CN113922721B - Model predictive control method for permanent magnet synchronous linear motor with continuous control set - Google Patents

Abstract

The invention relates to a continuous control set permanent magnet synchronous linear motor model prediction control method, which comprises the steps of obtaining a stator current state equation under a rotating coordinate system by utilizing a mathematical model of a permanent magnet synchronous linear motor; determining a cost function according to a stator current state equation, and converting the cost function into a quadratic optimization equation; calculating an optimal solution of the quadratic optimization equation, and determining a sector in which the optimal solution is located; determining three voltage vectors of the sector synthesized optimal voltage vector, calculating the respective action time of the three voltage vectors, PWM modulating the time of the three voltage vectors, defining the error between the reference rotating speed and the feedback rotating speed of the motor as a state variable, determining a non-singular terminal sliding mode surface according to the state variable, and differentiating the sliding mode surface to obtain an output expression of the sliding mode controller. The invention reduces the online calculation amount of multi-step prediction, obtains an optimal switching state of non-Boolean quantity after the related constraint on the switching state is not considered, and remarkably improves the control performance.

Description

Model Predictive Control Method for Continuous Control Set Permanent Magnet Synchronous Linear Motor

technical field

The invention relates to the technical field of permanent magnet synchronous linear motor control, in particular to a continuous control set permanent magnet synchronous linear motor model predictive control method.

Background technique

The permanent magnet synchronous linear motor, because of the cancellation of the mechanical transmission link, has high speed, high precision and zero transmission characteristics, so its mechanical loss is small, the thrust density is high, and the dynamic response is fast, so it has attracted wide attention and has been widely used in elevators and semiconductor manufacturing. Precision applications such as equipment and computer numerical control machine tools.

Currently, vector control, direct torque control and finite control set model predictive control are widely used. Compared with direct torque control, model predictive control is more accurate and effective in vector selection. It selects the optimal voltage vector at the current moment by predicting the state of the motor, so that better steady-state performance can be obtained. The above model predictive control has the characteristics of fast dynamic response, good current control performance, easy consideration of system nonlinear constraints, and flexible control. The traditional current predictive control can get a better control effect through one-step current prediction, but the one-step current predictive control method ignores the time-consuming algorithm calculation and system sampling. If the sampling time is small, the calculation time will be long. There will be a time delay problem, the system will always use the switch state at the previous moment, and the current prediction will deviate, resulting in inaccurate control accuracy. When the system enters the steady state, the speed fluctuates greatly and the current harmonics larger. In addition, although the multi-step predictive control using the traditional ergodic method can bring better control effects, it is followed by an exponentially increasing calculation amount, which is not conducive to the online execution of the system. Among them, the finite control set model predictive control only selects one switch state in one cycle and directly sends it to the inverter, which avoids PWM modulation and is easy to control, but this algorithm will bring large current ripples and torque ripples. The accuracy is poor. Moreover, the traditional sliding mode control algorithm generally uses a linear sliding mode surface, which takes a long time to converge state errors and causes serious chattering problems.

Contents of the invention

Therefore, the technical problem to be solved by the present invention is to overcome the problems existing in the prior art, and to propose a model predictive control method for continuous control of integrated permanent magnet synchronous linear motors, which is of great significance for realizing high-performance control of permanent magnet synchronous linear motors.

In order to solve the above technical problems, the present invention provides a model predictive control method for continuous control integrated permanent magnet synchronous linear motor, comprising the following steps:

Using the mathematical model of the permanent magnet synchronous linear motor, the state equation of the stator current in the rotating coordinate system is obtained;

determining a cost function according to the stator current state equation, and converting the cost function into a quadratic optimization equation;

Calculating the optimal solution of the quadratic optimization equation, obtaining the continuous switching state of the inverter in an ideal state, and determining the sector where the optimal solution is located;

Determine the three voltage vectors of the sector-combined optimal voltage vectors, calculate the respective action times of the three voltage vectors, perform PWM waveform modulation on the time of the three voltage vectors, and input the modulated PWM waveforms to the In the above inverter, the error between the reference speed and the feedback speed of the motor is defined as the state variable at the same time, and the non-singular terminal sliding mode surface is determined according to the state variable, and the sliding mode surface is differentiated to obtain the sliding mode controller. output expression.

