Model-free predictive direct speed control method and system for SPMSM drive system

Abstract

The present invention provides a model-free predictive direct speed control method and system for an SPMSM drive system, comprising: S1, establishing a mathematical model of the SPMSM under parameter disturbance; S2, establishing a hyperlocal model of the SPMSM under parameter disturbance based on the mathematical model to predict the current and speed under a finite number of switch states, and observing unknown disturbances through an extended sliding mode observer; S3, constructing a model-free predictive direct speed controller based on the hyperlocal model of the SPMSM and the extended sliding mode observer, adding the speed directly as the control target into the cost function, selecting the switch state corresponding to the predicted value of the optimal state and outputting it to the three-phase inverter to control the speed and current. The designed MFPDSC method not only retains the advantage of model-free control that does not require a precise model, but also improves the anti-disturbance capability and dynamic performance of the traditional model predictive direct speed control strategy.

Description

Technical Field

[0001] The present invention belongs to the technical field of permanent magnet synchronous motor control, and in particular relates to a model-free prediction direct speed control method and system for an SPMSM drive system. Background Art

[0002] To improve dynamic response and simplify the control structure, model predictive direct speed control (MPDSC) has been applied to permanent magnet synchronous motor drives in recent years. MPDSC directly adds speed as a control objective to the cost function. It also predicts the speed and current at the next moment based on the motor's speed and current prediction models and selects the optimal control state by minimizing the cost function. MPDSC leverages the flexible constraints of model predictive control, integrates the speed loop and current loop, and simplifies the control system structure.

[0003] However, as with most model-based control methods, the performance of the MPDSC approach depends heavily on accurate prediction models. Therefore, achieving good control targets requires knowledge of stable real-world parameters for the multiple parameters used in MPDSC, such as inductance, flux linkage, and moment of inertia. In reality, when a motor operates in a real-world environment, its parameters are affected by various internal and external disturbances.

[0004] Due to temperature rise and magnetic circuit saturation, the inductance and flux are subject to varying degrees of disturbance, which can lead to steady-state current errors or even oscillations, seriously affecting the stability of the control system. Furthermore, external disturbances are not considered in the system when establishing the prediction model. Traditional MPDSC is based on a nominal model, which assumes that the load disturbance is zero or a fixed value. External load disturbances can degrade speed control performance and affect the dynamic and static performance of the system. To enhance the robustness of traditional MPDSC, several improvement methods have been proposed, including parameter identification and observer-based methods. However, these methods do not simultaneously consider multi-parameter perturbations and only address the perturbation of a single parameter. Summary of the Invention

[0005] The present invention provides a model-free predictive direct speed control method and system for an SPMSM drive system to solve at least one of the above-mentioned problems existing in the prior art.

[0006] According to a first aspect of the present invention, one or more embodiments of the present application provide a model-free predictive direct speed control method for an SPMSM drive system, comprising the following steps:

[0007] S1. Establish a mathematical model of SPMSM under parameter disturbance;

[0008] S2. Establishing a hyperlocal model of the SPMSM under parameter disturbance based on the mathematical model to predict the current and speed under a finite number of switching states, wherein the parameter disturbance includes a modeled part and an unknown disturbance; observing the unknown disturbance by extending the sliding mode observer;

[0009] S3. Based on the super-local model of SPMSM and the extended sliding mode observer, a model-free predictive direct speed controller is constructed. The speed is directly added as the control target into the cost function, and each predicted state of the super-local model of SPMSM is evaluated by the cost function. The switching state corresponding to the predicted value of the optimal state is selected and output to the three-phase inverter to control the speed and current.

[0010] Based on the above technical solution of the present invention, the following improvements can also be made:

[0011] Optionally, in step S1, when considering the motor parameter disturbance, the state equation of the SPMSM in the dq coordinate system is expressed as:

[0012]

[0013] Where u d and u q are the d-axis and q-axis stator voltages respectively; i d and i q are the d-axis and q-axis stator currents respectively; R s is the stator resistance; L so and ψ ro are the nominal values ​​of stator inductance and permanent magnet flux linkage respectively; ω e is the electrical angular velocity;

[0014] Among them, δ d and δ q are the uncertainty disturbances of the d-axis and q-axis current loops, respectively, and their expressions are:

[0015]

[0016] Where ΔL s =L s -L so and Δψ r =ψ r -ψ ro are the changes in inductance and flux amplitude respectively; L s and ψ r are the actual stator inductance and flux linkage amplitude respectively;

[0017] Taking into account the parameter perturbations, the mechanical equation of the SPMSM is expressed as:

[0018]

[0019] Where n p is the extreme logarithm; J o and B represent the nominal value of the moment of inertia and the viscous friction coefficient respectively; ΔJ=JJ o is the rotational inertia error; ΔT e It is the electromagnetic torque disturbance caused by flux mismatch, ΔT L is the torque disturbance.

