Sliding mode control method for surface-mounted permanent magnet synchronous motor speed regulation system

Abstract

The invention discloses a sliding mode control method for a surface-mounted permanent magnet synchronous motor speed regulation system, and the method comprises the following steps: S1, obtaining an ideal mathematical model and an uncertainty disturbance actual mathematical model under a two-phase rotating coordinate system; s2, the three-phase current and the actual rotating speed of the SPMSM are detected, and the current iq under a two-phase rotating coordinate system is obtained through coordinate transformation; s3, the extended sliding mode disturbance observer estimates the lumped disturbance of the speed regulation system according to the obtained current iq and rotating speed omega m to obtain lumped disturbance tau; s4, taking the deviation between the reference rotating speed and the actual rotating speed and the estimated lumped disturbance as the input of a novel sliding mode controller, and taking the deviation between the output of the sliding mode controller and the current iq as the input of a PI controller; according to the invention, the sliding mode controller has a faster convergence rate, the buffeting phenomenon of the control system is weakened, the problems of slow response speed and serious buffeting of the existing sliding mode control method are solved, and the control performance and robustness of the permanent magnet synchronous motor speed regulation system are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of permanent magnet synchronous motor speed regulation sliding mode control, and in particular relates to a sliding mode control method for a surface mounted permanent magnet synchronous motor speed regulation system. Background Art

[0002] Since PMSM is a multivariable, strongly coupled nonlinear system, the traditional closed-loop PID control strategy cannot meet the high control performance requirements. It is necessary to adopt a more robust nonlinear control method to achieve high-precision control of PMSM. At present, the main nonlinear control methods of PMSM include adaptive control, fuzzy control, sliding mode control and model predictive control. Adaptive control realizes the control of the system by online identification of the controller parameters of the PMSM speed regulation system. Adaptive control is mainly divided into model reference adaptive control, self-correcting controller and parameter adaptive control. Fuzzy control can effectively control without an accurate PMSM model, and can maintain good control performance when the system is subject to external interference or parameter changes. However, since the design of its fuzzy rules depends on the designer's intuition or experience, this limits the control performance of fuzzy control. Sliding mode control is a control method commonly used in nonlinear systems. Its characteristics are that the structure of the control system changes with the change of the operating state, and the state of the system moves along the preset sliding mode trajectory during the control process. Therefore, it has strong robustness to internal parameter changes and external disturbances, and is simple to design. However, since the system motion trajectory of the sliding mode control will shuttle on the sliding mode surface until it moves to the sliding mode surface, the sliding mode control will have serious chattering phenomenon, which needs to be eliminated. Model predictive control is an optimization control method that predicts the future control effect by establishing a dynamic model of the motor and selecting the optimal control strategy. Therefore, it has strong robustness and adaptability, and is suitable for handling multi-variable and constrained control problems, but it depends on the accuracy of system parameters and models.

[0003] In actual operation, PMSM always has internal parameter perturbations and external uncertainty disturbances, which need to be compensated in the controller. However, since internal parameter perturbations and external load disturbances are unmeasurable, it is necessary to design an observer to estimate them so as to achieve precise control through feedforward compensation. Summary of the invention

[0004] The object of the present invention is to provide a sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system to solve the problems raised in the above background technology.

[0005] To achieve the above object, the present invention provides the following technical solution: a sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system, comprising the following steps:

[0006] S1. First, the speed controller of the SPMSM speed control system is designed. The voltage equation of the SPMSM in the three-phase stationary coordinate system is transformed into the two-phase (dq) rotating coordinate system by Clark transformation and Park transformation, so as to reduce the order and simplify the analysis of the SPMSM. Then, the stator voltage equation of the SPMSM in the two-phase rotating coordinate system is expressed as:

[0007]

[0008] In the formula, u d ,u q ,i d ,i q ,L d and L q are the voltage, current and inductance components of the stator of SPMSM in the dq coordinate system, R is the stator resistance, ψ f is the permanent magnet flux, ω e is the electrical angular velocity of the motor.

[0009] S2. Detect the three-phase current and actual speed of the SPMSM, and obtain the current in the two-phase rotating coordinate system through coordinate transformation. In order to effectively control the speed of the SPMSM, the difference between the motor speed reference value and the actual value is introduced as the state variable, and the state variable of the system is defined as:

[0010]

[0011] In the formula, δ1 and δ2 are the state variables of the system, is the derivative of the system state variable δ1, ω ref and ω m are the reference value and actual value of the motor speed respectively, and are the derivatives of the motor speed reference and actual values ​​respectively;

[0012] The proposed fast integration terminal sliding surface is designed as:

[0013]

[0014] Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, δ1 and δ2 are the state variables of the system, and sign(·) is a sign function that satisfies:

[0015]

[0016] The proposed bi-power reaching law is designed as:

[0017]

[0018] In the formula, η1, η2, u, and v are parameters to be designed, and η1 > 0, η2 > 0, 0 < u < 1, and v satisfies:

[0019]

[0020] where γ is a parameter to be designed, and γ > 1;

[0021] Proof: The Lyapunov stability theorem is used to prove the stability of the designed FITSMC. The candidate Lyapunov energy function is:

[0022]

[0023] Taking the derivative of the Lyapunov function gives:

[0024]

[0025] According to the Lyapunov stability theorem, when V ≥ 0, the system will converge to zero in a finite time. Therefore, the proposed FITSMC satisfies the stability condition;

[0026] S3. Considering that the motor parameters of the SPMSM will drift, there will be friction, and the load will change under actual working conditions. Therefore, the mechanical motion equation of the SPMSM considering both internal parameter changes and external disturbances is expressed as:

[0027]

[0028] where ΔJ, Δψ f , ΔB, and ΔT L are the uncertainty factors of the moment of inertia, permanent magnet flux linkage, damping coefficient, and load torque of the motor, respectively, and they are all bounded. τ is the lumped disturbance of the system, ψ f is the permanent magnet flux linkage, ω m is the mechanical angular velocity of the SPMSM, P n is the number of pole pairs, J is the moment of inertia, B is the damping coefficient, T L is the load torque of the SPMSM, and i q is the q-axis current.

