Model-free sliding mode single-loop control method for permanent magnet synchronous motor

Abstract

The invention discloses a model-free sliding mode single-loop control method for a permanent magnet synchronous motor. The method comprises the following steps: step 1, establishing a permanent magnet synchronous motor mathematical model under a d-q coordinate system; step 2, establishing a hyperlocal model of the permanent magnet synchronous motor; step 3, designing a system state equation, including establishing equations of state variables and matching disturbance, non-matching disturbance and q-axis stator voltage; 4, designing a finite time generalized proportional-integral observer for estimating matching disturbance and non-matching disturbance and estimating the change rate of the non-matching disturbance; and step 5, designing a single-loop model-free sliding mode speed controller to obtain the single-loop model-free sliding mode speed controller. According to the model-free sliding mode single-loop control method for the permanent magnet synchronous motor, the permanent magnet synchronous motor hyper-local model is established, the designed permanent magnet synchronous motor hyper-local model does not contain any motor parameter, the dependence on the motor parameter of the system is eliminated, and the anti-interference capability of the system is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor control, and in particular relates to a model-free sliding mode single-loop control method for a permanent magnet synchronous motor. Background Art

[0002] In recent years, permanent magnet synchronous motor (PMSM) drive systems have attracted widespread attention in industrial applications due to their high efficiency, high power density, and high reliability. Motor vector control based on PI control technology has become the mainstream motor control method due to its excellent dynamic performance, simple algorithm, and ease of engineering implementation. However, as the control performance requirements for motor drive systems continue to increase, the traditional PI method can no longer meet the requirements for high-performance control. Due to the nonlinear motion dynamics of PMSMs, the control accuracy, response speed, and interference immunity are no longer sufficient.

[0003] In addition, PI control technology is susceptible to interference and uncertainty factors from various sources, including external disturbances such as load torque changes and friction torque, parameter uncertainty including changes in mechanical and electrical parameters, and unmodeled dynamics including motor body design, inverter nonlinear factors and current measurement errors. Various uncertainties will affect the control performance of the system. Summary of the Invention

[0004] In order to solve the technical problems that the existing permanent magnet synchronous motor control method adopts speed-current cascade control, resulting in a complex control system structure, and the existing control method is subject to interference and uncertainty from multiple sources, resulting in poor anti-interference ability of the system, the present invention proposes a permanent magnet synchronous motor model-free sliding mode single-loop control method, which can solve the above problems.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] A model-free sliding mode single-loop control method for a permanent magnet synchronous motor, comprising:

[0007] Step 1: Establish a mathematical model of the permanent magnet synchronous motor in the dq coordinate system;

[0008] Step 2: Establish a super-local model of the permanent magnet synchronous motor, and transform the q-axis stator current in the mathematical model of the permanent magnet synchronous motor into the q-axis stator voltage and the q-axis lumped disturbance F q The mechanical angular velocity is represented by the q-axis stator current and the lumped disturbance F ω Indicates that F q and F ω is the lumped disturbance caused by the influence of motor parameters, model uncertainty and external unknown disturbance;

[0009] Step 3: Design the system state equation, including establishing the equations of state variables and matching disturbance, non-matching disturbance and q-axis stator voltage, among which non-matching disturbance and lumped disturbance F ω Correlation, matching disturbance and q-axis lumped disturbance F q Related;

[0010] Step 4: Design a finite-time generalized proportional-integral observer to estimate the matching disturbance and the non-matching disturbance, as well as the rate of change of the non-matching disturbance;

[0011] Step 5: Design a single-loop model-free sliding mode speed controller, including designing a fast non-singular terminal sliding mode surface and a sliding mode reaching law, to obtain a single-loop model-free sliding mode speed controller.

[0012] In some embodiments, the super-local model of the permanent magnet synchronous motor in step 2 is:

[0013]

[0014] Among them, i q is the stator current of the q axis, u q is the stator voltage of the q-axis, ω is the mechanical angular velocity, α1 is the q-axis voltage gain to be designed, and α2 is the stator q-axis current gain to be designed.

