CN106788098A - A kind of permanent magnetic linear synchronous motor is based on the sliding formwork control of varying index Reaching Law - Google Patents
A kind of permanent magnetic linear synchronous motor is based on the sliding formwork control of varying index Reaching Law Download PDFInfo
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- H—ELECTRICITY
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- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
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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 discloses the sliding formwork control that a kind of permanent magnetic linear synchronous motor is based on varying index Reaching Law, comprise the following steps：(1) coordinate transform is carried out to prototype machine equation, sets up Mathematical Modelings of the PMSLM under d/q coordinate systems；(2) the PMSLM two close cycles servo-control systems being made up of electric current loop and speed ring are set up；(3) linear switching function is chosen, index sliding formwork control ratio is obtained according to exponentially approaching rule；(4) using the sign function in saturation function substitution sliding formwork control；(5) integral element is introduced on the basis of switching function, varying index sliding formwork control ratio is obtained by varying index Reaching Law；(6) sliding formwork gain is made with velocity error into non-linear relation.The present invention uses rate of current double closed-loop decoupling control structure, for the buffeting problem in sliding formwork control, integration diverter surface and varying index Reaching Law are introduced on the basis of conventional sliding mode controller, the disturbance for effectively inhibiting load change to bring, significantly improves the tracking performance of speed and the robustness of system.
Description
Technical field
Varying index Reaching Law is based on the present invention relates to PMSLM servo-drive systems, more particularly to a kind of permanent magnetic linear synchronous motor
Sliding formwork control.
Background technology
With motor and its development of technology is controled, occur in that the permanent magnetic linear synchronous motor of direct drive, this straight line
Compared with traditional electric rotating machine adds ball screw, it eliminates intermediate gearing and directly drives load movement motor, keeps away
Exempt to bring influence because of machine driving, therefore, there is high efficiency, high speed, high acceleration.In high-speed, high precision processing
Machine tool field, although electric rotating machine adds, ball-screw drives and linear electric motors drive and can also and deposit significant period of time,
From the point of view of present trend, linear electric motors drive and are likely to ban the main flow that ball-screw drives as machine tool feed.
However, there is the non-linear factors such as Parameters variation, load disturbance in itself due to linear electric motors, if treatment is bad,
Can have a negative impact to the performance of servo-drive system, such as robustness weakens, and then have a negative impact to motor work, the lighter will
Influence production efficiency, severe patient can even cause any property loss and personal safety.
At present, the method for control PMSLM servo-control system stability is broadly divided into two major classes：First：PMSLM servo controls
System speed ring processed carries out speed regulation using conventional PI control device；Second：PMSLM vector control system medium velocity rings use base
The regulation of speed is carried out in the sliding mode controller of exponentially approaching rule.Method one can be such that mover speed reaches in a short period of time
Set-point, but motor thrust output can produce larger fluctuation with the change of mover given speed, illustrate the anti-interference of system
Can be low, robustness is not strong.Method two in the case of it there are heavy load disturbances in system, using based on exponentially approaching rule sliding formwork control
There is chattering phenomenon in the system of device.So there is certain limitation in the current techniques equipment higher for some precision requirements.
These limitation sexual stimuluses the adjustment and development of domestic high-end equipment manufacture.
Straight drive technology also has been enter into the industrial applications stage abroad.But, domestic research in this respect is still in rising
Step section, gap is also very big, and key technology is substantially that each giant manufacturer is grasped, and is considered as trade secret, it is difficult to from
Valuable detailed technology content is found in scientific and technical literature and network.Therefore, the high-speed machining center technology that develop China is built
Vertical related industry, must just walk the road of independent development.
The content of the invention
Goal of the invention：To weaken the buffeting that general sliding formwork control is brought, suppress the disturbance that load change brings, the present invention is carried
A kind of permanent magnetic linear synchronous motor has been supplied to be based on the sliding formwork control of varying index Reaching Law.