[0029]

[0030] In the formula, τ is the lumped disturbance of the system, ψ f is the permanent magnet flux linkage, ω m is the mechanical angular velocity of the SPMSM, P n is the number of pole pairs, J is the moment of inertia, B is the damping coefficient, TL is the load torque of SPMSM, ΔJ, Δψ f , ΔB and ΔT L are the uncertainty factors of the motor’s rotational inertia, permanent magnet flux, damping coefficient and load torque, i q is the q-axis current.

[0031] Assumption 1: Assume that the signal is continuously differentiable and the derivative is bounded;

[0032] Assumption 2: Assume that the lumped perturbation τ is unknown and bounded and satisfies |τ|≤κ1, and its derivative satisfies Among them, κ1 and κ2 are both positive real numbers;

[0033] Therefore, the q-axis reference input current considering internal parameter disturbance and external load disturbance is was modified to:

[0034]

[0035] Where P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, η1, η2, u and v are the parameters to be designed, c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, δ1 and δ2 are the state variables of the system, f sat (·) is the saturation function, is the derivative of the total disturbance of the system.

[0036] Since the internal and external disturbances of the motor cannot be measured under actual working conditions, it is necessary to estimate the internal and external disturbances so that the designed controller can compensate for the disturbances. According to the motor mechanical motion equation considering the uncertainty of internal and external disturbances, the lumped disturbance of the system is written as the extended disturbance state space expression:

[0037]

[0038] in, is the derivative of the mechanical angular velocity of the SPMSM, is the derivative of the total disturbance of the system, λ is the rate of change of the total disturbance τ, P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, i q is the q-axis current.

[0039] The proposed extended sliding mode disturbance observer is designed as follows:

[0040]

[0041] in, and They are the actual motor speed values ​​ω m and an estimate of the lumped disturbance τ, and They are the actual motor speed values ​​ω m and the derivative of the lumped perturbation τ estimate, is the gain of the sliding mode observer, P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, i q is the q-axis current, ζ is the sliding mode function of the observer, which is designed as:

[0042]

[0043] Among them, l1, l2 and l3 are positive real numbers, 0<ε1<1, 1<ε2, is the error between the estimated speed and the actual speed, sign(·) is the sign function;

[0044] The resulting lumped disturbance Substitute the q-axis reference input current In the modified equation, the corrected q-axis reference input current with disturbance compensation is obtained:

[0045]

[0046] Where P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, η1, η2, u and v are the parameters to be designed, c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, δ1 and δ2 are the state variables of the system, f sat (·) is the saturation function, is the derivative of the estimated value of the lumped disturbance τ;

[0047] In order to verify the stability of the designed extended sliding mode disturbance observer, the sliding mode surface of the designed observer is Using the same Lyapunov energy function formula as the selected Lyapunov energy function, the derivative of the Lyapunov function is obtained:

[0048]

[0049] Where J is the moment of inertia, B is the damping coefficient, l1, l2 and l3 are positive real numbers, 0<ε1<1, 1<ε2, is the error between the estimated speed and the actual speed, sign(·) is the sign function, is the error between the estimated value and the actual value of the lumped disturbance;

[0050] when Satisfies Lyapunov stability theorem When , the sliding mode disturbance observer is asymptotically stable, then when the proposed observer parameters are designed to meet the following conditions, the error of the sliding mode disturbance observer converges and is stable:

[0051]

[0052] Where, J is the moment of inertia, B is the damping coefficient, l1, l2 and l3 are positive real numbers, 0<ε1<1, 1<ε2;

[0053] S4. The deviation between the reference speed and the actual speed and the estimated lumped disturbance are used as the input of the sliding mode controller. The output of the sliding mode controller is related to the current i q The deviation is used as the input of the PI controller to form a dual closed-loop control of speed and current.

[0054] Preferably, the result calculated in step S2 enables the output of the sliding mode controller to be derived in combination with the formula in step S2:

[0055]

[0056] Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, sign(·) is the sign function, η1, η2, u and v are the parameters to be designed, and η1>0, η2>0, 0 <u<1,P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system.

[0057] because Therefore, the q-axis reference input current i of the SPMSM servo control system is * q for:

[0058]

[0059] Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, sign(·) is the sign function, η1, η2, u and v are the parameters to be designed, and η1>0, η2>0, 0 <u<1,P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system.

[0060] Preferably, an improved saturation function f is designed according to the calculation result in step S2. sat (·) replaces the sign function sign(·) in the sliding mode controller to suppress chattering, and the improved saturation function is designed as:

[0061]

[0062] Where, σ is the boundary layer thickness, k is a positive integer to be designed, and the switching speed of the improved saturation function at the origin;

[0063] Therefore, the q-axis reference input current i for chatter suppression is * qm is refactored to:

[0064]

[0065] Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, f sat (·) is a saturation function, η1, η2, u and v are the parameters to be designed, and η1>0, η2>0, 0 <u<1,P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system.

[0066] Preferably, when the state variables in step S2 and the formula defining the state variables of the system ignore the system speed reference value and the external load as constant values, the output of the controller is set to The error state space expression of the system is obtained:

[0067]

[0068] In the formula, and is the derivative of the system state variable, P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ fis the permanent magnet flux, δ1 and δ2 are the state variables of the system, is the derivative of the q-axis current.

[0069] Preferably, the permanent magnet synchronous motor is made into a multivariable, nonlinear, strongly coupled system by step S1, so its control system is decoupled. For the surface mounted permanent magnet synchronous motor, i d = 0 rotor magnetic field oriented control method to decouple: and the stator inductance of the surface-mounted permanent magnet synchronous motor meets L d =L q , so the mechanical motion equation of SPMSM is reconstructed as follows under this decoupling method:

[0070]

[0071] Where P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, i q is the q-axis current, T L is the load torque of SPMSM, ω m is the mechanical angular velocity of the motor.

[0072] The reconstructed mechanical motion equation contains the motor's mechanical angular velocity ω m , q-axis current i q , moment of inertia J, damping coefficient B and load torque T L .

