CN109617482B - L2 sliding mode control method of permanent magnet synchronous motor - Google Patents

L2 sliding mode control method of permanent magnet synchronous motor Download PDF

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CN109617482B
CN109617482B CN201811652554.4A CN201811652554A CN109617482B CN 109617482 B CN109617482 B CN 109617482B CN 201811652554 A CN201811652554 A CN 201811652554A CN 109617482 B CN109617482 B CN 109617482B
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permanent magnet
synchronous motor
magnet synchronous
current
axis
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CN109617482A (en
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程勇
彭超洋
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Chongqing Qiulong Technology Co ltd
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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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention discloses an L2 sliding mode control method of a permanent magnet synchronous motor, which comprises the following steps: firstly, obtaining a feedback position; secondly, obtaining a position error; thirdly, obtaining given current of a q axis; obtaining d-axis current and q-axis current; fifthly, obtaining alpha axis voltage and beta axis voltage; and sixthly, carrying out SVPWM control on the permanent magnet synchronous motor. The method has the advantages of simple steps, convenience in implementation, good position tracking effect, high response speed, strong anti-interference capability, good robustness, strong practicability, good use effect and convenience in popularization and use.

Description

L2 sliding mode control method of permanent magnet synchronous motor
Technical Field
The invention belongs to the technical field of permanent magnet synchronous motor control, and particularly relates to an L2 sliding mode control method of a permanent magnet synchronous motor.
Background
The Permanent Magnet Synchronous Motor (PMSM) has the advantages of high power density, high efficiency, small volume and reliable operation, and is a speed regulating motor with good control performance. When a permanent magnet synchronous motor is disturbed, a motor control system is required to effectively track a given position and suppress the disturbance. The method is particularly important in places with high position requirements, so that how to inhibit the disturbance of the permanent magnet synchronous motor and realize position tracking becomes a research hotspot in the field of permanent magnet synchronous motor research.
In the prior art, the most widely used position control method is PID control, i.e. proportional-integral control, where P represents Proportion (distribution), I represents integral (Integration), and D represents derivative (Differentiation). The permanent magnet synchronous motor generally adopts PI control, because the system noise interference is increased after the differentiation is added. The PI control has the advantages of simple structure, convenient parameter adjustment and the like. However, the system under the control of the PI has weak interference resistance and is sensitive to parameter changes. Pure fragmented PI control has not been able to meet the requirements of system control. In order to solve these problems, v.m.hemandez-Guzman and r.silva-origoza disclose the paper "PI Control current loop of permanent magnet synchronous motor" (PI Control plus electric current loops for PM synchronous motors) in the IEEE Control Systems Technology (IEEE Transactions on Control Systems Technology) at volume 4, 2011, 19, wherein the mentioned adaptive PID Control method is complicated in algorithm and difficult in parameter adjustment relative to pure PI Control; a paper "Pm synchronous motor speed control using a hybrid fuzzy PI with a novel switching function" (Pm synchronous motor speed controlled hybrid-PI with novel switching functions), which is disclosed in IEEE machines and trades (IEEE Transactions on Magnetics) at volume 10, 45, 2009, sant and k.r.rajagopal, wherein a hybrid control system is mentioned, which uses a fuzzy algorithm for speed control while using PID control when the speed reaches steady state.
The self-adaptive control can adjust various parameters of the controller by extracting some information of the model, so that the control effect of the optimal permanent magnet synchronous motor can be interfered by the outside when the permanent magnet synchronous motor runs, and the self-adaptive control has the defects of large calculated amount and long time for achieving the optimal effect. The concept of fuzzy control (fuzzy logic control theory) is proposed in 1965 by the teaching of l.a.zadeh, and is a rule-based control, and an accurate mathematical model of a controlled object does not need to be established from the control experience of field operators and the knowledge of experts, so that the control theory is easy to understand, the design is simple, and the application is simple and convenient. However, the fuzzy control has low control precision and limited adaptive capacity, and is easy to generate oscillation phenomenon, so that a reasonable fuzzy approximator is found in practice, and no determined method is available.