In one embodiment of the present invention, using the mathematical model of the permanent magnet synchronous linear motor to obtain the stator current state equation under the rotating coordinate system includes:

The state equation of the stator current is as follows:

Among them, u _d and u _q are stator direct axis voltage and electron quadrature axis voltage respectively, _id and i _q are stator direct axis current and stator quadrature axis current respectively, R _s is stator resistance, ψ _d and ψ _q are stator direct Shaft flux linkage and stator quadrature axis flux linkage, ψ _d =L _d i _d +ψ _f , ψ _q =L _q i _q , ψ _f is permanent magnet flux linkage.

In one embodiment of the present invention, after obtaining the state equation of the stator current, the differential form of the current is obtained according to Euler's formula, so that the current value of the k+1 period can be obtained from the kth period.

In one embodiment of the present invention, determining the cost function according to the stator current state equation includes:

define variable Δs(k|k)=s(k|k)-s(k-1|k), the form of the cost function is expressed as /> In the formula, λ>0 is the limit value of the weight factor current, Δs(k|k) is the switching loss between the front and rear switch states, and λ is the weight coefficient;

Introduce the switching sequence S(k|k)=[s(k|k) ^T ,...,s(k+N-1|k) ^T ] ^T to construct the stator cross-axis and direct-axis current prediction values in the rolling time domain The following vector form is as follows, where N is the number of prediction steps, S(k|k)∈M, s(k|k) represents the switch state of the switch position of the inverter at time k, and Ms×s...×s represents is the N times Cartesian product of the discrete switch state s:

x _dq (k+N|k)＝A ^N (k|k)x _dq (k|k)+[A ^N-1 (k|k)B+...+A ⁰ (k|k)B]s (k|k)+[A ^N-1 (k|k)F(k|k)+...+A ⁰ (k|k)F];

Let Y _dq represent the output of the predicted value of the orthogonal and direct axis current within the prediction step range from k+1 time to k+N time, and Y ^* _dq is the corresponding reference output:

Y _dq ＝Γx _dq (k|k)+YS(k|k)+Π

In the formula, Γ=[A, A ² ,…,A ^N ] ^T , />

Modify the cost function to and define:

Ξ(k|k)=((Γx _dq (k|k)-Ω(k|k)) ^T Υ-λ(Es(k-1|k)) ^T W) ^T , Q=Υ ^T Υ+λW ^T W;

Determine the cost function as J=ξ(k|k)+2(Ξ(k|k)) ^T S(k|k)+S(k|k) ^T QS(k|k), where

In one embodiment of the present invention, converting the cost function into a quadratic optimization equation includes:

Transform the cost function J=ξ(k|k)+2(Ξ(k|k)) ^T S(k|k)+S(k|k) ^T QS(k|k) into quadratic optimization by matrix transformation The equation is as follows:

J＝(S(k|k)+Q ^-1 Ξ(k|k)) ^T Q(S(k|k)+Q ^-1 Ξ(k|k))+c(k|k)

Among them, c(k) is a constant term.

In one embodiment of the present invention, calculating the optimal solution of the quadratic optimization equation includes:

Calculating the optimal solution of the quadratic optimization equation under unconstrained conditions is S _unc (k | k)=-HQ- ¹ Ξ (k), wherein the optimal solution S _unc (k | k) is the column of 3N rows Vector, the first three elements of which represent the optimal switch state s _opt =[S _unc (1) S _unc (2) S _unc (3)] ^T at a certain moment.

In an embodiment of the present invention, determining the sector where the optimal solution is located includes:

calculating the components u _a , u _β of the optimal switching state s _opt on the α-β axis;

Define the normalization vector and /> in get P with sector /> Relationship;

According to the P and sector The relationship of determines the sector where the optimal solution is located.

In one embodiment of the present invention, calculating the respective action times of the three voltage vectors includes:

make The action times of the three voltage vectors are obtained, wherein the three voltage vectors include one zero voltage vector and two non-zero voltage vectors.

In one embodiment of the present invention, the error between the reference speed and the feedback speed of the motor is defined as a state variable, and determining the non-singular terminal sliding surface according to the state variable includes:

Define the speed error e=v ^* -v, according to the electromagnetic thrust formula of the permanent magnet synchronous linear motor get the formula as />

Determine the non-singular terminal sliding mode surface as Among them, k, α, β are all greater than 0, g, h, p, q are all positive odd numbers, and 1<p/q<2, p/q<g/h.