[0020] Optionally, in step S2, for a single-input single-output system, the super-local model of the SPMSM is expressed as follows:

[0021]

[0022] Where y and u are the system output and control input respectively; F represents the known and uncertain parts of the system; α is the constant to be designed;

[0023] According to equations (1), (3) and (4), the super-local model of the SPMSM speed loop and current loop is expressed as:

[0024]

[0025] Where, x=[i d i q ω e ] T is a state variable; u=[u d u q i q ] T is the control input; α=diag(α d ,α q ,α ω ) is the design gain; F=[F d F q F ω ] T Represents the modeled parts and unknown disturbances in the SPMSM drive system.

[0026] Alternatively, based on the first-order forward Euler method, the discrete super-local model of SPMSM is obtained from equation (5):

[0027]

[0028] Where, and They represent the predicted values ​​of d-axis current, q-axis current and speed at the (k+1)th moment respectively; i d (k), i q (k) and ω e(k) are the measured values ​​of d-axis current, q-axis current and speed at the kth moment respectively; u d (k) and u q (k) are the d-axis and q-axis voltages selected at time k; T s is the current sampling time; T sp is the speed sampling time, T sp =10T s ; Based on the fact that the mechanical time constant is greater than the electrical time constant, the influence of current on speed is almost the same in adjacent sampling cycles, so the super-local model of SPMSM is adopted. Replace i q (k).

[0029] Optionally, the cost function is expressed as:

[0030]

[0031] Where, and Indicates the current and speed reference value; ω and λ d Represents the weight coefficient of speed and current, and its value is selected based on the compromise between current and speed response; C lim Indicates the maximum current limit:

[0032]

[0033] Where, I max is the maximum allowable current.

[0034] Optionally, in order to accurately estimate the unknown disturbances in the hyperlocal models of the SPMSM speed loop and current loop, the unknown disturbances in the hyperlocal model of the SPMSM are expanded into state variables to obtain an extended hyperlocal model and expressed as:

[0035]

[0036] Where, f=[f d f q f ω ] T is the rate of change of the corresponding unknown disturbance;

[0037] According to formula (9), the extended sliding mode observer is established as:

[0038]

[0039] Where, is the observed value of x, is the observed value of F, U smo=[U dsmo U qsmo U ωsmo ] T is the sliding mode control rate; G=diag(G d ,G q ,G ω ) is the parameter matrix;

[0040] Subtracting Equation (9) from Equation (10) yields the observation error dynamics:

[0041]

[0042] Where, e1=[e d e q e ω ] T , and e2=[e Fd e Fq e Fω ] T , and

[0043] Select s = e1 as the sliding surface. To improve the accuracy of the extended sliding mode observer, the sliding mode approach rate is selected as:

[0044]

[0045] Where k = diag(k1, k2, k3) and λ = diag(λ1, λ2, λ3) are parameter matrices, both of which are positive values;

[0046] Then substitute (12) into (11) to obtain:

[0047] e2-U smo =-λe1-ksgn(e1) (13)

[0048] Considering e2 as disturbance, the sliding mode control rate is designed as

[0049] U smo =λe1+ksgn(e1) (14).

[0050] According to another aspect of the present invention, a model-free predictive direct speed control system for an SPMSM drive system is provided, comprising a processor, a memory, and a computer program stored on the memory. When the processor executes the computer program, it implements any of the above-described model-free predictive direct speed control methods for the SPMSM drive system.

[0051] The present invention provides a model-free predictive direct speed control method and system for an SPMSM drive system. It also designs an MFPDSC method based on the SPMSM hyperlocal model, proposes an extended sliding mode observer, and accurately estimates the unknown component. Simulation results demonstrate that the designed MFPDSC method not only retains the advantages of model-free control without requiring a precise model, but also improves the disturbance rejection and dynamic performance of traditional model-predictive direct speed control strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a discrete block diagram of the ESMO of a model-free predictive direct speed control method for an SPMSM drive system according to an embodiment of the present invention.

