CN108964544A - A kind of permanent magnet linear synchronous motor multiple time scale model System with Sliding Mode Controller and method - Google Patents

Abstract

The invention discloses a dual-time-scale sliding mode control system and method for a permanent magnet linear synchronous motor, belonging to the field of linear motor control. Firstly, the mathematical model of the permanent magnet linear synchronous motor in the two-phase rotating orthogonal coordinate system is established; secondly, it is established as a dual time scale model of the permanent magnet linear synchronous motor; then, in order to improve the robustness of the system to external disturbances, the The quasi-sliding mode method and reaching law method design the sliding mode control laws corresponding to the fast and slow subsystems respectively, and then unify the time scales of the two subsystems to synthesize the combined control law of the permanent magnet linear synchronous motor. Finally, the stability of the system is analyzed using Lyapunov's stability theory. The most important feature of the present invention is that the designed dual-time-scale sliding mode controller enables the controlled system of the permanent magnet linear synchronous motor to have better static performance and good and fast dynamic performance, and makes the system highly robust to external disturbances sex.

Description

A dual-time-scale sliding mode control system and method for a permanent magnet linear synchronous motor

technical field

The invention relates to a dual-time-scale sliding mode control system and method for a permanent magnet linear synchronous motor, belonging to the technical field of linear synchronous motor control.

Background technique

As a linear induction motor, the permanent magnet linear synchronous motor has the advantages of low moment of inertia, small volume and weight, high efficiency, easy maintenance, and high reliability in addition to the excellent advantages of the linear motor itself. It is widely used in high-precision AC in the servo system. Although the linear motor has special advantages compared with the traditional rotary motor, it is similar to the rotary motor and is also a complex control object with high coupling, multi-variable, nonlinear and time-varying properties. In addition, it is affected by thrust fluctuations and Influenced by non-linear factors such as friction, the resistance to different degrees of external disturbance is weak, which brings great difficulty to the research of control strategy. In order to greatly improve the control performance and precision of permanent magnet linear synchronous motors, traditional control strategies have been difficult to meet the performance requirements of permanent magnet linear synchronous motor control systems, so it is very meaningful to study new control methods. Currently, the most commonly used The control strategy of the system is PID closed-loop control in the classical control field. This traditional control system has slow dynamic response and poor control precision.

Contents of the invention

Aiming at the problems existing in the above-mentioned prior art, the present invention provides a dual-time-scale sliding mode control system and method for permanent magnet linear synchronous motors, which can effectively improve the dynamic response speed of the control system, and at the same time be robust to parameter perturbations and external disturbances. Robust and easy to design and implement.

In order to achieve the above object, the technical solution adopted in the present invention is: a dual-time-scale sliding mode control system for permanent magnet linear synchronous motors, including a slow subsystem sliding mode surface module and a fast subsystem sliding mode surface module, the slow subsystem The sliding mode surface module is connected to the combined control law module through the slow subsystem sliding mode control law module; the fast subsystem sliding mode surface module is connected to the combined control law module through the fast subsystem sliding mode control law module; the combined control law module is connected to There is a permanent magnet linear synchronous motor, and the permanent magnet linear synchronous motor is also connected with an external interference signal. The permanent magnet linear synchronous motor is connected to the sliding surface module of the slow subsystem, and the actual speed of the permanent magnet linear synchronous motor is compared with the given The speed error signal is transmitted to the slow subsystem sliding surface module; the permanent magnet linear synchronous motor is connected to the fast subsystem sliding surface module through the fast variable estimation module, and the current id and iq of the permanent magnet linear synchronous motor are transmitted to the fast subsystem. In the variable estimation module, the fast variable current components idf and iqf obtained by subtracting the slow variable current components ids and iqs from the fast variable estimation module are transmitted to the fast subsystem sliding mode surface module.

