameters can be obtained by subtracting and sorting the two formulas
In the above method for identifying mechanical parameters of a permanent magnet synchronous motor based on the extended sliding-mode observer, in step 3), when the parameters B and J are accurately estimated, the original estimation B in the state equation is performed0And J0Estimated parameters
And
instead, the extended sliding-mode observer is then rewritten as:
at this time, the updated estimated disturbance
Expressed as:
it can be seen that the updated extended sliding-mode observer has the capability of estimating the load torque, and therefore, in practical applications, the proposed extended sliding-mode observer is used to estimate B and J, or to estimate the load torque T on-line in real time with B and J being knownL。
The invention has the beneficial effects that:
1. according to the problem that the control performance of the permanent magnet synchronous motor is influenced due to variable load conditions in an actual permanent magnet synchronous motor control system, the extended sliding mode observer can observe mechanical parameters of the permanent magnet synchronous motor control system in real time and feed back the mechanical parameters to the controller to adjust the parameters in time, so that system disturbance is restrained, and good dynamic performance and stable performance of the system are guaranteed.
2. The extended sliding-mode observer provided by the invention can be equivalent to a low-pass filter after sliding mode occurs, and the disturbance observation effect of the extended sliding-mode observer is equivalent to the output of filtering actual system disturbance. The cut-off frequency of the low-pass filter is m, and the low-pass filter can be designed arbitrarily according to the buffeting suppression requirement of the observer. Therefore, the output of the observer does not contain sliding mode buffeting caused by a low-pass filter and can be directly used for system control.
3. The invention can reduce the error value of the observer to zero in the effective time, has stronger anti-interference capability to external disturbance, simple structure and low sensitivity to system parameter change.
Drawings
Fig. 1 is a block diagram of estimation of mechanical parameters of a permanent magnet synchronous motor.
Fig. 2 is a schematic diagram of an extended sliding-mode observer.
Fig. 3 is a schematic diagram of an equivalent low-pass filter of an extended sliding-mode observer.
Fig. 4 is a schematic diagram of mechanical parameter estimation.
FIG. 5 is a graph of experimental results of expanding damping coefficients identified by a sliding-mode observer.
FIG. 6 is a graph of experimental results of expanding the rotational inertia identified by the sliding-mode observer.
Fig. 7 is a graph of experimental results of load torque identified by the extended sliding mode observer.
Detailed Description
The invention is further described below with reference to the figures and examples.
As shown in fig. 1, a method for identifying mechanical parameters of a permanent magnet synchronous motor based on an extended sliding-mode observer includes the following steps:
1) establishing a mathematical model of the surface-mounted permanent magnet synchronous motor, and performing coordinate transformation by adopting vector control: firstly, a mathematical model under an A-B-C three-phase static coordinate system is established to obtain an equation of each phase voltage, a flux linkage equation, a torque equation and a mechanical motion equation, and then the mathematical models under an alpha-beta two-phase static coordinate system and a d-q axis two-phase rotating coordinate system are obtained through Clark conversion and Park conversion in sequence, so that complete decoupling of exciting current and torque current is realized to facilitate control.