[0073] Preferably, in the stator voltage equation of the SPMSM in step S1, u d ,u q ,i d ,i q ,L d and L q are the voltage, current and inductance components of the stator of SPMSM in the dq coordinate system, R is the stator resistance, ψ f is the permanent magnet flux, ω e and ω m are the electrical angular velocity and mechanical angular velocity of the motor respectively, and the relationship between the two satisfies ω e =P n ω m , P n is the number of magnetic pole pairs.

[0074] Preferably, the formula in step S3 performs stability analysis on the sliding mode disturbance observer, and the dynamic error equation of the motor speed is obtained by subtracting the extended disturbance state space formula from the extended sliding mode disturbance observer formula:

[0075]

[0076] In the formula, and are the estimated errors of velocity and lumped disturbance respectively, J is the moment of inertia, B is the damping coefficient, ζ is the sliding mode function of the observer, is the gain of the sliding mode observer, λ is the rate of change of the lumped disturbance τ, is the error between the estimated speed and the actual speed, is the error between the estimated value and the actual value of the lumped disturbance.

[0077] Preferably, the mechanical motion equation of the SPMSM calculated according to the stator voltage equation of the SPMSM in step S1 is expressed as:

[0078]

[0079] In the formula, ω m is the mechanical angular velocity of the motor, J is the moment of inertia, T e and T L is the electromagnetic torque and load torque of SPMSM, B is the damping coefficient, P n is the number of magnetic pole pairs, i d and i q is the stator current component of the SPMSM in the dq coordinate system, L d and L q is the stator inductance component of the SPMSM in the dq coordinate system, ψ f is the permanent magnet flux, θ m is the mechanical angle of the motor.

[0080] Compared with the prior art, the technical effects and advantages of the present invention are as follows: the sliding mode control method for the surface-mounted permanent magnet synchronous motor speed control system, the present invention aims at the problem that the traditional PI control strategy cannot meet the high control performance requirements of the surface-mounted permanent magnet synchronous motor speed control system, and proposes a new sliding mode controller, the new sliding mode controller has a faster convergence speed, and weakens the jitter phenomenon of the control system, solves the problems of slow response speed and serious jitter of the existing sliding mode control method, and improves the control performance and robustness of the permanent magnet synchronous motor speed control system. In addition, in order to ensure that the permanent magnet synchronous motor can have sufficient robustness under internal parameter perturbations and external uncertainty disturbances, a new extended sliding mode disturbance observer is designed, and by feeding forward the estimated internal and external lumped disturbances to the sliding mode controller, accurate compensation for internal and external unknown disturbances is achieved, further improving the speed tracking performance and robustness of the surface-mounted permanent magnet synchronous motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 This is a structural block diagram of the fast integral terminal sliding mode control algorithm proposed by the present invention;

[0082] Figure 2 This is a structural block diagram of the extended sliding mode disturbance observer proposed in the present invention;

[0083] Figure 3 This is the complete structural block diagram of the composite sliding mode control of the SPMSM speed regulation system proposed in the present invention;

[0084] Figure 4 The speed tracking comparison curve of the control method proposed by the present invention, PI control and traditional sliding mode control when the reference speed n=200rpm is given;

[0085] Figure 5 For a given reference speed n = 400rpm, the speed tracking comparison curve of the control method proposed by the present invention, PI control and traditional sliding mode control is shown;

[0086] Figure 6 For a given reference speed n=600rpm, the speed tracking comparison curve of the control method proposed by the present invention, PI control and traditional sliding mode control is shown;

[0087] Figure 7 For a given reference speed n=800rpm, the speed tracking comparison curve of the control method proposed by the present invention, PI control and traditional sliding mode control is shown;

[0088] Figure 8 For a given reference speed n = 1000rpm, the speed tracking comparison curve of the control method proposed by the present invention, PI control and traditional sliding mode control is shown;

[0089] Fig. 9 T L =3N·m external load and when the sudden external load is removed, the estimated lumped disturbance torque curve of the extended sliding mode disturbance observer;

[0090] Fig.10 When the motor parameter perturbation is J+2J and the reference speed is given as n=1000rpm, the speed tracking comparison curve of the control method proposed by the present invention, PI control and traditional sliding mode control is shown;

[0091] Fig.11 The estimated lumped disturbance torque curve of the extended sliding mode disturbance observer when the motor parameter perturbation is J+2J and the reference speed is given as n=1000rpm;

[0092] Fig.12 The motor parameter perturbation is ψ f +20%ψ f , given a reference speed of n = 1000rpm, the speed tracking comparison curve of the control method proposed by the present invention, PI control and traditional sliding mode control;

[0093] Fig.13 The motor parameter perturbation is ψ f +20%ψ f , given a reference speed of n = 1000rpm, the estimated lumped disturbance torque curve of the extended sliding mode disturbance observer;

[0094] Fig.14 When the motor parameter perturbation is L+50%L and the reference speed is given as n=1000rpm, the speed tracking comparison curve of the control method proposed by the present invention, PI control and traditional sliding mode control is shown;

[0095] Fig.15 The estimated lumped disturbance torque curve of the extended sliding mode disturbance observer when the motor parameter perturbation is L+50%L and the reference speed is given as n=1000rpm;

[0096] Fig.16 It is a logic block diagram of the present invention. DETAILED DESCRIPTION

[0097] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0098] Example 1

[0099] The present invention provides a technical solution: a sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system, such as Fig.16 , characterized in that it comprises the following steps:

[0100] S1. Establishment of mathematical model of permanent magnet synchronous motor: In order to facilitate the design of speed controller of SPMSM speed control system, Clark transformation and Park transformation are used to transform the voltage equation of SPMSM in three-phase stationary coordinate system into two-phase (dq) rotating coordinate system, so as to reduce the order and simplify the analysis of SPMSM. Then the stator voltage equation of SPMSM in two-phase rotating coordinate system can be expressed as:

[0101]

[0102] The mechanical motion equation of SPMSM can be expressed as:

[0103]

[0104] In the formula, u d ,uq ,i d ,i q ,L d and L q are the voltage, current and inductance components of the stator of SPMSM in the dq coordinate system, R is the stator resistance, ψ f is the permanent magnet flux, ω e and ω m are the electrical angular velocity and mechanical angular velocity of the SPMSM, respectively, and the relationship between the two satisfies ω e =P n ω m ,θ m is the mechanical angle of the motor, P n is the number of magnetic pole pairs, J is the moment of inertia, B is the damping coefficient, T e and T L are the electromagnetic torque and load torque of SPMSM respectively.

