CN110061666B - Permanent magnet synchronous motor speed regulation performance improvement method based on full-order terminal sliding mode control - Google Patents

Permanent magnet synchronous motor speed regulation performance improvement method based on full-order terminal sliding mode control Download PDF

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CN110061666B
CN110061666B CN201811149141.4A CN201811149141A CN110061666B CN 110061666 B CN110061666 B CN 110061666B CN 201811149141 A CN201811149141 A CN 201811149141A CN 110061666 B CN110061666 B CN 110061666B
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sliding mode
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孙兰昕
牛子铭
王艳敏
买永锋
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Harbin Engineering University
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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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Abstract

The invention belongs to the technical field of motor speed regulation, and particularly relates to a permanent magnet synchronous motor speed regulation performance improvement method based on full-order terminal sliding mode control. The method comprises the following steps: (1) carrying out permanent magnet synchronous motor double-closed-loop sliding mode control based on full-order terminal sliding mode control; (2) carrying out full-order terminal sliding mode control on a rotating speed ring; (3) and (4) carrying out quadrature axis current loop full-order terminal sliding mode control (4) and carrying out direct axis current loop full-order terminal sliding mode control. The invention improves the control performance of the outer ring rotating speed ring and the inner ring current ring by utilizing the advantages of the special finite time control characteristic of full-order terminal sliding mode control, the fact that a robust differential estimator is not needed and the like, thereby improving the speed regulation performance of the whole system.

Description

Permanent magnet synchronous motor speed regulation performance improvement method based on full-order terminal sliding mode control
Technical Field
The invention belongs to the technical field of motor speed regulation, and particularly relates to a permanent magnet synchronous motor speed regulation performance improvement method based on full-order terminal sliding mode control.
Background
The traditional sliding mode control is mostly applied to the permanent magnet synchronous motor in a composite form such as 'outer ring PI + inner ring sliding mode control', and is difficult to expand to double closed-loop sliding mode control. At present, in the field of sliding mode control of permanent magnet synchronous motors, the application of a traditional sliding mode control method is mainly used, from the aspect of mathematical mechanism, the switching control characteristic of the sliding mode control method is related to a sign function sgn (), and double-closed-loop sliding mode control is difficult to realize.
Although the conventional continuous sliding mode control method can eliminate the switching control sgn (mean) term and expand the realization of the double-closed-loop sliding mode control of the permanent magnet synchronous motor, a robust differential estimator needs to be applied and the speed regulation performance of the permanent magnet synchronous motor is influenced. At present, an auxiliary robust differential estimator is needed in application of a continuous sliding mode control method, a certain engineering application value is achieved, influences of actual system measurement errors, input noise and the like can be overcome, the problem of buffeting induced by traditional sliding mode switching control sgn (normal) is eliminated, and application in a permanent magnet synchronous motor double closed loop control system can be expanded and realized. However, the robust differential estimator in this system is used to obtain the differential signal in real time, which is essentially an auxiliary observer, but due to the tracking process of the differential signal, the rotating speed of the permanent magnet synchronous motor has an inverse peak value in the initial stage, and the response speed is slow, which leads to the reduction of the speed regulation performance.
Disclosure of Invention
The invention aims to provide a permanent magnet synchronous motor speed regulation performance improvement method based on full-order terminal sliding mode control.