The specific process of the step 1) is as follows:
firstly, establishing a mathematical model under an A-B-C three-phase static coordinate system, wherein a voltage equation of the A-B-C three-phase static coordinate system is as follows:
wherein R issIs stator resistance, UA、UB、UCIs a stator three-phase voltage iA、iB、iCFor stator three-phase currents, ΨsA、ΨsB、ΨsCThe stator is a stator three-phase full magnetic linkage, and the vector form is as follows:
in the formula psisFor stator flux linkage, USIs the stator voltage; i.e. isIs the stator current;
the flux linkage equation is:
in the formula, ΨfA、ΨfB、ΨfCFlux linkage i for three-phase interlinkage of permanent magnet field and statorsA、isB、isCRespectively representing A, B, C three-phase stator currents, LsIn order to realize the synchronous inductance of the stator,
since the distribution of the air gaps is uniform, the rotor does not affect the self-inductance and the mutual inductance of the stator and A, B, C phases, so they are constant. L isA＝LB＝LC＝Lsσ+LmlWherein L isA、LB、LCFor self-induction of each phase, LmlExciting inductance for each phase; l isSσIs the leakage inductance of each phase;
the torque equation:
the electromagnetic torque is considered as a result of the interaction between the stator, rotor and armature, and is expressed as:
wherein p is the number of pole pairs, TeBeing electromagnetic torque, ΨfMagnetic linkage psi linking the permanent magnet field with the statorsA stator flux linkage;
mechanical equation of motion:
ωmas mechanical angular speed of the rotor, TLThe load torque is J, the moment of inertia is J, and the damping coefficient of the motor is B;
and finally obtaining a mathematical model under a d-q axis two-phase rotating coordinate system through Clark transformation and Park transformation to realize complete decoupling of exciting current and torque current so as to perform vector control:
the flux linkage equation:
in the formula, Ψd、ΨqIs the quadrature-direct component of the stator flux linkage, Ld、LqComponent of stator inductance in d, q axes, id、iqD and q axis stator currents;
voltage equation:
in the formula of Ud、UqThe quadrature-direct component, omega, of the stator voltageeRepresenting the rotor angular velocity.
The torque equation:
in the formula, Ld、LqThe inductance values are direct axis and quadrature axis inductance values; therefore, the decoupling of the torque is realized under the d-q axis, and the torque equation is as follows:
2) designing an extended sliding mode observer and determining observer related parameters: according to a mechanical motion equation of the PMSM, a damping coefficient parameter error, a rotational inertia parameter error and a load torque system disturbance are used as an extended system state, an extended state equation is established and used for designing an extended sliding mode observer, and the stability of the observer is ensured by considering a Lyapunov function.
The motor's kinetic equation is expressed as follows:
wherein B is0、J0Is a rough estimation of real parameters, Δ B, Δ J are parameter errors between the real system and its rough estimation, and the moment of inertia J ═ J0+ Δ J, damping coefficient B ═ B0+ Δ B, ω is the rotational speed, d represents disturbances including parameter errors and load disturbances;
considering the disturbance d as an extended system state, in order to perform parameter estimation, the extended sliding mode observer is designed as follows:
wherein,
is an estimate of the disturbance,
is an estimate of the velocity, m is a sliding mode parameter, usmoRepresents the sliding mode observer signal and usmoEta, sgn (S), eta is real number, S is sliding mode surface and negative value, and is designed as
The error equation is now obtained as follows:
error of the measurement
In order to ensure the sliding mode, parameters of the observer must be reasonably selected, namely the stable condition of the sliding mode variable structure must be met; thus, consider the following Lyapunov function: v is 0.5s2V and s represent the speed versus time in a motion system, differentiating V from time t:
namely:
in order to ensure the stability of the extended sliding-mode observer, a stability condition must be satisfied
Eta is<-|e2-B0e1In practical application, the following parameter adaptation law is adopted: eta ═ l | e2-B0e1|,l>1, l is the safety factor of the sliding mode; in general, l ═ 2 is sufficient to ensure the stability of the observer.
It can be seen that the error e1And derivatives thereof
Can converge to zero along a sliding mode occurring within a limited time, i.e.
Therefore, the error equation is simplified to
Namely, it is
Thus, e2The results of (a) are expressed as: e.g. of the type2＝e-mt[C+∫r·emtdt]Where e is a mathematical constant and C is a constant, in order to ensure a disturbance estimation error e2Converging to zero, and selecting sliding mode parameters as parameters m of disturbance estimation>0; therefore, the selection of the parameters of the extended sliding-mode observer is constrained by η and m;
as shown in FIG. 2, the speed after the sliding mode occurs
Observer equation simplification to
Thus, the equation is obtained:
the observer is equivalent to a low-pass filter after the sliding mode occurs, as shown in fig. 3; therefore, the disturbance observation effect of the extended sliding mode observer is equivalent to the output of the actual system disturbance of the filtering. Since the cut-off frequency of the low-pass filter is the same as the value of m, the design can be arbitrarily carried out according to the buffeting suppression requirement of the observer. Therefore, the output of the observer does not contain sliding mode buffeting caused by a low-pass filter and can be directly used for system control.