In one embodiment of the present invention, the output expression of the sliding mode controller obtained by differentiating the sliding mode surface includes:

make Differentiating the terminal sliding mode surface yields:

That is, the output of the sliding mode controller is Where ξ>0, γ>0;

define switch function Where δ=π/(2Δ), Δ is the thickness of the boundary layer, that is, the output of the sliding mode controller is />

The above technical solution of the present invention has the following advantages compared with the prior art:

The present invention converts the coupling multivariable cost function into an easy-to-calculate quadratic optimization equation through matrix conversion, reduces the online calculation amount of multi-step prediction through the quadratic optimization equation, and solves the time delay problem caused by algorithm calculation and system sampling, And without considering the relevant constraints on the switch state, a non-Boolean optimal switch state is obtained, which significantly improves the control performance. At the same time, the non-singular terminal sliding mode controller is used to improve the anti-disturbance ability of the entire system, which is beneficial to the realization of permanent magnet The high performance control of synchronous linear motor is of great significance.

Description of drawings

In order to make the content of the present invention more clearly understood, the present invention will be further described in detail below according to the specific embodiments of the present invention and in conjunction with the accompanying drawings.

Fig. 1 is a schematic flow chart of the method for model predictive control of the continuous control integrated permanent magnet synchronous linear motor of the present invention.

Fig. 2 is a system control block diagram of the method for model predictive control of the continuous control integrated permanent magnet synchronous linear motor of the present invention.

Fig. 3 is a block diagram of the inverter for the model predictive control method of the continuous control integrated permanent magnet synchronous linear motor of the present invention.

Fig. 4 is a schematic diagram of sector division of the method for model predictive control of the continuous control integrated permanent magnet synchronous linear motor of the present invention.

Fig. 5 is the sector of the model predictive control method for the continuous control set permanent magnet synchronous linear motor of the present invention Schematic diagram of the relationship with P.

Fig. 6 is an action time diagram of three voltage vectors in the model predictive control method of the continuous control integrated permanent magnet synchronous linear motor of the present invention.

Fig. 7 is a waveform diagram of the rotational speed under the three-step predictive control of the model predictive control method of the continuous control integrated permanent magnet synchronous linear motor of the present invention without disturbance compensation.

Fig. 8 is a waveform diagram of the rotational speed under the three-step predictive control and disturbance compensation of the model predictive control method of the continuous control integrated permanent magnet synchronous linear motor of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the examples given are not intended to limit the present invention.

Referring to FIGS. 1 to 6, this embodiment provides a model predictive control method for continuous control set permanent magnet synchronous linear motor, including the following steps:

S100: Using the mathematical model of the permanent magnet synchronous linear motor to obtain the state equation of the stator current in the rotating coordinate system;

S200: Determine a cost function according to the stator current state equation, and convert the cost function into a quadratic optimization equation;

S300: Calculate the optimal solution of the quadratic optimization equation, obtain the continuous switching state of the inverter in an ideal state, and determine the sector where the optimal solution is located;

S400: Determine the three voltage vectors of the sector-combined optimal voltage vectors, calculate the respective action times of the three voltage vectors, perform PWM waveform modulation on the time of the three voltage vectors, and input the modulated PWM waveforms In the inverter, the error between the reference speed and the feedback speed of the motor is defined as the state variable at the same time, and the non-singular terminal sliding mode surface is determined according to the state variable, and the sliding mode control is obtained by differentiating the sliding mode surface The output expression of the device.

The present invention converts the coupling multivariable cost function into an easy-to-calculate quadratic optimization equation through matrix conversion, reduces the online calculation amount of multi-step prediction through the quadratic optimization equation, and solves the time delay problem caused by algorithm calculation and system sampling, And without considering the relevant constraints on the switch state, a non-Boolean optimal switch state is obtained, which significantly improves the control performance. At the same time, the non-singular terminal sliding mode controller is used to improve the anti-disturbance ability of the entire system, which is beneficial to the realization of permanent magnet The high performance control of synchronous linear motor is of great significance.

Wherein, in step S100, using the mathematical model of the permanent magnet synchronous linear motor to obtain the state equation of the stator current in the rotating coordinate system includes:

The state equation of the stator current is as follows:

Among them, u _d and u _q are stator direct axis voltage and electron quadrature axis voltage respectively, _id and i _q are stator direct axis current and stator quadrature axis current respectively, R _s is stator resistance, ψ _d and ψ _q are stator direct Shaft flux linkage and stator quadrature axis flux linkage, ψ _d =L _d i _d +ψ _f , ψ _q =L _q i _q , ψ _f is permanent magnet flux linkage.