A control method for a dual-time-scale sliding mode control system of a permanent magnet linear synchronous motor, comprising the following steps:

A. Establish a mathematical model;

B. Establish a dual time scale model;

C. Design sliding mode control law;

D. Synthetic combination controller;

E. Stability analysis.

The beneficial effects of the present invention are: the control system has strong robustness to disturbance, and can realize accurate tracking of given speed signal; The quasi-sliding mode method and the reaching law method are used in the controller respectively, the inherent chattering phenomenon of the sliding mode control is greatly improved, and the control quantity is close to zero after the control system enters a steady state.

Description of drawings

Fig. 1 is the basic working principle figure of permanent magnet linear synchronous motor of the present invention;

Figure 2 is a block diagram of a dual-time-scale sliding mode control system for a permanent magnet linear synchronous motor;

Fig. 3 is the comparative schematic diagram of the speed response curve of dual-time scale sliding mode control and PID control of the present invention;

Fig. 4 is the comparative schematic diagram of the speed response curve of dual time scale control of the present invention and general sliding mode control;

Fig. 5 is the schematic diagram of the electromagnetic wave thrust curve of dual-time scale sliding mode control of the present invention;

Fig. 6 is the electromagnetic thrust of general sliding mode control;

Fig. 7 is a schematic diagram of the three-phase current of the motor under the dual-time-scale sliding mode control of the present invention.

In the figure: 1. Slow subsystem sliding mode surface module, 2. Fast subsystem sliding mode surface module, 3. Slow subsystem sliding mode control law module, 4. Fast subsystem sliding mode control law module, 5. Combined control law Module, 6, permanent magnet linear synchronous motor, 7, disturbance, 8, fast variable estimation module.

Detailed ways

The present invention will be further described below in conjunction with accompanying drawing.

As shown in Figure 2, a dual-time-scale sliding mode control system for permanent magnet linear synchronous motors includes a slow subsystem sliding mode surface module 1 and a fast subsystem sliding mode surface module 2, and the slow subsystem sliding mode surface module 1 The slow subsystem sliding mode control law module 3 is connected with the combined control law module 5; the fast subsystem sliding mode surface module 2 is connected with the combined control law module 5 through the fast subsystem sliding mode control law module 4; the combined control law module 5 is connected with a permanent magnet linear synchronous motor 6, the permanent magnet linear synchronous motor 6 is also connected with an external disturbance 7, the permanent magnet linear synchronous motor 6 is connected to the slow subsystem sliding surface module 1, and the permanent magnet linear synchronous motor The error signal between the actual speed of 6 and the given speed is transmitted to the slow subsystem sliding mode surface module 1; the permanent magnet linear synchronous motor 6 is connected to the fast subsystem sliding mode surface module 2 through the fast variable estimation module 8, and the permanent magnet The current i _d and i _q of the linear synchronous motor 6 are transmitted to the fast variable estimation module 8, and the fast variable current components i _df and i _qf obtained by subtracting the slow variable current components i _ds and i _qs from the fast variable estimation module 8 are transmitted to the Fast Subsystem Sliding Mode Surface Module2.

A control method for a dual-time-scale sliding mode control system of a permanent magnet linear synchronous motor, comprising the following steps:

A. Establish a mathematical model;

The basic working principle of the permanent magnet linear synchronous motor: refer to the rotating synchronous motor, cut it along its radial direction, and then tile the circumference of the rotating motor horizontally along the straight line to obtain a mechanical structure similar to that of the linear motor. The permanent magnet linear synchronous motor can be regarded as a development from the rotary synchronous motor. The permanent magnet linear synchronous motor is mainly divided into primary and secondary parts, the former corresponds to the stator part of the rotary synchronous motor, and the latter corresponds to the rotor part of the rotary synchronous motor. In order to generate the excitation magnetic field, the secondary is distributed with N and S permanent magnets which are longitudinally magnetized evenly and alternately along the straight line. In order to generate an air gap magnetic field, the primary iron core is distributed with cogs equipped with three-phase armature windings. When the linear motor is powered on, a traveling wave magnetic field will be generated to drive the linear motor to move horizontally along the guide rail; Its basic working principle is shown in Figure 1;