Technical scheme：To realize the purpose of the present invention, adopt the following technical scheme that：A kind of permanent magnetic linear synchronous motor is based on
The sliding formwork control of varying index Reaching Law, comprises the following steps：
(1) coordinate transform is carried out to prototype machine equation, sets up Mathematical Modelings of the PMSLM under d/q coordinate systems：
Wherein, ud、uqWith the dq axle components of three-phase windings voltage, id、iqIt is the dq axle components of three-phase windings electric current；ψd、ψq
It is the dq axle components of winding magnetic linkage；Ld、LqIt is the dq axle components of inductance；ψfIt is permanent magnet fundamental wave excitation flux linkage；R is every phase winding
Resistance；V is the speed of service of linear electric motor primary mover；τ is pole span, and n is mover number of pole-pairs, and M is mover quality, and B is viscous
Stagnant coefficient of friction, fLIt is external disturbance；
(2) PMSLM servo-control systems are set up, the system is the double loop system that electric current loop and speed ring are constituted；
(3) step (1) gained Mathematical Modeling is reduced to：
Definition status variable：Above formula is turned to：
In formula, a, b, d are time-varying parameter, fLIt is broad sense load disturbance；
If v*, v be respectively the set-point and value of feedback of speed, it is assumed that e=v*- v, x1=∫ edt,Then
The velocity error state equation of PMSLM is：
(4) linear switching function s=Cx is chosen1+x2, according to exponentially approaching ruleObtain sliding formwork control
Rule：
Wherein, ueqIt is sliding formwork equivalent control part, equivalent to the average value of switching control, as control system can determine
Part；And uvsIt is the uncertain part of control system, to ensure the robustness of system, by designing equivalent control part, can be with
Reduce the amplitude of switching control amount to a certain extent.
Knowable to above formula, the frequent switching of sign function sgn (s) is the main cause for causing buffeting in control law, may
Trigger the uncertainty of control effect, the buffeting that velocity of approach σ brings more greatly is bigger, therefore solve to buffet the name of the game just
It is process switching amount, generally, quasi- cunning is realized using sign function sgn (s) in saturation function sat (s) substitution sliding formwork control
Mould is controlled；
(5) using sign function sgn (s) in saturation function sat (s) substitution sliding formwork control, sliding mode controller is obtained
Control law is：
The switching of structure need not be carried out due to saturation function sat (s, Δ) boundary layer, so control law is in this region
It is continuous such that it is able to eliminate the problem that sliding formwork is buffeted to a certain extent；
(6) integral element is introduced on the basis of switching function s, then switching function isBy becoming
Exponentially approaching ruleObtaining sliding formwork control ratio is：
As long as suitably setting integration primary condition, so that it may so that the original state of system is on Fault slip rate, protect
The global robustness of system dynamic course is demonstrate,proved.In addition, increasing integral element can eliminate the steady-state error of system, so as to ensure
The tracking performance of system；Varying index Reaching Law makes the state variable e (velocity error) of speed ring with two kinds of speed of index and speed change
Rate is moved to sliding formwork diverter surface, and when diverter surface is reached, exponential term goes to zero, and speed change plays Main Function.When variable e is being
When being substantially equal to zero in the dynamic process of system, control law makes variable e be moved to equalization point after entering diverter surface, this fortune
Dynamic process can cause againConstantly reduce, final stabilization is in equalization point；System is stable after equalization point,
Cause to buffet the switching control-σ for producing | x1| the coefficient of sgn (s) becomes zero, so as to eliminate the buffeting that sliding formwork control causes ask
Topic；
(7) while in order that varying index Reaching Law largely can slacken buffeting, still with stronger robust
Property, Curve guide impeller is made to sliding formwork gain, make sliding formwork gain A as follows into nonlinear relation with error e：
Wherein, e is the difference of speed preset value and value of feedback, i.e. e=v*-v.
In step (1), the coordinate is transformed to " equivalent " conversion；Clarke is carried out between ABC coordinate systems and α β coordinate systems
Conversion, carries out Park conversion between α β coordinate systems and dq coordinate systems, thus further obtain the change that ABC coordinates are tied to dq coordinate systems
Change matrix；
In step (2), using PI controls, the method has the advantages that to control the simple, loss of electric machine small electric current loop.
Beneficial effect：Compared with prior art, the present invention uses current-velocity double closed-loop decoupling control structure, chooses line
Property diverter surface and exponentially approaching rule derive sliding formwork control ratio；For the buffeting problem in sliding formwork control, in conventional sliding formwork control
Integration diverter surface and varying index Reaching Law are introduced on the basis of device, not only at utmost weaken that general sliding formwork control brings trembles
Shake, and restrained effectively the load disturbance that brings of change, reduce the overshoot of speed and thrust, improve speed with
The robustness of track performance and system.
