A data-driven predictive current control method for permanent magnet synchronous motor

Abstract

The application discloses a kind of permanent magnet synchronous motor data-driven predictive current control methods, for five-phase permanent magnet synchronous motor drive system, comprising the following steps: S1, the model predictive current control MPCC based on virtual voltage vector is established step;S2, data-driven predictive control (DeePC) online rolling optimization step, using the data-driven predictive controller independent of parameterized motor model, is realized by two stages.The application has significant advantages in improving the robustness of system to motor parameter perturbation, enhancing current tracking accuracy and suppressing harmonic distortion.

Description

Technical Field

[0001] This invention relates to the field of five-phase permanent magnet synchronous motor (FP-PMSM) technology, specifically to a data-driven predictive current control method for permanent magnet synchronous motors. Background Technology

[0002] In recent years, driven by the rapid growth of the electric vehicle industry, the application of permanent magnet synchronous motors (PMSMs) in electric vehicles has received widespread attention. Compared with three-phase PMSMs, five-phase motors offer advantages such as lower torque ripple, stronger fault tolerance, higher degrees of freedom, and no increase in control complexity. Therefore, five-phase motors have a broader application scope. Furthermore, the decreasing cost of computer storage and the increasing computing power have made large-scale data storage and real-time analysis possible, leading to a growing focus on data-supported methods across various branches of science and engineering. This transformation has also profoundly impacted the development of control engineering. Unlike model-based predictive control, data-driven control design involves using data collected from real systems to synthesize controllers without defining and identifying parameterized models of the objects.

[0003] With the continuous advancement of modern control theory, parameterization methods and parameter identification techniques based on state-space models have developed into a comprehensive theoretical framework. Traditional model-based control methods typically follow a two-stage design process of "modeling-control": first, a mathematical model of the controlled object is established, and then a controller is designed based on this model. A typical representative of this methodology is the model predictive control strategy. In the field of permanent magnet synchronous motor (PMSM) control, most existing research uses the motor's state-space model (such as the stator voltage balance equation) to construct predictive controllers. It is particularly noteworthy that the design of the motor control system must fully consider key factors, including rotor topology, spatial distribution of permanent magnets, and stator winding configuration, to ensure the accuracy of the selected motor model. This is because the parameters of a PMSM, such as stator resistance and inductance, are sensitive to operating conditions, including temperature, frequency effects, magnetic saturation, and cross-saturation effects. In certain specific application scenarios, motor parameters may not be observable or usable in real time because they are not accessible during motor operation. Parameter uncertainty directly affects the accuracy of current prediction, thereby reducing the performance of VV-MPCC.

[0004] Faced with the uncertainty of motor parameters, many existing studies have explored online estimation of motor parameters by integrating different observers within the Model Predictive Control (MPC) framework. However, this approach inevitably increases the complexity of the control structure. For example, one study proposed a predictive current control algorithm utilizing an Extended State Observer (ESO) to enhance the robustness of inductor parameters and address system divergence caused by stator inductor parameter mismatch. Another effective approach to addressing the parameter sensitivity problem in MPC is to employ model-free (or parameter-free) prediction concepts in permanent magnet synchronous motor (PMSM) current control. Another paradigm of model-free predictive control involves using so-called hyperlocal models, which are updated online rather than relying on a parameterized mathematical model of the PMSM. However, it should be noted that the parameters involved in the hyperlocal models themselves still require estimation using additional techniques such as observers.

[0005] In contrast, data-driven predictive controllers fundamentally bypass the model identification stage, with their control laws directly derived from the system's input / output data (such as voltage and current measurements) during operation. This paradigm shift effectively addresses key challenges such as optimal model selection, real-time system adaptation, and parameter sensitivity, demonstrating significant advantages in industrial applications. A relatively comprehensive technical overview of data-driven control applications in industrial environments is available. Specifically in the field of motor drives, research has proposed using time-series subspace models to capture the dynamic relationships between system inputs and outputs, thereby effectively describing the dynamic characteristics of permanent magnet synchronous motor drive systems. Furthermore, novel data-supported predictive control algorithms have been applied to grid-connected power converters to achieve safe and optimal control. However, overall, instances of applying data-driven control methods to motor drives remain relatively few, and even rarer in the more complex field of five-phase motor control. Current explorations include: combining a data-enabled algorithm with traditional CCS predictive control for a three-phase permanent magnet synchronous motor drive module; and proposing a simplified finite control set data predictive current control strategy that drives a three-phase permanent magnet synchronous motor by directly exploring data relationships. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a data-driven predictive current control method for five-phase permanent magnet synchronous motor drive systems. The method employs offline continuous excitation signal acquisition of motor input-output data trajectories, constructing a non-parametric data-driven predictive model that fundamentally avoids model errors caused by motor parameter mismatch. During online operation, a data matrix is ​​constructed based on historical data trajectories, representing future current predictions as a linear combination of historical data trajectories. The optimal voltage command is directly solved by minimizing the future current tracking error. Simultaneously, adaptive rolling updates of the data model are achieved by injecting real-time data from the current cycle into the historical trajectory library. To further suppress the inherent harmonic current components of the five-phase motor, a set of virtual voltage vectors synthesized from large and medium vectors in a fixed ratio is designed. Utilizing the physical property of mutual cancellation of volt-second products in the harmonic subspace, the solved optimal voltage command is mapped to this virtual vector set, thus achieving both rapid dynamic response and excellent steady-state harmonic suppression performance. The results show that the present invention has significant advantages in improving the robustness of the system to motor parameter perturbations, enhancing current tracking accuracy, and suppressing harmonic distortion.

[0007] The specific plan is as follows:

[0008] A data-driven predictive current control method for permanent magnet synchronous motors includes the following steps:

[0009] S1. Steps for establishing Model Predictive Current Control (MPCC) based on Virtual Voltage Vector

[0010] In a rotating coordinate system, the voltage equation of a five-phase permanent magnet synchronous motor is decomposed into two subsystems: the fundamental plane and the harmonic plane. A current prediction model is established by discretization using the forward Euler method. A set of virtual voltage vectors is defined as a set of harmonic suppression constraints. The large and medium vectors aligned in the α-β subspace are selected, and their action time ratio is fixed to the golden ratio of 0.618. Volt-second balance is achieved in the xy harmonic subspace, and an effective voltage vector with constant amplitude in the α-β fundamental subspace is synthesized, thereby eliminating low-order harmonic components while generating an effective control voltage.