[0105] Since the permanent magnet synchronous motor is a multivariable, nonlinear, and strongly coupled system, it is very necessary to decouple its control system. d = 0 is decoupled by the rotor field oriented control method, which can achieve good control effect. And because the stator inductance of the surface mounted permanent magnet synchronous motor satisfies L d =L q , so the mechanical motion equation of SPMSM can be reconstructed as follows under this decoupling method:

[0106]

[0107] Where P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, i q is the q-axis current, T L is the load torque of SPMSM, ω m is the mechanical angular velocity of the motor.

[0108] The reconstructed mechanical motion equation involves the motor's mechanical angular velocity, q-axis current, moment of inertia, damping coefficient, and load torque. This equation can facilitate the subsequent design of the speed controller.

[0109] Example 2

[0110] S2. Design of a new sliding mode speed controller: In order to effectively control the speed of the SPMSM, the reconstructed mechanical motion equation is used to introduce the deviation between the motor speed reference value and the actual value as the state variable, and the state variable of the speed control system is defined as:

[0111]

[0112] In the formula, δ1 and δ2 are state variables of the system, is the derivative of the system state variable δ1, ω ref and ω m are the reference value and the actual value of the motor speed respectively, and are the derivatives of the reference value and the actual value of the motor speed respectively.

[0113] When ignoring the uncertainties of the system and considering the speed reference value and the external load as constant values, let the output of the controller and substitute Equation (3) into Equation (4) to obtain the error state space expression of the system:

[0114]

[0115] In the formula, and are the derivatives of the system state variables, P n is the number of pole pairs, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux linkage, δ1 and δ2 are the state variables of the system, is the derivative of the q-axis current.

[0116] For sliding mode control, the selection of the sliding mode surface determines the control performance of the system. To ensure that the speed control system has good dynamic performance and speed tracking accuracy, the fast integral terminal sliding mode surface proposed by the present invention is designed as:

[0117] s = δ2 + cδ1 + ∫(k1|δ1| α sign(δ1) + k2|δ2| β sign(δ2) + k3δ1)dt, (6)

[0118] In the formula, c, α, β, k1, k2 and k3 are parameters to be designed for the sliding mode surface, c > 0, 0 < α < 1, β = 2α / (1 + α), k1, k2 and k3 are all positive real numbers, δ1 and δ2 are the state variables of the system, sign(·) is the sign function, satisfying:

[0119]

[0120] To further ensure the dynamic response quality of the sliding mode controller in the approaching stage, a double power reaching law is designed:

[0121]

[0122] In the formula, η1, η2, u and v are parameters to be designed, and η1 > 0, η2 > 0, 0 < u < 1, v satisfies

[0123]

[0124] Among them, γ is the parameter to be designed, and γ>1.

[0125] Proof: In order to use the Lyapunov stability theorem to prove the stability of the designed FITSMC, the selected Lyapunov energy function is:

[0126]

[0127] Taking the derivative of the Lyapunov function we can get:

[0128]

[0129] According to the Lyapunov stability theorem, when V ≥ 0, , the system will converge to zero in a finite time, so the proposed FITSMC meets the stability conditions, and the SPMSM speed control system based on FITSMC is stable.

[0130] Therefore, when When , the output of the sliding mode controller can be derived by combining equations (5), (6) and (8):

[0131]

[0132] Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, sign(·) is the sign function, η1, η2, u and v are the parameters to be designed, and η1>0, η2>0, 0 <u<1,P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system.

[0133] Since the output of the controller Therefore, the q-axis reference input current i of the SPMSM speed control system is * q for:

[0134]

[0135] Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, sign(·) is the sign function, η1, η2, u and v are the parameters to be designed, and η1>0, η2>0, 0 <u<1,Pn is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system.

[0136] Theoretically, the state of the controlled system will continue to slide along the sliding surface to the equilibrium point after reaching the target sliding trajectory. However, in actual operation, due to the lag and delay of the controlled device, the system state cannot accurately reach the predetermined sliding trajectory, but fluctuates up and down on the sliding surface, resulting in chattering. Although the double power reaching law can suppress the chattering phenomenon of the system to a certain extent, the present invention designs an improved saturation function f sat (·) replaces the sign function sign(·) in the sliding mode controller to better suppress chattering. The improved saturation function is designed as:

[0137]

[0138] Among them, σ is the boundary layer thickness, k is a positive integer to be designed, which determines the switching speed of the improved saturation function at the origin.

[0139] The improved saturation function is introduced into the expression of the q-axis reference input current to replace the traditional sign switching function, and the q-axis reference input current i is used to suppress the chattering. * qm was modified to:

[0140]

[0141] Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, f sat (·) is a saturation function, η1, η2, u and v are the parameters to be designed, and η1>0, η2>0, 0 <u<1,P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system.

[0142] The obtained q-axis reference input current will be used as the reference value of the q-axis current controller, i d=0 is used as the reference value of the d-axis current controller. The current controller uses the deviation between the reference current and the actual current of the dq axis as input to obtain the control voltage of the dq axis. The control voltage is obtained by Park inverse transformation in the two-phase rotating (α-β) coordinate system, and then the SPMSM is driven by SVPWM and a three-phase inverter. The current sensor and speed sensor detect the three-phase current and mechanical angular velocity of the SPMSM in real time and feed back to the input of the speed controller and the current meter, thereby realizing the closed-loop sliding mode speed control of the SPMSM based on the rotor magnetic field oriented control.

[0143] Implementation Example 3. Design of a new extended sliding mode disturbance observer: Considering the parameter uncertainty in the establishment of the SPMSM mathematical model and the parameter drift, friction and load changes of the motor under actual working conditions, in order to achieve accurate speed tracking control of SPMSM, the internal parameter changes and external disturbances are considered in the mechanical motion equation of the motor. The mechanical motion equation of the motor with internal and external uncertainty disturbances can be expressed as:

[0144]

[0145] Among them, ΔJ, Δψ f , ΔB and ΔT L are the uncertainty factors of the motor's moment of inertia, permanent magnet flux, damping coefficient and load torque, and they are all bounded. τ is the lumped disturbance of the system, ψ f is the permanent magnet flux, ω m is the mechanical angular velocity of SPMSM, P n is the number of magnetic pole pairs, J is the moment of inertia, B is the damping coefficient, T L is the load torque of SPMSM, i q is the q-axis current.

