Composite control method and system for permanent magnet synchronous motor

Abstract

The invention relates to the technical field of model predictive control, in particular to a composite control method and system for a permanent magnet synchronous motor, and the method comprises the steps: building a state space model with load torque as an extended state variable, building an optimization problem based on a discrete state space model and a preset constraint condition, employing a multi-parameter quadratic programming problem, and carrying out the offline solving. And generating a partition lookup table of the state space and a corresponding segmented affine control law. During on-line operation, the load torque estimated in real time by a load observer based on a recursive least square method and the current rotating speed form a state vector together, and an optimal q-axis current reference instruction can be obtained through table look-up and one-time linear calculation. According to the method, complex online optimization is converted into efficient offline calculation and online table look-up, the real-time calculation complexity is remarkably reduced on the premise of ensuring global optimality and constraint satisfaction, and meanwhile, through disturbance observation and compensation, the load disturbance resistance robustness is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of model predictive control, in particular to a permanent magnet synchronous motor compound control method and system. BACKGROUND

[0002] Permanent magnet synchronous motor (PMSM) has become the preferred driving scheme in the new energy field due to its compact structure, high power density and other advantages. In the mid-20th century, with the advent of aluminum-nickel-cobalt and ferrite permanent magnet technology and its continuous performance improvement, various new permanent magnet motors have emerged and quickly popularized. The PMSM system model is a time-varying system with strong coupling, multi-variable and non-linear characteristics. The load carried by the PMSM system model continuously fluctuates, and its own parameters will also change accordingly due to changes in the environment and operating conditions. Therefore, to achieve reasonable use of the permanent magnet synchronous motor, a control strategy comparable to the permanent magnet synchronous motor is needed to take advantage of the high performance characteristics of the permanent magnet synchronous motor.

[0003] Model Predictive Control (MPC), an advanced control strategy based on optimal control theory, is widely used in PMSM drive control systems due to its fast dynamic performance and good steady-state performance. Compared with traditional PID control, a significant advantage of MPC is its ability to handle constraints, incorporating current and voltage constraints as control objectives into the cost function. In the field of motor control, MPC is divided into two control strategies based on the different control actions: Finite Control Set Model Predictive Control (FCS-MPC) and Continuous Control Set Model Predictive Control (CCS-MPC). FCS-MPC typically selects vectors through enumeration or optimization algorithms (such as exhaustive search). This control method allows FCS-MPC to directly output the inverter's switching state without a modulation module (SVPWM), thus exhibiting good dynamic response speed. However, its control accuracy is limited by the number of vectors, potentially generating current ripple, and the computational burden increases with the number of vectors (e.g., in three-level inverters with many vectors). CCS-MPC searches for the optimal voltage vector within the voltage vector space plane during the prediction process, and finally synthesizes and outputs the voltage vector through PWM modulation. Because there are infinitely many candidate voltage vectors in the continuous set, the optimization time for current and voltage constraints needs to be considered. Explicit Model Predictive Control (EMPC) shifts the online optimization problem offline, requiring only table lookups for calculation. However, motors are susceptible to load disturbances during operation. Load disturbances negatively impact the dynamic and steady-state performance and control accuracy of the entire motor system, leading to a decrease in predictive control accuracy.

[0004] In summary, existing model predictive control systems are all based on online prediction, which results in long optimization times and high computational burdens, leading to poor real-time control performance. Furthermore, existing technologies cannot observe load disturbances, which significantly deteriorates the dynamic and steady-state performance of the system and reduces control accuracy. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problems of low predictive control efficiency and poor accuracy caused by online optimization and neglect of load torque in the prior art.

[0006] To solve the above technical problems, the present invention provides a composite control method for a permanent magnet synchronous motor, comprising: In the dq coordinate system, a mathematical model of the permanent magnet synchronous motor is constructed based on the current, voltage, stator inductance of the d-axis and q-axis, as well as the rotor mechanical speed, number of pole pairs and excitation flux of the permanent magnet synchronous motor. Based on the mathematical model of permanent magnet synchronous motor, a state space model is constructed with rotor mechanical speed and load torque as state variables and q-axis current as input control variable, and then discretized to obtain a discrete state space model. Based on the discrete state-space model and preset constraints, an optimization problem is constructed. The optimization problem is solved offline by multi-parameter quadratic programming to generate a piecewise affine control law, which divides the state space into multiple critical regions. A lookup table is then established based on the geometric description of each critical region and its corresponding affine control law parameters. Based on the torque balance equation, a recursive least squares method with a forgetting factor is used to update the load estimate online, and a load observer is established to obtain the real-time load estimate. In each control cycle, based on the current q-axis current value, rotor mechanical speed and real-time load estimate, the current state variable is constructed, the corresponding affine control law parameters are retrieved from the lookup table, and the optimal q-axis voltage value is calculated.

