An inner model-based adaptive speed control method for permanent magnet synchronous motor

Abstract

This invention discloses an adaptive speed control method for permanent magnet synchronous motors (PMSMs) based on internal modeling. The method includes: establishing a mathematical model of the PMSM; describing the speed tracking and interference suppression problem of the PMSM under unknown external disturbance frequencies as an adaptive servo control problem; and designing the controller using a cascaded speed-current loop structure, where the speed loop employs an adaptive control method based on internal modeling, and the current loop employs a PI control method. This invention solves the problem of unknown external disturbance frequencies and the impact of motor parameter perturbations on tracking performance in practical control, exhibiting excellent speed tracking performance. Furthermore, the adaptive speed control method based on internal modeling proposed in this invention allows for the estimation of unknown motor parameters and enables the estimation of unknown disturbance frequencies.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor control, and more specifically to an adaptive speed control method for permanent magnet synchronous motors based on internal models. Background Technology

[0002] In modern AC servo systems, permanent magnet synchronous motors (PMSMs) are widely used in aerospace, CNC machine tools, robotics, and electric vehicles due to their advantages such as high power density, high efficiency, fast response, wide speed range, and low moment of inertia. However, PMSM models are characterized by multivariables, nonlinearity, and strong coupling, and are also affected by load torque disturbances and parameter uncertainties, making it often difficult to achieve good tracking control performance.

[0003] On the other hand, adaptive servo control has received widespread attention in the control field in recent decades. Internal model and adaptive techniques, as powerful tools for solving adaptive servo control problems, have the advantage of achieving multiple control objectives such as trajectory tracking, disturbance suppression, and robustness even when the external system contains unknown parameters. Applying internal model and adaptive techniques to permanent magnet synchronous motors not only achieves good speed tracking performance under conditions where the external disturbance frequency and motor parameters are unknown, but also enables the estimation of unknown disturbance frequencies. Summary of the Invention

[0004] Purpose of the invention: In order to overcome the shortcomings of the existing technology, the present invention provides an adaptive speed control method for permanent magnet synchronous motors based on internal models.

[0005] The technical solution of this invention is:

[0006] The present invention discloses an adaptive speed control method for a permanent magnet synchronous motor based on an internal model, the method comprising the following steps:

[0007] Step 1: Establish a mathematical model for the permanent magnet synchronous motor;

[0008] Step 2: Describe the speed tracking and interference suppression problem of permanent magnet synchronous motor under unknown external interference frequency as an adaptive servo control problem;

[0009] Step 3: Design the internal model to transform the adaptive servo control problem of the motor system into a robust stabilization problem of an augmented system consisting of the motor system and the internal model;

[0010] Step 4: Using a cascaded structure of speed-current loops, and based on the adaptive output regulation theory, design an adaptive state feedback controller for the speed loop;

[0011] Step 5: Using a cascaded structure of speed-current loop, design a PI controller for the current loop and provide the final controller.

[0012] Furthermore, an adaptive speed control method for a permanent magnet synchronous motor based on an internal model is characterized in that step 1 specifically comprises:

[0013] The mathematical model of a permanent magnet synchronous motor is:

[0014]

[0015] Where: u d u q These are the dq-axis components of the stator voltage, i d i q These are the dq-axis components of the stator current, where L is the armature inductance and R is the dq-axis component. s It is the stator resistance, p is the number of pole pairs, Φ v Represents the magnetic flux linkage of a permanent magnet, ω r It is the actual mechanical angular velocity, T L J is the load torque, J is the moment of inertia of the motor rotor, and B is the coefficient of viscous friction.

[0016] Furthermore, an adaptive speed control method for a permanent magnet synchronous motor based on an internal model is characterized in that step 2 specifically comprises:

[0017] 1) This method assumes a reference velocity ω d and load torque T L It can be generated by the following external systems:

[0018]

[0019] Where A1(σ), N1, and N2 are three constant matrices, but σ is an unknown constant. This external system is general and can generate commonly used signals in practice, such as constant signals, ramp signals, and sinusoidal signals.

[0020] 2) Let x = ω r , i q As the control input u (which will be used as i) q (Reference signal of the current loop). The velocity equation of system (1) can be written in the following form:

[0021]

[0022] 3) Define the tracking error as:

[0023] e = ω r -N1v. (4)

[0024] 4) Order in The nominal values ​​of various parameters of the permanent magnet synchronous motor, L, R s , Φ v J and B represent the actual values ​​of various parameters of the permanent magnet synchronous motor, ε∈R 5 This represents the deviation between the actual and nominal values ​​of the parameters of the permanent magnet synchronous motor. Formulas (1) and (2) can be written in the following compact form:

[0025]

[0026] where f(x,u,v,ε)=ax+bu-J -1 N2v,h(x,u,v,ε)=x-N1v.