Disclosure of Invention
The technical problem to be solved by the invention is to provide an L2 sliding mode control method of a permanent magnet synchronous motor aiming at the defects in the prior art, wherein the method has the advantages of simple steps, convenience in implementation, good position tracking effect, high response speed, strong anti-interference capability, good robustness, strong practicability, good use effect and convenience in popularization and use.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: an L2 sliding mode control method of a permanent magnet synchronous motor comprises the following steps:
step one, obtaining a feedback position: the position sensor periodically detects the position of the permanent magnet synchronous motor to obtain feedback positions at a plurality of moments and transmits the feedback positions to the processor;
step two, obtaining a position error: the processor calculates the difference between the feedback position and the given position to obtain a position error e; and calculating to obtain a derivative e' of the position error;
step three, obtaining given current of a q axis: the processor invokes the L2 synovial controller module based on the position error e and the derivative of the position error e', and based on the formula:
Figure BDA0001933279490000021
calculating q-axis given current
Figure BDA0001933279490000022
Wherein p is the pole pair number psi of the permanent magnet synchronous motorfIs the flux linkage of the permanent magnet synchronous motor, J is the rotational inertia of the permanent magnet synchronous motor, B is the friction factor of the permanent magnet synchronous motor, gamma is the suppression degree of given interference and gamma is>0, s is a sliding mode function, and the expression is:
s＝p1e+e′ (9)
wherein p is1Is a parameter of a sliding mode function and p1>0；
Step four, obtaining d-axis current and q-axis current: the A-phase current sensor detects the A-phase winding current of the stator of the permanent magnet synchronous motor and detects the A-phase winding current iaTransmitting to a processor; the B-phase current sensor detects the stator B-phase winding current of the permanent magnet synchronous motor and detects the detected B-phase winding current ibTransmitting to a processor; processor passes formula ic＝-(ia+ib) Calculating to obtain the stator C-phase winding current i of the permanent magnet synchronous motorcThen the A phase winding current iaPhase B winding current ibAnd C phase winding current icPerforming Clarke transformation to obtain alpha-axis current i under a two-phase static coordinate systemαAnd beta axis current iβFor the alpha axis current iαAnd beta axis current iβCarrying out Park conversion to obtain d-axis current idAnd q-axis current iq；
Step five, obtaining the alpha axis voltage and the beta axis voltage: processor definition d-axis given current
Figure BDA0001933279490000031
D-axis current idWith d-axis set current
Figure BDA0001933279490000032
Comparing to obtain d-axis current difference and comparing q-axis current iqWith q-axis set current
Figure BDA0001933279490000033
Comparing to obtain q-axis current difference, and respectively passing the d-axis current difference and the q-axis current difference through a current PI regulator to respectively output d-axis voltage udAnd q-axis voltage uqFor d-axis voltage udAnd q-axis voltage uqCarrying out Park inverse transformation to obtain alpha-axis voltage uαAnd beta axis current uβ；
Step six, carrying out SVPWM control on the permanent magnet synchronous motor: and calling the SVPWM control module by the processor to perform SVPWM control on the permanent magnet synchronous motor so that the permanent magnet synchronous motor reaches a given position.