A.1. Establish a dynamic model:

The dynamic equation of the permanent magnet linear synchronous motor is composed of voltage equation, flux linkage equation, electromagnetic thrust equation and motion equation; through coordinate transformation, the mathematical model application vector of the permanent magnet linear synchronous motor on the two-phase synchronous rotating orthogonal coordinate system is obtained The idea of control is to make the electromagnetic thrust proportional to the magnitude of the quadrature axis current component i _q and set the given value i _d of the direct axis current component to zero, and the simplified dynamic model of the permanent magnet linear synchronous motor on the dq coordinate system is as follows Formula (1) shows:

Among them, i _d , i _q , u _d , u _q are the current and voltage values of the d and q axes respectively, L is the inductance, R is the resistance value of the mover winding, ω=πv/τ is the angular velocity of the rotor, and v is speed, τ is the pole pitch of the magnetic pole, is the flux linkage of the permanent magnet, Fe is the electromagnetic thrust, M is the mass of the carrier, B is the viscous friction coefficient, F _L is the load torque, K _F is the electromagnetic thrust coefficient, and its expression is shown in the following formula (2):

Among them, p is the number of magnetic pole pairs of the motor;

A.2. Establish state equation:

Rewrite the dynamic model of the permanent magnet linear synchronous motor obtained in step A.1 into the state equation form, as shown in the following formula (3):

Among them, the state variable is v and i=[i _d i _q ] ^T , the control variable is u=[u _d u _q ] ^T ;

A.3. The standard form of singular perturbation:

From the mathematical model in the two-phase rotating orthogonal coordinate system, it can be seen that the degree of nonlinear coupling between the current and the current and between the current and the speed is very large, so it is necessary to find a corresponding method to achieve linear decoupling; consider the electrical time constant The value of L/R is far less than the value of the mechanical time constant M/B, so σ=LB/MR can be taken as the perturbation parameter with a small median value in the singular perturbation system, and the standard form of the singular perturbation of the motor is obtained as the formula ( 4) as shown:

B. Establish a dual time scale model;

B.1. Establish slow subsystem model:

Since the value of σ is very small, assuming the perturbation parameter σ→0, the full-order system model of the original permanent magnet linear synchronous motor is shown in the following formula (5):

Among them, v _s , i _ds , i _qs , u _ds , u _qs represent the slow-varying components corresponding to v, i, u respectively; Substitute the current value obtained from the second fraction in formula (5) into the first Fraction, the expression of the obtained slow subsystem model is shown in formula (6):

in, u _ds and u _qs are the control signals of the slow subsystem, K _F is the electromagnetic thrust coefficient, M is the mass of the carrier, is the flux linkage of the permanent magnet, F _L is the load torque, τ is the pole pitch of the magnetic pole, B is the viscous friction coefficient, L is the inductance, and R is the resistance value of the mover winding;

B.2. Establish fast subsystem model:

Compared to the slow subsystem, let v=constant, The fast-changing current component can be obtained as shown in formula (7):

Taking the fast time scale γ=t/σ, the mathematical model of the fast subsystem finally obtained is shown in formula (8):

Among them, if _f =[i _df i _qf ] ^T , u _df and u _qf are the control signals of the fast subsystem, K _F is the electromagnetic thrust coefficient, M is the mass of the carrier, is the flux linkage of the permanent magnet, F _L is the load torque, τ is the pole pitch of the magnetic pole, B is the viscous friction coefficient, L is the inductance, and R is the resistance value of the mover winding;

B.3. Derive the dual time scale model:

From equations (6) and (8), the dual time scale model of permanent magnet linear synchronous motor is obtained as shown in equation (9):

