Permanent magnet synchronous motor adaptive speed control method based on time-varying internal model

Abstract

The invention discloses a permanent magnet synchronous motor adaptive speed control method based on a time-varying internal model. The method comprises the following steps: S1, establishing a permanent magnet synchronous motor mathematical model; s2, describing a speed tracking and interference suppression problem of the permanent magnet synchronous motor under the condition that the external interference frequency is unknown and time-varying as a self-adaptive servo control problem; s3, designing a time-varying internal model, and converting an adaptive servo control problem of the motor system into a robust stabilization problem of an augmented system composed of the motor system and the time-varying internal model; and S4, a speed-current loop cascade structure is adopted, a self-adaptive controller based on a time-varying internal model is designed, a PI controller is designed for a current loop, and a final controller is given. According to the method, all motor parameters are allowed to be unknown, through the adaptive controller based on the time-varying internal model, the problem of high-precision speed tracking control of the permanent magnet synchronous motor under the conditions that the external interference frequency is unknown and the time is varying is solved, and good speed tracking performance is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motor control, and particularly to an adaptive speed control method for permanent magnet synchronous motors based on a time-varying internal model. Background Technique

[0002] Among various AC motor drive devices, permanent magnet synchronous motors have attracted much attention due to their advantages such as high efficiency, high power density, large torque-inertia ratio, low noise, and maintenance-free. Therefore, permanent magnet synchronous motor drive devices have been widely used in various industrial fields such as robotics, electric vehicles, and aerospace. As a complex multi-input multi-output nonlinear system, the operation process of permanent magnet synchronous motors will be affected by time-varying external disturbances and uncertain motor parameters. In addition, the frequency of external disturbances may be unknown. Therefore, the high-precision control of permanent magnet synchronous motor drive devices is quite challenging.

[0003] On the one hand, the nonlinear output regulation theory has received extensive attention in the past few decades. Among them, the internal model control method can achieve trajectory tracking and disturbance rejection of uncertain nonlinear systems. On the other hand, since adaptive control technology can handle unknown parameters, it is widely used in the field of nonlinear system control. When permanent magnet synchronous motors are subject to parameter uncertainties and external disturbances with unknown and time-varying frequencies, combining the internal model control with adaptive control technology can achieve high-precision speed tracking control of permanent magnet synchronous motors and allow all motor parameters to be unknown.

[0004] However, at present, when using the output regulation method to solve the high-precision speed control problem of permanent magnet synchronous motors, it is impossible to suppress the load torque disturbance with unknown and time-varying frequencies, which greatly limits the scope of use of this method. Summary of the Invention

[0005] The purpose of the present invention is to provide an adaptive speed control method for permanent magnet synchronous motors based on a time-varying internal model to solve the above defects.

[0006] To achieve the above purpose, the present invention provides the following technical solutions:

[0007] An adaptive speed control method for permanent magnet synchronous motors based on a time-varying internal model includes the following steps:

[0008] S1. Establish a mathematical model of the permanent magnet synchronous motor;

[0009] S2. Describe the speed tracking and disturbance rejection problem of the permanent magnet synchronous motor under the condition of unknown and time-varying external disturbance frequencies as an adaptive servo control problem;

[0010] S3. Design a time-varying internal model to transform the adaptive servo control problem of the motor system into a robust stabilization problem of the augmented system composed of the motor system and the time-varying internal model;

[0011] S4. Adopt a cascade structure of speed-current loops, design an adaptive controller based on the time-varying internal model for the speed loop, design a PI controller for the current loop, and give the final controller.

[0012] Preferably, in step S1, the mathematical model of the permanent magnet synchronous motor is described as follows:

[0013]

[0014] where ω r is the angular velocity of the motor rotor, u d , u q are the stator voltages on the d-q axes respectively, i d , i q are the stator currents on the d-q axes respectively, T L is the load torque of the motor, J is the moment of inertia of the motor, L is the armature inductance, R s is the stator resistance, p is the number of pole pairs of the motor, Φ v is the rotor flux linkage, F v is the viscous friction coefficient.