Brief description of the drawings
Fig. 1 is PMSLM servo-control systems block diagram of the present invention；
Fig. 2 is three kinds of motions dot characteristics on diverter surface of the present invention；
Fig. 3 is sliding formwork control theory diagram of the present invention；
Fig. 4 is PMSLM servo-control systems simulation model of the present invention；
Fig. 5 (a) and 5 (b) are motor thrust output of the present invention based on PI controllers and mover velocity wave form；
Fig. 6 is sliding mode controller simulation model of the present invention based on exponentially approaching rule；
Fig. 7 is system simulation model of the speed ring of the present invention using sliding mode controller；
Fig. 8 (a) and 8 (b) are motor thrust output of the present invention based on exponentially approaching rule and mover velocity wave form；
Fig. 9 is sliding mode controller simulation model of the present invention based on varying index Reaching Law；
Motor thrust output and mover velocity wave form when Figure 10 (a) and 10 (b) are speed change constant load of the present invention；
Motor thrust output and mover velocity wave form when Figure 11 (a) and 11 (b) are constant speed varying load of the present invention.
Specific embodiment
Technical scheme is described further with reference to specific embodiment.
A kind of permanent magnetic linear synchronous motor is based on the sliding formwork control of varying index Reaching Law, comprises the following steps：
(1) coordinate transform is carried out to prototype machine equation：
From " equivalent " coordinate transform, Clarke conversion transformation matrixs are carried out between ABC coordinate systems and α β coordinate systems as follows：
Park conversion is carried out between α β coordinate systems and dq coordinate systems, transformation matrix is：
ABC coordinates are tied to the transformation matrix of dq coordinate systems：
(2) Mathematical Modelings of the PMSLM under d/q coordinate systems is set up：
Primary (mover) voltage equation of permanent magnetic linear synchronous motor is：
Flux linkage equations are：
Can be obtained under dq coordinate systems by formula (7) and formula (8), the state equation of PMSLM is：
In formula, ud、uqWith the dq axle components of three-phase windings voltage, id、iqIt is the dq axle components of three-phase windings electric current；ψd、ψq
It is the dq axle components of winding magnetic linkage；Ld、LqIt is the dq axle components of inductance；ψfIt is permanent magnet fundamental wave excitation flux linkage；R is every phase winding
Resistance；V is the speed of service of linear electric motor primary (mover).
Electromagnetic power is：
Flux-linkage equations (8) are substituted into formula (10), can be obtained：
Electromagnetic power is made up of two parts：A part is due to secondary excitation field and primary armature supply quadrature axis component phase
The electromagnetic power that interaction causes；Another part is to cause L because primary and secondary magnetic resistance is unevend≠Lq, and in d-axis and friendship
Magnetic resistance electromagnetic power is produced under shaft current component collective effect.PMSLM produce electromagnetic power principal element be movement velocity and
The quadrature axis component of primary mover electric current.
PMSLM produce electromagnetic push be：
The mechanical motion equation of PMSLM is：
In above-mentioned formula, τ is pole span, and n is mover number of pole-pairs, and M is mover quality, and B is viscous friction coefficient, fLIt is outside
Disturbance.
Finally giving Mathematical Modelings of the PMSLM under dq coordinate systems is：
There is multiple mechanical variables and electromagnetism variable knowable to the model of above-mentioned linear electric motors, in system, and these become
Stronger coupling is there is between amount, in AC servo motor, is often required that and is realized vector controlled to improve control effect
Really.Using id=0 control method, the method has the advantages that to control the simple, loss of electric machine small.
From the double loop system that electric current loop and speed ring are constituted, set up PMSLM servo-control system theory diagrams and see
Fig. 1.
Electric current loop is in the inner ring of servo-control system, and its effect is to enable the electric current in electric mover coil quick accurate
Given current value really is tracked, so as to control the output of thrust, quick response, high performance control requirement is realized.If needed
Wanting servo-drive system has dynamic response faster, then the performance quality of electric current loop has conclusive effect, for AC servo
System, electric current generally uses id=0 control mode, i.e. electric current loop are typically controlled using PI.
(3) sliding mode controller of the design based on exponentially approaching rule：
Assuming that in the state space of the system, there is diverter surface s (x)=s (x1,x2,...,xn)=0, is also called out
Pass face, state space is divided into upper and lower two parts s by it>0 and s<0.Motion before reaching diverter surface is referred to as proper motion, and it takes
Certainly in the parameter and structure of the intrinsic part of system；Slip on diverter surface is referred to as sliding formwork motion, and system once enters sliding formwork
Motion, is solely dependent upon diverter surface s (x), just has robustness for external interference and parameter perturbation.System fortune on diverter surface
Moving point has three kinds of situations, as shown in Figure 2.