[0053] Figure 2 This is a block diagram of an MFPDAC for a PMSM drive using a model-free predictive direct speed control method for an SPMSM drive system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0054] In order to make the objectives, technical solutions and advantages of the present disclosure more clearly understood, the present disclosure is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

[0055] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in one or more embodiments of the present application should have the usual meanings understood by people with ordinary skills in the field to which the present disclosure belongs. The "first", "second" and similar words used in one or more embodiments of the present application do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0056] like Figure 1 and Figure 2 As shown, a model-free predictive direct speed control method for an SPMSM drive system in one or more embodiments of the present application includes the following steps:

[0057] S1. Establish a mathematical model of SPMSM under parameter disturbance;

[0058] In step S1, when considering the motor parameter disturbance, the state equation of the SPMSM in the dq coordinate system is expressed as:

[0059]

[0060] Where u d and u q are the d-axis and q-axis stator voltages respectively; i d and i q are the d-axis and q-axis stator currents respectively; R s is the stator resistance; L so and ψ ro are the nominal values ​​of stator inductance and permanent magnet flux linkage respectively; ω e is the electrical angular velocity;

[0061] Among them, δ d and δ q are the uncertainty disturbances of the d-axis and q-axis current loops, respectively, and their expressions are:

[0062]

[0063] Where ΔL s =L s -L so and Δψ r =ψ r -ψ ro are the changes in inductance and flux amplitude respectively; L s and ψ r are the actual stator inductance and flux linkage amplitude respectively;

[0064] Taking into account the parameter perturbations, the mechanical equation of the SPMSM is expressed as:

[0065]

[0066] Where n p is the extreme logarithm; J o and B represent the nominal value of the moment of inertia and the viscous friction coefficient respectively; ΔJ=JJ o is the rotational inertia error; ΔT e It is the electromagnetic torque disturbance caused by flux mismatch, ΔT L is the torque disturbance.

[0067] S2. Establishing a super-local model of the SPMSM under parameter disturbance based on the mathematical model to predict the current and speed under a finite number of switching states u0-u7, wherein the parameter disturbance includes the modeled part and the unknown disturbance; observing the unknown disturbance by extending the sliding mode observer;

[0068] To reduce the predictive controller's reliance on the actual model, this embodiment designs an ultra-local model (ULM) to predict current and speed. For a single-input single-output system, the first-order ULM can be expressed as follows:

[0069]

[0070] Where y and u are the system output and control input respectively; F represents the known and uncertain parts of the system; α is the constant to be designed so that αu and Keep the same order.

[0071] According to equations (1), (3) and (4), the super-local model of the SPMSM speed loop and current loop is expressed as:

[0072]

[0073] Where, x=[i d i q ω e ] T is a state variable; u=[u d u q i q ] T is the control input; α=diag(α d ,α q ,α ω ) is the design gain; F=[F d F q F ω ] T Represents the modeled parts and unknown disturbances in the SPMSM drive system.

[0074] S3. Based on the super-local model of SPMSM and the extended sliding mode observer, a model-free predictive direct speed controller is constructed. The speed is directly added as the control target into the cost function, and each predicted state of the super-local model of SPMSM is evaluated by the cost function. The switching state corresponding to the predicted value of the optimal state is selected and output to the three-phase inverter to control the speed and current.

[0075] Based on the first-order forward Euler method, the discrete hyperlocal model obtained from formula (5) is:

[0076]

[0077] Where, and They represent the predicted values ​​of d-axis current, q-axis current and speed at the (k+1)th moment respectively; i d (k), i q (k) and ω e(k) are the measured values ​​of d-axis current, q-axis current and speed at the kth moment respectively; u d (k) and u q (k) are the d-axis and q-axis voltages selected at time k; T s is the current sampling time; T sp is the speed sampling time, T sp =10T s ;

[0078] It is worth noting that since the mechanical time constant is greater than the electrical time constant, the effect of current on speed in adjacent sampling periods is almost the same. q (k) can be replace.

[0079] The proposed MFPDSC method evaluates each predicted state through a cost function and selects the best state to control speed and current. In the control objective, the speed error is considered first, and the current error is considered second. The cost function can be constructed as

[0080]

[0081] Where, and Indicates the current and speed reference value; ω and λ d Represents the weight coefficient of speed and current, and its value is selected based on the compromise between current and speed response. lim Indicates the maximum current limit:

[0082]

[0083] Where, I max is the maximum allowable current.