[0007] Preferably, the mathematical model of the permanent magnet synchronous motor is constructed, including: The operating speed of the permanent magnet synchronous motor is preset, and the d-axis current is controlled by PI. A d-axis current model and a q-axis current model are constructed, expressed as follows: ; ; By comprehensively controlling the q-axis current and the rotor mechanical speed, a mechanical motion model is constructed, which is expressed as: ; A mathematical model for a permanent magnet synchronous motor is constructed based on the d-axis current model, the q-axis current model, and the mechanical motion model. in, and These represent the d-axis current and the q-axis current, respectively. and These represent the d-axis voltage and the q-axis voltage, respectively. Indicates stator resistance. Indicates stator inductance, Indicates the number of pole pairs of the motor. Indicates the rotor's mechanical speed. Indicates the excitation flux linkage of a permanent magnet; Represents the moment of inertia. Indicates the coefficient of friction. This indicates the load torque.

[0008] Preferably, based on the mathematical model of a permanent magnet synchronous motor, a state-space model is constructed with rotor mechanical speed and load torque as state variables and q-axis current as input control variable, including: Define the state variable as Using q-axis voltage as control input Rotor electric angular velocity ; Keeping the load torque constant within the prediction step, a state-space model is constructed, represented as: ; in, Represents q-axis current The continuous-time derivative of a state variable is represented as follows. Indicates stator resistance. Indicates stator inductance, Indicates the number of pole pairs of the motor. Indicates the rotor's mechanical speed. Indicates the excitation flux linkage of a permanent magnet. Indicates the q-axis inductance; Represents the moment of inertia. This represents the coefficient of friction.

[0009] Preferably, a state-space model is constructed and discretized to obtain a discrete state-space model, including: The forward Euler method is used to discretize the state-space model to obtain a discrete state-space model containing the prediction model and the output model. The prediction model is represented as: ; The output model is represented as: ; Wherein, the state matrix , is represented as: , Indicates the sampling period; control matrix , represented as: ; express Predicted state variables at time 10:00 and They represent State variables and control inputs at any given time; .

[0010] Preferably, based on the discrete state-space model and preset constraints, an optimization problem is constructed, expressed as: ; ; ; ; ; ; ; ; in, Indicates the length of the prediction time domain. Indicates the relative step size in the prediction time domain. Output reference vector ; express The q-axis current reference value at time t is expressed as , express The actual q-axis current value at time t; express The reference rotor mechanical speed at any given time; , ; express Predicted state variables at time t; ; express The input q-axis voltage at time t and The difference in the input q-axis voltage at any given time; This represents the value of the q-axis current in the state variables. Indicates the rated current; Indicates in The prediction time domain of time 1 The absolute value of the input with a step size, Indicates the DC bus voltage. The state variable represents the initial static and unloaded state. This represents the initial control input.

[0011] Preferably, the optimization problem is solved offline using multi-parameter quadratic programming to generate piecewise affine control laws, dividing the state space into multiple critical regions; and a lookup table is established based on the geometric description of each critical region and its corresponding affine control law parameters, including: The prediction model is represented as: , , , , ; The optimization problem is transformed into a standard form of multi-parameter quadratic programming with the control sequence as the optimization variable and the current state variable as the parameter, expressed as: , ; definition ,but , ; Solving based on the first-order Kuhn-Tucker conditions and the effective constraint set of complementary relaxation conditions yields the piecewise affine function, expressed as: ; After obtaining the region that satisfies the preset affine constraint as the initial critical region, the entire state space is divided into multiple critical regions by gradually dividing it using the complement operation and redundant constraint removal. Store the geometric descriptions of each critical region and their corresponding affine control law parameters to form a lookup table; in, express Optimization variables at any given time; The coupling matrix is ​​expressed as follows: ; ; express State variables at time t; positive definite matrix , , , The dimension representing the state variable. Indicates the dimension of the input; , and It is a matrix determined by the system's preset constraints; Represents the constraint matrix. , This indicates the number of inequalities in the preset constraints. The number of free variables. ; Represents a constraint constant vector. ; express , This represents the constraint constant matrix.

[0012] Preferably, the preset affine constraint includes: , ; in, , and express , and The submatrix consists of vectors that belong to the effective constraint set.

[0013] Preferably, based on the torque balance equation, a recursive least squares method with a forgetting factor is used to update the load estimate online, a load observer is established, and the real-time load estimate is obtained, including: Based on the torque balance equation, construct Constant load torque The linear parametric model is expressed as: ; initialization , Iterative updates are performed using least squares with a forgetting factor to obtain... Real-time load estimate at time of day The iterative update process is represented as: ; ; ; in, express Electromagnetic torque at time t, Represents the moment of inertia. express The rotor mechanical speed at any given moment, Indicates the sampling period. Indicates the coefficient of friction; express Kalman gain at time step and They represent The regression vector at time t and its transpose. Indicates the forgetting factor, express The error covariance matrix at time t; This represents a pre-defined positive real number. Represents a unit vector. This represents the zero vector.

