CN110557070A - permanent magnet synchronous motor parameter identification method based on second-order sliding-mode observer - Google Patents
permanent magnet synchronous motor parameter identification method based on second-order sliding-mode observer Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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Abstract
The invention relates to the technical field of motor parameter identification, in particular to a permanent magnet synchronous motor parameter identification method based on a second-order sliding-mode observer, which comprises the following steps of: firstly, acquiring parameters of a permanent magnet synchronous motor under a dq axis reference coordinate system; secondly, constructing a sliding-mode observer capable of expanding by taking the mechanical angular velocity and the load torque as observation objects; and a third step of constructing a second-order sliding mode observer to identify the load torque of the permanent magnet synchronous motor by taking the mechanical angular speed and the load torque as observation objects on the basis of the second step, and a fourth step of identifying the rotational inertia of the permanent magnet synchronous motor by adopting a direct calculation method or a PI regulator method on the basis of the identified load torque. The invention considers the changes of the rotational inertia, the electromagnetic torque and the viscous friction, and can effectively inhibit buffeting while ensuring the precision of the load torque.
Description
Technical Field
the invention relates to the technical field of motor parameter identification, in particular to a permanent magnet synchronous motor parameter identification method based on a second-order sliding-mode observer.
Background
Permanent Magnet Synchronous Motor (PMSM) drives have found widespread use in various electromechanical servo systems over the last several decades. Parameters of a driving system such as load torque, rotational inertia and the like have important significance for improving controller design in industrial application. For example, when the moment of inertia is used to design a speed loop controller, the drive system will have a higher speed tracking accuracy. In addition, when the load torque is used as a feedforward term of the reference torque, the load disturbance resistance of the driving system is remarkably improved. However, the load torque is generally unknown, and the moment of inertia can vary significantly with the shape and size of the mechanical load. In some practical permanent magnet synchronous motor drive systems, the moment of inertia and load torque are time-varying and difficult to obtain online. In this case, the unmatched moment of inertia or load torque may not be strong enough to ensure the speed control performance of the drive system. For this purpose, recognition algorithms for load torque and moment of inertia are proposed.
The load torque identification method mainly comprises model reference adaptive control, a Kalman filter, a sliding-mode observer and the like. In practical research and application, the load torque is estimated by constructing various types of state observers. The sliding-mode observer has the advantages of simplicity in implementation, strong uncertainty resistance, strong anti-interference capability and the like, so that more and more attention is paid to the sliding-mode observer.
The sliding-mode observer is used for enabling the system structure to change along with the current state, so that the system moves up and down according to a given track, namely the sliding-mode observer is used for realizing the sliding-mode motion. The control has certain switching characteristics and is in an intermittent switching working state, so that the control has certain robustness on parameter conversion and disturbance. The main problem of the application of sliding-mode observers in servo systems is the well-known phenomenon of flutter, i.e. the generation of high frequency harmonics. Therefore, scholars at home and abroad propose several methods for overcoming buffeting, including a classical method, an intelligent method and an observer method. The classical methods mainly include a quasi-sliding mode method, an approach method and the like. Intelligent methods include fuzzy control, artificial neural networks, and the like. An advanced control theory is applied to the buffeting reduction, but the calculation amount is large, and the quick real-time control is difficult to realize. Buffeting caused by uncertainty can be well eliminated by adopting an observer method.
The rotational inertia identification method can be divided into an off-line identification method and an on-line identification method. The off-line identification method mainly comprises a direct calculation method, an acceleration and deceleration method and a limited torque acceleration method. The off-line identification method has the advantages that the calculation conditions can be set according to the algorithm, and meanwhile, the problem that the change of the rotational inertia cannot be reflected in real time is also obvious. The online rotational inertia identification method mainly comprises a sliding-mode observer, a Kalman filter, model reference adaptive control and the like. The Kalman filtering method takes the rotational inertia as a state variable, and the identification value of the rotational inertia is directly output by a filtering algorithm. The model reference adaptive observation technology takes the deviation of the speed as feedback, and the deviation of the speed model tends to zero through the identification of the rotational inertia value.