[0027] 5) At this time, the speed tracking and interference suppression problem of the permanent magnet synchronous motor under the condition of unknown external interference frequency has been described as an adaptive servo control problem. Its control objective is to make the closed-loop system stable and the steady-state tracking error of formula (5) asymptotically approach zero when the external system contains unknown parameters.

[0028] Furthermore, an adaptive speed control method for a permanent magnet synchronous motor based on an internal model is characterized in that step 3 specifically comprises:

[0029] 1) Solve the following regulator equation:

[0030]

[0031] Where x(v,ε) and u(v,σ,ε) are the steady-state state and steady-state input, respectively. The steady-state solutions for the state and input are obtained as follows:

[0032]

[0033] 2) There exist integers s and real numbers a1, a2, ..., a s Such that u(v,σ,ε) satisfies all trajectories v(t) and all ε of the external system.

[0034]

[0035] 3) Let And (Γ,Φ(σ)) is a pair of observable matrices as follows:

[0036]

[0037] 4) Construct the following steady-state generator to produce the steady-state solution:

[0038]

[0039] 5) Choose a pair of controllable matrices (M, N), where M is a Hurwitz matrix, and let θ(v,σ,ε) = T(σ)ξ(v,σ,ε), Ψ σ =ΓT -1 (σ) yields:

[0040]

[0041] Where T(σ) is any non-singular matrix satisfying the following Sylvester equation:

[0042] T(σ)Φ(σ)-MT(σ)=NΓ. (12)

[0043] 6) The inner mold is designed as follows:

[0044]

[0045] 7) Perform the following coordinate transformation and input transformation:

[0046]

[0047] The following error equation is obtained:

[0048]

[0049] 8) At this point, the adaptive servo control problem of system (5) has been transformed into the robust stabilization problem of system (15).

[0050] Furthermore, an adaptive speed control method for a permanent magnet synchronous motor based on an internal model is characterized in that step 4 specifically comprises:

[0051] 1) Definition make Where P is a positive definite symmetric matrix satisfying M P + PM = -I, and I is the identity matrix. For Ψ σ The estimated value is given by m, where m is a specific positive number. Therefore, there exists a sufficiently large gain k that satisfies the following inequality:

[0052]

[0053] 2) The following control law is obtained to solve the robust stabilization problem of system (15):

[0054]

[0055] 3) The speed loop controller is obtained in the following form:

[0056]

[0057] Furthermore, an adaptive speed control method for permanent magnet synchronous motors based on internal models is characterized by employing a cascaded structure of speed-current loops combined with... The vector control strategy, specifically step 5, is as follows:

[0058] 1) Using PI control, the controller for the current loop is:

[0059]

[0060] in

[0061] 2) Combining (18) and (19), the final controller is obtained as follows:

[0062]

[0063] The advantages of this invention are:

[0064] This invention solves the problems of unknown interference frequency and motor parameter perturbation affecting tracking performance in practical control, and has good speed tracking performance. In addition, the adaptive speed control method based on internal model proposed in this invention allows all motor parameters to be unknown and can estimate unknown interference frequency. Finally, the speed loop controller of this invention only needs to be designed based on the speed equation model of permanent magnet synchronous motor, which simplifies the model and makes it easy to apply in practice. Attached Figure Description

[0065] Figure 1 This is a block diagram of the permanent magnet synchronous motor control of the present invention;

[0066] Figure 2 This is the speed tracking curve of the present invention;

[0067] Figure 3 For the present invention i d Current curve;

[0068] Figure 4 For the present invention i q Current curve.

[0069] Figure 5 This is the frequency estimation curve for this invention. Detailed Implementation

[0070] The present invention will now be further described with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments.

[0071] The present invention discloses an adaptive speed control method for a permanent magnet synchronous motor based on an internal model, the method comprising the following steps:

[0072] Step 1: Establish a mathematical model for the permanent magnet synchronous motor;

[0073] Step 2: Describe the speed tracking and interference suppression problem of permanent magnet synchronous motor under unknown external interference frequency as an adaptive servo control problem;

[0074] Step 3: Design the internal model to transform the adaptive servo control problem of the motor system into a robust stabilization problem of an augmented system consisting of the motor system and the internal model;

[0075] Step 4: Using a cascaded structure of speed-current loops, and based on the adaptive output regulation theory, design an adaptive state feedback controller for the speed loop;

[0076] Step 5: Using a cascaded structure of speed-current loop, design a PI controller for the current loop and provide the final controller.