C. Design sliding mode control law;

C.1 Slow subsystem sliding mode function:

Combine the given speed v _s * with the actual speed v _s of the permanent magnet linear synchronous motor to get the speed error signal e _s and send it to the slow subsystem sliding mode surface module; the slow subsystem sliding mode surface module according to the speed error signal e _s gets the slow subsystem sliding mode function value S _s (e _s ) shown in formula (10):

Among them, C _s is the speed error coefficient, and C _s >0; and the speed error e _s = v*-v _s , v* is the given speed signal;

C.2 Equivalent control law of slow subsystem:

The sliding mode control law module of the slow subsystem operates according to the sliding mode function value S _s (e _s ) output by the sliding surface to obtain the control signal u _s ; the external disturbance d _s is not considered in formula (10), and is 0, and the sliding mode function is derived to obtain the form shown in formula (11):

The equivalent control law of the slow subsystem is obtained as shown in formula (12):

After considering the external disturbance ds, the designed handover robustness term is shown in Equation (13):

u _ss = K _s sign(S _s ) (13);

The sliding mode control law of the slow subsystem can be obtained from formula (12) and formula (13), as shown in formula (14):

In order to effectively weaken the chattering phenomenon, the sign function can be replaced by a saturation function, so the slow subsystem control law formula (14) is rewritten as the following formula (15):

where δ is the thickness of the boundary layer;

C.3 Fast subsystem sliding mode function:

The fast variable estimation module subtracts the current _{id , i q from} the slow-varying current components _ids , i _qs respectively to obtain the fast-varying current components _idf , i _qf , and sends them to the fast subsystem sliding mode surface module; the tachyon The sliding mode surface module of the system obtains the sliding mode function value S _f of the fast subsystem shown in formula (16) according to the fast-changing current signals i _df and i _qf ;

Among them, C _f is the sliding mode surface coefficient of the fast subsystem, and C _f >0;

C.4 Equivalent control law of fast subsystem:

The sliding mode control law module of the fast subsystem operates according to the sliding mode function value S _f output by the sliding mode function to obtain the control signal u _f (γ); in order to weaken the chattering phenomenon existing in the system, the reaching law design is adopted

Among them, ε _f =diag(ε _df ,ε _qf ), S _f =[S _1f S _2f ] ^T , K _f =diag(K _df ,K _qf );

Solving equation (17), the fast subsystem sliding mode control law is obtained as shown in equation (18):

in, u _f represents the control signal of the tachyon system, M is the mass of the carrier, is the permanent magnet flux linkage, K _F is the electromagnetic thrust coefficient, τ is the pole pitch of the magnetic pole, B is the viscous friction coefficient, L is the inductance, R is the resistance value of the mover winding, S _f is the sliding mode surface function of the fast subsystem ;

D. Synthetic combination controller;

Send the control signal u _s and control signal u _f (γ) to the combined control law module to synthesize the combined controller; the combined controller sends the control signal of the full-order system to the permanent magnet linear synchronous motor;

Simultaneous formula (14) and formula (18), the slow subsystem plays a major role in the system, at this time, the time scale can be unified as the time scale t of the slowly varying subsystem; then formula (14) and formula (18) The control laws shown are added together, and finally the control signal of the full-order system shown in equation (19) is obtained:

u = u _s + u _f (19);

E. Stability analysis:

For the slow subsystem (6), define the Lyapunov function as formula (20):

Taking the derivative of time with respect to L _s , we can get:

in, Satisfy It can be obtained that the slow subsystem is stable;

For the tachyon system (8), define the Lyapunov function as formula (22):

Taking the time derivative of L _f , we can get

for inequality solution as It can be seen that L _f (t) converges exponentially to 0, and the convergence speed depends on K _f , so the fast subsystem is exponentially stable.

It can be obtained from the above that, according to the principle of singular perturbation, stable control laws are designed respectively for fast and slow systems, and the resulting combined control laws are stable.