[0015] Preferably, step S2 is specifically as follows:

[0016] S21. Assume that the reference speed ω d and the load torque T L are generated by the following time-varying external system:

[0017]

[0018] where represents the derivative of the external system state variable, S(t,σ) is a sufficiently smooth matrix, the constant σ usually represents the magnitude of the unknown disturbance frequency in practice, τ represents the external system state variable, R, Q are constant matrices; t represents time, assume that for all t≥0, the solution of the external system (2) exists and is bounded, and this external system can generate not only constant signals and sine signals, but also periodic signals with time-varying frequencies;

[0019] S22. Let x = ω r , A = -F v / J, B = 3pΦ v / (2J), regard i q in the motion equation of the permanent magnet synchronous motor mathematical model formula (1) as the control input u, and after making a variable substitution and combining it with formula (2), the following form can be obtained:

[0020]

[0021] wherein, is expressed as the derivative of the rotor angular velocity;

[0022] S23. Define the tracking error e as:

[0023] e = x - Rτ (4),

[0024] wherein, e represents the tracking error of the rotor angular velocity;

[0025] S24. Considering the system parameter perturbation caused by uncertain factors, let

[0026] represent the nominal values of the parameters of the permanent magnet synchronous motor, represent the deviation between the actual value and the nominal value of the parameters of the permanent magnet synchronous motor;

[0027] Write formula (1) and the external system formula (2) in the following compact form, as shown in formula (5):

[0028]

[0029] e = x - Rτ (5);

[0030] S25. At this time, the speed tracking and disturbance rejection problem of the permanent magnet synchronous motor under the condition that the external disturbance frequency is unknown and time-varying has been described as an adaptive servo control problem. Its control objective is that when the external disturbance frequency is unknown and time-varying, the steady-state tracking error of formula (5) asymptotically approaches zero, and at the same time, the closed-loop system is ensured to be stable.

[0031] Preferably, the step S3 is specifically:

[0032] S31. Solve the following regulator equation:

[0033]

[0034] 0 = x(t, τ, ε) - Rτ (6),

[0035] Obtain the steady-state state x(t, τ, ε) = Rτ and the steady-state input u(t, τ, ε, σ) = B -1 (-AR + RS(t, σ) + J -1 Q)τ;

[0036] S32. Assume that there exists an integer s. For all t, τ, ε, and σ, the steady-state input u(t, τ, ε, σ) satisfies the following formula (7):

[0037]

[0038] where the sufficiently smooth function \(b\) i (t,σ), \(i = 0, 1, \ldots, s - 1\) and its \(n\) - th derivatives are uniformly bounded for \(n = 1, \ldots, l\), where \(l\) is a sufficiently large integer; furthermore, there exist smooth vector - valued functions and vector - valued function such that

[0039] S33. For all \(\varepsilon\), \(\tau\) and \(\sigma\), the following steady - state generator is obtained as shown in formula (8):

[0040]

[0041] where \(\xi(t,\tau,\varepsilon,\sigma)\) is the state of the steady - state generator, is the derivative of \(\xi(t,\tau,\varepsilon,\sigma)\), is a sufficiently smooth matrix, \(\Gamma_0=[1\ 0\ \ldots\ 0]\) is a row vector;

[0042] \(\varPhi_0(t,\sigma)\) can be re - described as:

[0043] \(\varPhi_0(t,\sigma)=\varPhi\) b +b(t,\sigma)\(\Gamma_0\) (9),

[0044] where is a constant matrix, is a smooth vector - valued function;

[0045] The matrix pair \((\varPhi\) b ,\(\Gamma_0)\) is observable, and the column vector such that is a Hurwitz matrix;

[0046] S34. Let \(G_0(t,\sigma)=L_0 + b(t,\sigma)\) and \(\beta_0(t)=1\), and define \(L\) i (\sigma)=\text{col}(\psi s-1,i ,\ldots,\psi 0,i ) and \(\beta(t)=\text{col}(\beta_1(t),\ldots,\beta i (t))\), where \(\beta i (t)\) is a scalar function, and from the following formula (10) can be obtained:

[0047] \(G_0(t,\sigma)=L_0\beta_0(t)+L_1(\sigma)\beta_1(t)+\ldots+L ρ (\sigma)\beta ρ (t)\) (10),

[0048] S35. Let

[0049] where F g is a block diagonal

[0050]

[0051] matrix, G g (t) is a sufficiently smooth matrix, H g (σ) is a constant matrix, F0 T is a Hurwitz matrix, Γ0 T is a column vector; L0 T , is a row vector;

[0052] Design the time-varying internal model in the following form, as shown in Equation (11):

[0053]

[0054] where η represents the state variable of the time-varying internal model, represents the derivative of the state variable of the time-varying internal model;

[0055] S36. Perform the following coordinate and input transformations on the augmented system composed of Equation (5) and Equation (11):

[0056]

[0057] where, is a continuously differentiable matrix, and the following error equation is obtained:

[0058]

[0059] where, represents 's derivative, represents the derivative of e, represents the derivative of G g (t);

[0060] At this time, the adaptive servo control problem of Equation (5) has been transformed into the robust stabilization problem of Equation (13).

[0061] Preferably, the step S4 is specifically:

[0062] S41. Design the following controller to solve the robust stabilization problem of Equation (13), as shown in Equation (14):

[0063]

[0064] where k is a positive number;

[0065] S42. Define and let where \(P\) is a positive definite symmetric matrix satisfying \(F\) g T \(P + PF\) g \(= -I\), where \(I\) is the identity matrix; is the estimate of \(H\) g (\(\sigma\)), \(m\) is a positive number; thus, there exists a sufficiently large gain \(k\) satisfying the following inequality (15):

[0066]

[0067] In the formula,[[]]END]] represents the derivative of;

[0068] S43. The controller formula (16) of the speed loop is in the following form:

[0069]

[0070] In the formula,[[]]END]] represents the derivative of;

[0071] S44. Adopting the PI control method, the controller of the current loop is as shown in formula (17):

[0072]

[0073] In the formula,[[]]END]]

[0074] S45. Combining formula (16) and formula (17), the final controller is as shown in formula (18):

[0075]

[0076] The beneficial effects of the present invention are as follows:

[0077] A permanent magnet synchronous motor adaptive speed control method based on a time-varying internal model according to the present invention solves the problem of high-precision speed tracking control of a permanent magnet synchronous motor under the conditions of unknown and time-varying external disturbance frequencies through an adaptive controller based on a time-varying internal model, and has good speed tracking performance. At the same time, the permanent magnet synchronous motor adaptive speed control method based on a time-varying internal model according to the present invention allows all motor parameters to be unknown; the speed loop controller of the present invention only needs to be designed according to the speed equation model of the permanent magnet synchronous motor, simplifies the model, and is easy to apply in practice. Description of the Drawings

[0078] Figure 1 : Control framework diagram of the permanent magnet synchronous motor of the method of the present invention;

[0079] Figure 2: Permanent magnet synchronous motor speed tracking curve of the method of the present invention;

[0080] Figure 3 : i of the method of the present invention d Current curve;

[0081] Figure 4 : i of the method of the present invention q Current curve. Detailed implementation manners

[0082] The present invention will be further described below in conjunction with embodiments. It should be noted that this is only an example and explanation of the inventive concept. Those skilled in the art of the present technology can make various modifications or supplements to the described specific embodiments or use similar methods for substitution, as long as they do not deviate from the inventive concept or exceed the scope defined by this claim book, they should be regarded as falling within the protection scope of the present invention.

