Permanent magnet synchronous motor sensorless model prediction speed control method

Abstract

The invention discloses a permanent magnet synchronous motor sensorless model prediction speed control method, which comprises the following steps of: firstly, modeling a mathematical model of a permanent magnet synchronous motor to obtain the mathematical model of the permanent magnet synchronous motor; then constructing and designing a sliding-mode observer with adaptive gain; carrying out permanent magnet flux linkage parameter identification by adopting a multi-new information extended Kalman filtering method based on a forgetting factor least square method; the parameter identification value of the permanent magnet flux linkage is introduced into a motor rotating speed estimation and model prediction module, and the stator current at the k + 1 moment and the rotating speed at the k + 2 moment are predicted; and finally, designing a cost function, and adding a weight coefficient to realize the optimal control performance of the permanent magnet synchronous motor. According to the method, the problem of position sensorless control robustness performance prediction by a traditional model in the prior art is solved.

Description

Technical Field

[0001] This invention belongs to the field of high-performance permanent magnet synchronous motor control technology, specifically relating to a sensorless model predictive speed control method for permanent magnet synchronous motors. Background Technology

[0002] With the rapid development of scientific theories, production technologies, and modern industry, the position and speed control of high-performance permanent magnet synchronous motor servo drive systems, characterized by fast response and high precision, are widely used in 3D printers, robots, universal joint mechanisms, machine tools, medical equipment, and other applications.

[0003] In recent years, model predictive control (MMC) has received widespread attention in the field of motor control as an advanced control strategy. Traditional MMC employs a dual-closed-loop structure consisting of an outer speed control loop and an inner model predictive control loop. The speed loop parameters require adjustment, increasing system complexity. Model predictive speed control eliminates the speed loop, adopting a single-loop control structure and improving the system's dynamic response speed.

[0004] High-performance control and stable, reliable operation of permanent magnet synchronous motors rely heavily on rotor position information. When using a voltage-source inverter to power the motor, voltage and current sensors installed on the inverter's output side can measure the stator voltage and current. However, obtaining rotor position information often requires a position sensor. High-precision position sensors are not only expensive but also reduce system reliability. Sensorless control technology can solve many problems that mechanical sensors bring to speed control systems; therefore, sensorless technology has become one of the cutting-edge technologies in the field of electrical speed control.

[0005] Meanwhile, the performance of model predictive control heavily depends on the accuracy of the motor's mathematical model. In actual operation, motor parameters (such as permanent magnet flux linkage) can change due to factors such as temperature rise and saturation, leading to model mismatch, reduced prediction accuracy, and consequently affecting the stability and dynamic performance of the entire sensorless control system. Therefore, obtaining accurate motor parameters online has become a key challenge in improving the performance of model predictive sensorless control of permanent magnet synchronous motors. Summary of the Invention

[0006] The purpose of this invention is to provide a sensorless model predictive speed control method for permanent magnet synchronous motors, which solves the problem of robust performance of traditional model predictive sensorless control in the prior art.

[0007] The technical solution adopted in this invention is a sensorless model predictive speed control method for permanent magnet synchronous motors, which is implemented according to the following steps: Step 1: Model the mathematical model of the permanent magnet synchronous motor to obtain the mathematical model of the permanent magnet synchronous motor; Step 2: Construct and design an adaptive gain sliding mode observer; Step 3: Identify the flux linkage parameters of the permanent magnet using the multi-new information extended Kalman filter method based on the forgetting factor least squares method; Step 4: Introduce the parameter identification of the permanent magnet flux linkage into the motor speed estimation and model prediction module. Step 5: Predict the stator current at time k+1 and the rotational speed at time k+2; Step 6: Design the cost function and add weighting coefficients to achieve the optimal control performance of the permanent magnet synchronous motor.

[0008] The invention is further characterized in that, Step 1 is implemented in the following steps: At three-phase rest abc A mathematical model of a surface-mounted permanent magnet synchronous motor (SPMSM) is established in a coordinate system, under three-phase stationary conditions. abc Coordinate transformation to two-phase rotation in coordinate system d - q coordinate system, obtained d - q The mathematical model in the coordinate system is shown below: Voltage equation: (1) In the formula, , for d shaft and q Shaft-stator voltage components, , for d shaft and q Shaft stator current components, , for d shaft and q Shaft stator flux linkage components, R s For stator resistance, This refers to the rotor angular velocity; The flux linkage equation is: (2) In the formula, For permanent magnet flux linkage, SPMSM quadrature and direct axis inductance ; The torque equation is: (3) In the formula, p It is the extreme logarithm; The equation of motion is: (4) In the formula, For load torque, For rotational inertia, For electromagnetic torque, B The coefficient of viscous friction, This refers to the mechanical angular velocity.