In this embodiment, in order to verify the effectiveness and advantages of the designed system, this embodiment builds a model and simulates a permanent magnet linear synchronous motor dual-time scale sliding mode control system and method: parameter setting of permanent magnet linear synchronous motor The coefficient of viscous friction is B=0.22, the mass of the carrier is M=100kg, the pitch of the magnetic poles is τ=3.6cm, and in the flux linkage of the permanent magnet, the number of pairs of magnetic poles of the motor is p=3. The parameters of the slow subsystem controller are set as follows C _s ＝[0.4 0.4] ^T , K _s ＝diag(0,81), δ＝0.01; the parameter settings for the fast subsystem controller are as follows C _f ＝diag(1,1), ε _f ＝diag(30, 30), K _f =diag(300,300); the speed input is a step signal of 1r/s, the permanent magnet linear synchronous motor starts without load, and a load disturbance of TL=100N is suddenly added at t=0.5s; the permanent magnet linear synchronous motor The simulation results of the dual-time-scale sliding mode control system for synchronous motors are shown in Figure 3 to Figure 7; Figure 3 to Figure 7 are the speed response curves of dual-time-scale sliding mode control and PID control, and the The speed response curve of the control, the electromagnetic wave thrust curve of the dual-time-scale sliding mode control, the electromagnetic thrust curve of the general sliding-mode control, and the three-phase current schematic curve of the motor under the dual-time-scale sliding mode control; it can be seen from Fig. 3 that the dual-time Compared with PID control, scale sliding mode control has faster dynamic response speed, better dynamic performance, and better robustness to external disturbances; it can be seen from Figure 4 that the quasi-sliding mode method and reaching law Compared with the general equivalent sliding mode control method, the dynamic quality of the system is better, and the robustness to external disturbances is stronger; comparing Figure 5 with Figure 6, it can be seen that the quasi-sliding mode method and reaching law method are adopted Compared with the general equivalent sliding mode control, the dual-time-scale sliding mode control has a stronger ability to suppress chattering and weaken the influence of thrust fluctuations. At the same time, when the external load disturbance is applied, the electromagnetic thrust can also overcome its impact on The interference of the performance of the motor system; the schematic curve of the three-phase current of the motor under dual-time scale sliding mode control is shown in Figure 7, and it can also be seen that the chattering phenomenon of the system has improved. It should be pointed out that the excellent performance shown in this embodiment is used to explain the present invention, rather than to limit the present invention.

The above describes the design process and ideas of a dual-time-scale sliding mode control system and method for a permanent magnet linear synchronous motor. It is established as a dual-time-scale model of permanent magnet linear synchronous motor, and the sliding mode control laws corresponding to the fast and slow subsystems are designed by using the quasi-sliding mode method and the approaching law method, and then the time scales of the two subsystems are unified to synthesize The combined controller of the permanent magnet linear synchronous motor is obtained. At the same time, the stability of the system is analyzed by using Lyapunov's stability theory. The simulation results show that the control system not only has a fast dynamic response, but also has strong robustness to external disturbances, and can accurately track a given speed signal. In addition, the chattering phenomenon of sliding mode control has also been greatly improved.

Claims (2)