[0011] S2. Data-Driven Predictive Control (DeePC) Online Rolling Optimization Steps

[0012] A data-driven predictive controller, independent of the parameterized motor model, is employed and implemented through the following two stages:

[0013] (1) Offline data preparation stage: excite the system to collect the voltage input signal and current output signal of the time series, construct the input Hankel matrix and the output Hankel matrix respectively, and divide them into past sub-blocks and future sub-blocks;

[0014] (2) Online adaptive control stage: At each sampling time, using a length of T ini The initial voltage and current trajectories are obtained, and the input and output trajectories for the next N steps are predicted based on the column linear combination of the offline Hankel matrix. The constrained DeePC optimization problem is solved to calculate the optimal solution vector, thereby obtaining the current estimate at the current sampling time. The data matrix is ​​dynamically updated using the current estimate and the measured voltage value, and the optimal input voltage vector is directly calculated. The α-β axis components of the optimal input voltage vector are used as references to select the corresponding switching signal from the set of virtual voltage vectors for control.

[0015] Furthermore, step S1 specifically includes:

[0016] S11, Mathematical Modeling of Five-Phase Permanent Magnet Synchronous Motor System

[0017] The voltage equation of a five-phase permanent magnet synchronous motor in a synchronously rotating coordinate system is decomposed into two subsystems: the fundamental plane and the harmonic plane; the stator voltage u d1 u q1 u d3 u q3 With current i d1 i q1 i d3 i q3 The following relationship must be satisfied:

[0018] (1)

[0019] Among them, R s L is the stator phase resistance. d and L q Let L be the d-axis and q-axis inductance of the fundamental plane. ls For leakage, ω e It is the rotor electrical angular velocity, Ψ f It is a permanent magnet flux linkage, and matrix L is the inductance matrix;

[0020] Then, the forward Euler method is used to discretize the above model and establish a current prediction model;

[0021] (2)

[0022] Where k is the index of the current discrete sampling time, k+1 is the next sampling time, and T s The sampling period is given by matrix A, which is the state transition matrix, and matrix B is the input matrix.

[0023] At sufficiently high sampling frequencies, the error introduced by Euler discretization is within acceptable limits. This model neglects cross-saturation, iron saturation, and back EMF harmonic effects. Subsequent demonstrations will show that the data-driven control strategy employed in this invention, because it does not rely on such explicit parameterized model structures, can fundamentally overcome a series of control problems caused by the aforementioned model inaccuracies.

[0024] S12. Definition of Virtual Voltage Vector

[0025] The five-phase voltage source inverter has five bridge arms, and the upper and lower power transistors of each bridge arm adopt complementary switching states (dead time not considered); the switching states are determined by S. x (x=a,b,c,d,e) represents that S x =0 indicates that the upper bridge arm is off, S x =1 indicates that the upper bridge arm is conducting, with a total of 2. 5 Various combinations; these combined voltage vectors are further classified into V L1 -V L10 V M1 -V M10 V S1 -V S10 And two additional zero vectors;

[0026] Define and employ a set of virtual voltage vectors V v1 -V v10 This serves as a set of harmonic suppression constraints; the synthesis of this set of vectors is based on the following principle: selecting a large vector V aligned in the α-β subspace. L1 With the mid-vector V M1 By utilizing the inherent amplitude ratio between the two in the xy subspace and fixing their action time ratio to the golden ratio of 0.618, volt-second balance is achieved in the xy subspace. The resulting vector is an effective voltage vector with constant amplitude in the α-β fundamental subspace, while the voltage is zero in the xy harmonic subspace. Thus, while generating an effective control voltage, low-order harmonic components are effectively eliminated.

[0027] Based on the above principle of vector composition, the magnitude of the virtual vector in the α-β and xy subspaces is quantitatively represented as follows:

[0028] (3)

[0029] Where, k v Indicates each control interval T s Duty cycle of the internal large voltage vector, V v V is a virtual voltage vector. dc It is the DC bus voltage; k v Substituting 0.618 into (3) gives:

[0030] (4)

[0031] Furthermore, step S2 specifically includes:

[0032] The core of this invention lies in a data-driven predictive controller that does not rely on a parameterized motor model as shown in formula (2). This controller directly constructs a predictive model and solves the control law by processing the historical and real-time input and output data trajectories of the system, thus achieving non-parametric characterization and control of the motor dynamics. This control method employs a hybrid architecture, specifically implemented through the following two stages: combining an offline-prepared data matrix with a real-time adaptive component to construct a self-optimizing control framework that can dynamically adapt to system changes.

[0033] The two distinct operational phases of the implementation protocol for this data-driven controller are as follows:

[0034] 1) Offline Data Preparation Phase: This initial phase involves systematic data collection through comprehensive system stimuli, followed by complex offline matrix configuration. This process establishes a rich behavioral database, capturing the dynamic characteristics of the system under various operational scenarios.

[0035] 2) Online Adaptive Control Phase: Real-time implementation employs a two-layer optimization architecture. The main control layer uses a pre-configured data matrix as a time constraint to solve the current tracking optimization problem, while integrating real-time input / output data streams for dynamic model optimization. Subsequent control iterations employ a rolling time-domain strategy with N-step predictive optimization, integrating virtual voltage vector synthesis to enhance constraint management. This adaptive mechanism achieves continuous performance improvement through progressive data assimilation, effectively balancing historical system knowledge with current operating conditions to achieve precise voltage regulation.

[0036] This layered implementation strategy ensures computational efficiency while maintaining adaptability, utilizing historical system information and real-time runtime data to optimize transient performance and steady-state accuracy.

[0037] S21. Data Collection and Processing

[0038] The modern design paradigm of data-driven controllers follows a standard procedure that begins with collecting time-series input / output data of length T from the system;

[0039] The development of nonparametric models requires preprocessing the collected data; specifically, constructing two Hankel matrices: one based on the control input sequence u. c The exported H(u) c ), and the current response sequence i c The formed H(i) c );

[0040] The number of columns in a Hankel matrix, denoted by L, is determined by the following formula:

[0041] (5)

[0042] Where T is the total number of data points collected, T ini is an adjustable parameter representing the minimum lag order, and N represents the prediction time domain length;

[0043] (6)

[0044] Among them, u t Let t be the voltage vector at the t-th sampling time during the offline acquisition phase (t=1,2,…,T);

[0045] Output Hankel matrix H(i) c The same method is used to measure the current sequence i c Construct; subsequently, H(u) c ) and H(i c They are all divided into past and future sub-blocks;

[0046] (7)

[0047] Among them, the historical input trajectory sub-block U P Includes H(u) c ) the front T ini One block of rows, i.e., 4*T ini Okay, predict the time-domain input trajectory sub-block U F Contains the remaining 4*N block rows; Hankel matrix sub-block I P and I F Obtained in the same manner;

[0048] S22, Solver for Constrained DeePC Problems

[0049] The DeePC controller is designed in a purely data-driven manner. It directly utilizes the Hankel matrix constructed from input and output data, defined in (5). It is rooted in the basic principles of behavioral systems theory, which states that under continuous input excitation, any valid future trajectory is uniquely represented as a linear combination of columns in the Hankel matrix.