[0146]

[0147] Where τ is the total disturbance of the system, ψ f is the permanent magnet flux, ω m is the mechanical angular velocity of SPMSM, P n is the number of magnetic pole pairs, J is the moment of inertia, B is the damping coefficient, T L is the load torque of SPMSM, ΔJ, Δψ f , ΔB and ΔT L are the uncertainty factors of the motor’s rotational inertia, permanent magnet flux, damping coefficient and load torque, i q is the q-axis current.

[0148] Assumption 1: Assume that the signal is continuously differentiable and its derivative is bounded.

[0149] Assumption 2: Assume that the lumped disturbance τ is unknown and bounded and satisfies |τ|≤κ1, and its derivative satisfies |τ|≤κ2, where κ1 and κ2 are both positive constants.

[0150] Substituting equation (17) into equation (4), we get the error state space expression of the system with uncertain disturbances:

[0151]

[0152] In the formula, and is the derivative of the system state variable, P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system, u is the output of the controller, is the derivative of the lumped disturbance.

[0153] According to the q-axis reference input current design steps in implementation example 2, the q-axis reference input current under the condition of internal and external uncertainty disturbance is considered. was modified to:

[0154]

[0155] Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, f sat (·) is a saturation function, η1, η2, u and v are the parameters to be designed, and η1>0, η2>0, 0 <u<1,P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system, is the derivative of the lumped disturbance.

[0156] Since the internal and external uncertain disturbances of the motor cannot be directly measured under actual working conditions, it is necessary to estimate the internal and external disturbances so that the designed controller can accurately compensate for them. According to the motor mechanical motion equation considering internal and external uncertain disturbances, the lumped disturbance of the system can be written as the extended disturbance state space expression as follows:

[0157]

[0158] in, is the derivative of the mechanical angular velocity of the SPMSM, is the derivative of the total disturbance of the system, λ is the rate of change of the total disturbance τ, P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψf is the permanent magnet flux, i q is the q-axis current.

[0159] The proposed extended sliding mode disturbance observer is designed as follows:

[0160]

[0161] in, and They are the actual motor speed values ​​ω m and an estimate of the lumped disturbance τ, and They are the actual motor speed values ​​ω m and the derivative of the lumped perturbation τ estimate, is the gain of the sliding mode observer, P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, i q is the q-axis current, ζ is the sliding mode function of the observer, which is designed as:

[0162]

[0163] Among them, l1, l2 and l3 are positive real numbers, 0<ε1<1, 1<ε2, is the error between the estimated speed and the actual speed, and sign(·) is the sign function.

[0164] Different from the traditional Romberg observer, the extended sliding mode observer proposed in this invention replaces the linear output error of Romberg by designing a sliding mode function, and the sliding mode function is also used as the rate of change of the estimated disturbance, which improves the estimation speed and accuracy of the observer. Substituting into equation (20) instead of τ, we can obtain the modified q-axis reference input current with disturbance compensation:

[0165]

[0166] Where P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, η1, η2, u and v are the parameters to be designed, c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, δ1 and δ2 are the state variables of the system, f sat (·) is the saturation function, is the derivative of the estimated value of the lumped disturbance τ.

[0167] The stability analysis of the sliding mode disturbance observer is carried out. By subtracting (21) from (22), the dynamic error equation of the motor speed is obtained:

[0168]

[0169] In the formula, and are the estimated errors of velocity and lumped disturbance respectively, J is the moment of inertia, B is the damping coefficient, ζ is the sliding mode function of the observer, is the gain of the sliding mode observer, λ is the rate of change of the lumped disturbance τ, is the error between the estimated speed and the actual speed, is the error between the estimated value and the actual value of the disturbance.

[0170] In order to verify the stability of the designed extended sliding mode disturbance observer, the sliding mode surface of the observer is selected as Using the same Lyapunov energy function as in formula (10), the derivative of the Lyapunov function can be obtained:

[0171]

[0172] Where J is the moment of inertia, B is the damping coefficient, l1, l2 and l3 are positive real numbers, 0<ε1<1, 1<ε2, is the error between the estimated speed and the actual speed, sign(·) is the sign function, is the error between the estimated value and the actual value of the lumped disturbance.

[0173] when Satisfies Lyapunov stability theorem When , the sliding mode disturbance observer is asymptotically stable, then when the proposed observer parameters are designed to meet the following conditions, the error of the sliding mode disturbance observer converges and is stable:

[0174]

[0175] Where J is the moment of inertia, B is the damping coefficient, l1, l2 and l3 are positive real numbers, 0<ε1<1, 1<ε2.

[0176] Implementation Example 4. Surface-mounted permanent magnet synchronous motor composite sliding mode control model: The composite sliding mode controller designed according to Implementation Examples 1, 2 and 3 of the present invention, the fast integral terminal sliding mode control algorithm structure block diagram, the extended sliding mode disturbance observer structure block diagram, the complete control structure block diagram and logic block diagram of the SPMSM speed regulation system are shown in the figure below. Figure 1 , Figure 2 , Figure 3 , Fig.16 shown.

[0177] Figure 1 The fast integral terminal sliding mode control algorithm in the paper obtains the equivalent control law by designing the sliding surface related to the speed error and its derivative, and designs the double power reaching law as the switching control law to output the reference current required by the current controller, thus forming a complete fast integral terminal sliding mode control algorithm.

[0178] Figure 2 The extended sliding mode disturbance observer in the paper takes the actual q-axis current and mechanical angular velocity of the motor as the input of the observer. The error between the actual value and the estimated value of the angular velocity is combined with the q-axis current through the sliding mode function, and the estimated value of the lumped disturbance is calculated by the mechanical motion equation of the motor. It is fed forward to the sliding mode controller to obtain the compensated q-axis reference current.