in conventional sliding-mode observer based methods, the sign function will cause high frequency flutter and buffeting problems, which may cause system oscillation, performance degradation, and even system instability. Therefore, most of the existing load torque identification methods based on the sliding mode observer are mainly focused on inhibiting buffeting, and influence of parameter distortion on identification performance is ignored. Although useful information of the estimated parameters can be obtained by adding a low-pass filter, the introduction of the low-pass filter causes a phase delay, thereby affecting the estimation accuracy and the performance of the driving system. Therefore, appropriate compensation is needed to mitigate the effects of the low pass filter, especially when estimating a continuous phase delayed ac signal. Meanwhile, in some load torque identification methods, the rotational inertia is considered to be constant, and when the rotational inertia changes, no analysis is performed on the observation performance. When the transmission system is in a dynamic state, the rotational inertia has great influence on the observation precision of the load moment.
In the aspect of identifying the rotational inertia, in the off-line identification method, in order to simplify the problem, a direct calculation method only calculates the rotational inertia of the rotor of the servo motor and ignores the friction torque, and the influence of the friction torque is weakened by taking the average value of the speed and the acceleration and deceleration time of the rotor. The method has no error iterative convergence process, so that the online tracking cannot be realized and the identification result fluctuates to a certain extent. The acceleration and deceleration method and the limited torque acceleration method are widely applied to offline rotational inertia identification, but the methods are low in precision, long in identification time and large in storage space. The on-line identification method has a large calculation amount and requires a digital signal processor to have higher data processing speed and storage capacity. And when the load disturbance in the transient process is changed in a large range, the old load torque estimation value still participates in the recursion process, so that the identification distortion is caused.
Disclosure of Invention
To solve the above technical problems, the present invention aims to: the method for identifying the parameters of the permanent magnet synchronous motor based on the second-order sliding-mode observer considers the changes of rotational inertia, electromagnetic torque and viscous friction, and can effectively inhibit buffeting while ensuring the precision of load torque.
The technical scheme adopted by the invention for solving the technical problem is as follows:
the permanent magnet synchronous motor parameter identification method based on the second-order sliding-mode observer specifically comprises the following steps:
firstly, acquiring parameters of the permanent magnet synchronous motor under a dq-axis reference coordinate system, wherein the parameters comprise the number of pole pairs P and voltage components u of stator voltage on d and q axesd、uqCurrent component i of stator current in d and q axesd、iqinductance component L of stator inductance on d and q axesd、LqStator resistance Rscomponent ψ of flux linkage in d and q axesd、ψqangular velocity ω of motorm；
and secondly, taking the mechanical angular velocity and the load torque as observation objects, and describing the extended sliding mode observer as follows:
In formula (1), J, Te、TLF and omegamRespectively rotational inertia, electromagnetic torque, load torque, viscous friction coefficient and motor angular velocity,andRespectively, moment of inertia, electromagnetic torqueEstimated values of load torque, viscous friction coefficient and motor angular velocity; k is sliding mode gain, g is feedback gain;
And thirdly, on the basis of the second step, taking the mechanical angular velocity and the load torque as observation objects, and constructing a second-order sliding mode observer for identifying the load torque of the permanent magnet synchronous motor, wherein the second-order sliding mode observer is as follows:
In the formulaωsIs a control law of the sliding-mode observer, h is a feedback gain,AndEstimated values of electromagnetic torque, load torque, viscous friction coefficient and mechanical angular velocity, respectively;
control law gamma of sliding-mode observerωsthe expression is as follows:
in the formula (3), the reaction mixture is,γ、lgand c are sliding mode control rate design parameters and meet min (gamma, l)gC) > 0, p, q are odd numbers and satisfy p/q>1，Sωfor second-order slip-form switching surfaces, SωThe expression is as follows:
In the formula Is fωthe first derivative of (a).
Preferably, the method for identifying parameters of the permanent magnet synchronous motor based on the second-order sliding-mode observer further includes the following steps:
And fourthly, on the basis of the identified load torque, identifying the rotational inertia of the permanent magnet synchronous motor by adopting a direct calculation method or a PI regulator method.