[0050] (8)

[0051] Among them, u ini i ini ∈R 4Tini These are the past d1q1-d3q3 axis voltage and current samples, i,u∈R. 4NIt is the future trajectory starting from this initial condition; each control cycle allows for the existence of a unique g∈R L*1 This ensures that the Hankel matrix based on the current / voltage trajectory satisfies the given constraints;

[0052] Controller design must incorporate robustness analysis and optimization to handle potential data disturbances and incomplete data frames. Since the system's input and output signals are typically transmitted together within a shared data frame, the design must consider two key practical challenges: random frame loss and measurement noise affecting both input and output channels simultaneously; for the control system, the received output data u m (t) and input data i m (t) represents the following:

[0053] (9)

[0054] Among them, u ini (t) and i ini (t) represents the actual input and output data of the controlled system, u d (t) and i d (t) represents noise interference, u r (t) and i r (t) is a random variable characterizing whether the actual data was successfully transmitted, defined as follows:

[0055] (10)

[0056] During online operation, the controller uses a length of T. ini The initial trajectory is used to predict future voltage I / current O trajectories in the time domain over N steps; this prediction is based on offline collected data, which are presented in a time domain with T... ini The Hankel matrix of each block row is structured; the solution vector g is expressed in explicit form:

[0057] (11)

[0058] Where † represents the Moore-Penrose pseudo-inverse operator, and Φ represents a set of bases of the kernel space of M; matrices Φ and M are computed offline using standard numerical linear algebra methods; in the implementation, the vector w obtained by decomposing the vector g is used as an intermediate variable in the subsequent optimization problem (8); this decomposition strategy effectively reduces the computational complexity during online execution.

[0059] To compute the optimal future control input, the DeePC algorithm solves the following optimization problem at each sampling time:

[0060] (12)

[0061] Among them, ir Let U represent the desired reference value, Q and R represent the additional weight matrices in the system, and finally, U is the set of virtual voltage vectors V of the input voltage. 3 s; optimal solution vector g opt From w using formula (7) opt The calculations established the relationship between the optimization variables and the data-driven control law;

[0062] S23. Data-based current estimation and optimal input voltage determination

[0063] Based on (12), the intermediate variables that meet the requirements are solved, and the current estimate at sampling time (k+1) is obtained by the following formula:

[0064] (13)

[0065] The data matrix is ​​dynamically updated using the current estimate derived from the data-driven method (13) to calculate the optimal input voltage for the next control cycle;

[0066] The proposed DeePC framework handles computational delay through a single-step compensation method. Unlike traditional MPC, which extends the prediction time domain to mitigate delay, this method first estimates the current in (k+1) steps to compensate for system delay, and then directly determines (k+1)T from the running data. s The optimal voltage vector for the control cycle; this simplified process eliminates the need for multi-step prediction while maintaining control accuracy, significantly reducing computational complexity compared to traditional methods. The data-driven nature of this solution ensures efficiency and reliability in practical applications.

[0067] During online operation, the data-driven prediction model is updated on a rolling basis based on real-time data. Specifically, in each control cycle, the controller dynamically updates the prediction data matrix using the calculated current estimate and the measured voltage value of the current cycle. During this update process, the storage location of the data is determined by the prediction time domain N, thereby ensuring the efficiency of data organization.

[0068] To simplify subsequent calculations, the data matrix is ​​updated as follows:

[0069] (14)

[0070] (15)

[0071] (16)

[0072] (17)

[0073] in, and For the updated voltage and current data vectors, and For the updated input Hankel matrix sub-block, and For the updated output Hankel matrix sub-block;

[0074] The data matrix (14-17) is dynamically updated by integrating the reference current value and the real-time current estimate obtained in the current control cycle, thereby generating an updated matrix [u m i m ] T This process ensures continuous synchronization between the predicted and actual system states, while maintaining data consistency throughout the control cycle.

[0075] Unlike traditional FCS-MPC (which requires calculating the current response under all voltage vector excitations based on a predictive model and selecting the optimal voltage vector through cost function evaluation), DeePC directly determines the optimal input voltage vector based on online collected data. This method effectively avoids the enumeration computational burden caused by objective function evaluation in traditional methods, thus significantly improving computational efficiency. The control period is (k+1)T. s The optimal input voltage is obtained through the following equation:

[0076] (18)

[0077] Among them, u opt The optimal input voltage vector. To obtain the optimal solution vector g opt The sub-vectors extracted from the future control input trajectory;

[0078] The optimal input voltage is calculated by integrating offline collection and online feedback of input and output data, independent of motor system parameters. By dynamically coupling real-time running feedback with pre-characterized offline data, control performance is maintained during changes in motor parameters.

[0079] In the FCS predictive control scheme, the candidate input is limited to the set of discrete voltage vectors generated by the VSI switching states. Therefore, the optimal input voltage u derived from (15) is... opt It cannot be used directly as a control signal. Instead, it serves as a reference vector, whose α-β axes determine the appropriate virtual voltage vector to be implemented; by using a vector selection method, the corresponding switching signals are calculated and executed to achieve precise motor control.

[0080] In summary, the proposed DeePC mainly includes current and voltage data updates, input calculation, and optimal vector output. The control flow of the proposed DeePC is as follows:

[0081] The first step of this method is to collect voltage and current data offline. Then, using these two datasets, a Hankel matrix is ​​constructed, a query sequence is defined, and intermediate variables are solved to perform data-driven current estimation. In the third stage, the dataset is updated using the estimated current and the corresponding input voltage. Finally, the required voltage can be calculated directly in a completely data-driven manner without relying on a system model of the permanent magnet synchronous motor or without system parameter identification. For the calculated input voltage, a location-based intuitive method is used to select a non-zero virtual voltage vector.

[0082] The beneficial effects of this invention are:

[0083] 1) Parameter decoupling design at the structural level of the predictive model. The constructed data-driven predictive model uses only historical input-output data trajectories as its sole information source, and its prediction mechanism does not involve explicit expressions of motor physical parameters such as resistance, inductance, and flux linkage. This structural feature decouples the prediction accuracy of the control system from motor parameter perturbations, fundamentally eliminating the control performance degradation problem caused by parameter mismatch in traditional model predictive control.

[0084] 2) Harmonic suppression embedded design at the modulation strategy level. Harmonic suppression is embedded within the synthesis mechanism of the virtual voltage vector. Utilizing the natural cancellation property of the volt-second product of the large and medium vectors in the harmonic subspace, the output voltage vector is simultaneously optimized in both fundamental frequency tracking and harmonic suppression dimensions. This design avoids the hierarchical cascade structure of predictive control and harmonic compensation in traditional methods, simplifying the system architecture while ensuring steady-state current quality.

[0085] 3) Online adaptive design at the model evolution mechanism level. Unlike the offline training paradigm with a fixed dataset, the proposed strategy continuously feeds real-time running data back to the historical trajectory database, driving the prediction model to dynamically reconstruct as the operating conditions evolve. This closed-loop update mechanism endows the control system with the ability to autonomously adapt to sudden load changes and gradual parameter variations, ensuring the consistency of prediction accuracy and dynamic quality across a wide range of operating conditions. Attached Figure Description

[0086] Figure 1 This is a topology diagram of a five-phase permanent magnet synchronous motor inverter.