[0014] Preferably, based on the current q-axis current value, rotor mechanical speed, and real-time load estimate, a current state variable is constructed. The corresponding affine control law parameters are then retrieved from a lookup table, and the optimal q-axis voltage value is calculated, including: The current q-axis current value, rotor mechanical speed, and real-time load estimate are obtained to form the current state vector; Compare the current state vector with the descriptive inequalities of each critical region in the lookup table to determine its critical region; Calculate the current optimal q-axis voltage value based on the affine control law parameters of the critical region.

[0015] This embodiment provides a permanent magnet synchronous motor control system based on the composite control method for permanent magnet synchronous motors as described above, including: The load observer takes the electromagnetic torque output by the permanent magnet synchronous motor, the rotor mechanical speed at the current moment and the previous moment as input, and outputs a real-time load estimate. The explicit model predictive controller takes the current q-axis current value, rotor mechanical speed and real-time load estimate as inputs, and outputs the optimal q-axis voltage value. The Clack converter module takes three-phase stator current as input and outputs two-phase stator current in the stationary coordinate system. The Park transformation module takes the two-phase stator current in the stationary coordinate system as input and outputs the d-axis current value and the q-axis current value. The d-axis PI controller takes the d-axis current value as input and outputs the d-axis voltage value. The Park inverse transform module takes the d-axis voltage value and the optimal q-axis voltage value as input and outputs the voltage value in the stationary coordinate system. The SVPWM module takes the voltage value in the stationary coordinate system as input and outputs a PWM wave. A three-phase inverter, using PWM waves as input, supplies power to a permanent magnet synchronous motor.

[0016] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: The permanent magnet synchronous motor composite control method described in this invention extends the load torque into a state variable, establishing a state-space model with rotor mechanical speed and load torque as states and q-axis current as input. Simultaneously, based on the torque balance equation, a recursive least squares method with a forgetting factor is used to update the load estimate online, establishing a load observer to achieve real-time observation of active disturbances. This organic combination of explicit model predictive control and the load observer significantly improves the system's ability to suppress load disturbances while ensuring rapid response, enabling the model predictive controller to anticipate and compensate for the impact of disturbances. Based on a state-space model and pre-defined constraints, an optimization problem is constructed with the control sequence as the variable and the current state as the parameter. This problem is solved offline using multi-parameter programming (MPP). While ensuring that voltage and current constraints are met, the explicit expression of the optimal control law is obtained. The state space is divided into multiple critical regions, and a lookup table is constructed so that the optimal control law can be obtained online with only a simple region lookup and a single matrix multiplication and addition operation. By combining offline MPP with online lookup tables, the complex online QP solution is transformed into a simple region lookup and linear calculation. Furthermore, the offline lookup table occupies a fixed amount of memory, and the online algorithm is deterministic and simple, greatly reducing the real-time computational burden. This achieves high-performance, high-precision, and robust predictive control of permanent magnet synchronous motors. Attached Figure Description

[0017] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein: Figure 1 This is a flowchart of the steps of the permanent magnet synchronous motor composite control method of the present invention; Figure 2 This is a schematic diagram of the critical region division; Figure 3 This is a structural diagram of a permanent magnet synchronous motor control system; Figure 4 This is a Simulink simulation diagram of a permanent magnet synchronous motor control system; Figure 5 It is a speed tracking curve under sudden load; Figure 6 It is a speed tracking curve for sudden load reduction; Figure 7 This is a schematic diagram of steady-state current FFT analysis under no-load conditions; Figure 8 This is a schematic diagram of steady-state current FFT analysis under load conditions; Figure 9 This is a comparison chart of the actual and estimated values ​​of the load torque. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0019] Reference Figure 1 The flowchart of the composite control method for permanent magnet synchronous motors of the present invention is shown below, and the specific steps are shown in S101-S105.

[0020] S101: In the dq coordinate system, based on the current, voltage, stator inductance of the d-axis and q-axis, as well as the rotor mechanical speed, number of pole pairs and excitation flux of the permanent magnet synchronous motor, a mathematical model of the permanent magnet synchronous motor is constructed.

[0021] S101-1: Establish the PMSM mathematical model in the dq rotating coordinate system and preset the electrode running speed.

