A finite set model-free predictive current control method for permanent magnet synchronous motors

Abstract

The present invention discloses a finite set model-free predictive current control method for a permanent magnet synchronous motor, comprising the following steps: 1: establishing a PMSM mathematical model, which includes the conditions of internal parameter perturbations and external disturbances of the motor, and establishing a current prediction model based on the PMSM mathematical model; 2: establishing a new hyperlocal model of the PMSM based on the hyperlocal model principle, and designing an extended sliding mode observer to observe the unknown disturbances therein; and 3: based on the result obtained in step 2, adopting a finite set predictive current control method, and outputting the switching state corresponding to the selected optimal voltage vector on the inverter. The present invention only utilizes the input and output of the system without considering specific parameters, and observes unknown disturbances through an extended sliding mode observer, and has stronger robustness to parameters. When the motor undergoes parameter perturbations, good performance can be maintained, which is specifically manifested in lower current pulsation and torque pulsation, as well as accurate d‑q axis current tracking capability.

Description

Technical Field

[0001] The present invention relates to the technical field of high-performance permanent magnet synchronous motor control, and in particular to a finite set model-free predictive current control method for a permanent magnet synchronous motor. Background Art

[0002] In recent years, permanent-magnet synchronous motors (PMSMs) have been widely used in the industrial sector due to their high precision, high efficiency, and excellent control performance. They are able to meet the stringent technical requirements of key national development areas and emerging industries, such as high-tech ships, advanced rail transit, high-end CNC machine tools, and high-performance automobiles. While promoting the development of high-end equipment manufacturing, PMSMs also show promising application prospects in reducing motor system energy consumption. However, despite their widespread application, PMSMs also face numerous challenges under complex operating conditions.

[0003] Model Predictive Control (MPC) has become a hot topic of research for scholars both domestically and internationally in recent years due to its multi-objective, multi-variable, and multi-constrained control properties. First proposed in the 1970s by several companies in the United States and France, MPC has been successfully applied in various process control fields, including petroleum, chemical engineering, aerospace, and energy, since the 1980s. However, due to limitations in the computing speed of processors at the time, its application to fast dynamic response systems, such as motor control, was not until the 20th century. Finite Control Set Model Predictive Control (FCS-MPC) uses the switching signals of the inverter power devices as control actions and is not constrained by the converter modulation strategy. It is highly versatile and practical in AC motor drive systems, but it is highly dependent on parameters. Model-free control, a control method that only utilizes the system's input and output without considering specific parameters, can effectively address the shortcomings of finite set model predictive control methods, which suffer from significant performance degradation due to motor parameter perturbations. Summary of the Invention

[0004] In order to overcome the deficiencies in the prior art, the present invention provides a finite set model-free predictive current control method for a permanent magnet synchronous motor, which effectively reduces the impact of disturbances such as motor parameter perturbations on motor performance.

[0005] In order to achieve the above-mentioned purpose of the invention, the technical solutions adopted to solve the technical problems are as follows:

[0006] A finite set model-free predictive current control method for a permanent magnet synchronous motor comprises the following steps:

[0007] Step 1: Establish a PMSM mathematical model that includes the perturbations of the motor's internal parameters and external disturbances, and establish a current prediction model based on the PMSM mathematical model;

[0008] Step 2: Based on the principle of hyperlocal model, a new hyperlocal model of PMSM is established, and an extended sliding film observer is designed to observe the unknown disturbances.

[0009] Step 3: Based on the result obtained in step 2, a finite set predictive current control method is used to output the switching state corresponding to the selected optimal voltage vector on the inverter.

[0010] Furthermore, the step 1 specifically includes:

[0011] Ignoring the influence of complex factors such as PMSM hysteresis eddy current loss and magnetic field cross-coupling, the voltage equation of the three-phase PMSM in the dq coordinate system is:

[0012]

[0013] Where u d and u q are the dq axis components of the stator voltage respectively; i d and i q are the dq axis components of the stator current respectively; R is the stator resistance; ψ d and ψ q are the dq axis components of the stator flux, ψ d =L d i d +ψ f , ψ q =L q i q , where L d and L q The dq axis components of the stator inductance are respectively selected, and the surface type PMSM is selected, so L d =L q =L;ψ f is the permanent magnet flux; ω e is the rotor electrical angular velocity;

[0014] Taking into account the internal parameter perturbations and external disturbances of the motor, the voltage equation is:

[0015]

[0016] Where R0, L0, ψ f0 are the nominal values of the corresponding parameters; ΔR, ΔL, Δψ f are the change values of the corresponding parameters when the motor parameters are perturbed; f d and f qare the components of the unknown disturbance in the dq axis respectively;

[0017] Taking into account the internal parameter perturbations and external disturbances of the motor, the discretized predicted current model is:

[0018]

[0019] Where, and It is the predicted current value of the system at time k+1 when considering the internal parameter perturbation of the motor and external disturbance.