[0084] In order to accurately estimate the unknown disturbances in the hyperlocal model of the SPMSM speed loop and current loop, the unknown disturbances in the hyperlocal model of the SPMSM are expanded into state variables, and the extended hyperlocal model is obtained and expressed as:

[0085]

[0086] Where, f=[f d f q f ω ] T is the rate of change of the corresponding unknown part.

[0087] According to formula (9), the extended sliding mode observer (ESMO) can be established as

[0088]

[0089] Where, is the observed value of x, is the observed value of F, U smo =[U dsmo U qsmo U ωsmo ] T is the sliding mode control rate; G=diag(G d ,G q ,G ω ) is the parameter matrix.

[0090] Subtracting Equation (9) from Equation (10) yields the observation error dynamics:

[0091]

[0092] Where, e1=[e d e q e ω ] T , and e2=[e Fd e Fq e Fω ] T , and

[0093] Select s = e1 as the sliding surface. To improve the accuracy of the ESMO observer, the sliding mode approach rate can be selected as

[0094]

[0095] Where k = diag(k1, k2, k3) and λ = diag(λ1, λ2, λ3) are parameter matrices, both of which are positive values.

[0096] Then substitute (12) into (11) to obtain:

[0097] e2-U smo =-λe1-ksgn(e1) (13)

[0098] Considering e2 as a disturbance, the sliding mode control rate can be designed as:

[0099] U smo =λe1+ksgn(e1) (14).

[0100] verify:

[0101] Choose the following positive definite function V as the Lyapunov function

[0102]

[0103] Differentiate the Lyapunov function (15) and substitute (11) and (14) into (15) to obtain

[0104]

[0105] Where ‖·‖ is the norm of the vector, and k4 = min{k1,k2,k3}.

[0106] According to the Lyapunov stability criterion, the error e1 will approach zero in a finite time.

[0107] Based on the sliding mode equivalence principle, when the system state reaches the sliding mode surface, we can get Therefore, formula (11) can be simplified to

[0108]

[0109] The solution for e2 can be given as follows:

[0110] e2=e -Gt [C1+∫f·e -Gt dt] (18)

[0111] Where C1 is a constant matrix. From this, we can conclude that the parameter matrix G must be positive to ensure the convergence of the unknown partial error e2 of the observer, and the convergence rate is related to G.

[0112] like Figure 1 As shown, using the first-order forward Euler method, the designed ESMO discrete expression can be expressed as

[0113]

[0114] Where, Indicates the current prediction value at the next sampling moment; Represents the predicted value of the unknown part of the hyperlocal model at the next sampling moment. smo (k) Satisfy U smo (k)=λe1(k)+ksgn(e1(k)), where

[0115] in conclusion:

[0116] This embodiment provides an MFPDSC method for suppressing multi-parameter mismatch and external disturbances in an SPMSM drive. It primarily designs an MFPDSC method based on the SPMSM hyperlocal model, proposes an extended sliding mode observer, and accurately estimates the unknown components. Simulation results demonstrate that the proposed MFPDSC method not only retains the advantages of model-free control without requiring a precise model, but also improves the disturbance rejection and dynamic performance of traditional model-predictive direct speed control strategies.

[0117] In another embodiment, a model-free predictive direct speed control system for an SPMSM drive system is provided, comprising a processor, a memory, and a computer program stored on the memory. When the processor executes the computer program, it implements any of the above-described model-free predictive direct speed control methods for the SPMSM drive system.

[0118] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0119] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A system that specifies the functions of a box or boxes.