[0022] S101-2: Order Only the d-axis current is controlled by PI (proportional-integral), while the q-axis current is combined with the motor speed for comprehensive control. Differential equations for voltage, motor torque balance, and speed dynamics are established for the surface-mounted permanent magnet synchronous motor. In the dq rotating coordinate system, the d-axis current model, q-axis current model, and mechanical motion model of the permanent magnet synchronous motor are established, expressed as: ; in, and These represent the d-axis current and the q-axis current, respectively. and These represent the d-axis voltage and the q-axis voltage, respectively. Indicates stator resistance. Indicates stator inductance, Indicates the number of pole pairs of the motor. Indicates the rotor's mechanical speed. Indicates the excitation flux linkage of a permanent magnet; Represents the moment of inertia. Indicates the coefficient of friction. This indicates the load torque.

[0023] In this embodiment, the stator resistance Number of pole pairs of motor Rotor mechanical speed Permanent magnet excitation flux coefficient of friction .

[0024] S102: Based on the mathematical model of permanent magnet synchronous motor, a state space model is constructed with rotor mechanical speed and load torque as state variables and q-axis current as input control variable, and then discretized to obtain a discrete state space model.

[0025] S102-1: The mechanical rotational speed at time k External load As a state variable, the q-axis current A velocity loop state-space model is established using the input control variables, and a state vector is defined. The control input is The voltage is the q-axis voltage, and the electric angular velocity is... Then the state-space expression of the system model is reconstructed, and it is assumed that the load torque remains constant within the prediction step, which means and They are equivalent, among which Then, the state-space model can be re-expressed as: ; in, The continuous-time derivative of a state variable is represented as follows. Indicates stator resistance. Indicates stator inductance, Indicates the number of pole pairs of the motor. Indicates the excitation flux linkage of a permanent magnet. Indicates the q-axis inductance; Represents the moment of inertia. This represents the coefficient of friction.

[0026] S102-2: Discretize the state-space model using the forward Euler method to obtain a discrete state-space model containing the prediction model and the output model; The prediction model is represented as: ; The output model is represented as: ; Wherein, the state matrix , represented as: , Indicates the sampling period; control matrix , represented as: ; express Predicted state variables at time 10:00 and They represent State variables and control inputs at any given time; .

[0027] In this embodiment, the system output is defined as the q-axis current output value and the mechanical speed output value, that is: Periodic sampling k is the kth sampling time, the control input. This is the q-axis voltage. and These are the state matrix and the control matrix, This is a predicted value for the next moment. Furthermore, since the discrete model composed of the q-axis current equation, motion loop equation, and load torque is a linear model, the requirement for offline storage space is significantly reduced, making the entire control process more efficient and economical.

[0028] S103: Based on the discrete state-space model and preset constraints, construct the optimization problem; solve the optimization problem offline through multi-parameter quadratic programming to generate a piecewise affine control law, divide the state space into multiple critical regions; and establish a lookup table based on the geometric description of each critical region and its corresponding affine control law parameters. S103-1: The core objective of the explicit model predictive controller is to quickly and accurately track the preset speed tracking value of the system, while ensuring stable operation of the motor system current to achieve optimal control performance. The implementation of this control strategy not only improves the motor's response speed and control accuracy, but also significantly enhances the stability and reliability of the entire system in practical applications, bringing a new breakthrough to the field of motor control. Therefore, the optimization problem can be designed as follows: ; ; ; ; ; ; ; ; in, Indicates the length of the prediction time domain. Indicates the relative step size in the prediction time domain. Output reference vector ; express The q-axis current reference value at time t is expressed as , express The actual q-axis current value at time t; express The reference rotor mechanical speed at any given time; , ; express Predicted state variables at time t; ; express The input q-axis voltage at time t and The difference in the input q-axis voltage at any given time; This represents the value of the q-axis current in the state variables. Indicates the rated current; Indicates in The prediction time domain of time 1 The absolute value of the input with a step size, Indicates the DC bus voltage. The state variable represents the initial static and unloaded state. This represents the initial control input.

[0029] This embodiment addresses this optimization problem by reducing current fluctuations, thereby suppressing current harmonic components.

[0030] S103-2: Based on the system requirements and configuration state, the system model and constraints are established. At this point, the discrete state-space equations of the system can be explicitly expressed. The single-loop model of the motor is represented by the d-axis current model, the q-axis current model, and the mechanical motion model. It reflects how the system state at time k is updated through a linear transformation and control input, and how the corresponding output is generated. The equations are: ; in , and These are the system's state variables, control variables, and output variables, respectively; the system's constraints are represented as follows: ; in, , , , Therefore, the control objective is: ; in For the prediction time domain, Q and R are symmetric non-negative weight matrices, which represent the penalty state and control input, respectively, in the above equation. The prediction model for calculating the future state trajectory in the prediction time domain is shown in the following equation: ; ; ; matrix , ; Transforming the optimization problem into the standard form of a multi-parameter quadratic programming problem with the control sequence as the optimization variable and the current state variable as the parameter, the cost function of the MPC problem is: ; in, express Optimization variables at any given time; The coupling matrix is ​​expressed as follows: ; ; express State variables at time t; positive definite matrix , , , The dimension representing the state variable. Indicates the dimension of the input; , and It is a matrix determined by the system's preset constraints; Represents the constraint matrix. , This indicates the number of inequalities in the preset constraints. The number of free variables. ; Represents a constraint constant vector. ; express , This represents the constraint constant matrix.