[0179] Figure 3 The controller in the complete control structure block diagram of the SPMSM speed regulation system includes a current loop and a speed loop. The current loop adopts traditional PI control, while the speed loop adopts the fast integral terminal sliding mode control proposed in this invention. The input of the speed controller is the speed tracking error, and the output is the q-axis reference current. The designed extended sliding mode disturbance observer takes the actual speed of the SPMSM and the q-axis current in the two-phase rotating coordinate system as input, estimates the internal and external uncertainty disturbances of the SPMSM, and then converts the estimated lumped disturbance into The output of the observer is fed forward to the FITSMC controller to accurately compensate for the lumped disturbance, thereby improving the speed tracking performance and robustness of the FITSMC controller.

[0180] Implementation Example 5. Simulation Verification of the Proposed Sliding Mode Control Method

[0181] The effectiveness of the composite sliding mode control method proposed in the present invention is verified by simulation on the MATLAB / Simulink simulation platform. In the simulation platform, the SPMSM speed control system models of traditional PI control, traditional sliding mode control (CSMC) based on extended sliding mode disturbance observer (ESMDO) and novel fast integral terminal sliding mode control (FITSMC) are established, and simulation comparison and verification are carried out. The nominal parameters of the SPMSM in the simulation model are: rated speed n = 1500rpm, number of magnetic poles Pn = 5, stator resistance R = 0.885Ω, stator inductance L d =L q =0.012H, permanent magnet flux ψ f =0.14373Wb, moment of inertia J = 0.001395Kg·m 2 , damping coefficient B = 0.00007403N·m·s.

[0182] In order to verify the effectiveness of the proposed sliding mode control method for the SPMSM speed control system, the given reference speeds of the system are n = 200rpm, n = 400rpm, n = 600rpm, n = 800rpm and n = 1000rpm, and the system is started in no-load mode. In order to further verify that the system still has good speed tracking performance under the condition of external load, when the SPMSM speed control system is running at 0.25s, the load torque is suddenly increased from the no-load state to T L =3N·m, and remove the external load when running to 0.5s, and set the total simulation time of the system to 0.75s.

[0183] Figures 4 to 8 The speed tracking comparison curves of the control method proposed by the present invention, PI control and traditional sliding mode control are shown for given reference speeds n=200rpm, n=400rpm, n=600rpm, n=800rpm and n=1000rpm respectively. Figures 4 to 8 It can be concluded that, given different reference speeds, the control method proposed in the present invention has a faster startup speed and no overshoot compared to PI control and traditional sliding mode control, and the maximum speed error and recovery time under the influence of load torque changes are also minimized. Here, only the case where the given reference speed is n = 200rpm is specifically analyzed.

[0184] When the reference speed is given as n=200rpm and the SPMSM is started in a no-load state, the control method proposed in the present invention can reach the given speed in about 0.0065s, with the fastest response speed and no overshoot; the traditional sliding mode control method reaches the given speed in 0.042s, with the second fastest response speed and no overshoot; and the PI control stabilizes to the given speed at 0.075s after a period of overshoot, with an overshoot of about 8.95% and the slowest response speed.

[0185] At 0.25s, the system suddenly changes from a no-load state to a load torque of T L =3N·m and 0.5s when the load torque is removed, the control method proposed in this paper has the smallest maximum speed error compared with the other two control methods, which is about ±32rpm, and the recovery time under the influence of load torque change is about 0.074s, the fastest response speed, and strong robustness to load disturbances. The maximum speed error of PI control is about ±46.6rpm, and the recovery time is about 0.0943s, while the maximum speed error of the traditional sliding mode control method is about ±50rpm, and the recovery time is about 0.0783s.

[0186] The maximum speed error of sliding mode control is slightly larger than that of PI control, but the recovery time is faster than that of PI control, which is basically consistent with the control method proposed in this paper. This shows that sliding mode control has better control effect on nonlinear systems such as SPMSM than PI control. And from the speed tracking curves under different given reference speeds, it can be seen that the SPMSM speed regulation system will have obvious vibration when it is in a low-speed operation state, while the vibration will be weakened when it is in high-speed operation. This is because the angular frequency of the magnetic flux harmonics caused by the permanent magnet magnetic flux and the tooth slot gap is related to and proportional to the given reference speed. The larger the given reference speed, the larger the angular frequency of the magnetic flux harmonics and the smaller the speed fluctuation.

[0187] Fig. 9 T L =3N·m external load and when the sudden external load is removed, the estimated lumped disturbance torque curve of the extended sliding mode disturbance observer. Fig. 9 It can be concluded that the extended sliding mode disturbance observer proposed in the present invention can quickly and accurately (about 0.095s) estimate the lumped disturbance torque of the system after the sudden load is added at 0.25s, which proves that the extended sliding mode disturbance observer can quickly and accurately estimate the uncertainty disturbance of the system.

[0188] Figure 10 to Figure 11 Assuming that the motor parameter perturbation is the motor rotation inertia J+2J, the speed tracking comparison curve of the control method proposed by the present invention, PI control and traditional sliding mode control and the estimated lumped disturbance torque curve of the extended sliding mode disturbance observer are shown.

[0189] analyze Fig.10 When the motor moment of inertia perturbation is J+2J, the overshoot of the speed tracking curve of the PI control is large at the startup stage, about 33.6%, and it stabilizes to the given reference speed after experiencing an oscillation of 0.243s. The overshoot of the conventional sliding mode control and the sliding mode control method of the present invention are 10.4% and 7.8% respectively, and they stabilize to the given speed at 0.213s and 0.135s respectively. However, the speed tracking curve of the conventional sliding mode control method oscillates and has a certain steady-state error, indicating that the sliding mode control method proposed in the present invention has a faster response speed and better robustness to the moment of inertia perturbation.

[0190] And from Fig.11 It can be seen that the maximum lumped disturbance torque of the system under the moment of inertia perturbation estimated by the extended sliding mode disturbance observer is T D =-7.502N·m, indicating that the moment of inertia perturbation belongs to the external load disturbance and reaches stability at 0.146s.

[0191] Figure 12 to Figure 13 Assume that the motor parameter perturbation is the motor permanent magnet flux ψ f +20%ψf When the control method proposed in the present invention is used, the speed tracking comparison curve between PI control and traditional sliding mode control and the estimated lumped disturbance torque curve of the extended sliding mode disturbance observer are obtained.