The L2 sliding mode control method of the permanent magnet synchronous motor adopts an L2 sliding mode control method in the formula (16) in the third step, and the specific process is as follows:
step 301, defining a torque equation of the permanent magnet synchronous motor as follows:
Figure BDA0001933279490000034
and the torque equation of the permanent magnet synchronous motor is expressed as follows:
Figure BDA0001933279490000035
wherein, TeIs the electromagnetic torque of the permanent magnet synchronous motor, theta is the feedback position, T is the time, TLIs the load torque;
step 302, defining a synovial membrane solution function H as:
Figure BDA0001933279490000041
wherein V' is the derivative of a positive definite and differentiable function V (x), and V (x) is ≧ 0; the value of V' satisfies:
Figure BDA0001933279490000042
d is interference amount, and Z is system evaluation signal;
step 303, defining that the feedback control law u satisfies the formula:
Figure BDA0001933279490000043
wherein the content of the first and second substances,
Figure BDA0001933279490000044
defining a first derivative of the position error for a given position
Figure BDA0001933279490000045
Defining the second derivative of the position error
Figure BDA0001933279490000046
Substituting equation (7) into equation (5) yields:
u＝Je″+Be′+TL (8)
from equation (8) and equation (9):
Figure BDA0001933279490000047
according to the formula (3), let
Figure BDA0001933279490000048
Then V ═ s × Js'; combining equation (10) yields:
V′＝-Bs2+Jp1e′s+Bp1es+us-TLs (11)
step 304, designing a control law u as follows:
Figure BDA0001933279490000049
wherein k is a constant greater than 0;
step 305, substituting the formula (12) into the formula (7) and combining the formula (4) to obtain:
Figure BDA00019332794900000410
in the L2 sliding-mode control method for the permanent magnet synchronous motor, in step 302, the value of Z is equal to the sliding-mode function s, and Z ═ s ═ p1e+e′。
In the L2 sliding mode control method of the permanent magnet synchronous motor, the obtaining process of the control law u in step 304 is as follows:
step 3041 represented by formula (13), formula (11), and Z ═ s ═ p1e + e' gives:
Figure BDA0001933279490000051
when equation (14) is satisfied:
Figure BDA0001933279490000052
then, the control law u is solved as follows:
Figure BDA0001933279490000053
the L2 sliding mode control method of the permanent magnet synchronous motor described above, p in step three1Is 25.
In the L2 sliding mode control method of the permanent magnet synchronous motor, in the third step, the value of γ is 0.0001.
According to the L2 sliding mode control method of the permanent magnet synchronous motor, the position sensor is an incremental encoder, and the processor is a DSP digital signal processor.
Compared with the prior art, the invention has the following advantages:
1. the method of the invention has simple steps and convenient realization.
2. The L2 sliding mode control method of the permanent magnet synchronous motor has the characteristics of good position tracking effect, high response speed and easiness in realization of controllers such as a DSP (digital signal processor).
3. The L2 sliding mode control method of the permanent magnet synchronous motor can achieve the purpose of inhibiting the load torque disturbance, has strong anti-interference capability and improves the robustness of the system.
4. The invention has strong practicability and good use effect and is convenient for popularization and use.
In conclusion, the method has the advantages of simple steps, convenience in implementation, good position tracking effect, high response speed, strong anti-interference capability, good robustness, strong practicability, good use effect and convenience in popularization and use.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a block diagram of the process flow of the present invention.
Fig. 2 is a schematic diagram of the present invention.
Fig. 3.1 is a position tracking comparison diagram of the permanent magnet synchronous motor when no-load starting is performed during simulation in the embodiment of the present invention.
Fig. 3.2 is an electromagnetic speed comparison diagram when the permanent magnet synchronous motor is started in no-load mode during simulation in the embodiment of the invention.
Fig. 3.3 is a comparison diagram of position tracking when the pmsm is started with a load in simulation according to the embodiment of the present invention.
Fig. 3.4 is an electromagnetic rotation speed comparison diagram when the permanent magnet synchronous motor is started with a load in simulation in the embodiment of the invention.
Fig. 4 is a connection diagram of a hardware control circuit employed in the present invention.
Description of reference numerals:
1-a processor; 2-position sensor.