[0031] S103-3: Definition Then the above optimization problem can be written as follows: ; in, , ; This represents the state vector at this moment and can be viewed as a parameter vector. Because the matrix... ,so The number of inequalities in the above system is represented by... Let represent the free variables: Therefore, there is , , , , .

[0032] S103-4: After a series of changes, an MPC optimization problem is transformed into a multi-parameter programming problem, which is then solved using the first-order Kuhn-Tucker conditions. The first-order Kuhn-Tucker condition is expressed as: ; ; ; ; in, It is a Lagrange multiplier. The first constraint represents the first constraint. Okay, we can deduce that: ; This leads to the complementary relaxation condition: The Lagrange multiplier λ is divided into effective constraints. and invalid constraints For invalid constraints For valid constraints to be satisfied: Therefore, we can solve the following: ; in, , and Let be the submatrix corresponding to the valid constraints, and The rows are linearly independent, ensuring the existence of the inverse matrix, and further derivation... The expression: ; at this time, Both λ and λ are affine functions of the state variable x.

[0033] S103-5: The critical region can be determined using the following inequalities. : ; ; Taking a two-dimensional state space as an example, such as Figure 2 The diagram shown is a schematic representation of the critical region division. It is a polyhedral region (such as a pentagon) defined by affine constraints, and the remaining region Through the gradual division using complement operations and redundant constraint removal, the entire state space is eventually divided into several critical regions.

[0034] S103-6: Within each critical region, the control input U is a piecewise affine function of state x: .

[0035] S104: Based on the torque balance equation, the recursive least squares method with a forgetting factor is used to update the load estimate online, and a load observer is established to obtain the real-time load estimate.

[0036] S104-1: Based on the torque balance equation, construct... Constant load torque The linear parametric model is expressed as: .

[0037] S104-2: Initialization , Iterative updates are performed using least squares with a forgetting factor to obtain... Real-time load estimate at time of day The iterative update process is represented as: ; ; ; in, express Electromagnetic torque at time t, Represents the moment of inertia. express The rotor mechanical speed at any given moment, Indicates the sampling period. express Kalman gain at time step and They represent The regression vector at time t and its transpose. Indicates the forgetting factor, express The error covariance matrix at time t; This represents a pre-defined positive real number. Represents a unit vector. This represents the zero vector.

[0038] In this embodiment, a forgetting factor is set for the least squares method. ; It is a sufficiently large positive real number. It is a unit vector. It is a sufficiently small positive real vector or zero vector, the regressor. Therefore, the parameter model can be updated using only one identification result.

[0039] S105: In each control cycle, based on the current q-axis current value, rotor mechanical speed, and real-time load estimate, construct the current state variable, look up the corresponding affine control law parameters in the lookup table, and calculate the optimal q-axis voltage value, including: Obtain the current q-axis current value, rotor mechanical speed, and real-time load estimate. This constitutes the current state vector. ; Compare the current state vector with the descriptive inequalities of each critical region in the lookup table to determine its critical region; Based on the affine control law parameters of the critical region, calculate the current optimal q-axis voltage value and output it to the Park inverse transform module.

[0040] This embodiment generates a piecewise affine control law offline using multi-parameter quadratic programming, dividing the state space into critical regions. The optimal control quantity u(k) is obtained by looking up a table based on the current state x(k), and then output... It acts on the motor again.

[0041] This embodiment maps the solution to the optimization problem to a piecewise affine function in the state space through offline computation, simplifying online computation to state partition lookup and affine control law invocation, thereby significantly reducing the real-time computation burden. Simultaneously, based on explicit model predictive control, this invention improves the original non-cascaded model framework by utilizing a load observer to monitor load torque in real time, addressing current and voltage constraints in the motor system while mitigating the impact of load disturbances. The load is estimated online using the recursive least squares method, and state and input constraints are configured according to system operating requirements. Combined with the established system model and constraints, a multi-parameter programming solver is used to generate state space partitions and corresponding piecewise affine control laws, improving the system's disturbance rejection performance while ensuring voltage and current constraints are met.