[0020] Furthermore, step 2 specifically includes:

[0021] Step 2.1: Design a new hyperlocal PMSM model in the dq coordinate system:

[0022]

[0023]

[0024] Where, α d and α q are the dq axis voltage gains respectively; β d and β q Current gain of dq axis respectively; F d and F d They represent the components of the unknown disturbance of the system on the dq axis respectively; f d and f d Represents F d and F d rate of change;

[0025] The discretized hyperlocal prediction model is:

[0026]

[0027]

[0028] Where, T s is the system sampling period;

[0029] Step 2.2: In order to accurately observe the unknown disturbance F, the synovial observer is designed as follows:

[0030]

[0031]

[0032] Where, and Respectively represent the estimated values of dq axis current; and They represent the components of the unknown disturbance estimate on the dq axis respectively; g d and g q is the gain coefficient of the synovial observer to be designed; I dsmo and I qsmo is the synovial control function;

[0033] Define the current error and disturbance error as:

[0034]

[0035]

[0036] Where, e d and e q are the errors between the estimated dq axis current and the feedback current respectively; e fd and e fq are the errors between the estimated value and the actual value of the unknown disturbance of dq axis respectively;

[0037] Subtracting equations (4) and (5) from equations (8) and (9) respectively, the error equation is:

[0038]

[0039]

[0040] Select e d and e q As a synovial surface, that is:

[0041]

[0042] In order to ensure that the error can quickly converge to the sliding surface within a limited time, the exponential convergence law is selected as:

[0043]

[0044] Where, s=[s d s q ], sgn is the sign function, ε and λ are the parameters to be designed;

[0045] Further, substituting formula (15) into formula (12) and formula (13), we have:

[0046]

[0047] e fd and e fq Considered as a disturbance, the synovial control function is:

[0048]

[0049] The designed observer needs to satisfy Lyapunov stability, and the Lyapunov function is selected:

[0050]

[0051] The derivative of V is:

[0052]

[0053] According to the Lyapunov stability criterion, the designed synovial observer must meet the following requirements:

[0054]

[0055] Will s d 、s q 、 Substituting into formula (20), the stability condition is:

[0056]

[0057]

[0058] Then the parameters ε and λ must satisfy:

[0059]

[0060] In summary, when appropriate parameters are set, the designed observer is asymptotically stable;

[0061] Discretize the observer as:

[0062]

[0063]

[0064] Furthermore, in step 3, the unknown disturbance observation value and the current observation value obtained in step 2 are used to realize motor control through a finite set predictive current control method;

[0065] In order to ensure accurate current tracking, a value function is required to judge the current prediction error under different voltage vectors, select the voltage vector that minimizes the predicted current error, and output the corresponding switching state on the inverter in the next cycle. In the case of a three-phase two-level inverter, its specific expression is:

[0066]

[0067] Where, and They are the current given values of dq axis respectively, using i d =0 control method, that is Output from the PI controller of the speed loop; i=0,1,……,7, and They are the components of the current prediction values on the dq axes under the eight switching states of the inverter.

[0068] Due to the adoption of the above technical solution, the present invention has the following advantages and positive effects compared with the prior art:

[0069] This paper presents a finite set model-free predictive current control method for a permanent magnet synchronous motor. Compared to traditional model-predictive current control, this method utilizes only the system's input and output without considering specific parameters. It also uses an extended sliding mode observer to observe unknown disturbances, resulting in a more robust control method. When the motor's parameters are perturbed, the control method maintains good performance, demonstrated by low current and torque ripple, and accurate dq-axis current tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following is a brief introduction to the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without inventive work. In the drawings:

[0071] Figure 1 The present invention is a flowchart of a finite set model-free predictive current control method for a permanent magnet synchronous motor. DETAILED DESCRIPTION

[0072] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0073] This embodiment discloses a finite set model-free predictive current control method for a permanent magnet synchronous motor, comprising the following steps:

[0074] Step 1: Establish a PMSM mathematical model that includes the perturbations of the motor's internal parameters and external disturbances, and establish a current prediction model based on the PMSM mathematical model;

[0075] Step 2: Based on the principle of hyperlocal model, a new hyperlocal model of PMSM is established, and an extended sliding film observer is designed to observe the unknown disturbances.

[0076] Step 3: Based on the result obtained in step 2, a finite set predictive current control method is used to output the switching state corresponding to the selected optimal voltage vector on the inverter.