Usual point X：When system motion point is reached near diverter surface, diverter surface is passed through by point X, into state space
Another part.
Starting point Y：When system motion point is reached near diverter surface, point Y is left from the both sides of diverter surface.
Terminating point Z：When system motion point is reached near diverter surface, point Z is intended to from the both sides of diverter surface.
The theory diagram of sliding formwork control is as shown in Figure 3.
PMSLM vector control system medium velocity rings carry out the regulation of speed using sliding mode controller, and speed ring is given below
The design process of sliding mode controller.
By after vector, the simplified Mathematical Modeling that can obtain PMSLM by formula (14) is：
Following state variable is defined first：
IfWhen, formula (15) can be turned to：
In formula, a, b, d are time-varying parameter, fLIt is broad sense load disturbance.
If v*, v be respectively the set-point and value of feedback of speed, it is assumed that e=v*- v, x1=∫ edt,Then
Then the velocity error state equation of PMSLM is：
Desin speed error sliding formwork switching function, chooses linear switching surface first
S=Cx1+x2 (19)
Local derviation, convolution (18) is asked formula (19) to obtain
According to exponentially approaching rule：
Control law can be obtained is：
Wherein, ueqIt is sliding formwork equivalent control part, equivalent to the average value of switching control, as control system can determine
Part；And uvsIt is the uncertain part of control system, to ensure the robustness of system, by designing equivalent control part, can be with
Reduce the amplitude of switching control amount to a certain extent.
Knowable to formula (22), the frequent switching of sign function sgn (s) is the main cause for causing buffeting in control law, can
The uncertainty of control effect can be triggered, the buffeting that velocity of approach σ brings more greatly is bigger, therefore solve to buffet the name of the game
It is exactly process switching amount, the present invention realizes standard using sign function sgn (s) in saturation function sat (s) substitution sliding formwork control
Sliding formwork control.
Use obtain after saturation function substitute symbol function switching control form for：
Now, the control law of sliding mode controller is：
In formula (25), the switching of structure need not be carried out due to saturation function sat (s, Δ) boundary layer, so control law exists
It is continuous in this region such that it is able to eliminate the problem that sliding formwork is buffeted to a certain extent.
(4) varying index Reaching Law sliding mode controller is designed
Desin speed error sliding formwork switching function first, in order to ensure the robustness in system dynamic course, in formula (19)
Integral element is introduced on the basis of switching function s, then switching function is
Local derviation, convolution (18) is asked formula (26) to obtain
General exponentially approaching rule is disadvantageous in that when motor point is moved near sliding-mode surface the track of system is in
Existing banding, when motor point is moved to diverter surface s=0, produces buffeting near origin, and is unable to convergence to origin, this buffeting
Not only increase the loss of motor, and system may be caused to be modeling dynamic, cause stability to reduce.In order to overcome basic index
The defect of Reaching Law, further improvement is made to it, draws a kind of new Reaching Law, i.e. varying index Reaching Law：
Obtained by formula (27) and formula (28)
Control law can be obtained is：
Varying index Reaching Law makes the state variable e (velocity error) of speed ring be cut to sliding formwork with two kinds of speed of index and speed change
Face motion is changed, when diverter surface is reached, exponential term goes to zero, speed change plays Main Function.When variable e is in the dynamic mistake of system
When being substantially equal to zero in journey, control law makes variable e be moved to equalization point after entering diverter surface, the meeting again of this motion process
CauseConstantly reduce, final stabilization is in equalization point.System stabilization is caused to buffet and produced after equalization point
Raw switching control-σ | x1| the coefficient of sgn (s) becomes zero, so as to eliminate the buffeting problem that sliding formwork control causes.
(6) Curve guide impeller sliding formwork gain
From analysis, varying index Reaching Law can largely suppression system buffeting, but there is also deficiency not
Place, while suppressing to buffet, can make the robustness of system decrease, and the essence of varying index Reaching Law is using sliding formwork gain
The control mode proportional to error e weakens buffeting, and when error reaches zero, sliding formwork gain is also zero, and this is inevitably resulted in
System robustness can be reduced.While in order that varying index Reaching Law largely can slacken buffeting, still with stronger
Robustness, here, the present invention makes Curve guide impeller to sliding formwork gain, make sliding formwork gain A and error e into nonlinear relation such as
Under：
In formula, e is the difference of speed preset value and value of feedback, i.e. e=v*-v.