[0042] Reference Figure 3 The diagram shown is a structural diagram of a permanent magnet synchronous motor control system. The permanent magnet synchronous motor control system of this embodiment includes: The load observer takes the electromagnetic torque output by the permanent magnet synchronous motor, the rotor mechanical speed at the current moment and the previous moment as input, and outputs a real-time load estimate. The explicit model predictive controller takes the current q-axis current value, rotor mechanical speed and real-time load estimate as inputs, and outputs the optimal q-axis voltage value. The Clack converter module takes three-phase stator current as input and outputs two-phase stator current in the stationary coordinate system. The Park transformation module takes the two-phase stator current in the stationary coordinate system as input and outputs the d-axis current value and the q-axis current value. The d-axis PI controller takes the d-axis current value as input and outputs the d-axis voltage value. The Park inverse transform module takes the d-axis voltage value and the optimal q-axis voltage value as input and outputs the voltage value in the stationary coordinate system. The SVPWM module takes the voltage value in the stationary coordinate system as input and outputs a PWM wave. A three-phase inverter, using PWM waves as input, supplies power to a permanent magnet synchronous motor.

[0043] Based on the above embodiments, this embodiment uses a Simulink model for verification, referring to... Figure 4 The image shows a Simulink simulation diagram of a permanent magnet synchronous motor control system. First, a Simulink framework design is established, including an EMPC module, a Park converter module, an SVPWM module, an inverter, a Clark converter module, and a load observer. Then, in the initial simulation phase, an initial tracking speed is set, followed by a sudden change after 0.05 seconds to examine the speed tracking capability. First, motor parameters are defined, selecting a surface-mounted permanent magnet synchronous motor as the research object. PI (proportional-integral) control is applied to the d-axis, with the load torque as an extended variable. Then, Euler's formula is used to discretize the system, obtaining a discretized model. Then, the load estimate is updated online based on the torque balance equation. An adaptive forgetting factor mechanism and an online adjustment strategy for the covariance matrix are designed to construct an integrated estimation-control architecture. The recursive least squares (RLS) load estimation method is adopted, and state constraints and input constraints are configured according to system requirements. Based on the established system model and constraints, a multi-parameter programming solver is used to generate state space partitions and corresponding piecewise affine (PWA) control laws. The final results are saved in the form of a lookup table. Finally, the lookup table operation is implemented with the help of tools such as MPT3.0 to generate explicit control laws and output appropriate values ​​to the motor.

[0044] Specifically, the design of the Simulink model architecture is divided into two parts. One part is the part that is built directly in Simulink, including the Park Transformer module, SVPWM module, inverter, and Clark Transformer module. The explicit model predictive controller part is compiled using MATLAB and is also the core part of the entire control system.

[0045] In the initial simulation phase, the initial tracking speed was set to 500 r / min. After 0.2 seconds, a sudden change was made to examine the speed tracking capability. In the simulation, the motor showed only a slight delay after the speed change, and then completed the adjustment within a short time. The speed tracking performance was excellent and basically matched the ideal curve. To verify the effectiveness of the proposed scheme, a load was applied at 0.2 seconds. Perform load operation, refer to Figure 5 The image shows the speed tracking curve under sudden load; the load is reduced at 0.2 seconds. Perform unloaded operation, refer to Figure 6 The figure shown is a speed tracking curve for sudden load reduction. Based on Figure 5 and Figure 6 As can be seen, when applying and reducing the load, there is a small fluctuation in the speed, and then the motor speed gradually returns to a stable value and tends to the set speed value; thus, the controller has good robustness.

[0046] Reference Figure 7 The diagram shown illustrates the steady-state current FFT analysis under no-load conditions; refer to... Figure 8 The figure shows a schematic diagram of steady-state current FFT analysis under load. Figure 7 and Figure 8 FFT analysis of a single phase of the steady-state three-phase current of the motor under no-load and load conditions is presented respectively. Under no-load conditions, the THD value obtained by explicit model predictive control is 2.50%; under a given load torque... Under these conditions, the THD value of the motor after reaching steady state is 1.89%.

[0047] Reference Figure 9 As shown, this is a comparison chart of the actual and estimated load torque values. In the process of using the least squares method to update the torque balance equation online to estimate the load torque, the calculated predicted value (TLe) is highly consistent with the actual applied load torque (TL). The trends and steady-state values ​​of both are almost completely identical, indicating that this method can accurately reflect changes in external load torque under both dynamic and steady-state conditions, achieving high-precision online load estimation.

[0048] The simulation results above lead to the following conclusions: When the motor accelerates from its initial standstill (0 r / min) to the target speed of 500 r / min, the model predictive control (MPC) system constructed in this study exhibits excellent dynamic characteristics. Specifically, the system achieves a fast response time of 0.003 seconds during the startup phase. This fast, overshoot-free tracking characteristic and strong robustness are attributed to the unique feedforward-feedback composite control mechanism of model predictive control: multi-step prediction is performed using the built-in discrete state-space model of the permanent magnet synchronous motor, combined with the cost function for the coordinated optimization of q-axis current and speed deviations, achieving precise feedforward compensation of electromagnetic torque; simultaneously, by solving the quadratic programming problem online in each control cycle, the control quantity weight coefficients are dynamically adjusted, effectively balancing the dialectical relationship between system response speed and disturbance rejection performance.