3) Observing system disturbance information by using the proposed extended sliding-mode observer, and extracting a damping coefficient, a rotational inertia and a load torque from the system disturbance information: firstly, the permanent magnet synchronous motor runs at two different steady-state speeds, the damping coefficient is estimated by utilizing the actually measured speed information and the estimated disturbance, then the rotary inertia is estimated by respectively running the permanent magnet synchronous motor at two different constant acceleration or constant deceleration, and finally, the damping coefficient and the rotary inertia are directly used for estimating the load torque.
As shown in fig. 4, when the motor is operating at a first steady-state rotational speed ω (t), based on the extended sliding-mode observer and the disturbance d, the following disturbance estimate is obtained:
after a time delay τ of the motor, the disturbance of the second steady speed ω (t + τ) is estimated as follows,
when the permanent magnet synchronous motor control system reaches the steady-state rotating speed, the load torque TLRegarded as a constant, the above two equations are subtracted:
therefore, the temperature of the molten metal is controlled,
writing:
therefore, the temperature of the molten metal is controlled,obtaining an estimated parameter
Comprises the following steps:
when the motor is in a first constant acceleration state ac1When the method is operated, based on an extended sliding-mode observer and a disturbance equation, the B estimation value obtained in the previous step is substituted, and the following disturbance estimation value can be obtained:
then, by ensuring that the two different constant accelerations correspond exactly to two different time periods, respectively, after a time delay τ, the second constant acceleration state ac2The interference estimate of (c) is given by:
the estimation parameters can be obtained by subtracting and sorting the two formulas
Raw estimate B in the equation of state when parameters B and J are accurately estimated0And J0Estimated parameters
And
instead, the extended sliding-mode observer is then rewrittenComprises the following steps:
at this time, the updated estimated disturbance
Expressed as:
it can be seen that the updated extended sliding-mode observer has the capability of estimating the load torque, and therefore, in practical applications, the proposed extended sliding-mode observer is used to estimate B and J, or to estimate the load torque T on-line in real time with B and J being knownL。
The method for identifying the mechanical parameters is simulated by using a Matlab simulation platform, a system template adopts a vector control structure, and i is selecteddThe identification results of the three parameters are respectively shown in fig. 5, 6 and 7, and the comparison of the actual data of the motor can find that the identification results are substantially consistent with the actual values. Therefore, the validity of the mechanical parameter identification algorithm is verified.
In summary, according to the actual control system of the permanent magnet synchronous motor, aiming at the problem that the control performance of the permanent magnet synchronous motor is affected due to variable load conditions, the extended mechanical parameter sliding mode observer provided by the invention can observe the mechanical parameters of the permanent magnet synchronous motor in real time and feed back the mechanical parameters to the controller to adjust the parameters in time, so that system disturbance is inhibited, and good dynamic performance and stability of the system are ensured; compared with the prior art, the mechanical parameter identification based on the extended sliding-mode observer provides an effective way for improving the self-regulation control of the permanent magnet synchronous motor under the condition of variable load, and can be widely applied to a system of complex systems such as an electric automobile, a flywheel energy storage system, a wind energy conversion system and the like.