[0015] In some embodiments, the state variables in step 3 include x1 and x2:

[0016]

[0017] Among them, ω r The state variables x1 and x2 are derived as the reference speed, and the following is obtained by combining the permanent magnet synchronous motor super-local model:

[0018]

[0019] Among them, d1 is the non-matching disturbance, d2 is the matching disturbance, d2=-α2F q , α f =-α2α1, ω r The derivative value of .

[0020] In some embodiments, the finite-time generalized proportional-integral mismatched disturbance observer in step 4 is:

[0021]

[0022] The matched disturbance observer is designed as:

[0023]

[0024] Among them, k1, k2, k3, k6, k7, k8, β1, β2, β3, β4, β5, β6 are observer parameters, represents the observed value of the state variable x1, express The derivative of , represents the observed value of d1, express The derivative of , represents the derivative of d1, express The observed value of express The derivative of ;

[0025] represents the observed value of the state variable x2, express The derivative of , represents the observed value of d2, express The derivative of , represents the derivative of d2, express The observed value of express The derivative value of .

[0026] In some embodiments, the fast non-singular terminal sliding surface designed in step 5 is:

[0027]

[0028] in, Represents the derivative value of x1, σ1>0,σ2>0,0<λ1<2,λ2>λ1.

[0029] In some embodiments, step five further includes taking the derivative of s to obtain:

[0030]

[0031] in, Represents the quadratic derivative of x1;

[0032] The sliding mode reaching law designed in step 5 is:

[0033]

[0034] Where, 0<α<1, k4>0, k5>0, δ is any positive real number;

[0035]

[0036] In some embodiments, the single-loop model-free sliding mode speed controller in step 5 is:

[0037]

[0038] In some embodiments, the permanent magnet synchronous motor mathematical model established in step 1 is:

[0039]

[0040] Among them, R s is the stator resistance; L d and L q are the d-axis and q-axis stator inductances respectively; u d and u q are the d-axis and q-axis stator voltages respectively; i d and i q are the stator currents of the d-axis and q-axis respectively; n p is the pole pair number; T e is the electromagnetic torque; J is the moment of inertia; ω is the mechanical angular velocity; B is the friction coefficient; Φ is the permanent magnet flux; f d and f q and f ω is the disturbance caused by the changes in model parameters and external loads.

[0041] In some embodiments, f d and f q and f ω for:

[0042]

[0043] Where, ΔR s =R st -R s , ΔL d =L dt -L d , ΔL q =L qt -L q , ΔB=B t -B, ΔΦ=Φ t -Φ, ΔJ=J t -J is the parameter change value, R st , L dt , L qt , B t , Φ t , J t is the actual parameter τ during motor operation L is the external load torque.

[0044] Compared with the prior art, the advantages and positive effects of the present invention are as follows: the model-free sliding mode single-loop control method for permanent magnet synchronous motor of the present invention first establishes a super-local model of permanent magnet synchronous motor, and expresses the lumped disturbance generated by the influence of motor parameters, model uncertainty and external unknown disturbance as F q and F ω , the q-axis stator current and mechanical angular velocity in the mathematical model of permanent magnet synchronous motor are determined by the q-axis stator current and F q and F ω The designed permanent magnet synchronous motor super-local model does not contain any motor parameters, gets rid of the dependence on the system motor parameters, and improves the system's anti-interference ability.

[0045] Secondly, in order to ensure the speed response performance and tracking performance, the present invention designs a single-loop speed controller with a fast non-singular terminal sliding surface. The controller adopts a non-cascade structure, simplifies the control system structure and can achieve direct speed control.

[0046] Furthermore, the present invention designs a finite-time generalized proportional-integral observer to estimate the system's unknown disturbances. This observer boasts high estimation accuracy and fast response, effectively improving the system's anti-interference capability. Furthermore, the estimated disturbance is used for feedforward compensation, further enhancing the system's control accuracy.