[0049] The permanent magnet synchronous motor composite control method described in this invention extends the load torque into a state variable, establishing a state-space model with rotor mechanical speed and load torque as states and q-axis current as input. Simultaneously, based on the torque balance equation, a recursive least squares method with a forgetting factor is used to update the load estimate online, establishing a load observer to achieve real-time observation of active disturbances. This organic combination of explicit model predictive control and the load observer significantly improves the system's ability to suppress load disturbances while ensuring rapid response, enabling the model predictive controller to anticipate and compensate for the impact of disturbances. Based on a state-space model and pre-defined constraints, an optimization problem is constructed with the control sequence as the variable and the current state as the parameter. This problem is solved offline using multi-parameter programming (MPP). While ensuring that voltage and current constraints are met, the explicit expression of the optimal control law is obtained. The state space is divided into multiple critical regions, and a lookup table is constructed so that the optimal control law can be obtained online with only a simple region lookup and a single matrix multiplication and addition operation. By combining offline MPP with online lookup tables, the complex online QP solution is transformed into a simple region lookup and linear calculation. Furthermore, the offline lookup table occupies a fixed amount of memory, and the online algorithm is deterministic and simple, greatly reducing the real-time computational burden. This achieves high-performance, high-precision, and robust predictive control of permanent magnet synchronous motors.

[0050] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0051] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0052] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0053] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0054] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for hybrid control of a permanent magnet synchronous motor, characterized in that, Comprise: Under the d-q coordinate system, based on the current, voltage, stator inductance of d-axis and q-axis, and the rotor mechanical speed, motor pole pair number and permanent magnet excitation flux linkage of permanent magnet synchronous motor, a mathematical model of permanent magnet synchronous motor is constructed; Based on the mathematical model of permanent magnet synchronous motor, taking the rotor mechanical speed and load torque as state variables, and taking the q-axis current as input control variable, a state space model is constructed, and is discretized to obtain a discrete state space model; Based on the discrete state space model and the preset constraint condition, an optimization problem is constructed; The optimization problem is solved offline by multi-parameter quadratic programming to generate a segmented affine control law, which divides the state space into multiple critical regions; and a lookup table is established based on the geometric description of each critical region and the corresponding affine control law parameters; Based on the torque balance equation, the recursive least squares method with forgetting factor is used to update the load estimate value online to establish a load observer to obtain a real-time load estimate value; In each control cycle, based on the current q-axis current value, rotor mechanical speed and real-time load estimate value, the current state variable is constructed, the corresponding affine control law parameters are obtained in the lookup table, and the optimal q-axis voltage value is calculated.

2. The method of claim 1, wherein, The mathematical model of permanent magnet synchronous motor is constructed, comprising: The preset permanent magnet synchronous motor running speed, PI control is performed on the d-axis current, the d-axis current model and the q-axis current model are constructed, and are expressed as: ； ； The q-axis current and the rotor mechanical speed are comprehensively controlled, and a mechanical motion model is constructed, which is expressed as: ； Based on the d-axis current model, the q-axis current model and the mechanical motion model, the mathematical model of permanent magnet synchronous motor is composed; wherein, and idand iqdenote the d-axis and q-axis currents, respectively, and idand iqdenote the d-axis and q-axis voltages, respectively; idand iqdenote the stator resistance, idand iqdenote the stator inductance, idand iqdenote the number of motor pole pairs, idand iqdenote the rotor mechanical speed, idand iqdenote the permanent magnet excitation flux linkage; idand iqdenote the moment of inertia, idand iqdenote the friction coefficient, idand iqdenote the load torque.

3. The method of claim 1, wherein, Based on the mathematical model of permanent magnet synchronous motor, taking the rotor mechanical speed and load torque as state variables, and taking the q-axis current as input control variable, a state space model is constructed, comprising: The state variables are defined as with q-axis voltage as control input , rotor electrical angular velocity ; Let the load torque in the prediction step remain constant, and construct a state space model, which is expressed as: ； wherein, represents the q-axis current, represents the continuous-time derivative of the state variable representation, represents the stator resistance, represents the stator inductance, represents the number of motor pole pairs, represents the rotor mechanical rotational speed, represents the permanent magnet excitation flux linkage, represents the q-axis inductance; represents the moment of inertia, represents the friction coefficient.

4. The compound control method of permanent magnet synchronous motor according to claim 3, characterized in that, The state space model is constructed and discretized to obtain a discrete state space model, comprising: The state space model is discretized by forward Euler method to obtain a discrete state space model containing a prediction model and an output model; A prediction model, denoted as: ; An output model is represented as: ; where the state matrix is given by , denotes the sampling period; the control matrix is given by ; denotes the predicted state variable at time , and denote the state variable and the control input at time ; .