[0077] Furthermore, the step 1 specifically includes:

[0078] Ignoring the influence of complex factors such as PMSM hysteresis eddy current loss and magnetic field cross-coupling, the voltage equation of the three-phase PMSM in the dq coordinate system is:

[0079]

[0080] Where u d and u q are the dq axis components of the stator voltage respectively; i d and i q are the dq axis components of the stator current respectively; R is the stator resistance; ψ d and ψ q are the dq axis components of the stator flux, ψ d =L d i d +ψ f , ψ q =L q i q , where L d and L q The d and q axis components of the stator inductance are respectively. In this embodiment, a surface PMSM is selected, so L d =L q =L;ψ f is the permanent magnet flux; ω e is the rotor electrical angular velocity;

[0081] Taking into account the internal parameter perturbations and external disturbances of the motor, the voltage equation is:

[0082]

[0083] Where R0, L0, ψ f0 are the nominal values of the corresponding parameters; ΔR, ΔL, Δψ f are the change values of the corresponding parameters when the motor parameters are perturbed; f d and f q are the components of the unknown disturbance in the dq axis respectively;

[0084] Taking into account the internal parameter perturbations and external disturbances of the motor, the discretized predicted current model is:

[0085]

[0086] Where, and It is the predicted current value of the system at time k+1 when considering the internal parameter perturbation of the motor and external disturbance.

[0087] Furthermore, step 2 specifically includes:

[0088] Step 2.1: Design a new hyperlocal PMSM model in the dq coordinate system:

[0089]

[0090]

[0091] Where, α d and α q are the dq axis voltage gains respectively; β d and β q Current gain of dq axis respectively; F d and F d They represent the components of the unknown disturbance of the system on the dq axis respectively; f d and f d Respectively represent F d and F d rate of change;

[0092] The discretized hyperlocal prediction model is:

[0093]

[0094]

[0095] Where, T s is the system sampling period;

[0096] Step 2.2: In order to accurately observe the unknown disturbance F, the synovial observer is designed as follows:

[0097]

[0098]

[0099] Where, and Respectively represent the estimated values of dq axis current; and They represent the components of the unknown disturbance estimate on the dq axis respectively; g d and g q is the gain coefficient of the synovial observer to be designed; I dsmo and I qsmo is the synovial control function;

[0100] Define the current error and disturbance error as:

[0101]

[0102]

[0103] Where, e d and e q are the errors between the estimated dq axis current and the feedback current respectively; e fd and e fq are the errors between the estimated value and the actual value of the unknown disturbance of dq axis respectively;

[0104] Subtracting equations (4) and (5) from equations (8) and (9) respectively, the error equation is:

[0105]

[0106]

[0107] Select e d and e q As a synovial surface, that is:

[0108]

[0109] In order to ensure that the error can quickly converge to the sliding surface within a limited time, the exponential convergence law is selected as:

[0110]

[0111] Where, s=[s d s q ], sgn is the sign function, ε and λ are the parameters to be designed;

[0112] Further, substituting formula (15) into formula (12) and formula (13), we have:

[0113]

[0114] e fd and e fq Considered as a disturbance, the synovial control function is:

[0115]

[0116] The designed observer needs to satisfy Lyapunov stability, and the Lyapunov function is selected:

[0117]

[0118] The derivative of V is:

[0119]

[0120] According to the Lyapunov stability criterion, the designed synovial observer must meet the following requirements:

[0121]

[0122] Will s d 、s q 、 Substituting into formula (20), the stability condition is:

[0123]

[0124]

[0125] Then the parameters ε and λ must satisfy:

[0126]

[0127] In summary, when appropriate parameters are set, the designed observer is asymptotically stable;

[0128] Discretize the observer as:

[0129]

[0130]

[0131] Furthermore, in step 3, the unknown disturbance observation value and the current observation value obtained in step 2 are used to realize motor control through a finite set predictive current control method;

[0132] In order to ensure accurate current tracking, a value function is required to judge the current prediction error under different voltage vectors, select the voltage vector that minimizes the predicted current error, and output the corresponding switching state on the inverter in the next cycle. In the case of a three-phase two-level inverter, its specific expression is:

[0133]

[0134] Where, and are the current given values of the d and q axes respectively. In this embodiment, i d =0 control method, that is Output from the PI controller of the speed loop; i=0,1,……,7, and They are the components of the current prediction values on the dq axes under the eight switching states of the inverter.

[0135] like Figure 1 As shown, the voltage u in the stationary three-phase coordinate system is measured by the Hall sensorab 、u bc and current i a 、i b , the voltage u in the two-phase rotating coordinate system is obtained by coordinate transformation d (k),u q (k) and current i d (k), i q (k). The motor speed is measured by the encoder, and the speed error is output to the PI controller of the speed loop, whose output is the reference value of the q-axis current. set up The current speed ω e (k), voltage u(k), and current i(k) are output to the extended sliding film observer to obtain the unknown disturbance observation value at the next moment and current observations Considering the time delay problem of the actual controller, the first-order delay compensation method is used to convert the predicted unknown disturbance observation value into and current observations As the input of the improved super-local prediction model, another prediction step is performed. The current prediction values under the eight voltage vectors u0~u7 are substituted into the value function respectively. The switching state corresponding to the voltage vector that minimizes the value function is selected and output to the inverter to achieve high-performance control of the permanent magnet synchronous motor.