[0083] Embodiment 1:

[0084] An adaptive speed control method for a permanent magnet synchronous motor based on a time-varying internal model, characterized by including the following steps:

[0085] S1. Establish a mathematical model of the permanent magnet synchronous motor. The mathematical model of the permanent magnet synchronous motor is described as follows:

[0086]

[0087] In the formula, ω r is the angular velocity of the motor rotor, u d , u q are the stator voltages of the d-q axes respectively, i d , i q are the stator currents of the d-q axes respectively, T L is the load torque of the motor, J is the moment of inertia of the motor, L is the armature inductance, R s is the stator resistance, p is the number of pole pairs of the motor, Φ v is the rotor flux, and F v is the viscous friction coefficient.

[0088] S2. Describe the speed tracking and disturbance rejection problems of the permanent magnet synchronous motor under the condition that the external disturbance frequency is unknown and time-varying as an adaptive servo control problem. The specific steps are as follows:

[0089] S21. Assume that the reference speed ω d and the load torque T L are generated by the following time-varying external system:

[0090]

[0091] In the formula, Denote the derivative of the external system state variable. \(S(t,\sigma)\) is a sufficiently smooth matrix. The constant \(\sigma\) usually represents the magnitude of the unknown disturbance frequency in practice. \(\tau\) represents the external system state variable, \(R\) and \(Q\) are constant matrices, and \(t\) represents time. Assume that for all \(t\geq0\), the solution of the external system (2) exists and is bounded. It should be noted that this external system can generate not only constant signals and sine signals, but also periodic signals with time-varying frequencies.

[0092] S22. Let \(x = \omega\) r , \(A=-F\) v / J, \(B = 3p\varPhi\) v / (2J). Regarding \(i\) in the motion equation of the permanent magnet synchronous motor mathematical model formula (1) q as the control input \(u\), and after making a variable substitution and combining it with formula (2), the following form can be obtained:

[0093]

[0094] In the formula, denotes the derivative of the rotor angular velocity.

[0095] S23. Define the tracking error \(e\) as:

[0096] \(e=x - R\tau\) (4),

[0097] In the formula, \(e\) represents the tracking error of the rotor angular velocity.

[0098] S24. Considering the system parameter perturbation caused by uncertain factors, let where \(L\), \(R\) s , \(\varPhi\) v , \(J\), \(F\) v are the actual values of the various parameters of the permanent magnet synchronous motor, denotes the nominal values of the various parameters of the permanent magnet synchronous motor, represents the deviation between the actual value and the nominal value of the parameters of the permanent magnet synchronous motor.

[0099] Write formula (1) and the external system formula (2) in the following compact form, as shown in formula (5):

[0100]

[0101] \(e=x - R\tau\) (5).

[0102] S25. At this time, the speed tracking and disturbance rejection problem of the permanent magnet synchronous motor under the condition that the external disturbance frequency is unknown and time-varying has been described as an adaptive servo control problem. Its control objective is that when the external disturbance frequency is unknown and time-varying, the steady-state tracking error of formula (5) asymptotically approaches zero, and at the same time, the closed-loop system is ensured to be stable.

[0103] S3. Design a time-varying internal model to transform the adaptive servo control problem of the motor system into a robust stabilization problem of the augmented system composed of the motor system and the time-varying internal model. The specific steps are as follows:

[0104] S31. Solve the following regulator equation:

[0105]

[0106] 0 = x(t, τ, ε) - Rτ (6),

[0107] Obtain the steady-state state x(t, τ, ε) = Rτ and the steady-state input u(t, τ, ε, σ) = B -1 (-AR + RS(t, σ) + J -1 Q)τ.

[0108] S32. Assume that there exists an integer s such that for all t, τ, ε, and σ, the steady-state input u(t, τ, ε, σ) satisfies the following formula (7):

[0109]

[0110] where the sufficiently smooth functions b i (t, σ), i = 0, 1, …, s - 1 and their nth-order derivatives are uniformly bounded, n = 1, …, l, where l is a sufficiently large integer; in addition, there exist smooth vector-valued functions and the vector-valued function such that

[0111] S33. For all ε, τ, and σ, obtain the following steady-state generator, as shown in formula (8):

[0112]

[0113] where ξ(t, τ, ε, σ) is the state of the steady-state generator, is the derivative of ξ(t, τ, ε, σ), is a sufficiently smooth matrix, and Γ0 = [1 0 … 0] is a row vector.