[0087] Figure 2 It is a virtual vector projection image.

[0088] Figure 3 This is a data collection flowchart.

[0089] Figure 4 This is the control structure diagram of the DeePC method.

[0090] Figure 5 This is the control flow diagram of the DeePC method.

[0091] Figure 6 This is an analysis of the prediction accuracy of the d1q1 axis voltage. (a) prediction error of ud1, (b) prediction error of uq1, (c) prediction error of ud3, (d) prediction error of uq3.

[0092] Figure 7 These are steady-state performance diagrams for speed, q1-axis current, torque, and A-phase current. (a) VV-MPCC. (b) DeePC.

[0093] Figure 8 These are the THD diagrams of phase A current under two methods: (a) VV-MPCC, (b) DeePC.

[0094] Figure 9 The steady-state performance is measured at 350 rpm under the control method of switching from the conventional VV-MPCC with a current of 0.5 Ls to the proposed DeePC.

[0095] Figure 10 These are the THD diagrams of the phase current under two methods: (a) VV-MPCC, (b) DeePC.

[0096] Figure 11 The figure shows the steady-state performance at 1600 rpm under the control method of switching from the conventional 2LsVV-MPCC to the proposed DeePC.

[0097] Figure 12 These are the THD diagrams of the phase current under two methods: (a) VV-MPCC, (b) DeePC.

[0098] Figure 13 These are dynamic response performance diagrams of speed, q1-axis current, and torque to load changes. (a) VV-MPCC, (b) DeePC.

[0099] Figure 14 These are dynamic performance diagrams of the current response to load changes along the d1-d3-q3 axes. (a) VV-MPCC, (b) DeePC.

[0100] Figure 15 This is a dynamic performance graph of the response speed. (a) Increased speed, (b) Decelerated speed. Detailed Implementation

[0101] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0102] This invention provides a data-driven predictive current control method for permanent magnet synchronous motors, comprising the following steps:

[0103] S1. Steps for establishing Model Predictive Current Control (MPCC) based on Virtual Voltage Vector

[0104] In a rotating coordinate system, the voltage equation of a five-phase permanent magnet synchronous motor is decomposed into two subsystems: the fundamental plane and the harmonic plane. A current prediction model is established by discretization using the forward Euler method. A set of virtual voltage vectors is defined as a set of harmonic suppression constraints. The large and medium vectors aligned in the α-β subspace are selected, and their action time ratio is fixed to the golden ratio of 0.618. Volt-second balance is achieved in the xy harmonic subspace, and an effective voltage vector with constant amplitude in the α-β fundamental subspace is synthesized, thereby eliminating low-order harmonic components while generating an effective control voltage.

[0105] S2. Data-Driven Predictive Control (DeePC) Online Rolling Optimization Steps

[0106] A data-driven predictive controller, independent of the parameterized motor model, is employed and implemented through the following two stages:

[0107] (1) Offline data preparation stage: excite the system to collect the voltage input signal and current output signal of the time series, construct the input Hankel matrix and the output Hankel matrix respectively, and divide them into past sub-blocks and future sub-blocks;

[0108] (2) Online adaptive control stage: At each sampling time, using a length of T ini The initial voltage and current trajectories are obtained, and the input and output trajectories for the next N steps are predicted based on the column linear combination of the offline Hankel matrix. The constrained DeePC optimization problem is solved to calculate the optimal solution vector, thereby obtaining the current estimate at the current sampling time. The data matrix is ​​dynamically updated using the current estimate and the measured voltage value, and the optimal input voltage vector is directly calculated. The α-β axis components of the optimal input voltage vector are used as references to select the corresponding switching signal from the set of virtual voltage vectors for control.

[0109] In this embodiment, step S1 specifically includes:

[0110] S11, Mathematical Modeling of Five-Phase Permanent Magnet Synchronous Motor System

[0111] The voltage equation of a five-phase permanent magnet synchronous motor in a synchronously rotating coordinate system is decomposed into two subsystems: the fundamental plane and the harmonic plane; the stator voltage u d1 u q1 u d3 u q3 With current i d1 i q1 i d3 i q3 The following relationship must be satisfied:

[0112] (1)

[0113] Among them, R s L is the stator phase resistance. d and L q Let L be the d-axis and q-axis inductance of the fundamental plane. ls For leakage, ω e It is the rotor electrical angular velocity, Ψ f It is a permanent magnet flux linkage, and matrix L is the inductance matrix;

[0114] Then, the forward Euler method is used to discretize the above model and establish a current prediction model;

[0115] (2)

[0116] Where k is the index of the current discrete sampling time, k+1 is the next sampling time, and T s The sampling period is given by matrix A, which is the state transition matrix, and matrix B is the input matrix.

[0117] At sufficiently high sampling frequencies, the error introduced by Euler discretization is within acceptable limits. This model neglects cross-saturation, iron saturation, and back EMF harmonic effects. Subsequent demonstrations will show that the data-driven control strategy employed in this invention, because it does not rely on such explicit parameterized model structures, can fundamentally overcome a series of control problems caused by the aforementioned model inaccuracies.

[0118] S12. Definition of Virtual Voltage Vector

[0119] like Figure 1 As shown, the five-phase voltage source inverter has five bridge arms, and the upper and lower power transistors of each bridge arm adopt complementary switching states (dead time is not considered); the switching states are determined by S x (x=a,b,c,d,e) represents that S x =0 indicates that the upper bridge arm is off, S x =1 indicates that the upper bridge arm is conducting, with a total of 2. 5 Various combinations; these combined voltage vectors are further classified into V L1 -V L10 V M1 -V M10 V S1 -V S10 And two additional zero vectors;

[0120] like Figure 2 As shown, a set of virtual voltage vectors V is defined and used. v1 -V v10 This serves as a set of harmonic suppression constraints; the synthesis of this set of vectors is based on the following principle: selecting a large vector V aligned in the α-β subspace.L1 With the mid-vector V M1 By utilizing the inherent amplitude ratio between the two in the xy subspace and fixing their action time ratio to the golden ratio of 0.618, volt-second balance is achieved in the xy subspace. The resulting vector is an effective voltage vector with constant amplitude in the α-β fundamental subspace, while the voltage is zero in the xy harmonic subspace. Thus, while generating an effective control voltage, low-order harmonic components are effectively eliminated.

[0121] Based on the above principle of vector composition, the magnitude of the virtual vector in the α-β and xy subspaces is quantitatively represented as follows:

[0122] (3)

[0123] Where, k v Indicates each control interval T s Duty cycle of the internal large voltage vector, V v V is a virtual voltage vector. dc It is the DC bus voltage; k v Substituting 0.618 into (3) gives:

[0124] (4)

[0125] In this embodiment, step S2 specifically includes:

[0126] The core of this invention lies in a data-driven predictive controller that does not rely on a parameterized motor model as shown in formula (2). This controller directly constructs a predictive model and solves the control law by processing the historical and real-time input and output data trajectories of the system, thus achieving non-parametric characterization and control of the motor dynamics. This control method employs a hybrid architecture, specifically implemented through the following two stages: combining an offline-prepared data matrix with a real-time adaptive component to construct a self-optimizing control framework that can dynamically adapt to system changes.