Preferably, the direct calculation method is suitable for the driving system just entering the steady state, and the specific algorithm is as follows:
When the drive system enters a steady state at T ═ x, the load torque T is loaded at that timeL(x) Can be expressed as:
TL(x)＝Te(x)-Fωm(x) (5)
TL(x) From t-x to t-x1is kept constant, the moment of inertia is directly calculated by the following expression:
In the formulathe value of the moment of inertia at t x,Estimated load torque for initial moment of inertia value
Let Δ x be x-x1If Δ x is too large, it is difficult to satisfy the assumption that the load torque is constant in the Δ x time. If Δ x is too small, there may be large computational errors due to sampling noise or other non-idealities.
preferably, the PI regulator method is suitable for the moment when the driving system is just switched into the dynamic state from any steady state, and the load torque observation error always exists in the drivingdynamic state of the system, load torque observation error fTThe discrete form is expressed as follows:
The rule for identifying the moment of inertia using a PI regulator is as follows:
In the formula kpand kiproportional and integral gains, T, respectivelysis the sampling time, sT(x) The expression of (a) is as follows:
sT(x)＝sign[Te(x)-TL(x)-Fωm(x)] (9)
J/[ T ] when the drive system goes to steady statee(x)-TL(x)-Fωm(x)]the term tends to be infinite, possibly leading to recognition failure, so s is usedT(x) Alternative J/[ T ]e(x)-TL(x)-Fωm(x)]。
Preferably, a cut-off frequency ofThe low-pass filter of (a) suppresses the buffeting signal of a second order sliding mode observer, wherein,k is the sliding mode gain, g is the feedback gain,is an estimate of the moment of inertia.
compared with the prior art, the invention has the following beneficial effects:
the invention provides a novel load torque second-order sliding mode observer, which considers the changes of rotational inertia, electromagnetic torque and viscous friction, can effectively inhibit buffeting while ensuring the precision of the load torque, has higher estimation precision and faster convergence speed, and provides two methods for estimating the rotational inertia.
Drawings
FIG. 1 is a block flow diagram of the present invention.
Detailed Description
example 1:
as shown in fig. 1, the method for identifying parameters of a permanent magnet synchronous motor based on a second-order sliding-mode observer includes the following steps:
firstly, acquiring parameters of the permanent magnet synchronous motor under a dq-axis reference coordinate system, wherein the parameters comprise the number of pole pairs P and voltage components u of stator voltage on d and q axesd、uqCurrent component i of stator current in d and q axesd、iqInductance component L of stator inductance on d and q axesd、LqStator resistance Rscomponent ψ of flux linkage in d and q axesd、ψqangular velocity ω of motorm；
And secondly, taking the mechanical angular velocity and the load torque as observation objects, and describing the extended sliding mode observer as follows:
In formula (1), J, Te、TLF and omegamRespectively rotational inertia, electromagnetic torque, load torque, viscous friction coefficient and motor angular velocity,AndRespectively obtaining estimated values of rotational inertia, electromagnetic torque, load torque, viscous friction coefficient and motor angular speed; k is sliding mode gain, g is feedback gain;
and thirdly, on the basis of the second step, taking the mechanical angular velocity and the load torque as observation objects, and constructing a second-order sliding mode observer for identifying the load torque of the permanent magnet synchronous motor, wherein the second-order sliding mode observer is as follows:
in the formulaωsIs a control law of the sliding-mode observer, h is a feedback gain,andestimated values of electromagnetic torque, load torque, viscous friction coefficient and mechanical angular velocity, respectively;
Control law gamma of sliding-mode observerωsThe expression is as follows:
In the formula (3), the reaction mixture is,γ、lgand c are sliding mode control rate design parameters and meet min (gamma, l)gc) > 0, p, q are odd numbers and satisfy p/q>1，SωFor second-order slip-form switching surfaces, SωThe expression is as follows:
in the formula Is fωThe first derivative of (a);
and fourthly, on the basis of the identified load torque, identifying the rotational inertia of the permanent magnet synchronous motor by adopting a direct calculation method or a PI regulator method.