[0120] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction system that is implemented in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0121] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0122] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0123] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. Model-free predictive direct speed control method for SPMSM drive system, characterized by: It includes the following steps: S1. Establish a mathematical model of SPMSM under parameter disturbance; S2. Establishing a hyperlocal model of the SPMSM under parameter disturbance based on the mathematical model to predict the current and speed under a finite number of switching states, wherein the parameter disturbance includes a modeled part and an unknown disturbance; observing the unknown disturbance by extending the sliding mode observer; S3. Based on the SPMSM hyperlocal model and extended sliding mode observer, a model-free predictive direct speed controller is constructed. The speed is directly added as the control target in the cost function. The cost function is used to evaluate each predicted state of the SPMSM hyperlocal model. The switching state corresponding to the predicted value of the optimal state is selected and output to the three-phase inverter to control the speed and current. The cost function is expressed as: Where, and Respectively represent the current and speed reference values; λ ω and λ d Represent the weight coefficients of speed and current respectively, and their values ​​are selected based on the compromise between current and speed response; C lim Indicates the maximum current limit: Where, I max is the maximum allowable current; In order to accurately estimate the unknown disturbances in the hyperlocal model of the SPMSM speed loop and current loop, the unknown disturbances in the hyperlocal model of the SPMSM are expanded into state variables, and the extended hyperlocal model is obtained and expressed as: Where, f=[f d f q f ω ] T is the rate of change of the corresponding unknown disturbance; According to formula (9), the extended sliding mode observer is established as: Where, is the observed value of x, is the observed value of F, U smo =[U dsmo U qsmo U ω smo] T is the sliding mode control rate; G=diag(G d ,G q ,G ω ) is the parameter matrix; Subtracting Equation (10) from Equation (9) yields the observation error dynamics: Where, e1=[e d e q e ω ] T , and e2=[e Fd e Fq e Fω ] T , and Select s = e1 as the sliding surface. To improve the accuracy of the extended sliding mode observer, the sliding mode approach rate is selected as: Where k = diag(k1, k2, k3) and λ = diag(λ1, λ2, λ3) are parameter matrices, both of which are positive values; Then substitute (12) into (11) to obtain: e2-U smo =-λe1-ksgn(e1) (13) Considering e2 as disturbance, the sliding mode control rate is designed as: U smo =λe1+ksgn(e1) (14).

2. The model-free predictive direct speed control method for the SPMSM drive system according to claim 1, wherein: In step S1, when considering the motor parameter disturbance, the state equation of the SPMSM in the dq coordinate system is expressed as: Where u d and u q are the d-axis and q-axis stator voltages respectively; i d and i q are the d-axis and q-axis stator currents respectively; R s is the stator resistance; L so and ψ ro are the nominal values ​​of stator inductance and permanent magnet flux linkage respectively; ω e is the electrical angular velocity; Among them, δ d and δ q are the uncertainty disturbances of the d-axis and q-axis current loops, respectively, and their expressions are: Where ΔL s =L s -L so and Δψ r =ψ r -ψ ro are the changes in inductance and flux amplitude respectively; L s and ψ r are the actual stator inductance and flux linkage amplitude respectively; Taking into account the parameter perturbations, the mechanical equation of the SPMSM is expressed as: Where n p is the extreme logarithm; J o and B represent the nominal value of the moment of inertia and the viscous friction coefficient respectively; ΔJ=JJ o is the rotational inertia error; ΔT e It is the electromagnetic torque disturbance caused by flux mismatch, ΔT L is the torque disturbance.

3. The model-free predictive direct speed control method for the SPMSM drive system according to claim 2, wherein: In step S2, for a single-input single-output system, the super-local model of the SPMSM is expressed as follows: Where y and u are the system output and control input respectively; F represents the known and uncertain parts of the system; α is the constant to be designed; According to equations (1), (3) and (4), the super-local model of the SPMSM speed loop and current loop is expressed as: Where, x=[i d i q ω e ] T is a state variable; u=[u d u q i q ] T is the control input; α=diag(α d ,α q ,α ω ) is the design gain; F=[F d F q F ω ] T Represents the modeled parts and unknown disturbances in the SPMSM drive system.

4. The model-free predictive direct speed control method for the SPMSM drive system according to claim 3, wherein: Based on the first-order forward Euler method, the super-local model of the discrete SPMSM is obtained from formula (5): Where, and They represent the predicted values ​​of d-axis current, q-axis current and speed at the (k+1)th moment respectively; i d (k), i q (k) and ω e (k) are the measured values ​​of d-axis current, q-axis current and speed at the kth moment respectively; u d (k) and u q (k) are the d-axis and q-axis voltages selected at time k; T s is the current sampling time; T sp is the speed sampling time, T sp =10T s ; Based on the fact that the mechanical time constant is greater than the electrical time constant, the influence of current on speed is almost the same in adjacent sampling cycles, so the super-local model of SPMSM is adopted. Replace i q (k).

5. A model-free predictive direct speed control system for an SPMSM drive system, comprising a processor, a memory, and a computer program stored in the memory, characterized in that: When the processor executes the computer program, the model-free predictive direct speed control method for the SPMSM drive system according to any one of claims 1 to 4 is implemented.

Images