Stability analysis：
It can be seen from liapunov function stability condition, System with Sliding Mode Controller stabilization need to meet following condition：
Again σ ＞ 0, k ＞ 0, it is ensured that s withContrary sign, meets the condition of stability, i.e.,Therefore, PMSLM systems
Speed ring is stable using the sliding mode controller based on varying index Reaching Law.
Comparative example 1：Conventional PI control device is emulated
Speed ring first in PMSLM servo-control systems carries out speed regulation using conventional PI control device, and such as Fig. 4 takes
Complete simulation model is built, parameter is set, l-G simulation test is carried out, the parameter of PMSLM is as follows：DC bus-bar voltage Udc=
310V；M=5.1Kg；Ac-dc axis inductance Ld=Lq=0.0325H；Pole span τ=0.032m；Number of pole-pairs n=1；Per phase winding resistance R
=2.1 Ω；Viscous friction factor B=0.1；Electric current loop PI controller parameters Kp=200；Ki=50；Speed ring PI controllers Kp=
30；Ki=8；Given mover initial velocity v*=0.6m/s, step is to 0.8m/s during 0.8s；Load 150N.Based on speed ring PI
Shown in the thrust output of controller and mover velocity wave form such as Fig. 5 (a), Fig. 5 (b).
As can be seen from Figure 5, when speed ring uses PI controllers, under conditions of thrust output regulation is met, mover speed is deposited
In certain overshoot, slightly larger than given speed.Meanwhile, when 0.5s changes speed preset value, although speed can be when very short
Interior (less than 0.05s) reaches set-point, but motor thrust output can produce larger fluctuation with the change of mover given speed,
The interference free performance of explanation system is low, and robustness is not strong, in some precision machined lathe equipments, for wanting for control system
Seeking PI control strategies relatively very high, traditional can not well suppress the change of the parameter of electric machine, it is clear that be difficult to meet high performance
It is required that.In order to improve the robust performance of PMSLM servo-control systems, new controller need to be introduced, make up the deficiency of PI controllers.
Comparative example 2：Sliding mode controller emulation based on exponentially approaching rule
According to the control law equation of formula (25), the speed sliding mode controller based on exponentially approaching rule is built in SIMULINK
Simulation model is as shown in Figure 6.
When speed ring uses exponentially approaching rule sliding mode controller, PMSLM system simulation models as shown in fig. 7, with Fig. 4 not
With the PI controllers of speed ring are replaced by SMC, and electric current loop remains unchanged using PI to adjust.
The parameter of PMSLM：DC bus-bar voltage Udc=310V；M=5.1Kg；Ac-dc axis inductance Ld=Lq=0.0325H；
Pole span τ=0.032m；Number of pole-pairs n=1；Per phase winding resistance R=2.1 Ω；Viscous friction factor B=0.1；Electric current loop PI is controlled
Device parameter takes Kp=200；Ki=50；Take the C=2 of Reaching Law sliding mode controller；K=80；σ=0.2；
In order to verify the speed tracing performance of motor, formed using conventional PI control device with speed ring and compared, set identical
Motor operating state, i.e., it is 150N that starting load is constant, and initial velocity is 0.6m/s, and 0.5s moment given speeds step is extremely
0.8m/s.The thrust output of motor, mover velocity wave form are as shown in Figure 8.
The sliding mode controller of speed ring use can be seen that relative to traditional PI by the simulation waveform of comparison diagram 5 and Fig. 8
Controller, speed is not only in response to fast, and tracking performance is very strong.It is disadvantageous in that, when system has the feelings of heavy load disturbances
Under condition, knowable to thrust curve of output, there is chattering phenomenon in the system using sliding mode controller.
Embodiment 1：Sliding mode controller emulation based on varying index Reaching Law
Varying index Reaching Law sliding mode controller simulation model using integration diverter surface is as shown in Figure 9：Controller parameter sets
It is set to：C0=5, C1=2, k=40, a=0.01, b=0.5.Other specification is same as above during emulation.
Be control performance of the checking using the control system after sliding mode controller, set after load constant speed starts loading and
Constant load accelerates the working condition of two kinds of motors to be emulated after starting, and obtains under two kinds of running statuses, when motor works
Output waveform.