[0127] The two distinct operational phases of the implementation protocol for this data-driven controller are as follows:

[0128] 1) Offline Data Preparation Phase: This initial phase involves systematic data collection through comprehensive system stimuli, followed by complex offline matrix configuration. This process establishes a rich behavioral database, capturing the dynamic characteristics of the system under various operational scenarios.

[0129] 2) Online Adaptive Control Phase: Real-time implementation employs a two-layer optimization architecture. The main control layer uses a pre-configured data matrix as a time constraint to solve the current tracking optimization problem, while integrating real-time input / output data streams for dynamic model optimization. Subsequent control iterations employ a rolling time-domain strategy with N-step predictive optimization, integrating virtual voltage vector synthesis to enhance constraint management. This adaptive mechanism achieves continuous performance improvement through progressive data assimilation, effectively balancing historical system knowledge with current operating conditions to achieve precise voltage regulation.

[0130] This layered implementation strategy ensures computational efficiency while maintaining adaptability, utilizing historical system information and real-time runtime data to optimize transient performance and steady-state accuracy.

[0131] S21. Data Collection and Processing

[0132] The modern design paradigm for data-driven controllers follows standard procedures (such as...) Figure 3 As shown), the process begins from the system (in this study, specifically the voltage and current signals, Figure 3 The superscript "c" in the text indicates data acquired during the acquisition phase. Time series input / output data of length T are collected; it must be emphasized that, for example... Figure 3 As shown, the selection of the input signal must strictly comply with the virtual voltage vector constraint;

[0133] The development of nonparametric models requires preprocessing the collected data; specifically, constructing two Hankel matrices: one based on the control input sequence u. c The exported H(u) c ), and the current response sequence i c The formed H(i) c );

[0134] The number of columns in a Hankel matrix, denoted by L, is determined by the following formula:

[0135] (5)

[0136] Where T is the total number of data points collected, T ini is an adjustable parameter representing the minimum lag order, and N represents the prediction time domain length;

[0137] (6)

[0138] Among them, u t Let t be the voltage vector at the t-th sampling time during the offline acquisition phase (t=1,2,…,T);

[0139] Output Hankel matrix H(i) c The same method is used to measure the current sequence i cConstruct; subsequently, H(u) c ) and H(i c They are all divided into past and future sub-blocks;

[0140] (7)

[0141] Among them, the historical input trajectory sub-block U P Includes H(u) c ) the front T ini One block of rows, i.e., 4*T ini Okay, predict the time-domain input trajectory sub-block U F Contains the remaining 4*N block rows; Hankel matrix sub-block I P and I F Obtained in the same manner;

[0142] S22, Solver for Constrained DeePC Problems

[0143] The DeePC controller is designed in a purely data-driven manner. It directly utilizes the Hankel matrix constructed from input and output data, defined in (5). It is rooted in the basic principles of behavioral systems theory, which states that under continuous input excitation, any valid future trajectory is uniquely represented as a linear combination of columns in the Hankel matrix.

[0144] (8)

[0145] Among them, u ini i ini ∈R 4Tini These are the past d1q1-d3q3 axis voltage and current samples, i,u∈R. 4N It is the future trajectory starting from this initial condition; each control cycle allows for the existence of a unique g∈R L*1 This ensures that the Hankel matrix based on the current / voltage trajectory satisfies the given constraints;

[0146] Controller design must incorporate robustness analysis and optimization to handle potential data disturbances and incomplete data frames. Since the system's input and output signals are typically transmitted together within a shared data frame, the design must consider two key practical challenges: random frame loss and measurement noise affecting both input and output channels simultaneously; for the control system, the received output data u m (t) and input data i m (t) represents the following:

[0147] (9)

[0148] Among them, u ini (t) and i ini(t) represents the actual input and output data of the controlled system, u d (t) and i d (t) represents noise interference, u r (t) and i r (t) is a random variable characterizing whether the actual data was successfully transmitted, defined as follows:

[0149] (10)

[0150] During online operation, the controller uses a length of T. ini The initial trajectory is used to predict future voltage I / current O trajectories in the time domain over N steps; this prediction is based on offline collected data, which are presented in a time domain with T... ini The Hankel matrix of each block row is structured; the solution vector g is expressed in explicit form:

[0151] (11)

[0152] Where † represents the Moore-Penrose pseudo-inverse operator, and Φ represents a set of bases of the kernel space of M; matrices Φ and M are computed offline using standard numerical linear algebra methods; in the implementation, the vector w obtained by decomposing the vector g is used as an intermediate variable in the subsequent optimization problem (8); this decomposition strategy effectively reduces the computational complexity during online execution.

[0153] To compute the optimal future control input, the DeePC algorithm solves the following optimization problem at each sampling time:

[0154] (12)

[0155] Among them, i r Let U represent the desired reference value, Q and R represent the additional weight matrices in the system, and finally, U is the set of virtual voltage vectors V of the input voltage. 3 s; optimal solution vector g opt From w using formula (7) opt The calculations established the relationship between the optimization variables and the data-driven control law;

[0156] S23. Data-based current estimation and optimal input voltage determination

[0157] Based on (12), the intermediate variables that meet the requirements are solved, and the current estimate at sampling time (k+1) is obtained by the following formula:

[0158] (13)

[0159] The data matrix is ​​dynamically updated using the current estimate derived from the data-driven method (13) to calculate the optimal input voltage for the next control cycle;

[0160] The proposed DeePC framework handles computational delay through a single-step compensation method. Unlike traditional MPC, which extends the prediction time domain to mitigate delay, this method first estimates the current in (k+1) steps to compensate for system delay, and then directly determines (k+1)T from the running data. s The optimal voltage vector for the control cycle; this simplified process eliminates the need for multi-step prediction while maintaining control accuracy, significantly reducing computational complexity compared to traditional methods. The data-driven nature of this solution ensures efficiency and reliability in practical applications.

[0161] During online operation, the data-driven prediction model is updated on a rolling basis based on real-time data. Specifically, in each control cycle, the controller dynamically updates the prediction data matrix using the calculated current estimate and the measured voltage value of the current cycle. During this update process, the storage location of the data is determined by the prediction time domain N, thereby ensuring the efficiency of data organization.

[0162] To simplify subsequent calculations, the data matrix is ​​updated as follows:

[0163] (14)

[0164] (15)

[0165] (16)

[0166] (17)

[0167] in, and For the updated voltage and current data vectors, and For the updated input Hankel matrix sub-block, and For the updated output Hankel matrix sub-block;

[0168] The data matrix (14-17) is dynamically updated by integrating the reference current value and the real-time current estimate obtained in the current control cycle, thereby generating an updated matrix [u m i m ] T This process ensures continuous synchronization between the predicted and actual system states, while maintaining data consistency throughout the control cycle.