[0047] Other features and advantages of the present invention will become more apparent after reading the detailed description of the embodiments of the present invention in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a block diagram of the speed-current structure of a permanent magnet synchronous motor using the method of the present invention to design a controller and an observer;

[0049] Figure 2 The speed curves of the three control strategies when the permanent magnet synchronous motor model-free sliding mode single-loop control method proposed in the present invention is started at a desired speed of 200 r / min;

[0050] Figure 3 The speed curves of the three control strategies when the permanent magnet synchronous motor model-free sliding mode single-loop control method proposed in the present invention is started at a desired speed of 1000 r / min;

[0051] Figure 4 The speed curves of the three control strategies before and after sudden load increase and decrease when the desired speed is 200 r / min for the model-free sliding mode single-loop control method for the permanent magnet synchronous motor proposed in the present invention are as follows;

[0052] Figure 5The speed curves of the three control strategies before and after sudden load increase and decrease when the desired speed of the permanent magnet synchronous motor model-free sliding mode single-loop control method proposed in the present invention is 1000 r / min;

[0053] Figure 6 These are the torque response curves of the three control strategies when the expected speed of the permanent magnet synchronous motor model-free sliding mode single-loop control method proposed in the present invention is 200 r / min. DETAILED DESCRIPTION

[0054] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings 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 making creative efforts shall fall within the scope of protection of the present invention.

[0056] It should be noted that, in the description of the present invention, the terms "upper", "lower", "left", "right", "vertical", "horizontal", "inside", "outside" and the like indicating directions or positional relationships are based on the directions or positional relationships shown in the accompanying drawings. This is merely for the convenience of description and does not indicate or imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it cannot be understood as a limitation on the present invention. In addition, the terms "first" and "second" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance. In the description of the present invention, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0057] In the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," "connect," "fixed," etc. should be understood broadly. For example, they may refer to fixed connection, detachable connection, or integration; mechanical connection or electrical connection; direct connection or indirect connection through an intermediate medium; internal communication between two components or interaction between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0058] In a first embodiment, the present invention proposes a model-free sliding mode single-loop control method for a permanent magnet synchronous motor, comprising:

[0059] Step 1: Establish a mathematical model of the permanent magnet synchronous motor in the dq coordinate system.

[0060] Step 2: Establish a super-local model of the permanent magnet synchronous motor, and transform the q-axis stator current in the mathematical model of the permanent magnet synchronous motor into the q-axis stator voltage and the q-axis lumped disturbance F q The mechanical angular velocity is represented by the q-axis stator current and the lumped disturbance F ω Indicates that F q and F ω is the lumped disturbance caused by the influence of motor parameters, model uncertainty and external unknown disturbance.

[0061] The super-local model of the permanent magnet synchronous motor established in this step is represented by the lumped disturbance caused by the influence of motor parameters, model uncertainty and external unknown disturbance as F q and F ω , the q-axis stator current and mechanical angular velocity in the mathematical model of permanent magnet synchronous motor are determined by the q-axis stator current and F q and F ω The designed permanent magnet synchronous motor super-local model does not contain any motor parameters, gets rid of the dependence on the system motor parameters, and improves the system's anti-interference ability.

[0062] Step 3: Design the system state equation, including establishing the equations of state variables and matching disturbance, non-matching disturbance and q-axis stator voltage, among which non-matching disturbance and lumped disturbance F ω Correlation, matching disturbance and q-axis lumped disturbance F q Related.

[0063] Step 4: Design a finite-time generalized proportional-integral observer to estimate the matched disturbance and the non-matched disturbance, as well as the rate of change of the non-matched disturbance.

[0064] To improve the robustness of the system, a finite-time generalized proportional-integral observer is used to estimate the unknown disturbances of the system, addressing both matched and mismatched disturbances. This observer achieves finite-time convergence and effectively estimates not only the disturbance but also the rate of change of the disturbance, further improving estimation accuracy. The estimated unknown disturbances are then used for feedforward compensation, enhancing the system's interference rejection capability. This observer boasts high estimation accuracy and fast response, effectively improving the system's interference rejection capability. Furthermore, the estimated disturbances are used for feedforward compensation, further enhancing the system's control accuracy.