[0114] Φ0(t, σ) can be re-described as:

[0115] Φ0(t, σ) = Φ b + b(t, σ)Γ0 (9),

[0116] where is a constant matrix, is a smooth vector-valued function;

[0117] Note that the matrix pair (Φ b, (Γ0) is observable, so there exists a column vector such that is a Hurwitz matrix.

[0118] S34. Let G0(t, σ) = L0 + b(t, σ) and β0(t) = 1, and define L i (σ) = col(ψ s-1,i , …, ψ 0,i ) and β(t) = col(β1(t), …, β i (t)), where β i (t) is a scalar function, and from the following formula (10) can be obtained:

[0119] G0(t, σ) = L0β0(t) + L1(σ)β1(t) + … + L ρ (σ)β ρ (t) (10).

[0120] S35. Let

[0121] where F g is a block diagonal

[0122]

[0123] matrix, G g (t) is a sufficiently smooth matrix, H g (σ) is a constant matrix, F0 T is a Hurwitz matrix, Γ0 T is a column vector, L0 T , is a row vector;

[0124] Design the time-varying internal model in the following form, as shown in formula (11):

[0125]

[0126] where η represents the state variable of the time-varying internal model, represents the derivative of the state variable of the time-varying internal model.

[0127] S36. Perform the following coordinate and input transformation on the augmented system composed of formula (5) and formula (11):

[0128]

[0129] where is a continuously differentiable matrix, and the following error equation is obtained:

[0130]

[0131] In the formula, represents the derivative of, represents the derivative of e, represents G g (t) the derivative of;

[0132] At this time, the adaptive servo control problem of formula (5) has been transformed into the robust stabilization problem of formula (13).

[0133] S4. Adopt the cascade structure of the speed-current loop, design an adaptive controller based on the time-varying internal model for the speed loop, design a PI controller for the current loop and give the final controller. The specific steps are as follows:

[0134] S41. Design the following controller to solve the robust stabilization problem of formula (13), as shown in formula (14):

[0135]

[0136] In the formula, k is a positive number;

[0137] S42. Define and let where P is a positive definite symmetric matrix satisfying F g T P + PF g = -I, I is the identity matrix, is the estimated value of H g (σ), m is a positive number; thus there exists a sufficiently large gain k that satisfies the following inequality (15):

[0138]

[0139] In the formula, represents the derivative of.

[0140] S43. Obtain the controller formula (16) of the speed loop in the following form:

[0141]

[0142] In the formula, represents the derivative of.

[0143] S44. Adopt the PI control method, and the controller of the current loop is as shown in formula (17):

[0144]

[0145] In the formula,

[0146] S45. Combining formula (16) and formula (17), the final controller is obtained as shown in formula (18):

[0147]

[0148] To verify the effectiveness of the above-mentioned method, the selected permanent magnet synchronous motor has specific parameters shown in Table 1 in the appendix.

[0149] Table 1: Nominal values of permanent magnet synchronous motor parameters;

[0150]

[0151] Load torque T L = 0.3sin(σsint)+0.3sin(σcost) N·m, reference signal ω d = 1500 r / min, then the external system parameters are as follows:

[0152] R = [1 0 0], Q = [0 1 0].

[0153] The controller parameters are selected as follows:

[0154] k = 50,

[0155]

[0156] Among them,

[0157] i d and i q The PI parameters of the current loop are respectively:

[0158] k p1 = 30, k i1 = 15, k p2 = 30, k i2 = 15.

[0159] In addition, we use a linear tracking differentiator to prevent excessive control voltage during the motor startup phase, where is the desired speed trajectory and δ = 3.