[0009] Step 2 is implemented in the following steps: Step 201: Select the mathematical model established in Step 1 and transform it to a two-phase stationary state. Design a sliding mode observer in a coordinate system, with both phases stationary. Voltage equation in coordinate system: (5) In the formula, , for shaft and Shaft-stator voltage components, , for shaft and Shaft stator current components, and express The extended back electromotive force of the shaft, Rotor position; Convert equation (5) into the form of a current state equation: (6) Design the Sliding Mode Observer (SMO) expression: (7) In the formula, and This represents the estimated current value. and The control input for the sliding mode observer is expressed as: (8) In the formula, h For sliding mode gain, when the estimated current value is greater than the actual value, the control input of the sliding mode observer is a positive number, and the sign function is selected. This is the switching function; Step 202: Analyze the requirements that the sliding mode gain should meet when the observer is stable. Subtracting equation (6) from equation (7) yields the error equation for the stator current: (9) In the formula, , It is an error in current observation. Sliding mode gain in equation (8) h Regarding current observations and Whether it converges and converges to the actual value and The velocity is determined by defining the sliding surface function. Steps 1 and 2 define the sliding surface: (10) For the sliding surface in step 1, select an appropriate sliding gain. h When the observed current and the actual current satisfy the sliding surface equation (10), and the difference between them is 0, then the state... It will reach and remain on the sliding surface. To analyze the stability of the sliding observer, the Lyapunov equation is defined: (11) According to the Lyapunov stability principle, when the Lyapunov equations satisfy... When the system is asymptotically stable, taking the derivative of equation (11) gives: (12) For SMO to be stable and convergent, according to equation (12), the following must be satisfied: (13) Based on equation (13), the sliding mode gain requirement is derived and simplified to obtain: (14) At this point, the system state reaches the sliding surface, and the current observation error is 0. Therefore, equation (9) can be written as: (15) According to equation (8), we have: (16) Step 203: The super-twisting algorithm addresses the discontinuous parts in the sliding mode switching term. Integral calculations were performed, and the trajectory within the second-order sliding mode control surface hovers around the origin, with the basic form as follows: (17) In the formula, For system state variables, For the first i The error between the actual and estimated values ​​of each state variable Indicates the first i The perturbation of each state variable k i It is the first i The sliding mode gain of each state variable, and k i >0; In the above formula, "." represents the derivative of the variable, and the same applies below; Combining equations (7) and (17), the sliding mode observer based on the super-twistin algorithm is designed as follows: (18) In the formula, h 1 and h 2 is the sliding mode gain; Combining equations (17) and (18), the disturbance coefficient is designed as follows: (19) Subtracting equation (6) from equation (18) yields the current error equation: (20) In the formula, , It is an error in current observation; When the sliding mode observer system reaches stability, i.e., the estimation error reaches... At this point, the estimated value is approximately the actual value, and the estimated back electromotive force is obtained according to equation (20): (twenty one) Step 204: Introduce a linear correction term for the observation error to improve the observer performance. Compare equation (17) by adding the correction term. and The specific structure is as follows: (twenty two) In the formula, h 1 ，h 2 ，h 3 ，h 4 represents the sliding mode gain, where the perturbation coefficient must satisfy the following formula: (twenty three) In the formula, the parameters Used to adjust the proportion of each part, requiring ; for Combining equations (22) and (18), the SMO based on the linear super-twisting algorithm with added correction terms is obtained as follows: (twenty four) At this point, subtracting equation (6) from equation (24) yields the current error equation: (25) In the formula, Let be the disturbance quantity, represented by the linear component of the disturbance and other small disturbances. The sum of these is: (26) The estimated back electromotive force is obtained from equation (25): (27) Step 205: Traditional fixed-gain SMOs struggle to simultaneously achieve convergence speed and chatter suppression. This invention employs adaptive gain, which automatically adjusts the gain according to operating conditions. Based on step 204, a time-varying gain is designed. The specific structure of the SMO is improved according to equation (24): (28) The adaptive gain design is as follows: (29) In the formula, As the integration factor, the initial gain is set to a small positive number, always satisfying... Therefore, the back electromotive force of the adaptive gain SMO is estimated by equation (28). , Similarly; (30) Step 206: Based on the calculations in step 205 and The position and angle information of the rotor are calculated using the arctangent function. Then, the angular velocity is obtained by differentiating the angle. ,Right now: (31) (32).