[0065] Step 5: Design a single-loop model-free sliding mode speed controller, including designing a fast non-singular terminal sliding mode surface and a sliding mode reaching law, to obtain a single-loop model-free sliding mode speed controller.

[0066] The single-loop model-free sliding mode speed controller designed in this embodiment adopts a speed-current single-loop sliding mode control strategy instead of the traditional speed-current cascade control. The controller adopts a non-cascade structure, simplifies the control system structure and can achieve direct speed control, simplifies the control system structure, and ensures speed response performance and tracking performance.

[0067] In addition, the designed model-free sliding mode control strategy based on non-cascade structure can be easily extended to other second-order systems.

[0068] like Figure 1 As shown in the figure, the speed-current structure block diagram of the permanent magnet synchronous motor using the controller and observer designed by the present invention is shown in the figure. Figure 1 It can be seen that the controller adopts a speed-current single-loop control structure to replace the traditional cascade control. The control system designed in this scheme adopts a non-cascade control structure and uses a finite-time generalized proportional-integral observer for disturbance estimation and compensation of the controller; the d-axis adopts id*=0 control to ensure constant magnetic flux; ω r is the reference speed.

[0069] In some embodiments, the mathematical model of the permanent magnet synchronous motor in the dq coordinate system established in step 1 is:

[0070]

[0071] Among them, R s is the stator resistance; L d and L q are the d-axis and q-axis stator inductances respectively; u d and u q are the d-axis and q-axis stator voltages respectively; i d and i q are the stator currents of the d-axis and q-axis respectively; n p is the pole pair number; T e is the electromagnetic torque; J is the moment of inertia; ω is the mechanical angular velocity; B is the friction coefficient; Φ is the permanent magnet flux; f d and f q and f ω is the disturbance caused by the changes in model parameters and external loads.

[0072] In some embodiments, f d and f q and f ω It can be defined as:

[0073]

[0074] Where, ΔR s =R st -R s , ΔLd =L dt -L d , ΔL q =L qt -L q , ΔB=B t -B, ΔΦ=Φ t -Φ, ΔJ=J t -J is the parameter change value, R st , L dt , L qt , B t , Φ t , J t is the actual parameter τ during motor operation L is the external load torque.

[0075] Conventional permanent magnet synchronous motor speed control typically uses a cascade control structure with an outer speed loop and an inner current loop, with PI controllers regulating speed and current, respectively. To simplify the structure and improve transient response and interference immunity, this invention replaces the traditional cascade structure with a single-loop speed-current control structure based on a finite-time generalized proportional-integral observer and a model-free sliding mode control strategy.

[0076] In step 2, the super-local model of the permanent magnet synchronous motor, according to the super-local model theory, in some embodiments, the second and third equations of the mathematical model of the permanent magnet synchronous motor in the dq coordinate system can be expressed as:

[0077]

[0078] Among them, i q is the stator current of the q axis, u q is the stator voltage of the q-axis, ω is the mechanical angular velocity, α1 is the q-axis voltage gain to be designed, and α2 is the stator q-axis current gain to be designed.

[0079] In some embodiments, the state variables in step 3 include x1 and x2:

[0080]

[0081] Among them, ω r The state variables x1 and x2 are derived as the reference speed, and the following is obtained by combining the permanent magnet synchronous motor super-local model:

[0082]

[0083] Among them, d1 is the non-matching disturbance, d2 is the matching disturbance, d2=-α2F q , α f =-α2α1, ωr The derivative value of .