The purpose of the invention is realized as follows:
the permanent magnet synchronous motor speed regulation performance improvement method based on full-order terminal sliding mode control comprises the following steps:
(1) carrying out permanent magnet synchronous motor double-closed-loop sliding mode control based on full-order terminal sliding mode control;
AC and DC shaft inductance equal L of surface-mounted permanent magnet synchronous motord＝LqThe rotor is provided with an undamped winding, a magnetic circuit is linear and unsaturated, the motor is provided with a sinusoidal back electromotive force, and the current is three-phase symmetrical current, so that a model of the permanent magnet synchronous motor under a dq coordinate system is obtained
Figure RE-GDA0001947855700000011
In the formula ud，uq，id，iq，ψd，ψq，Ld，LqThe voltage and current of stator, stator flux linkage, and direct and alternating components of stator winding inductance, RsIs stator resistance,. psifIs the flux linkage generated in the rotating process of the permanent magnet rotor, J is the moment of inertia, TmAs motor torque, TLIs the load torque, B is the friction coefficient, p is the pole pair number, omega is the angular velocity;
decomposing a permanent magnet synchronous motor control system into outer partsA ring speed ring and an inner ring current ring; the outer ring is a speed ring, the speed error is tracked, and the output value is a given value i of the quadrature axis currentq *(ii) a The inner ring is a current ring, the direct-axis current and the quadrature-axis current are respectively controlled by decoupling, and the tracked d-axis current given value i is set in a direct-axis current controllerd *Is zero, and the output control value is the direct-axis voltage udQuadrature axis voltage uq；
(2) Carrying out full-order terminal sliding mode control on a rotating speed ring;
the output value of the rotating speed loop controller is a quadrature axis current set value signal iq *Error in rotational speed eωIs eω＝ω*ω, ring offset:
Figure RE-GDA0001947855700000021
the full-order terminal sliding mode controller comprises a sliding mode surface and a control law, wherein the sliding mode surface is as follows:
Figure RE-GDA0001947855700000022
design parameter c1>0，α∈(1-,1)，∈(0,1)；
When the rotating speed error system reaches the sliding mode surface sωWhen 0, the system dynamics can be characterized as:
Figure RE-GDA0001947855700000023
realizing the convergence of the system state within a limited time;
setting the initial condition of the system state when the system state reaches the sliding mode surface as eω(0) Not equal to 0, then from eω(0) To eω(ts) Time t required for not more than 0sIs composed of
Figure RE-GDA0001947855700000024
Obtained by direct forward-backward differentiation:
Figure RE-GDA0001947855700000025
τ is a time delay, and has a value of 0.5< <1,
Figure RE-GDA0001947855700000026
arrival conditions of slip form
Figure RE-GDA0001947855700000027
Control law iq *Comprises the following steps:
Figure RE-GDA0001947855700000028
iqeq *as an equivalent control term, iqn *For switching control items, T is discrete sampling time, k1>0 is the switching gain;
(3) carrying out quadrature axis current loop full-order terminal sliding mode control;
defining quadrature axis current error variable eq＝iq *-iq
The corresponding quadrature axis current error system is
Figure RE-GDA0001947855700000031
To quadrature axis current error system, slip form surface sqThe design is as follows:
Figure RE-GDA0001947855700000032
design parameter c2>0，
Control law uqIs composed of
Figure RE-GDA0001947855700000033
Wherein u isqeqIs an equivalent control term, and uqnFor switching control items, k2>0 is the switching gain;
(4) carrying out straight-axis current loop full-order terminal sliding mode control;
error variable e of direct axis currentd＝id *-id
The corresponding direct axis current error system is
Figure RE-GDA0001947855700000034
Slip form surface sdIs composed of
Figure RE-GDA0001947855700000035
Design parameter c3>0, control law udThe design is as follows:
Figure RE-GDA0001947855700000036
udeqas an equivalent control term, udnFor switching control items, k3>0 is the switching gain.
The invention has the beneficial effects that: the invention provides a permanent magnet synchronous motor double-closed-loop sliding mode control scheme based on novel full-order terminal sliding mode control, and overcomes the defects of the traditional composite control form of 'outer loop PI + inner loop sliding mode control' and the continuous sliding mode control form based on a robust differential estimator. The control performance of an outer ring rotating speed ring and an inner ring current ring is improved by utilizing the advantages of the characteristic finite time control characteristic of full-order terminal sliding mode control, the fact that a robust differential estimator is not required and the like, and the speed regulation performance of the whole system is further improved.