[0169] Unlike traditional FCS-MPC (which requires calculating the current response under all voltage vector excitations based on a predictive model and selecting the optimal voltage vector through cost function evaluation), DeePC directly determines the optimal input voltage vector based on online collected data. This method effectively avoids the enumeration computational burden caused by objective function evaluation in traditional methods, thus significantly improving computational efficiency. The control period is (k+1)T. s The optimal input voltage is obtained through the following equation:

[0170] (18)

[0171] Among them, u opt The optimal input voltage vector. To obtain the optimal solution vector g opt The sub-vectors extracted from the future control input trajectory;

[0172] The optimal input voltage is calculated by integrating offline collection and online feedback of input and output data, independent of motor system parameters. By dynamically coupling real-time running feedback with pre-characterized offline data, control performance is maintained during changes in motor parameters.

[0173] In the FCS predictive control scheme, the candidate input is limited to the set of discrete voltage vectors generated by the VSI switching states. Therefore, the optimal input voltage u derived from (15) is... opt It cannot be used directly as a control signal. Instead, it serves as a reference vector, whose α-β axes determine the appropriate virtual voltage vector to be implemented; by using a vector selection method, the corresponding switching signals are calculated and executed to achieve precise motor control.

[0174] In summary, the schematic diagram of the proposed DeePC is as follows: Figure 4 As shown, the main functions include current and voltage data updates, input calculations, and optimal vector output. The control flow of the proposed DeePC is as follows:

[0175] The first step of this method is to collect voltage and current data offline. Then, using these two datasets, a Hankel matrix is ​​constructed, a query sequence is defined, and intermediate variables are solved to perform data-driven current estimation. In the third stage, the dataset is updated using the estimated current and the corresponding input voltage. Finally, the required voltage can be calculated directly in a completely data-driven manner without relying on a system model of the permanent magnet synchronous motor or without system parameter identification. For the calculated input voltage, a location-based intuitive method is used to select a non-zero virtual voltage vector. The structure and detailed flowchart are shown below. Figure 5 As shown.

[0176] Experimental verification

[0177] The performance of the proposed method was evaluated using a five-phase permanent magnet synchronous motor drive system. The test bench consisted of an oscilloscope, an inverter, a real-time control system (RTU-BOX206), a five-phase instrument, and a load motor driven by a load cabinet. The system operated at a sampling frequency of 10 kHz with the DC bus voltage set to 310 V. To ensure full system excitation while maintaining operational safety, the voltage amplitude was carefully selected from a uniform distribution within the range of [-0.5527 Vdc, 0.5527 Vdc], balancing three key requirements: (1) maximizing the excitation range to cover different operating conditions, (2) preventing overcurrent through the upper voltage limit, and (3) avoiding low signal-to-noise ratio measurements by maintaining a sufficient excitation level. This virtual voltage vector method produces zero net voltage and current averages, resulting in zero average torque and eliminating the need for rotor locking. It still provides effective data acquisition across the entire operating range, with all current measurements systematically recorded synchronously with their corresponding applied voltage sequences according to the theoretical framework.

[0178] Since this design applies data-driven control only in the current loop, the reference currents for the d1-axis and d3 / q3-axis currents are set to zero, and the q1-axis current reference is provided by a PI speed regulator. Using the VV-MPCC control framework, the prediction time domain length N is set to 2. For data-driven control methods, this value represents a good trade-off between accuracy and computational complexity. Since the system hysteresis of the considered application is known (i.e., l=1), T is set... ini =1. Considering the motor speed range and computational burden, the number of offline data samples T is chosen to be 100. Furthermore, Q is the identity matrix, and R is the identity matrix scaled by a factor of 0.001, consistent with the VV-MPCC evaluation function.

[0179] A. Data-driven prediction accuracy

[0180] In DeePC, current estimation is achieved not through model-based prediction, but through a data-driven approach. This distinction has prompted research into the accuracy of data-driven current predictors. Here, VV-MPCC is used as a benchmark comparison to evaluate the predictive performance of the DeePC method.

[0181] The experiment was conducted during steady-state operation of the motor, using the same selected operating conditions and parameters. The objective was to observe the error trends of the estimated and measured voltages of the d1q1-d3q3 axes under the two control methods. The experimental results are as follows: Figure 6 As shown. Measurement data are processed as percentages (i.e., estimated value minus measured value, then divided by measured value). From Figure 6 It is evident that both control methods achieve good prediction accuracy. The proposed data-based method exhibits a very small error between the estimated and measured values, fluctuating within -3% to 3%, indicating good prediction accuracy.

[0182] B. Stability performance

[0183] The focus is on the control effect of DeePC in steady-state performance, and comparative experiments are conducted in conjunction with VV-MPCC. First, the motor speed is set to 850 rpm to observe its operation, and real-time motor data is recorded according to the observation parameters set in the software. This includes speed, q1 shaft current, and torque (T). e The waveforms of phase A and phase A current are as follows: Figure 7 As shown. From Figure 7 As can be seen from (b), the DeepPC exhibits stable performance in terms of speed, torque, q1-axis current, and phase current, with fluctuations in each value remaining within a reasonable range. Figure 7 Compared with VV-MPCC in (a), the two have similar performance in terms of speed and q1 axis current; in terms of torque, the DeePC control effect fluctuates slightly more; in terms of phase current, the peak current fluctuation of DeePC is also slightly greater than that of VV-MPCC.

[0184] like Figure 7 As shown, there are still subtle differences between DeePC and VV-MPCC, which will be further investigated by analyzing phase current fluctuations. Figure 8 The total harmonic distortion (THD) of the phase current induced by two methods is reported. The results show that the THD of DeePC is slightly greater than that of VV-MPCC, which also explains the difference in phase current total harmonic distortion (THD) caused by both methods. Figure 7 The differences.

[0185] Based on the above analysis, the motor driven by DeePC achieved the expected control effect.

[0186] Since traditional VV-MPCCs are sensitive to parameter uncertainties, studying the control performance of DeePCs under parameter mismatch is crucial. Considering that the motor's intrinsic parameters cannot be modified, only the parameters in the controller can be adjusted. However, DeePCs themselves do not handle motor parameters. Therefore, voltage and current data from the VV-MPCC under parameter mismatch were input into the DeePC to simulate parameter mismatch. The experiment was conducted at a speed of 350 rpm and a torque of 6 Nm. The motor inductance was changed to 0.5L for 0.2 seconds, followed by 1.2 seconds of switching to DeePC operation. The experimental results are as follows: Figure 9 As shown. From Figure 9 It can be seen that with the activation of the proposed DeePC, the dq-axis current is positively regulated, and the current deviation caused by parameter mismatch is effectively reduced, although the velocity waveform exhibits fluctuations. The corresponding harmonic analysis of the phase current is as follows: Figure 10 As shown.