[0084] In order to improve the robustness of the system, the present invention designs a finite-time generalized proportional integral observer to estimate the system disturbance for the matched and mismatched disturbances in the system. This observer can achieve finite-time convergence, not only effectively estimating the disturbance, but also accurately estimating the rate of change of the disturbance, further improving the estimation accuracy. In some embodiments, the finite-time generalized proportional integral mismatched disturbance observer in step 4 is:

[0085]

[0086] The matched disturbance observer is designed as:

[0087]

[0088] Among them, k1, k2, k3, k6, k7, k8, β1, β2, β3, β4, β5, β6 are observer parameters, represents the observed value of the state variable x1, express The derivative of , represents the observed value of d1, express The derivative of , represents the derivative of d1, express The observed value of express The derivative of ;

[0089] represents the observed value of the state variable x2, express The derivative of , represents the observed value of d2, express The derivative of , represents the derivative of d2, express The observed value of express The derivative value of .

[0090] In some embodiments, the fast non-singular terminal sliding surface designed in step 5 is:

[0091]

[0092] in, Represents the derivative value of x1, σ1>0,σ2>0,0<λ1<2,λ2>λ1.

[0093] In some embodiments, step five further includes taking the derivative of s to obtain:

[0094]

[0095] in, Represents the second derivative of x1.

[0096] In order to increase the sliding mode arrival speed and reduce chattering, the sliding mode reaching law designed in step 5 is:

[0097]

[0098] Among them, 0<α<1, k4>0, k5>0, are the parameters to be designed, and δ is any positive real number;

[0099]

[0100] In some embodiments, based on the two designed sliding surfaces and their reaching laws, the single-loop model-free sliding mode speed controller in step five is:

[0101]

[0102] In some embodiments, MATLAB / Simulink is also used to verify the superiority of the single-loop model-free sliding mode control strategy based on the finite-time generalized proportional-integral observer of this embodiment.

[0103] In order to better verify the speed tracking performance and anti-interference ability of the control strategy designed in the present invention, it is compared with the model-free sliding mode controller based on the extended state observer and the PI controller.

[0104] First, two different reference speeds were input into the system, and speed tracking experiments were performed in sequence to verify the transient response performance and robustness of the three control strategies. The two sets of experimental conditions are as follows:

[0105] Experiment 1: Starting test of the motor with no load.

[0106] like Figure 2 、 Figure 3 The figures show the speed curves of the three control strategies for the proposed model-free sliding mode single-loop control method for a permanent magnet synchronous motor at a desired starting speed of 1000 r / min, as well as the speed curves of the three control strategies before and after a sudden load increase or decrease at a desired speed of 200 r / min. The experimental results show that compared with the PI control strategy, this system has less overshoot and faster response time. Compared with the MFSMC+ESO control strategy, the response time is shortened and the steady-state error is smaller. These results demonstrate that this method outperforms other control strategies.

[0107] Experiment 2: Robustness test under variable load.

[0108] like Figure 4 、 Figure 5 As shown, the speed curves of the three control strategies before and after sudden addition and subtraction of the load when the expected speed is 200r / min for the model-free sliding mode single-loop control method for the permanent magnet synchronous motor proposed in the present invention, and the speed curves of the three control strategies before and after sudden addition and subtraction of the load when the expected speed is 1000r / min. It can be seen from the figure that the traditional PI control has a large speed fluctuation, and it takes longer for the speed to return to a stable state when the load is suddenly added. Compared with MFSMC+ESO, the motor speed fluctuation is smaller, and it can reach a stable state in a shorter time after a sudden load is added. As shown in the figure, the speed of the motor fluctuates less when the load is suddenly added. Figure 6 As shown, the control strategy of the present invention has smaller torque fluctuation and smaller transient response.

[0109] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A model-free sliding mode single-loop control method for a permanent magnet synchronous motor, characterized in that: include: Step 1: Establish a mathematical model of the permanent magnet synchronous motor in the dq coordinate system; Step 2: Establish a super-local model of the permanent magnet synchronous motor, and transform the q-axis stator current in the mathematical model of the permanent magnet synchronous motor into the q-axis stator voltage and the q-axis lumped disturbance F q The mechanical angular velocity is represented by the q-axis stator current and the lumped disturbance F ω Indicates that F q and F ω is the lumped disturbance caused by the influence of motor parameters, model uncertainty and external unknown disturbance; Step 3: Design the system state equation, including establishing the equations of state variables and matching disturbance, non-matching disturbance and q-axis stator voltage, among which non-matching disturbance and lumped disturbance F ω Correlation, matching disturbance and q-axis lumped disturbance F q Related; Step 4: Design a finite-time generalized proportional-integral observer to estimate the matching disturbance and the non-matching disturbance, as well as the rate of change of the non-matching disturbance; Step 5: Design a single-loop model-free sliding mode speed controller, including designing a fast non-singular terminal sliding mode surface and a sliding mode reaching law, to obtain a single-loop model-free sliding mode speed controller.