Drawings
FIG. 1a is a control block diagram of a conventional "outer loop PI + inner loop sliding mode control";
FIG. 1b is a block diagram of a continuous sliding mode control based on a robust differential estimator;
FIG. 1c is a block diagram of a permanent magnet synchronous motor double closed-loop sliding mode control based on full-order terminal sliding mode control;
FIG. 2a is a schematic diagram of a system hardware configuration of a permanent magnet synchronous motor experiment platform based on the DSP TSMS320F 28335;
FIG. 2b is a schematic diagram of a data acquisition interface of a PMSM experimental platform based on the DSP TSMS320F 28335;
FIG. 2c is a schematic diagram of a selection interface of a PMSM experiment platform controller based on DSP TSMS320F 28335;
FIG. 3a is a diagram of the effect of the dual closed loop PI control on the rotating speed performance of the permanent magnet synchronous motor;
FIG. 3b is a diagram of the control effect of a double closed-loop continuous sliding mode based on a differential estimator for the rotating speed performance of a permanent magnet synchronous motor;
fig. 3c is a double closed loop full-order terminal sliding mode control of the rotating speed performance of the permanent magnet synchronous motor.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
(1) Establishment of permanent magnet synchronous motor double-closed-loop sliding mode control scheme based on full-order terminal sliding mode control
The surface-mounted permanent magnet synchronous motor researched by the paper has equal inductance L of the alternating axis and the direct axisd＝LqIf the rotor is assumed to have no damping winding, the magnetic circuit is linear and the saturation is not considered, the motor has sinusoidal back electromotive force, and the current is three-phase symmetrical current, a mathematical model of the permanent magnet synchronous motor in the dq coordinate system can be obtained.
Figure RE-GDA0001947855700000041
In the formula ud，uq，id，iq，ψd，ψq，Ld，LqThe voltage and current of stator, stator flux linkage, and direct and alternating components of stator winding inductance, RsIs stator resistance,. psifIs the flux linkage generated in the rotating process of the permanent magnet rotor, J is the moment of inertia, TmAs motor torque, TLThe load torque, B the coefficient of friction, p the number of pole pairs, and ω the angular velocity.
First, the permanent magnet synchronous motor control system (1) is decomposed into an outer ring speed ring and an inner ring current ring based on a vector control technology, as shown in fig. 1. Wherein, the outer ring is a speed ring which tracks speed error, and the output value is a given value i of quadrature axis currentq *(ii) a The inner ring is a current ring, the direct-axis current and the quadrature-axis current are respectively controlled by decoupling, and the tracked d-axis current given value i is set in a direct-axis current controllerd *Is zero, and the output control value is the direct-axis voltage udQuadrature axis voltage uq。
With reference to fig. 1, wherein (a) is a composite control form of "outer loop PI + inner loop sliding mode control" based on conventional sliding mode control, and cannot be extended to dual-loop sliding mode control, which is mainly because the differential of its switching control sgn (·) is difficult to obtain; and the graph (b) is a continuous sliding mode control method adopting a robust differential estimator, but the robust differential estimator needs to be additionally added, the design is complicated, and the tracking characteristic of the differential estimator can cause an inverse sharp peak value to exist in the initial stage, the response speed is slow, and further the speed regulation performance is reduced. Compared with the prior art, the control block diagram in the diagram (c) is directly a conventional double-closed-loop control structure, only three controllers are needed to adopt a full-order terminal sliding mode control method, and upgrading and transformation of a traditional double-closed-loop permanent magnet synchronous motor control system are facilitated.
(2) Design of full-order terminal sliding mode controller of rotating speed ring
The rotating speed loop controller requires accurate tracking of a given speed, the system has strong robustness to external load disturbance and internal parameter perturbation influence, and the output value is a quadrature axis current given value signal iq *. Defining a rotational speed error eωIs eω＝ω*- ω, from a given mathematical model (1) of the motor, a ring deviation of the rotation speed of
Figure RE-GDA0001947855700000051
The design of the full-order terminal sliding mode controller comprises a sliding mode surface and a control law, and is directed to the formula (2), wherein the sliding mode surface is designed to be
Figure RE-GDA0001947855700000052
Wherein the design parameter c1>0，α∈(1-,1)，∈(0,1)。
Once the system reaches the sliding mode surface s with the rotation speed error of the formula (2)ωThe system dynamics can be characterized as:
Figure RE-GDA0001947855700000053
it can be seen that convergence of the system state within a limited time is achieved. Assuming that the initial condition of the system state when the system state reaches the sliding mode surface is eω(0) Not equal to 0, then from eω(0) To eω(ts) Time t required for not more than 0sIs composed of
Figure RE-GDA0001947855700000054
It is noted from equation (3) that the full-order terminal sliding mode control surface is the same as the robust differential estimator-based continuous sliding mode control method in fig. 1(b), and the system state e also needs to be obtainedωDifferentiation, as is evident for a system (2) with a relative order of 1
Figure RE-GDA0001947855700000055
Are not available in real time. Therefore, it is considered here that the actual system differentiation implementation is obtained by direct forward and backward differentiation in many ways, i.e. there is
Figure RE-GDA0001947855700000056
Where τ is a time delay and has a value of 0.5< <1,
Figure RE-GDA0001947855700000057
according to the sliding mode arrival condition
Figure RE-GDA0001947855700000058
Accordingly, control law iq *Is designed as
Figure RE-GDA0001947855700000059
Wherein iqeq *Is an equivalent control term, and iqn *For switching control items, T is discrete sampling time, k1>0 is the switching gain.