[0010] Step 3 is implemented in the following steps: Step 301: The essence of the least squares method is to obtain unknown data based on known data. Assume... and Given two sets of data matrices, we have n Group data input, with the following formula: (33) In the formula, For the input observation matrix, Let be the matrix of parameters to be observed. To output the observation matrix; make Substituting the parameter matrix estimate into equation (33) yields the fitted output observation matrix: The residual is defined as: The residuals are used to evaluate whether the estimated matrix of the observed parameters is close to the true matrix of the observed parameters. The analytical solution of the parameter matrix estimate obtained by the least squares method is: (34) The solution to the observation parameter matrix obtained from equation (34) is: (35) The least squares method minimizes the sum of squares of the residuals, enabling the algorithm to converge quickly. Step 302: Recursive Least Squares (RLS) avoids redundant calculations in traditional least squares methods. k Time data correction k- For data at time 1, the recursive least squares method can be expressed as: (36) In the formula, for k Time-based RLS estimation of the observation parameter matrix; for k- Estimate the observation parameter matrix at time 1; for k Time correction value; The recursive expression for RLS is: (37) In the formula, P ( k ) is the RLS covariance matrix. K ( k ) is the RLS gain matrix. I It is the identity matrix; Step 303: The permanent magnet synchronous motor rotates in two phases. d - q In the coordinate system, neglecting the inductor voltage drop in steady state, the voltage equation simplifies to: (38) According to equation (38), let the input matrix Parameter matrix to be identified Output matrix ; Based on the RLS in step 302, a forgetting factor is introduced into the data before the current time step. According to equation (37), the recursive least squares (FFRLS) expression with forgetting factor is obtained as follows: (39) In the formula, P ( k ) is the FFRLS covariance matrix. K ( k) is the FFRLS gain matrix. I For identity matrix, forgetting factor Take a value between 0 and 1, and let the initial state be... , ,in To ensure large real numbers, For sufficiently small real numbers; In summary, the inductance is obtained L Estimate the predicted value; Step 304: The state equations and measurement equations of the Kalman filter system under linear system conditions are expressed as follows: (40) In the formula, A ( t )for n × n The state transition matrix, x ( t )for n dimensional state vector, Differentiate the state vector. B ( t )for n × r The control matrix, u ( t )for r × n Dimensional control input vector, m ( t )for n Dimensional process noise, y ( t )for m 3D measurement vector, C ( t )for m × n The measurement transformation matrix, v ( t )for m Measurement noise, with a mean of zero and a variance of . R ( k Its value has no effect on the system noise in the state equation; Equation (40) represents the state equation and measurement equation of a continuous nonlinear system, and a Taylor series expansion is performed: (41) In the formula, , State estimate x The function, for x The estimated value, u As the system input, equation (41) is expressed in the form of an estimate as follows: (42) Ignore the higher-order terms in equation (41) and And by subtracting from equation (42), we get: (43) In the formula, Indicates the difference. F ( t )and H ( t The Jacobian matrix of partial derivative terms is defined as follows: (44) The state equation and measurement equation obtained after discretizing equation (43) are as follows: (45) Among them, when sampling time T s When the value is sufficiently small, the nonlinear system is transformed into a linear system, and the state transition matrix is... and measurement matrix Represented as: (46) When the system is running, In order to be in k The best result obtained from parameter estimation at any given time is set as the optimal estimate; if at this time, using... k Before and k Estimate from the measurement of time have to , is defined as the posterior estimate; conversely, if using k Before that time, it did not include k The time can be estimated to get , defined as the prior estimate, and the optimal estimate at the previous time step: (47) Therefore, the five recursive formulas of the EKF algorithm for discrete nonlinear systems are as follows: (1) State prediction The prior estimate is obtained from the posterior estimate at time k-1 and the control input to predict the prior estimate at time k, according to equation (47). (48) (2) Covariance prediction The uncertainty used to calculate the prior state estimate is expressed by combining equation (46) as follows: (49) Among them, due to process noise covariance matrix ,but for The covariance matrix, the covariance of the prior estimation error , The covariance of the state estimation error; (3) Calculate the Kalman gain To weigh the reliability of prior state estimates against observed values, combined with equations (46) and (49), it can be expressed as: (50) In the formula, To measure noise The covariance matrix; (4) Status update use k Time observation value Corrected prior state estimation Combining equations (45), (46), (48), and (50), we obtain k Posterior state estimation at time step: (51) (5) Covariance update The uncertainty used to update the posterior state estimate, combined with the expressions (46), (49), and (50), is as follows: (52) Step 305: Define the new information as: (53) In the formula, For the latest information at the current moment, Given the information system from the previous time step, we have: (54) The gain matrix of MIEKF is expressed as: (55) Combining equations (54) and (55), we obtain the posterior optimal estimate. p* The length of new information is represented by an average weighted average. (56) Based on equations (48), (49), (50), (51), (52) obtained in step 304 and equation (56), the five recursive formulas for the discrete nonlinear system MIEKF are as follows: (57) Step 306: When using MIEKF to identify the parameters of the PMSM, it is approximately assumed that the motor speed remains basically unchanged. The state equation of the PMSM is: (58) Discretize equation (58) using the Euler discretization method of the preceding term: (59) The estimated values ​​of the motor parameters, ignoring noise, are as follows: The output equation is: Set the measurement matrix: .