The direct calculation method is suitable for the driving system just entering a steady state, and the specific algorithm is as follows:
When the drive system enters a steady state at T ═ x, the load torque T is loaded at that timeL(x) Can be expressed as:
TL(x)＝Te(x)-Fωm(x) (5)
TL(x) From t-x to t-x1is kept constant, the moment of inertia is directly calculated by the following expression:
In the formulaThe value of the moment of inertia at t x,Estimated load torque for initial moment of inertia value
let Δ x be x-x1if Δ x is too large, it is difficult to satisfy the assumption that the load torque is constant in the Δ x time. If Δ x is too small, there may be large computational errors due to sampling noise or other non-idealities.
The PI regulator method is suitable for the situation that a driving system just enters a dynamic state from any steady state, at the moment, a load torque observation error always exists in the dynamic state of the driving system, and a load torque observation error fTthe discrete form is expressed as follows:
The rule for identifying the moment of inertia using a PI regulator is as follows:
in the formula kpAnd kiProportional and integral gains, T, respectivelysIs the sampling time, sT(x) The expression of (a) is as follows:
sT(x)＝sign[Te(x)-TL(x)-Fωm(x)] (9)
J/[ T ] when the drive system goes to steady statee(x)-TL(x)-Fωm(x)]The term tends to be infinite, possibly leading to recognition failure, so s is usedT(x) Alternative J/[ T ]e(x)-TL(x)-Fωm(x)]。
With a cut-off frequency ofthe low-pass filter of (a) suppresses the buffeting signal of a second order sliding mode observer, wherein,k is the sliding mode gain, g is the feedback gain,Is an estimate of the moment of inertia.
The determination process of the second-order sliding mode observer is as follows:
in the dq-axis reference frame, the voltage equation of the permanent magnet synchronous motor can be expressed as:
U in formula (10)d、uqthe voltage components of the stator voltage in d and q axes, id、iqThe current components of the stator current in d and q axes, Ld、Lqthe inductance component of the stator inductance in d and q axes, RsIs stator resistance, #d、ψqcomponent of the flux linkage in the d and q axes, ωefor electrical angular velocity, psi, of the motorfIs a permanent magnetmagnetic flux linkage.
The electromagnetic torque equation of the permanent magnet synchronous motor is as follows:
in the formula TeIs the electromagnetic torque, and P is the pole pair number.
the equation of motion of a permanent magnet synchronous motor is as follows:
wherein J is moment of inertia, TLFor load torque, F is the viscous friction coefficient.
When the motor is at a constant speed, the load torque can be expressed as:
TL＝Te-Fωm (13)
In an actual permanent magnet synchronous motor drive system, the electromagnetic torque can be calculated by equation (11), where ψf、Ld、Lqthe estimation can be performed by a suitable parameter identification method. In addition, under no-load condition, by F ═ Te/ωmThe coefficient of viscous friction at different speeds was calculated and then approximated by a curve fitting method.
Assuming that the load torque remains constant for a short time, i.e.then, according to equation (3), an extended state equation of the permanent magnet synchronous motor can be obtained:
With mechanical angular velocity and load torque as the observation targets, the extended sliding-mode observer can be described as:
Formula (III) J, Te、TLF and omegamRespectively rotational inertia, electromagnetic torque, load torque, viscous friction coefficient and motor angular velocity,AndRespectively obtaining estimated values of rotational inertia, electromagnetic torque, load torque, viscous friction coefficient and motor angular speed; k is the sliding mode gain and g is the feedback gain. Order to Subtracting equation (14) from equation (15) yields the following equation:
With the mechanical angular velocity and the load torque as observation objects, a second-order sliding-mode observer is designed as follows:
In the formulaωsis a control law of the sliding-mode observer, and h is a feedback gain.
Subtracting equation (14) from equation (17) yields the following equation:
Defining a second order sliding mode switching surface Sω,SωThe expression is as follows:
in the formula, gamma is a sliding mode design parameter, and p and q are odd numbers, so that p/q is more than 1.