Detailed Description
As shown in fig. 1, fig. 2 and fig. 4, the L2 sliding mode control method of the permanent magnet synchronous motor of the present invention includes the following steps:
step one, obtaining a feedback position: the position sensor 2 periodically detects the position of the permanent magnet synchronous motor to obtain feedback positions at a plurality of moments and transmits the feedback positions to the processor 1;
step two, obtaining a position error: the processor 1 calculates the difference between the feedback position and the given position to obtain a position error e; and calculating to obtain a derivative e' of the position error;
step three, obtaining given current of a q axis: processor 1 invokes the L2 synovial controller module based on the position error e and the derivative of the position error e', and based on the formula:
Figure BDA0001933279490000061
calculating q-axis given current
Figure BDA0001933279490000062
Wherein p is the pole pair number psi of the permanent magnet synchronous motorfIs the flux linkage of the permanent magnet synchronous motor, J is the rotational inertia of the permanent magnet synchronous motor, B is the friction factor of the permanent magnet synchronous motor, gamma is the suppression degree of given interference and gamma is>0, s is a sliding mode function, and the expression is:
s＝p1e+e′ (9)
wherein p is1Is a parameter of a sliding mode function and p1>0; only p1>0, the permanent magnet synchronous motor can be ensured to track the given rotating speed.
In this embodiment, formula (16) in step three is obtained by using an L2 slip film control method, which specifically comprises the following steps:
step 301, defining a torque equation of the permanent magnet synchronous motor as follows:
Figure BDA0001933279490000071
and the torque equation of the permanent magnet synchronous motor is expressed as follows:
Figure BDA0001933279490000072
wherein, TeIs the electromagnetic torque of the permanent magnet synchronous motor, theta is the feedback position, T is the time, TLIs the load torque;
step 302, defining a synovial membrane solution function H as:
Figure BDA0001933279490000073
wherein V' is the derivative of a positive definite and differentiable function V (x), and V (x) is ≧ 0; the value of V' satisfies:
Figure BDA0001933279490000074
d is interference amount, and Z is system evaluation signal;
in this embodiment, the value of Z in step 302 is equal to the sliding mode function s, and Z ═ s ═ p1e+e′。
Step 303, defining that the feedback control law u satisfies the formula:
Figure BDA0001933279490000075
wherein the content of the first and second substances,
Figure BDA0001933279490000076
defining a first derivative of the position error for a given position
Figure BDA0001933279490000077
Defining the second derivative of the position error
Figure BDA0001933279490000081
Substituting equation (7) into equation (5) yields:
u＝Je″+Be′+TL (8)
from equation (8) and equation (9):
Figure BDA0001933279490000082
according to the formula (3), let
Figure BDA0001933279490000083
Then V ═ s × Js'; combining equation (10) yields:
V′＝-Bs2+Jp1e′s+Bp1es+us-TLs (11)
step 304, designing a control law u as follows:
Figure BDA0001933279490000084
wherein k is a constant greater than 0;
in this embodiment, the obtaining process of the control law u in step 304 is as follows:
step 3041 represented by formula (13), formula (11), and Z ═ s ═ p1e + e' gives:
Figure BDA0001933279490000085
when equation (14) is satisfied:
Figure BDA0001933279490000086
then, the control law u is solved as follows:
Figure BDA0001933279490000087
step 305, substituting the formula (12) into the formula (7) and combining the formula (4) to obtain:
Figure BDA0001933279490000088
in this example, p is described in step three1Is 25.
In this embodiment, γ in step three is 0.0001. For any given positive number γ, when there is a positive definite and differentiable function V (x) ≧ 0 and satisfaction
Figure BDA0001933279490000089
When the gain F of the L2 is smaller than the given positive number gamma, the purpose of suppressing the interference is achieved.