[0192] analyze Fig.12 , the flux perturbation of the permanent magnet of the motor is ψ f +20%ψ f The speed tracking curve of PI control shows an overshoot of 11.5% in the startup phase and then stabilizes at 1031rpm at 0.053s, while the speed drops at 0.187s and stabilizes to the given reference speed at 0.317s. The speed responses of the conventional sliding mode control and the sliding mode control method of the present invention do not have overshoot, and the sliding mode control method of the present invention has a faster response speed.

[0193] And from Fig.13 It can be seen that the maximum lumped disturbance torque of the system under the permanent magnet flux perturbation estimated by the extended sliding mode disturbance observer is T D =0.8495N·m, indicating that the permanent magnet flux perturbation belongs to the electromagnetic torque disturbance and reaches stability at 0.141s.

[0194] Figure 14 to Figure 15 Assuming that the motor parameter perturbation is the motor dq axis inductance L+50%L, the speed tracking comparison curve of the control method proposed by the present invention, PI control and traditional sliding mode control and the estimated lumped disturbance torque curve of the extended sliding mode disturbance observer are shown.

[0195] analyze Fig.14 , when the motor dq axis inductance perturbation is L+50%L, the overshoot of the speed tracking curve of PI control is 30% in the startup phase, and stabilizes to the given reference speed at 0.166s. However, the speed response of the conventional sliding mode control and the sliding mode control method of the present invention does not have overshoot, and the sliding mode control method of the present invention has a faster response speed. Fig.15 It can be seen that the maximum lumped disturbance torque of the system under the dq-axis inductance perturbation estimated by the extended sliding mode disturbance observer is T D =0.02788N·m, indicating that the dq-axis inductance perturbation also belongs to the electromagnetic torque disturbance, and it reaches stability at 0.111s.

[0196] Combination pair Figures 10 to 15According to the analysis, in the SPMSM speed regulation system, under the three perturbations of moment of inertia, permanent magnet flux and dq-axis inductance, the moment of inertia perturbation has the greatest impact on the system, followed by the permanent magnet flux perturbation, and the inductance perturbation has the least impact. Under the three control methods, the sliding mode control method proposed in the present invention estimates the system lumped disturbance through an extended sliding mode disturbance observer and feedforward compensates it. It has stronger anti-interference ability and better robustness. The traditional sliding mode control method is second. Since PI control does not compensate for system disturbances and only controls through proportional integral, its anti-interference ability and robustness are the worst, and the control performance of the SPMSM speed regulation system cannot meet the control requirements.

[0197] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system, characterized in that: It includes the following steps: S1. First, design the speed controller of the SPMSM speed regulation system. Use Clark transformation and Park transformation to transform the voltage equation of the SPMSM in the three-phase static coordinate system into the two-phase (d-q) rotating coordinate system, and perform reduced-order and simplified analysis on the SPMSM. Then, the stator voltage equation of the SPMSM in the two-phase rotating coordinate system is expressed as: S2. Detect the three-phase current and actual speed of the SPMSM, and obtain the current in the two-phase rotating coordinate system through coordinate transformation. Introduce the difference between the reference value and the actual value of the motor speed as the state variable, and define the state variables of the system as: In the formula, δ1 and δ2 are the state variables of the system, is the derivative of the system state variable δ1, ω ref and ω m are the reference value and actual value of the motor speed respectively, and are the derivatives of the motor speed reference and actual values ​​respectively; The proposed fast integral terminal sliding mode surface is designed as: s=δ2+cδ1+∫(k1|δ1| α sign(δ1)+k2|δ2| β sign(δ2)+k3δ1)dt, where c, α, β, k1, k2, and k3 are the parameters to be designed for the sliding mode surface, c>0, 0<α<1, β = 2α / (1 + α), k1, k2, and k3 are all positive real numbers, δ1 and δ2 are the state variables of the system, and sign(·) is the sign function, satisfying: The proposed double power reaching law is designed as: In the formula, η1, η2, u, and v are the parameters to be designed, and η1>0, η2>0, 0<u<1, and v satisfies: where γ is the parameter to be designed, and γ>1; Prove the stability of the FITSMC using the Lyapunov stability theorem. The selected Lyapunov energy function is: Derive the derivative of the Lyapunov function to obtain: According to the Lyapunov stability theorem, when V ≥ 0, When , the system converges to 0 in a finite time; S3. After the motor parameters of the SPMSM change during operation, the motor mechanical motion equation under the internal parameter change and external disturbance of the SPMSM is: Among them, ΔJ, Δψ f , ΔB and ΔT L are the uncertainty factors of the motor's moment of inertia, permanent magnet flux, damping coefficient and load torque, and they are all bounded, ψ f is the permanent magnet flux, ω m is the mechanical angular velocity of SPMSM, P n is the number of magnetic pole pairs, J is the moment of inertia, B is the damping coefficient, T L is the load torque of SPMSM, i q is the q-axis current, τ is the total disturbance of the system; In the formula, ψ f is the permanent magnet flux, ω m is the mechanical angular velocity of SPMSM, P n is the number of magnetic pole pairs, J is the moment of inertia, B is the damping coefficient, T L is the load torque of SPMSM, ΔJ, Δψ f , ΔB and ΔT L are the uncertainty factors of the motor’s rotational inertia, permanent magnet flux, damping coefficient and load torque, i q is the q-axis current; Assumption 1: Assume that the signal is continuously differentiable and its derivative is bounded; Assumption 2: Assume that the lumped perturbation τ is unknown and bounded and satisfies |τ|≤κ1, and its derivative satisfies Among them, κ1 and κ2 are both positive real numbers; Q-axis reference input current under internal parameter disturbance and external load disturbance was modified to: Where P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, η1, η2, u and v are the parameters to be designed, c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, δ1 and δ2 are the state variables of the system, f sat (·) is the saturation function; Perform calculations on the internal and external disturbances. According to the motor mechanical motion equation considering the uncertainty of the internal and external disturbances, the lumped disturbance of the system is written as an extended disturbance state space expression: in, is the derivative of the mechanical angular velocity of the SPMSM, is the derivative of the total disturbance of the system, λ is the rate of change of the total disturbance τ, P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, i q is the q-axis current; Obtain the formula for the extended sliding mode disturbance observer as: in, and They are the actual motor speed values ​​ω m and an estimate of the lumped disturbance τ, and They are the actual motor speed values ​​ω m and the derivative of the lumped perturbation τ estimate, is the gain of the sliding mode observer, P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, i q is the q-axis current, ζ is the sliding mode function of the observer, which is designed as: Among them, l1, l2 and l3 are positive real numbers, 0<ε1<1, 1<ε2, is the error between the estimated speed and the actual speed, sign(·) is the sign function; The resulting lumped disturbance Substitute the q-axis reference input current In the modified equation, the q-axis reference input current with disturbance compensation is obtained Where P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, η1, η2, u and v are the parameters to be designed, c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, δ1 and δ2 are the state variables of the system, f sat (·) is the saturation function, is the derivative of the estimated value of the lumped disturbance τ; The stability of the extended sliding mode disturbance observer is obtained by Using the same Lyapunov energy function formula as the selected Lyapunov energy function, the derivative of the Lyapunov function is obtained: Where J is the moment of inertia, B is the damping coefficient, l1, l2 and l3 are positive real numbers, 0<ε1<1, 1<ε2, is the error between the estimated speed and the actual speed, sign(·) is the sign function, is the error between the estimated value and the actual value of the lumped disturbance; when Satisfies Lyapunov stability theorem When , the sliding mode disturbance observer is asymptotically stable. When the observer parameters are designed to meet the following conditions, the error of the sliding mode disturbance observer converges and is stable: In the formula, J is the moment of inertia, B is the damping coefficient, l1, l2, and l3 are positive real numbers, 0<ε1<1, 1<ε2; S4. The deviation between the reference speed and the actual speed and the calculated lumped disturbance are used as the input of the sliding mode controller. The output of the sliding mode controller is related to the current i q The deviation is used as the input of the PI controller to achieve dual closed-loop control of speed and current.