First, in order to verify the speed tracing performance of motor, motor operating state is set：Load constant is set to 150N, initially
Speed is 0.6m/s, 0.5s moment given speed steps to 0.8m/s.The thrust output of motor, mover speed are as shown in Figure 10.
By the simulation curve of comparison diagram 8 and Figure 10 it is seen that, using exponentially approaching rule and the cunning of varying index Reaching Law
The system speed tracking performance of mould controller has no too big difference, is exactly the latter slightly longer on the speed responsive time, this
It is the effect from Integral Sliding Mode face.But contrasted from thrust output result as can be seen that using after varying index Reaching Law, system exists
In the case of heavy load disturbances, preferable dynamic characteristic is shown, eliminate the chattering phenomenon in sliding formwork control.
In order to verify the interference free performance of motor, for the sliding mode controller based on varying index Reaching Law, other one is set
Kind operational factor be：Given speed is 0.6m/s, applies 150N initial loads and starts, and it is 200N that increase is loaded in 0.5s,
The thrust output of motor, mover velocity wave form are as shown in figure 11.
Analysis of simulation result：Identical motor operating parameter is set, Comprehensive Correlation example 1, comparative example 2 and the present embodiment it is imitative
True result can draw, after the speed ring of PMSLM servo-control systems is using the sliding mode controller based on varying index Reaching Law,
The buffeting that sliding formwork control is brought not only at utmost is weakened, and restrained effectively the disturbance that load change brings, reduced
The overshoot of speed and thrust, improves the tracking performance of speed and the robustness of system.
The present invention uses current-velocity double closed-loop decoupling control structure, chooses linear switching surface and exponentially approaching rule is derived
The functional relation gone out between the given current value and electric mover velocity error of sliding formwork control ratio, i.e. q axles.For in sliding formwork control
Buffeting problem, integration diverter surface and varying index Reaching Law are introduced on the basis of conventional sliding mode controller, design improved speed
Degree ring sliding mode controller, by setting the simulation result that different working conditions are obtained, the control law gone out by the algorithmic derivation,
Control effect has obtained obvious improvement, has not only obtained the smooth thrust of fast speed and speed responsive, restrained effectively negative
The disturbance of load, while also demonstrating system with stronger robustness.
Claims (3)
1. a kind of permanent magnetic linear synchronous motor is based on the sliding formwork control of varying index Reaching Law, it is characterised in that comprise the following steps：
(1) coordinate transform is carried out to prototype machine equation, sets up Mathematical Modelings of the PMSLM under d/q coordinate systems：
Wherein, ud、uqWith the dq axle components of three-phase windings voltage, id、iqIt is the dq axle components of three-phase windings electric current；ψd、ψqBe around
The dq axle components of group magnetic linkage；Ld、LqIt is the dq axle components of inductance；ψfIt is permanent magnet fundamental wave excitation flux linkage；R is the electricity of every phase winding
Resistance；V is the speed of service of linear electric motor primary mover；τ is pole span, and n is mover number of pole-pairs, and M is mover quality, and B rubs for viscous
Wipe coefficient, fLIt is external disturbance；
(2) the PMSLM two close cycles servo-control systems being made up of electric current loop and speed ring are set up；
(3) step (1) gained Mathematical Modeling is reduced to：
Definition status variable：Above formula is turned to：
In formula, a, b, d are time-varying parameter, fLIt is broad sense load disturbance；
If v*, v be respectively the set-point and value of feedback of speed, it is assumed that e=v*- v, x1=∫ edt,Then
The velocity error state equation for obtaining PMSLM is：
(4) linear switching function s=Cx is chosen1+x2, according to exponentially approaching ruleObtain sliding formwork control ratio：
Wherein, ueqIt is sliding formwork equivalent control part, uvsIt is the uncertain part of control system；
(5) using sign function sgn (s) in saturation function sat (s) substitution sliding formwork control, the control law of sliding mode controller is：
(6) integral element is introduced on the basis of step (4) switching function s, then switching function is
By varying index Reaching LawObtaining sliding formwork control ratio is：
(7) make sliding formwork gain A as follows into nonlinear relation with error e：
Wherein, e is the difference of speed preset value and value of feedback, i.e. e=v*-v.
2. the sliding formwork control based on varying index Reaching Law according to claim 1, it is characterised in that：It is described in step (1)
Coordinate is transformed to " equivalent " conversion.
3. the sliding formwork control based on varying index Reaching Law according to claim 1, it is characterised in that：In step (2), electric current
Ring is using PI controls.
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