[0187] Another experiment was conducted at a speed of 1600 rpm and a torque of 6 Nm. The motor inductance was changed to 2L within 0.2 seconds, and then switched to DeePC operation after 1.2 seconds. The experimental results are as follows: Figure 11 As shown. Similarly, current deviation and ripple caused by parameter mismatch can be observed. Switching to the proposed DeePC enables timely adjustment of motion behavior, thus proving the effectiveness of the proposed DeePC. The harmonic analysis of the corresponding phase current is shown below. Figure 12 As shown.

[0188] C. Dynamic performance

[0189] The DeePC method is used to predict system behavior from collected data. Studying the system's behavior at various operating points under different operating conditions is crucial. Similar to steady-state performance studies, the dynamic performance of this control method is analyzed and compared with the dynamic performance of VV-MPCC.

[0190] In this test, the load variation of the motor was controlled by directly controlling the equipped magnetic powder brake. The load torque changed in a step from 6 Nm to 10 Nm. Because the proposed DeePC uses direct exploration of the raw input / output data, online updates of the initial data can be completed at a sufficiently high sampling rate, and theoretically, accurate modeling of system behavior and reliable optimization of control inputs can still be achieved under transients (i.e., sudden changes in load torque). Figure 13 As shown, during increased load operation, the traditional VV-MPCC and DeepPC exhibit differences in speed and torque (T) e The response time of the q1-axis current and the system settling time are basically the same. Meanwhile, the d1-d3-q3 axis current data were also compiled and compared, with the results as follows: Figure 14 As shown, this demonstrates good control performance. Furthermore, the DeePC control method achieves satisfactory suppression of harmonic plane current components, which is attributed to the effect of the virtual voltage vector constraint introduced when determining the optimal voltage vector.

[0191] In addition to the dynamic performance study based on variable load, the changes in the dynamic response of the control system under different speeds were compared between the two control methods. In this experiment, the speed changed from 500 rpm to 1300 rpm, and then from 1300 rpm back to 500 rpm; the experimental results are as follows. Figure 15 As shown (the red line represents the actual rotational speed), DeePC's speed overshoot and response time are slightly greater than VV-MPCC's. There is no significant difference between the two methods in terms of dynamic performance and subsequent steady-state response. The setting parameters of the speed loop PI controller can be optimized in practical applications, but this is not investigated in this invention. It can be concluded that DeePC can also meet the system's response requirements in the face of speed variations.

[0192] Based on the above analysis, DeePC achieves superior control in terms of dynamic performance. Therefore, the traditional VV-MPCC and DeePC methods exhibit similar dynamic performance.

[0193] The VV-MPCC method reduces computational requirements by using only 11 virtual voltage vectors and omitting the prediction of the third harmonic current. This simplified approach not only simplifies the control algorithm but also significantly reduces the computational load, making real-time implementation more feasible. By focusing on the reduced set of virtual voltage vectors and eliminating the complex calculations associated with third harmonic current prediction, the VV-MPC method achieves faster processing time without compromising control performance. The specific computation time of this control method is as follows.

[0194] Current measurement, position sensing, and Park transformation (converting three-phase currents to dq-axis currents) take approximately 8 μs. State estimation time depends on the complexity of matrix operations; since H is a pre-constructed matrix with relatively small dimensions (400 rows in this invention), solving for g can be kept within 10-20 μs. The solution time for the optimization problem depends on the problem size and the solver's efficiency. This invention employs a custom quadratic programming solver, which can solve the problem within 50-70 μs. PWM signal generation time is very short, typically within 6 μs. The execution time of this specific algorithm is shown in Table I. The total execution time is 85 μs, significantly lower than the 100 μs sampling period, ensuring the system's real-time performance.

[0195] Table I. Control Algorithm Execution Decomposition

[0196]

[0197] In summary, this invention proposes a data-driven design method for FP-PMSM controllers. This method only requires the acquisition of voltage and current samples to replace the traditional motor electrodynamic model. Combined with a virtual voltage vector, the predicted voltage satisfies the inverter's pulse width modulation. Preliminary experimental tests show that the results predicted by DeePC have a strong correspondence with the actual measurement results. Furthermore, compared with the traditional VV-MPCC, DeePC exhibits better steady-state performance and dynamic response. Experimental results demonstrate that DeePC possesses excellent control performance.

[0198] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications are also considered within the scope of protection of this invention.

Claims

1. A data-driven predictive current control method for a permanent magnet synchronous motor, characterized in that, Includes the following steps: S1. Steps for establishing Model Predictive Current Control (MPCC) based on Virtual Voltage Vector In a rotating coordinate system, the voltage equation of a five-phase permanent magnet synchronous motor is decomposed into two subsystems: the fundamental plane and the harmonic plane. A current prediction model is established by discretization using the forward Euler method. A set of virtual voltage vectors is defined as a set of harmonic suppression constraints. The large and medium vectors aligned in the α-β subspace are selected, and their action time ratio is fixed to the golden ratio of 0.

618. Volt-second balance is achieved in the xy harmonic subspace, and an effective voltage vector with constant amplitude in the α-β fundamental subspace is synthesized, thereby eliminating low-order harmonic components while generating an effective control voltage. S2. Data-Driven Predictive Control (DeePC) Online Rolling Optimization Steps A data-driven predictive controller, independent of the parameterized motor model, is employed and implemented through the following two stages: (1) Offline data preparation stage: excite the system to collect the voltage input signal and current output signal of the time series, construct the input Hankel matrix and the output Hankel matrix respectively, and divide them into past sub-blocks and future sub-blocks; (2) Online adaptive control stage: At each sampling time, using a length of T ini The initial voltage and current trajectories are obtained, and the input and output trajectories for the next N steps are predicted based on the column linear combination of the offline Hankel matrix. The constrained DeePC optimization problem is solved to calculate the optimal solution vector, and then the current estimate at the current sampling time is obtained. The data matrix is ​​dynamically updated using the current estimate and the measured voltage value. The optimal input voltage vector is directly calculated. The α-β axis components of the optimal input voltage vector are used as a reference to select the corresponding switching signal from the set of virtual voltage vectors for control.