(3) Design of quadrature axis current loop full-order terminal sliding mode controller
Similar to the design process of a rotating speed full-order terminal sliding mode controller, the design results of a quadrature axis current loop sliding mode surface and the controller are directly given, and the process is not described in detail.
Defining quadrature axis current error variable eq＝iq *-iqThe motor mathematical model of formula (1) is used to calculate the corresponding quadrature axis current error system as
Figure RE-GDA0001947855700000061
For quadrature axis current error system (10), slip form surface sqIs designed as
Figure RE-GDA0001947855700000062
Wherein the design parameter c2>0, parameter α1The design of (2) follows the selection principle of the formula (3).
Accordingly, control law uqIs designed as
Figure RE-GDA0001947855700000063
Wherein u isqeqIs an equivalent control term, and uqnFor switching control items, k2>0 is the switching gain.
(4) Design of straight-axis current loop full-order terminal sliding mode controller
Defining the error variable e of the direct-axis currentd＝id *-idThe corresponding direct-axis current error system is represented by the mathematical model of the motor in the formula (1)
Figure RE-GDA0001947855700000064
Similarly, slip form surface sdIs designed as
Figure RE-GDA0001947855700000065
Wherein the design parameter c3>0, parameter α2The design of (2) follows the selection principle of the formula (3).
Accordingly, control law udIs designed as
Figure RE-GDA0001947855700000066
Wherein u isdeqIs an equivalent control term, and udnFor switching control items, k3>0 is the switching gain.
In order to verify the improved performance of the full-order terminal sliding mode control method on the double closed loop speed regulation performance of the permanent magnet synchronous motor, the method is compared with a PI (proportional integral) and continuous sliding mode control method based on a differential estimator. Fig. 2 shows a built permanent magnet synchronous motor experimental platform based on the DSPTSMS320F28335, wherein (a) is formed by system hardware. The permanent magnet synchronous motor is a small 24V motor, and a data acquisition system is developed, and the visualized operation interface is shown in the figures (b) and (c). The functions of the device comprise: the data acquisition interface display, the motor control instruction input interface and the controller parameter selection interface can realize the functions of parameter setting, motion mode selection, data acquisition and storage at will.
Aiming at a continuous nonsingular terminal sliding mode control scheme based on a differential estimator, the parameters of the permanent magnet synchronous motor in the formula (1) are as follows: rated speed of ne2000rpm, phase resistance Rs2.875 Ω, pole pair number pnPermanent magnet flux linkage psi ═ 3f0.8Wb, 33mH equivalent inductance L of winding, 0.011 kg.m inertia moment J2Coefficient of friction B is 0.002 N.m.s, given value of load torque TL0N m, speed step given N*1800 rmp. Applying a full-order terminal sliding mode control method, wherein the design parameter alpha of a rotating speed loop controller is 0.6, c1＝5，k1(ii) 5; design parameter alpha of quadrature axis current controller1＝0.6，c2＝3，k13; design parameter alpha of direct-axis current controller2＝0.6， c3＝0.1，k1＝0.25。
In order to compare the improvement effect of the full-order terminal sliding mode control method on the rotating speed performance of the permanent magnet synchronous motor, the method is compared with a double-closed-loop PI control method and a double-closed-loop continuous sliding mode control method, as shown in Table 1 and FIG. 3.
TABLE 1 comparison of control Performance of different control modes for PMSM
Figure RE-GDA0001947855700000071
By comparing three different double closed-loop control methods, it can be seen that the starting time of the full-order terminal sliding mode control method is 0.30s as the adjusting time of the PI control, while the adjusting time of the continuous sliding mode control method is slightly 0.83s as the tracking time of the robust differential estimator is adopted. For the maximum rotating speed error, the full-order terminal sliding mode control method is improved from 75rmp to 53rmp compared with the continuous sliding mode control method of the previous subject group; the relative steady-state error is reduced from 4.17% to 2.94%, and the speed regulation performance is obviously improved. Compared with the PI control performance commonly used in the current engineering, the performance of the full-order terminal sliding mode control reaches an acceptable range.