To SωTwo sides are derived:
to verify the stability of the observer, the Lee function was chosen to be V-0.5 s2And obtaining the following derivative of V:
in the formula
the sliding-mode observer control law expression is as follows:
known from the sliding mode variable structure control theory, the second-order sliding mode switching surface S is under the action of the control lawωwill converge in a limited time. After the second-order sliding mode switching surface converges, the variable fω、And entering a sliding mode motion state of the hybrid terminal and finally converging to zero. Thus the observation error is satisfiedTherefore, the sliding mode control law is a continuous and smooth signal and can be directly used for estimating the load torque.
from equation (16), this can be seen:
The error equation of the load torque can be derived from equation (23) as follows:
Order toTo obtain the following formula:
In the formulaBased on the stability theory, the stability condition of the load torque error equation represented in equation (24) is as follows:
the differential of equation (25) yields:
Wherein C is a constant. Because of the fact thatSo that the sliding mode gainAnd because ofg<0, so in formula (25)Gradually tending towards 0 with increasing t. Equation (27) can now be expressed as:
When the motor is in a constant rotating speed state, T is known from the formula (12)e-TL-FωmWhen 0, the expression of formula (28) is as follows:
fT＝ΔTe-ΔFωm (29)
Based on the above analysis, it can be found that the load torque observation error and Δ T are observed under the state of the rotation speed variationeΔ F and Jeit is related. Load torque observation error and J under constant rotation speed stateeIs irrelevant.
Frequency determination process for suppressing a chattering signal:
The main problem of the sliding mode observer is the phenomenon of buffeting, which reduces the discriminatory ability of load torque and moment of inertia. Therefore, in order to obtain better performance, it is necessary to suppress the chattering phenomenon in the load torque observer. Defining w as the dither signal, error equation (16) can be rewritten as follows:
From equation (30), the load torque error equation with dither signal w may be derived as follows:
The transfer function of equation (31) is as follows:
In the formulaas can be seen from the formula (32), the cutoff frequency isThe low pass filter of (3) suppresses the dither signal.
To further overcome the problem of buffeting in the proposed load torque observer, the sign function sign (x) is replaced by a saturation function sat (x), the expression of which is as follows:
Wherein Δ > 0. Based on the above analysis, smallerOr a larger Δ will improve the buffeting suppression effect of the load torque observer, but at the same time, the dynamic performance becomes worse, and it is necessary to select the parameters g, k, and Δ correctly in practice.
to derive a calculation expression for the moment of inertia, Δ T is ignoredeand Δ F, equation (28) may be expressed as:
when this is the case (34), there are only two unknowns, namely TLAnd J. Thus, if the drive system is in a dynamic state and the load torque is known, the moment of inertia J can be calculated directly, and the load torque can be obtained directly in the steady state by equation (13).
direct calculation error analysis:
Order toIs composed ofCombining equations (28) and (34) to obtain:
According to equation (6), in an actual permanent magnet synchronous motor drive, the moment of inertia can be calculated by the following expression:
By substituting formula (29) or formula (35) for formula (36), the following compounds are obtained:
And (6) and (37) are combined to obtain an error expression of the moment of inertia:
as can be seen from the formula (38),ΔTeAnd Δ F affects the error in the moment of inertia. The Δ T can be effectively reduced by some suitable parameter estimation methodeAnd Δ F. Furthermore, the formula (38) showsTo JeDCInfluence ratio of (1) Δ TeThe sum Δ F is larger, and in actual permanent magnet synchronous motor driving, in order to reduce the calculation error of the rotational inertia, a small value is usually selected
error analysis of the identification method of the PI regulator method:
The purpose of the PI regulator method is to makeminimization, when fTI | → 0, the exact moment of inertia is obtained. In a practical PMSM drive, if T is consideredeAnd time-varying of F, it is necessary to useto replace fTi, |, i.e.:
the combined type (28) and the formula (39) can obtain:
When the error of the identification method based on the PI regulator method is 0, that isthen, in combination with formula (40), the following formula is obtained:
In the PI regulator approach, the time to reach the convergence state is typically short, ωm(x) And ωm(x2) Are usually closed to each other, so that from equation (41) Δ F vs. J can be derivedePIThe effect of (a) is limited. At the same time, let Δ F ω because Δ F is usually smallm(x2)≈ΔFωm(x)，Fωm(x2)≈Fωm(x) In that respect Combining formula (13) and formula (41) to obtain the following formula:
Let Delta Te(x2)＝mTe(x2)，ΔTe(x)＝nTe(x) M and n are constants satisfying m>n>0, then equation (42) can be converted to:
From equation (43), the error in the estimation of the electromagnetic torque and the error J in the identification method based on the PI regulator method can be seenePIThere is a direct relationship. In order to reduce the identification error of the moment of inertia, the estimation accuracy and consistency of the electromagnetic torque should be ensured, i.e. the estimation error is reduced as much as possibleAndThe value of (c).