After obtaining the state equation of the stator current, the differential form of the current is obtained according to Euler's formula:

So that the current value of the k+1 period can be obtained from the kth period:

In the formula:

Among them, s(k) represents the switching state at time k, U _dc is the DC side voltage, G _2/2 and G _3/2 are coordinate transformation matrices. Let x _dq =[i _d ,i _q ] ^T is the state vector of the system, /> is the corresponding reference value. ·(k+i|k) is expressed as the value at time k+i predicted at time k.

Wherein, in step S200, determining the cost function according to the stator current state equation includes:

define variables Δs(k|k)=s(k|k)-s(k-1|k), considering the error between the current prediction value and the reference value and the switching loss caused by the switch change at the front and back moments, the form of the cost function is expressed for /> In the formula, λ>0 is the limit value of the weight factor current, Δs(k|k) is the switching loss between the front and rear switch states, and λ is the weight coefficient;

Introduce the switching sequence S(k|k)=[s(k|k) ^T ,...,s(k+N-1|k) ^T ] ^T to construct the stator cross-axis and direct-axis current prediction values in the rolling time domain The following vector form is as follows, where N is the number of prediction steps, S(k|k)∈M, s(k|k) represents the switching state of the switch position of the inverter at time k, M s×s...×s Expressed as N times Cartesian product of discrete switch states s:

x _dq (k+N|k)＝A ^N (k|k)x _dq (k|k)+[A ^N-1 (k|k)B+...+A ⁰ (k|k)B]s (k|k)+[A ^N-1 (k|k)F(k|k)+...+A ⁰ (k|k)F];

Let Y _dq represent the output of the predicted value of the orthogonal and direct axis current within the prediction step range from k+1 time to k+N time, and Y ^* _dq is the corresponding reference output:

Y _dq ＝Γx _dq (k|k)+YS(k|k)+Π

In the formula, Γ=[A, A ² ,…,A ^N ] ^T , />

Modify the cost function to and define:

Ξ(k|k)=((Γx _dq (k|k)-Ω(k|k)) ^T Υ-λ(Es(k-1|k)) ^T W) ^T , Q=Υ ^T Υ+λW ^T W;

Determine the cost function as J=ξ(k|k)+2(Ξ(k|k)) ^T S(k|k)+S(k|k) ^T QS(k|k), where

Convert the cost function into a quadratic optimization equation as J=(S(k|k)+Q- ¹ Ξ(k|k)) ^T Q(S(k|k)+Q- ¹ Ξ(k|k)) +c(k|k), where c(k) is a constant term that only changes when the sampling moment changes.

Wherein, in step S300, the optimal solution of the switch state under the unconstrained condition at time k is introduced here, because Q is positive definite, and the optimal solution S _unc (k|k)=-HQ ^-1 Ξ( k). It can be deduced from the previous calculation that S _unc (k|k) is a column vector of 3N rows, and its first three elements represent the optimal switch state s _opt = [S _unc (1) S _unc (2) S _unc (3)] ^T noticed that s _opt is not a Boolean quantity, it is a continuous switch state expression, so it cannot be directly fed into the inverter.

After obtaining the optimal continuous switching state, determine which sector the optimal voltage vector is in. Firstly, the components u _a , u _β of s _opt on the α-β axis are required:

Define a normalization vector here and /> in:

Finally get P and sector The relationship is shown in Figure 5.

Wherein, in step S400, calculating the respective action times of the three voltage vectors includes:

make Figure 6 shows the action time of the three voltage vectors, where the three voltage vectors include a zero voltage vector and two non-zero voltage vectors.

Wherein, in step S400, the error between the reference speed of the motor and the feedback speed is defined as the state variable, and the non-singular terminal sliding mode surface is determined according to the state variable, and the sliding mode surface is differentiated to obtain the output expression of the sliding mode controller formulas include:

Define the speed error e=v ^* -v, according to the electromagnetic thrust formula of the permanent magnet synchronous linear motor get the formula as /> Considering that the output frequency of the controller is much greater than the change frequency of the disturbance, the disturbance d can be regarded as a constant within a sampling period, so:

Determine the non-singular terminal sliding mode surface as Among them, k, α, β are all greater than 0, g, h, p, q are all positive odd numbers, and 1<p/q<2, p/q<g/h;

make Differentiating the terminal sliding mode surface yields:

That is, the output of the sliding mode controller is Where ξ>0, γ>0;

In order to reduce the chattering of the sliding mode surface, define the switching function Where δ=π/(2Δ), Δ is the thickness of the boundary layer, that is, the output of the sliding mode controller is /> After integration, the reference current of the entire q-axis is:

In order to further reduce the influence of the disturbance, the present invention also designs a disturbance observer to compensate the speed loop controller.