[0077] Furthermore, step 1 specifically includes:

[0078] The mathematical model of a permanent magnet synchronous motor is:

[0079]

[0080] Where: u d u q These are the dq-axis components of the stator voltage, i d i q These are the dq-axis components of the stator current, where L is the armature inductance and R is the dq-axis component. s It is the stator resistance, p is the number of pole pairs, Φ v Represents the magnetic flux linkage of a permanent magnet, ω r It is the actual mechanical angular velocity, T L J is the load torque, J is the moment of inertia of the motor rotor, and B is the coefficient of viscous friction.

[0081] Furthermore, an adaptive speed control method for a permanent magnet synchronous motor based on an internal model is characterized in that step 2 specifically comprises:

[0082] 1) This method assumes a reference velocity ω d and load torque T L It can be generated by the following external systems:

[0083]

[0084] Where A1(σ), N1, and N2 are three constant matrices, but σ is an unknown constant. This external system is general and can generate commonly used signals in practice, such as constant signals, ramp signals, and sinusoidal signals.

[0085] 2) Let x = ω r , i qAs the control input u (which will be used as i) q (Reference signal of the current loop). The velocity equation of system (1) can be written in the following form:

[0086]

[0087] 3) Define the tracking error as:

[0088] e = ω r -N1v. (4)

[0089] 4) Order in The nominal values ​​of various parameters of the permanent magnet synchronous motor, L, R s , Φ v J and B represent the actual values ​​of various parameters of the permanent magnet synchronous motor, ε∈R 5 This represents the deviation between the actual and nominal values ​​of the parameters of the permanent magnet synchronous motor. Formulas (1) and (2) can be written in the following compact form:

[0090]

[0091] where f(x,u,v,ε)=ax+bu-J -1 N2v,h(x,u,v,ε)=x-N1v.

[0092] 5) At this time, the speed tracking and interference suppression problem of the permanent magnet synchronous motor under the condition of unknown external interference frequency has been described as an adaptive servo control problem. Its control objective is to make the closed-loop system stable and the steady-state tracking error of formula (5) asymptotically approach zero when the external system contains unknown parameters.

[0093] Furthermore, step 3 specifically involves:

[0094] 1) Solve the following regulator equation:

[0095]

[0096] Where x(v,ε) and u(v,σ,ε) are the steady-state state and steady-state input, respectively. The steady-state solutions for the state and input are obtained as follows:

[0097]

[0098] 2) There exist integers s and real numbers a1, a2, ..., a s Such that u(v,σ,ε) satisfies all trajectories v(t) and all ε of the external system.

[0099]

[0100] 3) Let And (Γ,Φ(σ)) is a pair of observable matrices as follows:

[0101]

[0102] 4) Construct the following steady-state generator to produce the steady-state solution:

[0103]

[0104] 5) Choose a pair of controllable matrices (M, N), where M is a Hurwitz matrix, and let θ(v,σ,ε) = T(σ)ξ(v,σ,ε), Ψ σ =ΓT -1 (σ) yields:

[0105]

[0106] Where T(σ) is any non-singular matrix satisfying the following Sylvester equation:

[0107] T(σ)Φ(σ)-MT(σ)=NΓ. (12)

[0108] 6) The inner mold is designed as follows:

[0109]

[0110] 7) Perform the following coordinate transformation and input transformation:

[0111]

[0112] The following error equation is obtained:

[0113]

[0114] 8) At this point, the adaptive servo control problem of system (5) has been transformed into the robust stabilization problem of system (15).

[0115] Furthermore, step 4 specifically involves:

[0116] 1) Definition make Where P is a positive definite symmetric matrix satisfying M P + PM = -I, and I is the identity matrix. For Ψ σ The estimated value is given by m, where m is a specific positive number. Therefore, there exists a sufficiently large gain k that satisfies the following inequality:

[0117]

[0118] 2) The following control law is obtained to solve the robust stabilization problem of system (15):

[0119]

[0120] 3) The speed loop controller is obtained in the following form:

[0121]

[0122] Furthermore, a cascaded structure of speed-current loops is adopted in combination with... The vector control strategy, step 5 specifically is as follows:

[0123] 1) Using PI control, the controller for the current loop is:

[0124]

[0125] in

[0126] 2) Combining (18) and (19), the final controller is obtained as follows:

[0127]

[0128] To verify the effectiveness of the proposed method, an example of the present invention is provided.

[0129] The specific parameters of the selected permanent magnet synchronous motor are shown in Table 1.

[0130] Table 1: Nominal values ​​of parameters for permanent magnet synchronous motors;

[0131]

[0132] Load torque T L =0.3sin(4t)N·m, reference signal ω d =1200r / min, then the external system parameters are as follows:

[0133]

[0134] The controller parameters are selected as follows:

[0135]

[0136] i d and i q The current loop PI parameters are as follows:

[0137] k p1 =2,k i1 =10,k p2 =2,k i2 =10.