2. The model-free sliding mode single-loop control method for a permanent magnet synchronous motor according to claim 1, characterized in that: The super-local model of the permanent magnet synchronous motor in step 2 is: Among them, i q is the stator current of the q axis, u q is the stator voltage of the q-axis, ω is the mechanical angular velocity, α1 is the q-axis voltage gain to be designed, and α2 is the stator q-axis current gain to be designed.

3. The model-free sliding mode single-loop control method for a permanent magnet synchronous motor according to claim 2, characterized in that: The state variables in step 3 include x1 and x2: Among them, ω r The state variables x1 and x2 are derived as the reference speed, and the following is obtained by combining the permanent magnet synchronous motor super-local model: Among them, d1 is the non-matching disturbance, d2 is the matching disturbance, d2=-α2F q , α f =-α2α1, ω r The derivative value of .

4. The model-free sliding mode single-loop control method for a permanent magnet synchronous motor according to claim 3, characterized in that: The finite-time generalized proportional-integral non-matched disturbance observer in step 4 is: The matched disturbance observer is designed as: Among them, k1, k2, k3, k6, k7, k8, β1, β2, β3, β4, β5, β6 are observer parameters, represents the observed value of the state variable x1, express The derivative of , represents the observed value of d1, express The derivative of , represents the derivative of d1, express The observed value of express The derivative of ; represents the observed value of the state variable x2, express The derivative of , represents the observed value of d2, express The derivative of , represents the derivative of d2, express The observed value of express The derivative value of .

5. The model-free sliding mode single-loop control method for a permanent magnet synchronous motor according to claim 4, characterized in that: The fast non-singular terminal sliding surface designed in step 5 is: in, Represents the derivative value of x1, σ1>0,σ2>0,0<λ1<2,λ2>λ1.

6. The model-free sliding mode single-loop control method for a permanent magnet synchronous motor according to claim 5, characterized in that: Step 5 also includes taking the derivative of s, and obtaining: in, Represents the quadratic derivative of x1; The sliding mode reaching law designed in step 5 is: Where, 0<α<1, k4>0, k5>0, δ is any positive real number; 7. The model-free sliding mode single-loop control method for a permanent magnet synchronous motor according to claim 6, characterized in that: The single-loop model-free sliding mode speed controller in step 5 is:

8. The model-free sliding mode single-loop control method for a permanent magnet synchronous motor according to any one of claims 1 to 7, characterized in that: The mathematical model of the permanent magnet synchronous motor established in step 1 is: Among them, R s is the stator resistance; L d and L q are the d-axis and q-axis stator inductances respectively; u d and u q are the d-axis and q-axis stator voltages respectively; i d and i q are the stator currents of the d-axis and q-axis respectively; n p is the pole pair number; T e is the electromagnetic torque; J is the moment of inertia; ω is the mechanical angular velocity; B is the friction coefficient; Φ is the permanent magnet flux; f d and f q and f ω is the disturbance caused by the changes in model parameters and external loads.

9. The model-free sliding mode single-loop control method for a permanent magnet synchronous motor according to claim 8, characterized in that: f d and f q and f ω for: Where, ΔR s =R st -R s , ΔL d =L dt -L d , ΔL q =L qt -L q , ΔB=B t -B, ΔΦ=Φ t -Φ, ΔJ=J t -J is the parameter change value, R st , L dt , L qt , B t , Φ t , J t is the actual parameter τ during motor operation L is the external load torque.

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