The design of the disturbance observer is introduced below.

The first step: establish the following state space equation:

where x=[vd] ^T , u=F _e , The matrix looks like this:

The state observer is constructed according to the state equation as follows:

in Represents the observed value of x, K=[k ₁ k ₂ ] is the feedback coefficient matrix.

The second step: According to the above formula, the error equation can be obtained as;

The matrix characteristic equation can be obtained as:

Suppose the desired characteristic equation is:

η ² −(σ ₁ +σ ₂ ) η+σ ₁ σ ₂ =0.

Step 3: According to the expectation, the feedback coefficient can be obtained as follows:

Step 4: The final disturbance observer design is as follows:

Step 5: Compensate the output of the disturbance observer to obtain the sliding mode controller of the speed loop. The final output of the sliding mode controller is as follows:

in is the feedback gain.

Fig. 7 and Fig. 8 are respectively the rotational speed waveform diagram without disturbance compensation and the rotational speed waveform diagram with disturbance compensation in the present invention. From the comparison of the simulation results, it can be seen that under the condition that the load disturbance is constantly changing, the sliding mode controller is adopted The speed waveform is more stable. It can be seen that after the traditional PI controller is compensated by the observer, the speed stability has been significantly improved, but it is still not as good as the effect of the sliding mode controller with the load observer.

Those skilled in the art should understand that the embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present application is described with reference to flowcharts and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each procedure and/or block in the flowchart and/or block diagram, and a combination of procedures and/or blocks in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions may be provided to a general purpose computer, special purpose computer, embedded processor, or processor of other programmable data processing equipment to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing equipment produce a An apparatus for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions The device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions can also be loaded onto a computer or other programmable data processing device, causing a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby The instructions provide steps for implementing the functions specified in the flow chart or blocks of the flowchart and/or the block or blocks of the block diagrams.

Apparently, the above-mentioned embodiments are only examples for clear description, and are not intended to limit the implementation. For those of ordinary skill in the art, on the basis of the above description, other changes or changes in various forms can also be made. It is not necessary and impossible to exhaustively list all the implementation manners here. However, the obvious changes or changes derived therefrom are still within the scope of protection of the present invention.

Claims (8)

1. A continuous control set permanent magnet synchronous linear motor model prediction control method is characterized by comprising the following steps:

obtaining a stator current state equation under a rotating coordinate system by using a mathematical model of the permanent magnet synchronous linear motor;

determining a cost function according to the stator current state equation, and converting the cost function into a quadratic optimization equation;

calculating an optimal solution of the quadratic optimization equation to obtain an inverter continuous switch state in an ideal state, and determining a sector in which the optimal solution is located;

determining three voltage vectors of the sector synthesized optimal voltage vector, calculating the respective acting time of the three voltage vectors, carrying out PWM waveform modulation on the time of the three voltage vectors, inputting the modulated PWM waveform into the inverter, defining the error between the reference rotating speed and the feedback rotating speed of the motor as a state variable, determining a nonsingular terminal sliding mode surface according to the state variable, and differentiating the sliding mode surface to obtain an output expression of a sliding mode controller;

determining a cost function from the stator current state equation includes:

definition of variablesΔs (k|k) =s (k|k) -s (k-1|k), the form of the cost function is expressed as +.>Lambda in>0 is the limiting value of the weight factor current, deltas (k|k) is the switching loss between the front and back switching states, and lambda is the weight coefficient;

introducing a switching sequence S (k|k) = [ S (k|k) ^T ,...,s(k+N-1|k) ^T ] ^T The vector form of the stator alternating current and direct axis current predicted values under the rolling time domain is constructed as follows, wherein N is the predicted step number, S (k|k) epsilon M, S (k|k) represents the switch state of the switch position at the moment k of the inverter,expressed as N times cartesian product of discrete switch states s:

x _dq (k+N|k)＝A ^N (k|k)x _dq (k|k)+[A ^N-1 (k|k)B+...+A ⁰ (k|k)B]s(k|k)+[A ^N-1 (k|k)F(k|k)+...+A ⁰ (k|k)F]；

let Y _dq Output of the alternating current and direct current predicted value in the predicted step length range from time k+1 to time k+N is shown, Y ^* _dq For the corresponding reference output:

Y _dq ＝Γx _dq (k|k)+ΥS(k|k)+Π

in the method, in the process of the invention,Γ＝[A，A ² ,...,A ^N ] ^T ，/>

modifying a cost function toAnd defines:

Ξ(k|k)＝((Γx _dq (k|k)-Ω(k|k)) ^T Υ-λ(Es(k-1|k)) ^T W) ^T ，Q＝Υ ^T Υ+λW ^T W；

determining the cost function as j=ζ (k|k) +2 (xi (k|k)) ^T S(k|k)+S(k|k) ^T QS (k|k) where

Converting the cost function into a quadratic optimization equation includes:

cost function j=ζ (k|k) +2 (Σ (k|k)) ^T S(k|k)+S(k|k) ^T The conversion of QS (k|k) to the quadratic optimization equation is as follows:

J＝(S(k|k)+Q ^-1 Ξ(k|k)) ^T Q(S(k|k)+Q ^-1 Ξ(k|k))+c(k|k)

wherein c (k) is a constant term.

2. The continuous control set permanent magnet synchronous linear motor model predictive control method according to claim 1, characterized by comprising the steps of: the method for obtaining the stator current state equation under the rotating coordinate system by using the mathematical model of the permanent magnet synchronous linear motor comprises the following steps:

the stator current state equation is as follows:

wherein u is _d And u is equal to _q Respectively a stator straight axis voltage and a stator quadrature axis voltage, i _d And i _q Respectively, a stator straight axis current and a stator quadrature axis current, R _s Is stator resistance, ψ _d And psi is equal to _q Is the direct axis magnetic linkage of the stator and the quadrature axis magnetic linkage of the stator, ψ _d ＝L _d i _d +ψ _f ，ψ _q ＝L _q i _q ，ψ _f Is a permanent magnet flux linkage.

3. The continuous control set permanent magnet synchronous linear motor model predictive control method according to claim 2, characterized by comprising the steps of: after the stator current state equation is obtained, a differential form of the current is obtained according to the euler equation so that the current value of the k+1 period can be obtained from the kth period.

4. The continuous control set permanent magnet synchronous linear motor model predictive control method according to claim 1, characterized by comprising the steps of: calculating an optimal solution for the quadratic optimization equation includes:

calculating the optimal solution of the quadratic optimization equation as S under the unconstrained condition _unc (k|k)＝-HQ ^-1 Xi (k), where the optimal solution S _unc (k|k) is a column vector of 3N rows, the first three elements of which represent the optimal switching state s at a certain moment _opt ＝[S _unc (1) S _unc (2) S _unc (3)] ^T 。

5. The predictive control method for a continuous control set permanent magnet synchronous linear motor model according to claim 4, wherein the predictive control method comprises the following steps: determining the sector in which the optimal solution is located includes:

calculating the optimal switching state s _opt Component u in the alpha-beta axis _a ,u _β ；

Defining normalized vectorsAnd->Wherein->Get P and sector->Is a relationship of (2);

according to the P and the sectorAnd determining the sector where the optimal solution is located.

6. The predictive control method for a continuous control set permanent magnet synchronous linear motor model according to claim 5, wherein the predictive control method comprises the following steps: calculating the respective time of action of the three voltage vectors comprises:

order theAnd obtaining the acting time of the three voltage vectors, wherein the three voltage vectors comprise one zero voltage vector and two non-zero voltage vectors.

7. The predictive control method for a continuous control set permanent magnet synchronous linear motor model according to claim 6, wherein: defining an error between a reference rotational speed and a feedback rotational speed of the motor as a state variable, and determining a non-singular terminal sliding mode surface according to the state variable comprises:

defining a speed error e=v ^* V, electromagnetic thrust formula according to permanent magnet synchronous linear motorThe formula is +.>

Determining a nonsingular terminal slip plane asWherein k, alpha, beta are all greater than 0, g, h, p, q are all positive odd numbers, and 1<p/q<2，p/q<g/h。

8. The predictive control method for a continuous control set permanent magnet synchronous linear motor model according to claim 7, wherein: differentiating the sliding mode surface to obtain an output expression of the sliding mode controller comprises the following steps:

order theDifferentiating the terminal sliding mode surface to obtain:

i.e. the output of the slip-form controller isWherein xi>0,γ>0；

Defining a switching functionWhere δ=pi/(2Δ), Δ is the boundary layer thickness, i.e. the output of the slip-mode controller is +.>