[0136] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A finite set model-free predictive current control method for a permanent magnet synchronous motor, characterized in that: The following steps are involved: Step 1: Establish a PMSM mathematical model that includes the perturbations of the motor's internal parameters and external disturbances, and establish a current prediction model based on the PMSM mathematical model; Step 2: Based on the hyperlocal model principle, a PMSM hyperlocal model is established and an extended sliding film observer is designed to observe the unknown disturbances. Step 2 specifically includes: Step 2.1: Design the PMSM hyperlocal model in the dq coordinate system as follows: Where u d and u q are the dq axis components of the stator voltage respectively; i d and i q are the dq axis components of the stator current respectively; α d and α q are the dq axis voltage gains respectively; β d and β q Current gain of dq axis respectively; F d and F d They represent the components of the unknown disturbance of the system on the dq axis respectively; f d and f d Respectively represent F d and F d rate of change; The discretized hyperlocal prediction model is: Where, T s is the system sampling period; Step 2.2: In order to accurately observe the unknown disturbance F, the synovial observer is designed as follows: Where, and Respectively represent the estimated values of dq axis current; and They represent the components of the unknown disturbance estimate on the dq axis respectively; g d and g q is the gain coefficient of the synovial observer to be designed; I dsmo and I qsmo is the synovial control function; Define the current error and disturbance error as: Where, e d and e q are the errors between the estimated dq axis current and the feedback current respectively; e fd and e fq are the errors between the estimated value and the actual value of the unknown disturbance of dq axis respectively; Subtracting equations (4) and (5) from equations (8) and (9) respectively, the error equation is: Select e d and e q As a synovial surface, that is: In order to ensure that the error can quickly converge to the sliding surface within a limited time, the exponential convergence law is selected as: Where, s=[s d s q ], sgn is the sign function, ε and λ are the parameters to be designed; Further, substituting formula (15) into formula (12) and formula (13), we have: e fd and e fq Considered as a disturbance, the synovial control function is: The designed observer needs to satisfy Lyapunov stability, and the Lyapunov function is selected: The derivative of V is: According to the Lyapunov stability criterion, the designed synovial observer must meet the following requirements: Will s d 、s q 、 Substituting into formula (20), the stability condition is: Then the parameters ε and λ must satisfy: In summary, when appropriate parameters are set, the designed observer is asymptotically stable; Discretize the observer as: Step 3: Based on the result obtained in step 2, a finite set predictive current control method is used to output the switching state corresponding to the selected optimal voltage vector on the inverter.

2. A finite set model-free predictive current control method for a permanent magnet synchronous motor according to claim 1, characterized in that: The step 1 specifically includes: Ignoring the influence of complex factors such as PMSM hysteresis eddy current loss and magnetic field cross-coupling, the voltage equation of the three-phase PMSM in the dq coordinate system is: Where u d and u q are the dq axis components of the stator voltage respectively; i d and i q are the dq axis components of the stator current respectively; R is the stator resistance; ψ d and ψ q are the dq axis components of the stator flux, ψ d =L d i d +ψ f , ψ q =L q i q , where L d and L q The dq axis components of the stator inductance are respectively selected, and the surface type PMSM is selected, so L d =L q =L;ψ f is the permanent magnet flux; ω e is the rotor electrical angular velocity; Taking into account the internal parameter perturbations and external disturbances of the motor, the voltage equation is: Where R0, L0, ψ f0 are the nominal values of the corresponding parameters; ΔR, ΔL, Δψ f are the change values of the corresponding parameters when the motor parameters are perturbed; f d and f q are the components of the unknown disturbance in the dq axis respectively; Taking into account the internal parameter perturbations and external disturbances of the motor, the discretized predicted current model is: Where, and It is the predicted current value of the system at time k+1 when considering the internal parameter perturbation of the motor and external disturbance.

3. The method for finite set model-free predictive current control of a permanent magnet synchronous motor according to claim 1, characterized in that: Step 3, using the unknown disturbance observation value and current observation value obtained in step 2, the motor is controlled by a finite set predictive current control method; In order to ensure accurate current tracking, a value function is required to judge the current prediction error under different voltage vectors, select the voltage vector that minimizes the predicted current error, and output the corresponding switching state on the inverter in the next cycle. In the case of a three-phase two-level inverter, its specific expression is: Where, and They are the current given values of dq axis respectively, using i d =0 control method, that is Output from the PI controller of the speed loop; i=0,1,……,7, and They are the components of the current prediction values on the dq axes under the eight switching states of the inverter.

Images