2. The sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system according to claim 1, characterized in that: The calculation result in step S2 enables the output of the sliding mode controller to be derived in combination with the formula in step S2: Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, sign(·) is the sign function, η1, η2, u and v are the parameters to be designed, and η1>0, η2>0, 0 <u<1,P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system; Since u=i q , so the q-axis reference input current i of the SPMSM servo control system is * q for: Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, sign(·) is the sign function, η1, η2, u and v are the parameters to be designed, and η1>0, η2>0, 0 <u<1,P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system.

3. The sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system according to claim 2, characterized in that: The saturation function f obtained by calculation in step S2 sat (·) replaces the sign function sign(·) in the sliding mode controller to suppress chattering, and the improved saturation function is designed as: where σ is the boundary layer thickness and k is a positive integer, which determines the switching speed of the improved saturation function at the origin; Therefore, the q-axis reference input current i for chatter suppression is * qm is refactored to: Where c, α, β, k1, k2 and k3 are the parameters to be designed of the sliding surface, c>0, 0<α<1, β=2α / (1+α), k1, k2 and k3 are all positive real numbers, f sat (·) is a saturation function, η1, η2, u and v are the parameters to be designed, and η1>0, η2>0, 0 <u<1,P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system.

4. The sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system according to claim 1, characterized in that: According to the state variables in step S2, the formula defining the state variables of the system ignores the speed reference value of the system and the external load as constant values, and sets the output of the controller to The error state space expression of the system is obtained: In the formula, and is the derivative of the system state variable, P n is the number of magnetic poles, J is the moment of inertia, B is the damping coefficient, ψ f is the permanent magnet flux, δ1 and δ2 are the state variables of the system, is the derivative of the q-axis current.

5. The sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system according to claim 1, characterized in that: The step S1 makes the permanent magnet synchronous motor a multivariable, nonlinear, strongly coupled system, decouples the control system, and the surface-mounted permanent magnet synchronous motor adopts i d = 0 for rotor field oriented control: When the stator inductance of the surface mounted permanent magnet synchronous motor satisfies L d =L q , so the mechanical motion equation of SPMSM is reconstructed as follows under this decoupling method: The reconstructed mechanical motion equation contains the motor's mechanical angular velocity ω m , q-axis current i q , moment of inertia J, damping coefficient B and load torque T L , P n is the number of magnetic pole pairs, ψ f is the permanent magnet flux.

6. The sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system according to claim 1, characterized in that: In the stator voltage equation of the SPMSM in step S1, u d ,u q ,i d ,i q ,L d and L q are the voltage, current and inductance components of the stator of the SPMSM in the dq coordinate system, R is the stator resistance, ψ f is the permanent magnet flux, ω e and ω m are the electrical angular velocity and mechanical angular velocity of the motor respectively, and the relationship between the two satisfies ω e =P n ω m , P n is the number of magnetic pole pairs.

7. The sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system according to claim 1, characterized in that: Perform stability analysis on the sliding mode disturbance observer using the formula in step S3. Subtract the extended disturbance state space formula from the extended sliding mode disturbance observer formula to obtain the dynamic error equation of the motor speed: In the formula, and are the estimated errors of velocity and lumped disturbance respectively, J is the moment of inertia, B is the damping coefficient, ζ is the sliding mode function of the observer, is the gain of the sliding mode observer, λ is the rate of change of the lumped disturbance τ, is the error between the estimated speed and the actual speed, is the error between the estimated value and the actual value of the lumped disturbance.

8. The sliding mode control method for a surface mounted permanent magnet synchronous motor speed control system according to claim 1, characterized in that: The mechanical motion equation of the SPMSM calculated according to the stator voltage equation of the SPMSM in step S1 is expressed as: In the formula, ω m is the mechanical angular velocity of the motor, J is the moment of inertia, T e and T L is the electromagnetic torque and load torque of SPMSM, B is the damping coefficient, P n is the number of magnetic pole pairs, i d and i q is the stator current component of the SPMSM in the dq coordinate system, L d and L q is the stator inductance component of the SPMSM in the dq coordinate system, ψ f is the permanent magnet flux, θ m is the mechanical angle of the motor.

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