1. a permanent magnet linear synchronous motor double time scale sliding mode control system, is characterized in that, comprises slow subsystem sliding mode surface module (1) and fast subsystem sliding mode surface module (2), and described slow subsystem sliding mode surface module (2) Die surface module (1) is connected with combination control law module (5) by slow subsystem sliding mode control law module (3); Described fast subsystem sliding mode surface module (2) is through fast subsystem sliding mode control law module ( 4) A combined control law module (5) is connected; the combined control law module (5) is connected with a permanent magnet linear synchronous motor (6), and the permanent magnet linear synchronous motor (6) is also connected with external interference (7), so The permanent magnet linear synchronous motor (6) is connected to the slow subsystem sliding mode surface module (1); the permanent magnet linear synchronous motor (6) is connected to the fast subsystem sliding mode surface module ( 2). 2. A control method for a permanent magnet linear synchronous motor dual time scale sliding mode control system, characterized in that, comprising a permanent magnet linear synchronous motor dual time scale sliding mode control system according to claim 1, and comprising steps: A. Establish a mathematical model; A.1. Establish a dynamic model: The dynamic equation of the permanent magnet linear synchronous motor is composed of voltage equation, flux linkage equation, electromagnetic thrust equation and motion equation; through coordinate transformation, the mathematical model application vector of the permanent magnet linear synchronous motor on the two-phase synchronous rotating orthogonal coordinate system is obtained The idea of control is to make the electromagnetic thrust proportional to the magnitude of the quadrature axis current component i _q and set the given value i _d of the direct axis current component to zero, and the simplified dynamic model of the permanent magnet linear synchronous motor on the dq coordinate system is as follows Formula (1) shows: Among them, i _d , i _q , u _d , u _q are the current and voltage values of the d and q axes respectively, L is the inductance, R is the resistance value of the mover winding, ω=πv/τ is the angular velocity of the rotor, and v is speed, τ is the pole pitch of the magnetic pole, is the flux linkage of the permanent magnet, Fe is the electromagnetic thrust, M is the mass of the carrier, B is the viscous friction coefficient, F _L is the load torque, K _F is the electromagnetic thrust coefficient, and its expression is shown in the following formula (2): Among them, p is the number of magnetic pole pairs of the motor; A.2. Establish state equation: Rewrite the dynamic model of the permanent magnet linear synchronous motor obtained in step A.1 into the state equation form, as shown in the following formula (3): Among them, the state variable is v and i=[i _d i _q ] ^T , the control variable is u=[u _d u _q ] ^T ; A.3. The standard form of singular perturbation: From the mathematical model in the two-phase rotating orthogonal coordinate system, it can be seen that the degree of nonlinear coupling between the current and the current and between the current and the speed is very large, so it is necessary to find a corresponding method to achieve linear decoupling; consider the electrical time constant The value of L/R is far less than the value of the mechanical time constant M/B, so σ=LB/MR can be taken as the perturbation parameter with a small median value in the singular perturbation system, and the standard form of the singular perturbation of the motor is obtained as the formula ( 4) as shown: B. Establish a dual time scale model; B.1. Establish slow subsystem model: Since the value of σ is very small, assuming the perturbation parameter σ→0, the full-order system model of the original permanent magnet linear synchronous motor is shown in the following formula (5): Among them, v _s , i _ds , i _qs , u _ds , u _qs represent the slow-varying components corresponding to v, i, u respectively; Substitute the current value obtained from the second fraction in formula (5) into the first Fraction, the expression of the obtained slow subsystem model is shown in formula (6): in, u _ds and u _qs are the control signals of the slow subsystem, K _F is the electromagnetic thrust coefficient, M is the mass of the carrier, is the flux linkage of the permanent magnet, F _L is the load torque, τ is the pole pitch of the magnetic pole, B is the viscous friction coefficient, L is the inductance, and R is the resistance value of the mover winding; B.2. Establish fast subsystem model: Compared to the slow subsystem, let v=constant, The fast-changing current component can be obtained as shown in formula (7): Taking the fast time scale γ=t/σ, the mathematical model of the fast subsystem finally obtained is shown in formula (8): Among them, if _f =[i _df i _qf ] ^T , u _df and u _qf are the control