Step four, obtaining d-axis current and q-axis current: the A-phase current sensor detects the stator A-phase winding current of the permanent magnet synchronous motor and detects the detected A-phase winding current iaTransmitted to the processor 1; the B-phase current sensor detects the stator B-phase winding current of the permanent magnet synchronous motor and detects the detected B-phase winding current ibTransmitted to the processor 1; the processor 1 passes the formula ic＝-(ia+ib) Calculating to obtain the stator C-phase winding current i of the permanent magnet synchronous motorcThen, the A-phase winding current i is appliedaPhase B winding current ibAnd C phase winding current icPerforming Clarke transformation to obtain alpha-axis current i under a two-phase static coordinate systemαAnd beta axis current iβFor the alpha axis current iαAnd beta axis current iβCarrying out Park conversion to obtain d-axis current idAnd q-axis current iq；
Step five, obtaining the alpha axis voltage and the beta axis voltage: processor 1 defines d-axis given current
Figure BDA0001933279490000091
D-axis current idWith d-axis set current
Figure BDA0001933279490000092
Compared withObtaining d-axis current difference value and converting q-axis current iqWith q-axis set current
Figure BDA0001933279490000093
Comparing to obtain q-axis current difference, and respectively passing the d-axis current difference and the q-axis current difference through a current PI regulator to respectively output d-axis voltage udAnd q-axis voltage uqFor d-axis voltage udAnd q-axis voltage uqCarrying out Park inverse transformation to obtain alpha-axis voltage uαAnd beta axis current uβ；
Step six, carrying out SVPWM control on the permanent magnet synchronous motor: and the processor 1 calls the SVPWM control module to perform SVPWM control on the permanent magnet synchronous motor so that the permanent magnet synchronous motor reaches a given position.
The purpose of restraining the load torque disturbance can be achieved through the method.
In this embodiment, the position sensor 2 is an incremental encoder, and the processor 1 is a DSP digital signal processor.
The method of the third step of the invention is derived according to the following principle:
consider the following system:
Figure BDA0001933279490000094
wherein d is interference amount, Z is system evaluation signal, and a sliding mode function is defined as the evaluation signal in the L2 sliding mode derivation process; x is a variable, x' is a derivative of the variable x, f (x) is a part of the system function, the part changes correspondingly with the change of the variable x, g (x) is another part of the system function, the part changes are related to a disturbance variable d besides the change of the variable x, h (x) is a sliding mode function;
the L2 slip form has the following three features of the slip form: determining the existence of sliding mode dynamic, possessing accessibility requirement and having stability. The sliding mode movement comprises approach movement and sliding mode movement, the approach movement is the approach movement when the system approaches to the switching surface from any initial state, in the approach process, the system is controlled by a control function, and the movement of the system can reach the switching surface no matter where the starting point is in the state space, namely, the accessibility condition is met.
To express the interference rejection capability of the system, the following indexes are defined:
Figure BDA0001933279490000101
wherein T is the integral action time, which indicates how long the action time is. It can be seen that the smaller F is, the higher anti-interference capability is obtained when the system is in operation, and the design of the L2 sliding mode controller is that in a closed-loop system, the higher anti-interference capability and stability are obtained when the system is interfered, so that F can be smaller than a given value. If, for any given positive number γ, there is a positive definite and differentiable function V (x) ≧ 0 and satisfied:
Figure BDA0001933279490000102
then, F < gamma is shown, and the robust condition is established, so that the purpose of suppressing interference is achieved.
The L2 sliding mode control design for the permanent magnet synchronous motor needs to satisfy the following two conditions:
(1) when T isLWhen the system is stable for any initial state, the system position error is close to zero.
(2) When T isLWhen not equal to 0, for any disturbing signal, the following conditions are satisfied:
Figure BDA0001933279490000103
where T >0 is a finite time and γ >0 is a given positive number.