[0160] Figure 1 is the control framework diagram of the permanent magnet synchronous motor in the method of the present invention. As Figure 1 shown, a series of the above technical parameters are adopted and applied to the adaptive speed control method of the permanent magnet synchronous motor based on time-varying internal model disclosed in the present invention, and the obtained simulation results are as Figures 2-4 shown. Figure 2 is the speed tracking curve diagram of the permanent magnet synchronous motor in the method of the present invention, asFigure 2 It can be seen that the curve in the figure reflects that the designed controller has good speed tracking performance under the conditions of unknown and time-varying interference frequency and motor parameter perturbation. Figure 3 、 Figure 4 are respectively the i d 、i q current curve diagrams of the permanent magnet synchronous motor in the method of the present invention; as Figure 3 、 Figure 4 can be seen, they are all within the rated current of the permanent magnet synchronous motor, verifying the practical feasibility of the present invention.

[0161] An adaptive speed control method for a permanent magnet synchronous motor based on a time-varying internal model according to the present invention solves the problem of high-precision speed tracking control of a permanent magnet synchronous motor under the conditions of unknown and time-varying external interference frequency through an adaptive controller based on a time-varying internal model, and has good speed tracking performance. At the same time, the adaptive speed control method for a permanent magnet synchronous motor based on a time-varying internal model according to the present invention allows all motor parameters to be unknown; the speed loop controller of the present invention only needs to be designed according to the speed equation model of the permanent magnet synchronous motor, simplifies the model, and is easy to be applied in practice.

[0162] The above is an exemplary description of the invention. Obviously, the specific implementation of the present invention is not limited by the above methods. As long as such non-substantial improvements are made by adopting the method concept and technical solution of the present invention, or the concept and technical solution of the invention are directly applied to other occasions without improvement, they are all within the protection scope of the present invention.

Claims

1. A permanent magnet synchronous motor adaptive speed control method based on time-varying internal model, characterized in that: The following steps are involved: S1. Establish a mathematical model of permanent magnet synchronous motor; S2. Describe the speed tracking and interference suppression problem of a permanent magnet synchronous motor under the condition of unknown and time-varying external interference frequency as an adaptive servo control problem; S3. Design a time-varying internal model to transform the adaptive servo control problem of the motor system into a robust stabilization problem of the augmented system consisting of the motor system and the time-varying internal model. S4. Using the cascade structure of speed-current loop, an adaptive controller based on time-varying internal model is designed for the speed loop, and a PI controller is designed for the current loop and the final controller is given.

2. The method for adaptive speed control of a permanent magnet synchronous motor based on a time-varying internal model according to claim 1 is characterized in that: In step S1, the permanent magnet synchronous motor mathematical model is described as follows: In the formula, ω r is the motor rotor angular velocity, u d 、u q are the stator voltages of the dq axes, i d 、i q are the stator currents of the dq axis, T L is the load torque of the motor, J is the moment of inertia of the motor, L is the armature inductance, R s is the stator resistance, p is the number of motor pole pairs, Φ v is the rotor flux, F v is the coefficient of viscous friction.

3. The method for adaptive speed control of a permanent magnet synchronous motor based on a time-varying internal model according to claim 2 is characterized in that: The step S2 is specifically: S21, assuming reference speed ω d and load torque T L Produced by the following time-varying external systems: In the formula, represents the derivative of the state variable of the external system, S(t,σ) is a sufficiently smooth matrix, the constant σ usually represents the magnitude of the unknown disturbance frequency in practice, τ represents the state variable of the external system, R and Q are constant matrices, and t represents time; it is assumed that for all t≥0, the solution of the external system (2) exists and is bounded. This external system can generate not only constant value signals and sinusoidal signals, but also periodic signals with time-varying frequencies; S22, let x = ω r ,A=-F v / J,B=3pΦ v / (2J), replace i in the motion equation of the permanent magnet synchronous motor mathematical model formula (1) q As the control input u, after variable substitution and combining it with formula (2), we can get the following form: In the formula, Expressed as the derivative of the rotor angular velocity; S23. Define the tracking error e as: e=x-Rτ (4), Where, e represents the tracking error of the rotor angular velocity; S24. Consider the system parameter perturbation caused by uncertain factors, let in Indicates the nominal values ​​of various parameters of permanent magnet synchronous motor, Indicates the deviation between the actual value and the nominal value of the permanent magnet synchronous motor parameter; Formula (1) and external system formula (2) are written in the following compact form, as shown in formula (5): S25. At this time, the speed tracking and interference suppression problem of the permanent magnet synchronous motor under the condition of unknown and time-varying external interference frequency has been described as an adaptive servo control problem. Its control goal is to make the steady-state tracking error of formula (5) approach zero asymptotically when the external interference frequency is unknown and time-varying, while ensuring the stability of the closed-loop system.