[0138] Using the above series of parameters, the method of this invention is applied to control the permanent magnet synchronous motor, and the simulation results shown in the attached figure are obtained. Figure 2 The figure shows the speed tracking curve, which reflects the good speed tracking performance of the designed controller under conditions of unknown interference frequency and motor parameter perturbation. Figure 3 and Figure 4 These are permanent magnet synchronous motors i d and i q The current curves all fall within the rated current of the permanent magnet synchronous motor, verifying the practical feasibility of the invention. Figure 5 The curve in the figure represents the frequency estimation curve, which reflects the ability of the designed controller to accurately estimate the unknown frequency in the load torque disturbance.

[0139] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. An adaptive speed control method for a permanent magnet synchronous motor based on an internal model, characterized in that, Includes the following steps: Step 1: Establish the mathematical model of the permanent magnet synchronous motor. The mathematical model of the permanent magnet synchronous motor is as follows: (1) in: , These are the dq-axis components of the stator voltage. , These are the dq-axis components of the stator current, respectively. It is armature inductance. It is the stator resistance, and p is the number of pole pairs. Represents permanent magnet flux linkage. It is the actual mechanical angular velocity. is the load torque, J is the moment of inertia of the motor rotor, and B is the coefficient of viscous friction. Step 2: The speed tracking and interference suppression problem of a permanent magnet synchronous motor under unknown external disturbance frequency conditions is described as an adaptive servo control problem, as follows: 1) Set reference speed and load torque Generated by the following external systems: (2) in, There are three constant matrices, but It is an unknown constant; this external system is general and can generate signals commonly used in practice, including constant signals, ramp signals, and sine signals; 2) Order , As control input It will be used as The reference signal for the current loop; the speed equation of the mathematical model of the permanent magnet synchronous motor is written in the following form: ， (3) 3) Define the tracking error as: ， (4) 4) Order , , , , ,in , , , , These represent the nominal values ​​of various parameters of a permanent magnet synchronous motor. , , , , This represents the actual values ​​of various parameters of the permanent magnet synchronous motor. This represents the deviation between the actual and nominal values ​​of the parameters of the permanent magnet synchronous motor; the mathematical model and formula (2) of the permanent magnet synchronous motor are written in the following compact form: (5) in, ; 5) At this time, the speed tracking and interference suppression problem of the permanent magnet synchronous motor under the condition of unknown external interference frequency has been described as an adaptive servo control problem. Its control objective is to make the closed-loop system stable and the steady-state tracking error of formula (5) asymptotically approach zero when the external system contains unknown parameters. Step 3: Design the internal model, transforming the adaptive servo control problem of the motor system into a robust stabilization problem of an augmented system consisting of the motor system and the internal model, as detailed below: 1) Solve the following regulator equation: (6) in, Given the steady-state state and steady-state input, the steady-state solutions for the state and input are as follows: ， (7) 2) There exists an integer and real numbers Make All tracks of the external system trace and all All satisfied ， (8) 3) Let and The observable matrices are as follows: (9) 4) Construct the following steady-state generator to produce the steady-state solution: (10) 5) Select a pair of controllable matrices ,in Let be the Hurwitz matrix, let , We can obtain: (11) in, For any nonsingular matrix that satisfies the following Sylvester equation: (12) 6) The inner mold is designed in the following form: (13) 7) Perform the following coordinate transformation and input transformation: (14) The following error equation is obtained: (15) 8) At this point, the adaptive servo control problem of system (5) has been transformed into the robust stabilization problem of system (15); Step 4: Using a cascaded structure of speed-current loops, and based on the adaptive output regulation theory, design an adaptive state feedback controller for the speed loop; Step 5: Using a cascaded structure of speed-current loop, design a PI controller for the current loop and provide the final controller.

2. The adaptive speed control method for a permanent magnet synchronous motor based on an internal model according to claim 1, characterized in that, Step 4 specifically involves: 1) Definition ,make in For a positive definite symmetric matrix, satisfying , It is the identity matrix. for The estimated value, For a specific positive number; therefore, there exists a sufficiently large gain. The following inequalities are satisfied: (16) 2) The following control law is obtained to solve the robust stabilization problem of system (15): (17) 3) The speed loop controller is obtained in the following form: (18)。 3. The adaptive speed control method for a permanent magnet synchronous motor based on an internal model according to claim 2, characterized in that, A cascaded structure combining speed and current loops is adopted. The vector control strategy, specifically step 5, is as follows: 1) Using the PI control method, the controller for the current loop is: (19) in ; 2) Combining (18) and (19), the final controller is obtained as follows: (20)。

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