signals of the fast subsystem, K _F is the electromagnetic thrust coefficient, M is the mass of the carrier, is the flux linkage of the permanent magnet, F _L is the load torque, τ is the pole pitch of the magnetic pole, B is the viscous friction coefficient, L is the inductance, and R is the resistance value of the mover winding; B.3. Derive the dual time scale model: From equations (6) and (8), the dual time scale model of permanent magnet linear synchronous motor is obtained as shown in equation (9): C. Design sliding mode control law; C.1 Slow subsystem sliding mode function: Combine the given speed v _s * with the actual speed v _s of the permanent magnet linear synchronous motor to get the speed error signal e _s and send it to the slow subsystem sliding mode surface module; the slow subsystem sliding mode surface module according to the speed error signal e _s gets the slow subsystem sliding mode function value S _s (e _s ) shown in formula (10): Among them, C _s is the speed error coefficient, and C _s >0; and the speed error e _s = v*-v _s , v* is the given speed signal; C.2 Equivalent control law of slow subsystem: The sliding mode control law module of the slow subsystem operates according to the sliding mode function value S _s (e _s ) output by the sliding surface to obtain the control signal u _s ; the external disturbance d _s is not considered in formula (10), and is 0, and the sliding mode function is derived to obtain the form shown in formula (11): The equivalent control law of the slow subsystem is obtained as shown in formula (12): After considering the external disturbance ds, the designed handover robustness term is shown in formula (13): u _ss =K _s sign(S _s )(13); The sliding mode control law of the slow subsystem can be obtained from formula (12) and formula (13), as shown in formula (14): In order to effectively weaken the chattering phenomenon, the sign function can be replaced by a saturation function, so the slow subsystem control law formula (14) is rewritten as the following formula (15): where δ is the thickness of the boundary layer; C.3 Fast subsystem sliding mode function: The fast variable estimation module subtracts the current _{id , i q from} the slow-varying current components _ids , i _qs respectively to obtain the fast-varying current components _idf , i _qf , and sends them to the fast subsystem sliding mode surface module; the tachyon The sliding mode surface module of the system obtains the sliding mode function value S _f of the fast subsystem shown in formula (16) according to the fast-changing current signals i _df and i _qf ; Among them, C _f is the sliding mode surface coefficient of the fast subsystem, and C _f >0; C.4 Equivalent control law of fast subsystem: The sliding mode control law module of the fast subsystem operates according to the sliding mode function value S _f output by the sliding mode function to obtain the control signal u _f (γ); in order to weaken the chattering phenomenon existing in the system, the reaching law design is adopted Among them, ε _f =diag(ε _df ,ε _qf ), S _f =[S _1f S _2f ] ^T , K _f =diag(K _df ,K _qf ); Solving equation (17), the fast subsystem sliding mode control law is obtained as shown in equation (18): in, u _f represents the control signal of the tachyon system, M is the mass of the carrier, is the permanent magnet flux linkage, K _F is the electromagnetic thrust coefficient, τ is the pole pitch of the magnetic pole, B is the viscous friction coefficient, L is the inductance, R is the resistance value of the mover winding, S _f is the sliding mode surface function of the fast subsystem ; D. Synthetic combination controller; Send the control signal u _s and control signal u _f (γ) to the combined control law module to synthesize the combined controller; the combined controller sends the control signal of the full-order system to the permanent magnet linear synchronous motor; Simultaneous formula (14) and formula (18), the slow subsystem plays a major role in the system, at this time, the time scale can be unified as the time scale t of the slowly varying subsystem; then formula (14) and formula (18) The control laws shown are added together, and finally the control signal of the full-order system shown in formula (19) is obtained; u=u _s +u _f (19); E. Stability analysis: For the slow subsystem (6), define the Lyapunov function as formula (20): Taking the derivative of time with respect to L _s , we can get: in, Satisfy It can be seen that the slow subsystem is stable; For the tachyon system (8), define the Lyapunov function as formula (22): Taking the time derivative with respect to L _f , we get: for inequality solution as It can be seen that L _f (t) converges exponentially to 0, and the convergence speed depends on K _f . It can be seen that the fast subsystem is exponentially stable; according to the singular perturbation principle, stable control laws are designed for fast and slow systems respectively, and the resulting combined control law is stable.