Claims (1)

1. The method for improving the speed regulation performance of the permanent magnet synchronous motor based on full-order terminal sliding mode control is characterized by comprising the following steps of:
(1) carrying out permanent magnet synchronous motor double-closed-loop sliding mode control based on full-order terminal sliding mode control;
AC and DC shaft inductance equal L of surface-mounted permanent magnet synchronous motord＝LqAnd (2) obtaining a model of the permanent magnet synchronous motor under a dq coordinate system, wherein the rotor is provided with an undamped winding, a magnetic circuit is linear and unsaturated, the motor is provided with a sinusoidal back electromotive force, and the current is three-phase symmetrical current:
Figure RE-FDA0001947855690000011
in the formula ud，uq，id，iq，ψd，ψq，Ld，LqThe voltage and current of stator, stator flux linkage, and direct and alternating components of stator winding inductance, RsIs stator resistance,. psifIs the flux linkage generated in the rotating process of the permanent magnet rotor, J is the moment of inertia, TmAs motor torque, TLIs the load torque, B is the friction coefficient, p is the pole pair number, omega is the angular velocity;
decomposing a permanent magnet synchronous motor control system into an outer ring speed ring and an inner ring current ring; the outer ring is a speed ring, the speed error is tracked, and the output value is a given value i of the quadrature axis currentq *(ii) a The inner ring is a current ring, the direct-axis current and the quadrature-axis current are respectively controlled by decoupling, and the tracked d-axis current given value i is set in a direct-axis current controllerd *Is zero, and the output control value is the direct-axis voltage udQuadrature axis voltage uq；
(2) Carrying out full-order terminal sliding mode control on a rotating speed ring;
the output value of the rotating speed loop controller is a quadrature axis current set value signal iq *Error in rotational speed eωIs eω＝ω*ω, ring offset:
Figure RE-FDA0001947855690000012
the full-order terminal sliding mode controller comprises a sliding mode surface and a control law, wherein the sliding mode surface is as follows:
Figure RE-FDA0001947855690000013
design parameter c1>0，α∈(1-,1)，∈(0,1)；
When the rotating speed error system reaches the sliding mode surface sωWhen 0, the system dynamics can be characterized as:
Figure RE-FDA0001947855690000014
realizing the convergence of the system state within a limited time;
setting the initial condition of the system state when the system state reaches the sliding mode surface as eω(0) Not equal to 0, then from eω(0) To eω(ts) Time t required for not more than 0sIs composed of
Figure RE-FDA0001947855690000015
Obtained by direct forward-backward differentiation:
Figure RE-FDA0001947855690000021
τ is a time delay, and has a value of 0.5< <1,
Figure RE-FDA0001947855690000022
arrival conditions of slip form
Figure RE-FDA0001947855690000023
Control law iq *Comprises the following steps:
Figure RE-FDA0001947855690000024
iqeq *as an equivalent control term, iqn *For switching control items, T is discrete sampling time, k1>0 is the switching gain;
(3) full-order terminal sliding mode control of quadrature axis current loop
Defining quadrature axis current error variable eq＝iq *-iq
The corresponding quadrature axis current error system is
Figure RE-FDA0001947855690000025
To quadrature axis current error system, slip form surface sqThe design is as follows:
Figure RE-FDA0001947855690000026
design parameter c2>0，
Control law uqIs composed of
Figure RE-FDA0001947855690000027
Wherein u isqeqIs an equivalent control term, and uqnFor switching control items, k2>0 is the switching gain;
(4) full-order terminal sliding mode control of straight-axis current loop
Error variable e of direct axis currentd＝id *-id；
The corresponding direct axis current error system is
Figure RE-FDA0001947855690000028
Slip form surface sdIs composed of
Figure RE-FDA0001947855690000029
Design parameter c3>0, control law udThe design is as follows:
Figure RE-FDA0001947855690000031
udeqas an equivalent control term, udnFor switching control items, k3>0 is the switching gain.
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