In order to verify the effectiveness of the L2 sliding mode control method of the permanent magnet synchronous motor, Matlab is adopted to carry out the L2 sliding mode control method of the permanent magnet synchronous motorAnd (3) simulation, wherein basic parameters of the permanent magnet synchronous motor used in the simulation are as follows: j is 0.0008kg.m2，B＝0.0001，p＝4，ψf0.175 Wb. The given position signal is a square wave input signal. Fig. 3.1 and 3.2 show a position tracking comparison graph and a rotational speed comparison graph, respectively, in which the start load is 0n.m, and the load torque is suddenly applied to 4n.m at 4.72s (a time point after the start of the falling edge of the second square wave signal); fig. 3.3 and 3.4 show a position tracking comparison chart and a rotational speed comparison chart, respectively, when the start load torque is 2n.m and the load torque is suddenly applied to 4n.m at 4.72s (a time point after the start of the falling edge of the second square wave signal). By comparing with the simulation result of the conventional PID control method, the simulation result is shown in FIGS. 3.1-3.4.
As can be seen from fig. 3.1, both the L2 sliding mode control method and the PID control method can effectively track the given position when the permanent magnet synchronous motor is started in no-load mode. Compared with a PID control method, the time for the permanent magnet synchronous motor to reach a given position is shorter by adopting an L2 sliding mode control method. At 4.72s, the load torque is suddenly increased to 4N.m, as can be seen from comparison in FIG. 3.1, the tracking of the motor position is less affected by disturbance by using the L2 sliding mode control method, and the tracking to a given position can be realized in a short time. And after the same disturbance is applied, the position of the permanent magnet synchronous motor deviates from the given position due to insufficient anti-interference capability by adopting a common PID control method. Fig. 3.3 is a simulation result of the rotating speed response of the permanent magnet synchronous motor in the two control methods when the permanent magnet synchronous motor is started with a load, and a comparison analysis shows that the permanent magnet synchronous motor has a faster rise time and a smaller overshoot when the L2 sliding mode control method is adopted. The permanent magnet synchronous motor also shows strong anti-interference capability when disturbed. When the permanent magnet synchronous motor is started in a no-load mode and a loaded mode respectively, as shown in fig. 3.2 and fig. 3.4, the electromagnetic rotating speed of the permanent magnet synchronous motor is faster than the rotating speed response of the permanent magnet synchronous motor under the control of the ordinary PID (proportion integration differentiation) by adopting the L2 sliding mode control method, and the overshoot is small.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all simple modifications, changes and equivalent structural changes made to the above embodiment according to the technical spirit of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims (6)

1. An L2 sliding mode control method of a permanent magnet synchronous motor is characterized by comprising the following steps:
step one, obtaining a feedback position: the position sensor (2) periodically detects the position of the permanent magnet synchronous motor to obtain feedback positions at a plurality of moments and transmits the feedback positions to the processor (1);
step two, obtaining a position error: the processor (1) calculates the difference between the feedback position and the given position to obtain a position error e; and calculating to obtain a derivative e' of the position error;
step three, obtaining given current of a q axis: the processor (1) invokes the L2 sliding mode controller module based on the position error e and the derivative of the position error e', and based on the formula:
Figure FDA0003474563730000011
calculating q-axis given current
Figure FDA0003474563730000012
Wherein p is the pole pair number psi of the permanent magnet synchronous motorfThe magnetic linkage is a magnetic linkage of the permanent magnet synchronous motor, J is the rotational inertia of the permanent magnet synchronous motor, B is a friction factor of the permanent magnet synchronous motor, gamma is the suppression degree of given interference and gamma is more than 0, s is a sliding mode function, and the expression is as follows:
s＝p1e+e′ (9)
wherein p is1Is a parameter of a sliding mode function and p1＞0；