2. The data-driven predictive current control method for a permanent magnet synchronous motor according to claim 1, characterized in that: Step S1 includes: S11, Mathematical Modeling of Five-Phase Permanent Magnet Synchronous Motor System The voltage equation of a five-phase permanent magnet synchronous motor in a synchronously rotating coordinate system is decomposed into two subsystems: the fundamental plane and the harmonic plane; the stator voltage u d1 u q1 u d3 u q3 With current i d1 i q1 i d3 i q3 The following relationship must be satisfied: (1) Among them, R s L is the stator phase resistance. d and L q Let L be the d-axis and q-axis inductance of the fundamental plane. ls For leakage, ω e It is the rotor electrical angular velocity, Ψ f It is a permanent magnet flux linkage, and matrix L is the inductance matrix; Then, the forward Euler method is used to discretize the above model and establish a current prediction model; (2) Where k is the index of the current discrete sampling time, k+1 is the next sampling time, and T s The sampling period is given by matrix A, which is the state transition matrix, and matrix B is the input matrix. S12, Definition of Virtual Voltage Vector The five-phase voltage source inverter has five bridge arms, and the upper and lower power transistors of each bridge arm adopt complementary switching states; the switching states are determined by S. x (x=a,b,c,d,e) represents that S x =0 indicates that the upper bridge arm is off, S x =1 indicates that the upper bridge arm is conducting, with a total of 2. 5 Various combinations; these combined voltage vectors are further classified into V L1 -V L10 V M1 -V M10 V S1 -V S10 And two additional zero vectors; Define and use a set of virtual voltage vectors V v1 -V v10 This serves as a set of harmonic suppression constraints; the synthesis of this set of vectors is based on the following principle: selecting a large vector V aligned in the α-β subspace. L1 With the mid-vector V M1 By utilizing the inherent amplitude ratio between the two in the xy subspace, and fixing their action time ratio to the golden ratio of 0.618, volt-second balance is achieved in the xy subspace; the resulting vector is a constant effective voltage vector in the α-β fundamental subspace, while the voltage is zero in the xy harmonic subspace. Based on the above principle of vector composition, the magnitude of the virtual vector in the α-β and xy subspaces is quantitatively represented as follows: (3) Where, k v Indicates each control interval T s Duty cycle of the internal large voltage vector, V v V is a virtual voltage vector. dc It is the DC bus voltage; k v Substituting 0.618 into (3) gives: (4)。 3. The data-driven predictive current control method for a permanent magnet synchronous motor according to claim 2, characterized in that: Step S2 includes: S21. Data Collection and Processing The modern design paradigm of data-driven controllers follows a standard procedure that begins with collecting time-series input / output data of length T from the system; The development of nonparametric models requires preprocessing the collected data; specifically, constructing two Hankel matrices: one based on the control input sequence u. c The exported H(u) c ), and the current response sequence i c The formed H(i) c ); The number of columns in a Hankel matrix, denoted by L, is determined by the following formula: (5) Where T is the total number of data points collected, T ini is an adjustable parameter representing the minimum lag order, and N represents the prediction time domain length; (6) Among them, u t Let t be the voltage vector at the t-th sampling time during the offline acquisition phase, where t = 1, 2, ..., T; Output Hankel matrix H(i) c The same method is used to measure the current sequence i c Construct; subsequently, H(u) c ) and H(i c They are all divided into past and future sub-blocks; (7) Among them, the historical input trajectory sub-block U P Includes H(u) c ) the front T ini One block of rows, i.e., 4*T ini Okay, predict the time-domain input trajectory sub-block U F Contains the remaining 4*N block rows; Hankel matrix sub-block I P and I F Obtained in the same manner; S22, Solver for Constrained DeePC Problems The DeePC controller is designed in a purely data-driven manner. It directly utilizes the Hankel matrix constructed from input and output data, defined in (5). It is rooted in the basic principles of behavioral systems theory, which states that under continuous input excitation, any valid future trajectory is uniquely represented as a linear combination of columns in the Hankel matrix. (8) Among them, u ini i ini ∈R 4Tini These are the past d1q1-d3q3 axis voltage and current samples, i,u∈R. 4N It is the future trajectory starting from this initial condition; each control cycle allows for a unique coefficient vector g∈R L*1 This ensures that the Hankel matrix based on the current / voltage trajectory satisfies the given constraints; The controller design considers two key practical challenges: random frame loss and measurement noise that simultaneously affects both input and output channels; for the control system, the received output data u m (t) and input data i m (t) represents the following: (9) Among them, u ini (t) and i ini (t) represents the actual input and output data of the controlled system, u d (t) and i d (t) represents noise interference, u r (t) and i r (t) is a random variable characterizing whether the actual data was successfully transmitted, defined as follows: (10) During online operation, the controller uses a length of T. ini The initial trajectory is used to predict future voltage I / current O trajectories in the time domain over N steps; this prediction is based on offline collected data, which are presented in a time domain with T... ini The Hankel matrix of each block row is structured; the solution vector g is expressed in explicit form: (11) Where, † represents the Moore-Penrose pseudo-inverse operator, and Φ represents a set of bases of the kernel space of M; matrices Φ and M are computed offline using standard numerical linear algebra methods; in the implementation, the vector w obtained by decomposing the vector g is used as an intermediate variable for the subsequent optimization problem (8); To compute the optimal future control input, the DeePC algorithm solves the following optimization problem at each sampling time: (12) Among them, i r Let U represent the desired reference value, Q and R represent the additional weight matrices in the system, and finally, U is the set of virtual voltage vectors V of the input voltage. 3 s; optimal solution vector g opt From w using formula (7) opt The calculations established the relationship between the optimization variables and the data-driven control law; S23. Data-based current estimation and optimal input voltage determination Based on (12), the intermediate variables that meet the requirements are solved, and the current estimate at sampling time (k+1) is obtained by the following formula: (13) The data matrix is ​​dynamically updated using the current estimate derived from the data-driven method (13) to calculate the optimal input voltage for the next control cycle; The proposed DeePC framework handles computational delay through a single-step compensation method. It first estimates the current for (k+1) steps to compensate for system delay, and then directly determines (k+1)T from the running data. s The optimal voltage vector for the control cycle; During online operation, the data-driven prediction model is updated on a rolling basis based on real-time data. Specifically, in each control cycle, the controller dynamically updates the prediction data matrix using the calculated current estimate and the measured voltage value of the current cycle. During this update process, the storage location of the data is determined by the prediction time domain N. The data matrix is ​​updated as follows: (14) (15) (16) (17) in, and For the updated voltage and current data vectors, and For the updated input Hankel matrix sub-block, and For the updated output Hankel matrix sub-blocks; The data matrix (14-17) is dynamically updated by integrating the reference current value and the real-time current estimate obtained in the current control cycle, thereby generating an updated matrix [u m i m ] T ; DeePC determines the optimal input voltage vector directly based on online collected data; control period (k+1)T s The optimal input voltage is obtained through the following equation: (18) Among them, u opt The optimal input voltage vector. To obtain the optimal solution vector g opt The sub-vectors extracted from the future control input trajectory; The optimal input voltage is calculated by integrating offline collection and online feedback of input and output data, independent of motor system parameters. By dynamically coupling real-time running feedback with pre-characterized offline data, control performance is maintained during changes in motor parameters. The optimal input voltage u derived from (15) opt Used as a reference vector, its α-β axes determine the appropriate virtual voltage vector to be implemented; by using a vector selection method, the corresponding switching signals are calculated and executed to achieve precise motor control.

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