4. The method for adaptive speed control of a permanent magnet synchronous motor based on a time-varying internal model according to claim 3 is characterized in that: The step S3 is specifically: S31. Solve the following regulator equation: 0=x(t,τ,ε)-Rτ (6), We obtain the steady-state state x(t,τ,ε)=Rτ and the steady-state input u(t,τ,ε,σ)=B -1 (-AR+RS(t,σ)+J -1 Q)τ; S32. Assume that there exists an integer s, for all t, τ, ε and σ, the steady-state input u(t, τ, ε, σ) satisfies the following formula (7): In the formula, the sufficiently smooth function b i (t,σ),i=0,1,…,s-1 and its n-th derivative are uniformly bounded, n=1,…,l, l is a sufficiently large integer; in addition, there exists a smooth vector-valued function and vector-valued functions Make S33. For all ε, τ and σ, the following steady-state generator is obtained, as shown in formula (8): Where ξ(t,τ,ε,σ) is the state of the steady-state generator, is the derivative of ξ(t,τ,ε,σ), is a fully smooth matrix, Γ0=[1 0 … 0] is the row vector; Φ0(t,σ) can be restated as: Φ0(t,σ)=Φ b +b(t,σ)Γ0 (9), In the formula, is a constant matrix, is a smooth vector-valued function; Matrix pair (Φ b ,Γ0) observable, column vector Make is the Hurwitz matrix; S34. Let G0(t,σ)=L0+b(t,σ) and β0(t)=1, and define L i (σ)=col(ψ s-1,i ,…,ψ 0,i ) and β(t)=col(β1(t),…,β i (t)), where β i (t) is a scalar function, given by The following formula (10) can be obtained: G0(t,σ)=L0β0(t)+L1(σ)β1(t)+…+L ρ (s)b ρ (t) (10), S35, Order where F g It is a diagonal block Matrix, G g (t) is a sufficiently smooth matrix, H g (σ) is a constant matrix, is the Hurwitz matrix, is a column vector; is a row vector; The time-varying internal model is designed as follows, as shown in formula (11): In the formula, η represents the state variable of the time-varying internal model, represents the derivative of the time-varying internal model state variable; S36. Perform the following coordinate and input transformations on the augmented system composed of formula (5) and formula (11): In the formula, is a continuously differentiable matrix, and the following error equation is obtained: In the formula, express The derivative of represents the derivative of e, Represents G g The derivative of (t); At this point, the adaptive servo control problem of formula (5) has been transformed into the robust stabilization problem of formula (13).

5. The method for adaptive speed control of a permanent magnet synchronous motor based on a time-varying internal model according to claim 4 is characterized in that: The step S4 is specifically: S41. Design the following controller to solve the robust stabilization problem of formula (13), as shown in formula (14): In the formula, k is a positive number; S42. Definition And order Where P is a positive definite symmetric matrix satisfying I is the identity matrix, H g (σ) is an estimated value, m is a positive number; then there exists a sufficiently large gain k that satisfies the following inequality (15): In the formula, express The derivative of S43, the controller formula (16) of the speed loop is obtained as follows: In the formula, express The derivative of S44, using the PI control method, the controller of the current loop is shown in formula (17): In the formula, S45. Combining formula (16) and formula (17), the final controller is obtained as shown in formula (18):

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