Step four, obtaining d-axis current and q-axis current: the A-phase current sensor detects the A-phase winding current of the stator of the permanent magnet synchronous motor and detects the A-phase winding current iaTransmitting to the processor (1); the B-phase current sensor detects the stator B-phase winding current of the permanent magnet synchronous motor and detects the detected B-phase winding current ibTransmitting to the processor (1); the processor (1) passes the formula ic＝-(ia+ib) Calculating to obtain the stator C-phase winding current i of the permanent magnet synchronous motorcThen the A phase winding current iaPhase B winding current ibAnd C phase winding current icPerforming Clarke transformation to obtain alpha-axis current i under a two-phase static coordinate systemαAnd beta axis current iβFor the alpha axis current iαAnd beta axis current iβCarrying out Park conversion to obtain d-axis current idAnd q-axis current iq；
Step five, obtaining the alpha axis voltage and the beta axis voltage: the processor (1) defines a d-axis given current
Figure FDA0003474563730000013
D-axis current idWith d-axis set current
Figure FDA0003474563730000014
Comparing to obtain d-axis current difference and comparing q-axis current iqWith q-axis set current
Figure FDA0003474563730000015
Comparing to obtain q-axis current difference, and respectively passing the d-axis current difference and the q-axis current difference through a current PID regulator to respectively output d-axis voltage udAnd q-axis voltage uqFor d-axis voltage udAnd q-axis voltage uqCarrying out Park inverse transformation to obtain alpha-axis voltage uαAnd beta axis current uβ；
Step six, carrying out SVPWM control on the permanent magnet synchronous motor: the processor (1) calls the SVPWM control module to perform SVPWM control on the permanent magnet synchronous motor so that the permanent magnet synchronous motor reaches a given position;
in the third step, the formula (16) is obtained by adopting an L2 sliding mode control method, and the specific process is as follows:
step 301, defining a torque equation of the permanent magnet synchronous motor as follows:
Figure FDA0003474563730000021
and the torque equation of the permanent magnet synchronous motor is expressed as follows:
Figure FDA0003474563730000022
wherein, TeIs the electromagnetic torque of the permanent magnet synchronous motor, theta is the feedback position, T is the time, TLIs the load torque;
step 302, defining a sliding mode solving function H as:
Figure FDA0003474563730000023
wherein V' is the derivative of a positive definite and differentiable function V (x), and V (x) is ≧ 0; the value of V' satisfies:
Figure FDA0003474563730000024
d is interference amount, and Z is system evaluation signal;
step 303, defining that the feedback control law u satisfies the formula:
Figure FDA0003474563730000025
wherein the content of the first and second substances,
Figure FDA0003474563730000026
defining a first derivative of the position error for a given position
Figure FDA0003474563730000027
Defining the second derivative of the position error
Figure FDA0003474563730000028
Substituting equation (7) into equation (5) yields:
u＝Je″+Be′+TL (8)
from equation (8) and equation (9):
Figure FDA0003474563730000031
according to the formula (3), let
Figure FDA0003474563730000032
Then V ═ s × Js'; combining equation (10) yields:
V′＝-Bs2+Jp1e′s+Bp1es+us-TLs (11)
step 304, designing a control law u as follows:
Figure FDA0003474563730000033
wherein k is a constant greater than 0;
step 305, substituting the formula (12) into the formula (7) and combining the formula (4) to obtain:
Figure FDA0003474563730000034
2. the L2 sliding-mode control method of the permanent magnet synchronous motor according to claim 1, characterized in that: in step 302, the value of Z is equal to the sliding mode function s, and Z ═ s ═ p1e+e′。
3. The L2 sliding-mode control method of the permanent magnet synchronous motor according to claim 1, characterized in that: the obtaining process of the control law u in the step 304 is as follows:
step 3041 represented by formula (13), formula (11), and Z ═ s ═ p1e + e' gives:
Figure FDA0003474563730000035
when equation (14) is satisfied:
Figure FDA0003474563730000036
then, the control law u is solved as follows:
Figure FDA0003474563730000037
4. the L2 sliding-mode control method of the permanent magnet synchronous motor according to claim 1, characterized in that: p in step three1Is 25.
5. The L2 sliding-mode control method of the permanent magnet synchronous motor according to claim 1, characterized in that: in the third step, the value of gamma is 0.0001.
6. The L2 sliding-mode control method of the permanent magnet synchronous motor according to claim 1, characterized in that: the position sensor (2) is an incremental encoder, and the processor (1) is a DSP digital signal processor.
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