Claims (5)
1. A permanent magnet synchronous motor parameter identification method based on a second-order sliding-mode observer is characterized by comprising the following steps:
Firstly, acquiring parameters of the permanent magnet synchronous motor under a dq-axis reference coordinate system, wherein the parameters comprise the number of pole pairs P and voltage components u of stator voltage on d and q axesd、uqcurrent component i of stator current in d and q axesd、iqinductance component L of stator inductance on d and q axesd、LqStator resistance Rscomponent ψ of flux linkage in d and q axesd、ψqangular velocity ω of motorm；
And secondly, taking the mechanical angular velocity and the load torque as observation objects, and describing the extended sliding mode observer as follows:
in formula (1), J, Te、TLf and omegamrespectively rotational inertia, electromagnetic torque, load torque, viscous friction coefficient and motor angular velocity,AndRespectively obtaining estimated values of rotational inertia, electromagnetic torque, load torque, viscous friction coefficient and motor angular speed; k is sliding mode gain, g is feedback gain;
and thirdly, on the basis of the second step, taking the mechanical angular velocity and the load torque as observation objects, and constructing a second-order sliding mode observer for identifying the load torque of the permanent magnet synchronous motor, wherein the second-order sliding mode observer is as follows:
in the formulaωsis a control law of the sliding-mode observer, h is a feedback gain,AndEstimated values of electromagnetic torque, load torque, viscous friction coefficient and mechanical angular velocity, respectively;
Control law gamma of sliding-mode observerωsThe expression is as follows:
In the formula (3), the reaction mixture is,γ、lgAnd c are sliding mode control rate design parameters and meet min (gamma, l)gC) > 0, p, q are odd numbers and satisfy p/q>1，Sωfor second-order slip-form switching surfaces, SωThe expression is as follows:
In the formula Is fωthe first derivative of (a).
2. the method for identifying the parameters of the permanent magnet synchronous motor based on the second-order sliding-mode observer according to claim 1, further comprising the following steps of:
And fourthly, on the basis of the identified load torque, identifying the rotational inertia of the permanent magnet synchronous motor by adopting a direct calculation method or a PI regulator method.
3. The method for identifying the parameters of the permanent magnet synchronous motor based on the second-order sliding-mode observer according to claim 2, wherein the direct calculation method is suitable for a driving system just before entering a steady state, and the specific algorithm is as follows:
When the drive system enters a steady state at T ═ x, the load torque T is loaded at that timeL(x) Can be expressed as:
TL(x)＝Te(x)-Fωm(x) (5)
TL(x) From t-x to t-x1Is kept constant, the moment of inertia is directly calculated by the following expression:
In the formulaThe value of the moment of inertia at t x,Estimated load torque for initial moment of inertia value
4. the method for identifying the parameters of the permanent magnet synchronous motor based on the second-order sliding-mode observer according to claim 2, wherein the PI regulator method is suitable for the situation that a load torque observation error always exists in a dynamic state of a driving system when the driving system is just switched into the dynamic state from any stable state,load torque observation error fTThe discrete form is expressed as follows:
The rule for identifying the moment of inertia using a PI regulator is as follows:
In the formula kpand kiProportional and integral gains, T, respectivelysis the sampling time, sT(x) The expression of (a) is as follows:
sT(x)＝sign[Te(x)-TL(x)-Fωm(x)] (9)
J/[ T ] when the drive system goes to steady statee(x)-TL(x)-Fωm(x)]The term tends to be infinite, possibly leading to recognition failure, so s is usedT(x) Alternative J/[ T ]e(x)-TL(x)-Fωm(x)]。
5. the method for identifying the parameters of the permanent magnet synchronous motor based on the second-order sliding-mode observer according to claim 1, wherein a cut-off frequency is adoptedthe low-pass filter of (a) suppresses the buffeting signal of a second order sliding mode observer, wherein,k is the sliding mode gain, g is the feedback gain,is an estimate of the moment of inertia.
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