5. The method of claim 4, wherein, Based on the discrete state space model and the preset constraint condition, an optimization problem is constructed, which is expressed as: ； ； ； ； ； ； ； ； in, Indicates the length of the prediction time domain. Indicates the relative step size in the prediction time domain. Output reference vector ; express The q-axis current reference value at time t is expressed as , express The actual q-axis current value at time t; express The reference rotor mechanical speed at any given time; , ; express Predicted state variables at time t; ; express The input q-axis voltage at time t and The difference in the input q-axis voltage at any given time; This represents the value of the q-axis current in the state variables. Indicates the rated current; Indicates in The prediction time domain of time 1 The absolute value of the input with a step size, Indicates the DC bus voltage. The state variable represents the initial static and unloaded state. This represents the initial control input.

6. The method of claim 5, wherein, The optimization problem is solved offline by multi-parameter quadratic programming to generate a segmented affine control law, which divides the state space into multiple critical regions; And based on the geometric description of each critical region and the corresponding affine control law parameters, a lookup table is established, comprising: The prediction model is represented as: , , , , ; The optimization problem is converted into a multi-parameter quadratic programming standard form with control sequence as optimization variable and current state variable as parameter, which is expressed as: ， ； Definitions then , ; Based on the first order Kuhn-Tucker conditions and the active constraint set of complementary slackness conditions, the piecewise affine function is obtained as ; After obtaining the region satisfying the preset affine constraint as the initial critical region, the entire state space is divided into multiple critical regions by using the complement operation and redundant constraint elimination step by step; The geometric description of each critical region and the corresponding affine control law parameters are stored to form a lookup table; wherein, denotes the optimization variable at time instant denotes the coupling matrix, expressed as ; ; denotes the state variable at time instant , , , denotes the dimension of the state variable, denotes the dimension of the input; , and are matrices determined by the system preset constraints; denotes the constraint matrix, , denotes the number of inequalities in the preset constraints, is the number of free variables, ; denotes the constraint constant vector, ; denotes , denotes the constraint constant matrix.

7. The method of claim 6, wherein, The preset affine constraint comprises: ， ； wherein , with denotes , with the submatrix consisting of the vectors belonging to the active constraint set in 8. The method of claim 1, wherein, Based on the torque balance equation, the recursive least squares method with forgetting factor is used to update the load estimate value online to establish a load observer to obtain a real-time load estimate value, comprising: Based on the torque balance equation, a linear parameter model is constructed Load torque at time is expressed as ； Initialization , , the real-time load estimation value at time t is obtained by iterative updating using the least square method with a forgetting factor The iterative updating process is represented as:​ ； ； ； wherein, denotes electromagnetic torque at time instant, denotes moment of inertia, denotes rotor mechanical speed at time instant, denotes sampling period, denotes friction coefficient; denotes Kalman gain at time instant, and denote regression vector at time instant and its transpose, respectively, denotes forgetting factor, denotes error covariance matrix at time instant; denotes a pre-set positive real number, denotes unit vector, denotes zero vector.

9. The method of claim 1, wherein, Based on the current q-axis current value, rotor mechanical speed and real-time load estimation value, a current state variable is constructed, corresponding affine control law parameters are obtained by looking up in a lookup table, and an optimal q-axis voltage value is calculated, including: Obtaining the q-axis current value, rotor mechanical speed and real-time load estimation value at the current time to constitute a current state vector; Comparing the current state vector with the description inequalities of each critical region in the lookup table to determine the belonging critical region; According to the affine control law parameters of the belonging critical region, the current optimal q-axis voltage value is calculated.

10. A permanent magnet synchronous motor control system based on the permanent magnet synchronous motor compound control method according to any one of claims 1 to 9, characterized in that, Including: A load observer, taking the electromagnetic torque output by the permanent magnet synchronous motor, the rotor mechanical speed at the current time and the previous time as input, and outputting a real-time load estimation value; An explicit model predictive controller, taking the q-axis current value, rotor mechanical speed and real-time load estimation value at the current time as input, and outputting an optimal q-axis voltage value; A Clack transformation module, taking three-phase stator currents as input, and outputting two-phase stator currents in the stationary coordinate system; A Park transformation module, taking the two-phase stator currents in the stationary coordinate system as input, and outputting a d-axis current value and a q-axis current value; A d-axis PI controller, taking the d-axis current value as input, and outputting a d-axis voltage value; A Park inverse transformation module, taking the d-axis voltage value and the optimal q-axis voltage value as input, and outputting a voltage value in the stationary coordinate system; An SVPWM module, taking the voltage value in the stationary coordinate system as input, and outputting a PWM wave; A three-phase inverter, taking the PWM wave as input, and supplying power for the permanent magnet synchronous motor.

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