Claims (6)
1. A permanent magnet synchronous motor mechanical parameter identification method based on an extended sliding-mode observer is characterized by comprising the following steps:
1) establishing a mathematical model of the surface-mounted permanent magnet synchronous motor, and performing coordinate transformation by adopting vector control: firstly, establishing a mathematical model under an A-B-C three-phase static coordinate system to obtain a phase voltage equation, a flux linkage equation, a torque equation and a mechanical motion equation of each phase, and then obtaining the mathematical model under an alpha-beta two-phase static coordinate system and a d-q axis two-phase rotating coordinate system through Clark conversion and Park conversion in sequence to realize complete decoupling of exciting current and torque current so as to be convenient for control;
2) designing an extended sliding mode observer and determining observer related parameters: according to a mechanical motion equation of the PMSM, taking a damping coefficient parameter error, a rotational inertia parameter error and load torque system disturbance as an extended system state, establishing an extended state equation for designing an extended sliding mode observer, and ensuring the stability of the observer by considering a Lyapunov function;
3) observing system disturbance information by using the proposed extended sliding-mode observer, and extracting a damping coefficient, a rotational inertia and a load torque from the system disturbance information: firstly, the permanent magnet synchronous motor runs at two different steady-state speeds, the damping coefficient is estimated by utilizing the actually measured speed information and the estimated disturbance, then the rotary inertia is estimated by respectively running the permanent magnet synchronous motor at two different constant acceleration or constant deceleration, and finally, the damping coefficient and the rotary inertia are directly used for estimating the load torque.
2. The method for identifying the mechanical parameters of the permanent magnet synchronous motor based on the extended sliding-mode observer according to claim 1, wherein the specific process in the step 1) is as follows:
firstly, establishing a mathematical model under an A-B-C three-phase static coordinate system, wherein a voltage equation of the A-B-C three-phase static coordinate system is as follows:
wherein R issIs stator resistance, UA、UB、UCIs a stator three-phase voltage iA、iB、iCFor stator three-phase currents, ΨsA、ΨsB、ΨsCThe stator is a stator three-phase full magnetic linkage, and the vector form is as follows:
in the formula psisFor stator flux linkage, USIs the stator voltage; i.e. isIs the stator current;
the flux linkage equation is:
in the formula, ΨfA、ΨfB、ΨfCFlux linkage i for three-phase interlinkage of permanent magnet field and statorsA、isB、isCRespectively representing A, B, C three-phase stator currents, LsIn order to realize the synchronous inductance of the stator,
LA＝LB＝LC＝Lsσ+Lmlwherein L isA、LB、LCFor self-induction of each phase, LmlExciting inductance for each phase; l isSσIs the leakage inductance of each phase;
the torque equation:
the electromagnetic torque is considered as a result of the interaction between the stator, rotor and armature, and is expressed as:
wherein p is the number of pole pairs, TeBeing electromagnetic torque, ΨfMagnetic linkage psi linking the permanent magnet field with the statorsA stator flux linkage;
mechanical equation of motion:
ωmas mechanical angular speed of the rotor, TLThe load torque is J, the moment of inertia is J, and the damping coefficient of the motor is B;
and finally obtaining a mathematical model under a d-q axis two-phase rotating coordinate system through Clark transformation and Park transformation to realize complete decoupling of exciting current and torque current so as to perform vector control:
the flux linkage equation:
in the formula, Ψd、ΨqIs the quadrature-direct component of the stator flux linkage, Ld、LqComponent of stator inductance in d, q axes, id、iqD and q axis stator currents;
voltage equation:
in the formula of Ud、UqThe quadrature-direct component, omega, of the stator voltageeRepresenting the rotor angular velocity;
the torque equation:
in the formula, Ld、LqThe inductance values are direct axis and quadrature axis inductance values; therefore, the decoupling of the torque is realized under the d-q axis, and the torque equation is as follows:
3. the method for identifying the mechanical parameters of the permanent magnet synchronous motor based on the extended sliding-mode observer according to claim 2, wherein in the step 2), the kinetic equation of the motor is expressed as follows:
wherein B is0、J0Is a rough estimate of the true parameter, the moment of inertia J ═ J0+ Δ J, damping coefficient B ═ B0+ Δ B, Δ J are the parameter errors between the real system and its rough estimate, ω is the rotation speed, d represents the disturbance, including parameter errors and load disturbances;
considering the disturbance d as an extended system state, in order to perform parameter estimation, the extended sliding mode observer is designed as follows:
wherein,
is an estimate of the disturbance,
is an estimate of the velocity, m is a sliding mode parameter, usmoRepresents the sliding mode observer signal and usmoEta, sgn (S), eta is real number, S is sliding mode surface and negative value, and is designed as
The error equation is now obtained as follows:
error of the measurement
Intermediate volume
In order to ensure the occurrence of the sliding mode, the stable condition of the variable structure of the sliding mode must be met; thus, consider the following Lyapunov function: v is 0.5s2V and s represent the speed versus time in a motion system, differentiating V from time t:
namely:
in order to ensure the stability of the extended sliding-mode observer, a stability condition must be satisfied
Thus η<-|e2-B0e1In practical application, the following parameter adaptation law is adopted: eta ═ l | e2-B0e1|,l>1, l is the safety factor of the sliding mode; error e1And derivatives thereof
Can converge to zero along a sliding mode occurring within a limited time, i.e.
Therefore, the error equation is simplified to
Namely, it is
Thus, e2The results of (a) are expressed as: e.g. of the type2＝e-mt[C+∫r·emtdt]Where e is a mathematical constant and C is a constant, in order to ensure a disturbance estimation error e2Converging to zero, and selecting sliding mode parameters as parameters m of disturbance estimation>0; therefore, the selection of the parameters of the extended sliding-mode observer is constrained by η and m;
speed after occurrence of sliding mode
Observer equation simplification to
Thus, the equation is obtained:
the observer is equivalent to a low-pass filter after the sliding mode occurs; therefore, the disturbance observation effect of the extended sliding mode observer is equivalent to the output of the actual system disturbance of the filtering.
4. The method for identifying the mechanical parameters of the permanent magnet synchronous motor based on the extended sliding-mode observer according to claim 3, wherein in the step 3), the permanent magnet synchronous motor is operated at two different stable speeds, so as to estimate the damping coefficient B;
when the motor runs at a first steady-state rotating speed omega (t), based on the extended sliding-mode observer and the disturbance d, the following disturbance estimation is obtained:
after a time delay τ of the motor, the disturbance of the second steady speed ω (t + τ) is estimated as follows,
when the permanent magnet synchronous motor control system reaches the steady-state rotating speed, the load torque TLRegarded as a constant, the above two equations are subtracted:
therefore, the temperature of the molten metal is controlled,
writing:
thus, an estimated parameter is obtained
Comprises the following steps:
5. the method for identifying the mechanical parameters of the permanent magnet synchronous motor based on the extended sliding-mode observer according to claim 4, wherein in the step 3), when the motor is in the first constant acceleration state ac1When in operation, based on the extended sliding-mode observer and the disturbance equation, the previous steps are performedThe resulting B estimate is substituted, and the following disturbance estimate can be obtained:
then, by ensuring that the two different constant accelerations correspond exactly to two different time periods, respectively, after a time delay τ, the second constant acceleration state ac2The interference estimate of (c) is given by:
the estimation parameters can be obtained by subtracting and sorting the two formulas
6. The method for identifying the mechanical parameters of the permanent magnet synchronous motor based on the extended sliding-mode observer according to claim 5, wherein in the step 3), when the parameters B and J are accurately estimated, the original estimation B in the state equation is adopted0And J0Estimated parameters
And
instead, the extended sliding-mode observer is then rewritten as:
at this time, the updated estimated disturbance
Expressed as:
it can be seen that the updated extended sliding-mode observer has the capability of estimating the load torque, and therefore, in practical applications, the proposed extended sliding-mode observer is used to estimate B and J, or to estimate the load torque T on-line in real time with B and J being knownL。
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