[0011] The state transition matrix, expressed in terms of motor parameters, is as follows: (60) In the formula, and Expressed using motor parameters: (61) During parameter tuning, considering the complexity of parameter identification and the presence of noise interference, the initial values ​​of the covariance matrix, system noise matrix, and measurement noise matrix are tuned using a trial-and-error method. Substituting the parameters from step 306 into the above process in step 3 yields the online [parameters / values]. The parameters are identified, and the identified permanent magnet flux linkage parameters are denoted as follows: .

[0012] Step 4 is implemented in the following steps: Step 401: The estimated rotor position obtained in step 3 is as follows: (62) The estimated rotational speed can be obtained by differentiating the rotor position: (63) Step 402: According to equation (4), ignoring the influence of friction, and with p as the differential operator, construct the state equation of PMSM: (64) Based on equation (64), and taking motor speed and load torque as the observation objects, a sliding mode load torque observer is established as follows: (65) in: (66) In the formula, This is an estimated value for the rotor's mechanical angular velocity. k For sliding mode gain, U 0 represents the traditional approximation rate; Define the speed estimation error Subtracting equation (64) from equation (65) yields the sliding mode error equation: (67) The speed estimation error is defined as the sliding surface, i.e. According to sliding mode control theory, when the system enters steady state and slides around the sliding surface, the following condition is met: At this point, the load torque can be estimated as: (68) Considering the discontinuity of the sign function and the presence of high-frequency noise in the load torque observations, which may cause system chattering, a first-order low-pass filter is added. After filtering out higher harmonics, the estimated load torque value is expressed as follows according to equation (68): (69) In the formula, ω c This is the cutoff frequency of the low-pass filter; s For the Laplace operator.

[0013] Step 5 is implemented in the following steps: Substituting equation (3) into equation (4), and discretizing it using the Euler method of the first term, we introduce the SMO estimate. and identification parameters renew, To predict the step size, the discrete equation of motion is obtained as follows: (70) Discretize equation (1) using the Euler method for the first term, and introduce the estimated and identified parameters to obtain the predicted value of the stator current: (71) According to equation (70), in order to unify the timing of velocity prediction and current prediction, when predicting the current at time k+1, the velocity at time k+2 is predicted, while considering delay compensation, resulting in the prediction model: (72).

[0014] The corrected cost function for predictive speed control of the sensorless permanent magnet synchronous motor model constructed in step 6 is as follows: (73) In the formula, and Given a value, the limiting term .

[0015] Weighting factors of the cost function in step 6 and Select the per-unit value based on the given value: (74).

[0016] The beneficial effects of this invention are that the sensorless model predictive speed control method for permanent magnet synchronous motors introduces an adaptive gain sliding mode observer to estimate the rotor position of the motor. It uses a predictive model to predict and control the stator current and speed, and introduces a permanent magnet flux linkage parameter identification module to update the permanent magnet flux linkage in real time, thereby improving the performance of the observer and model predictive control.

[0017] First, addressing the challenge of traditional fixed-gain SMOs simultaneously achieving high convergence speed and chatter suppression, this invention designs a variable-gain sliding mode observer based on the super-twisting algorithm, taking into account the effects of external disturbances. The sliding mode gain can be automatically adjusted according to the stator current. For the discontinuous portion in the sliding mode switching term... Integral calculations were performed, resulting in continuity and improved system dynamic performance. The improved sliding mode observer is more suitable for practical applications because it does not require derivative values ​​of state variables, and its finite-time convergence is more accurate.

[0018] Secondly, FFRLS-MIEKF was used for online identification of permanent magnet flux linkage parameters. EKF can simultaneously identify parameters and states of nonlinear systems and effectively handle state parameter estimation and data correction in linear systems. It fully considers the influence of system noise and measurement noise. The input of more new information can improve estimation accuracy, reduce noise influence, and enhance system robustness. At the same time, the addition of FFRLS-assisted online identification of EKF also makes the identification results more accurate.

[0019] Finally, this invention employs model predictive speed control, eliminating the speed loop and using a single-loop control structure, thereby improving the dynamic response speed of the system.

[0020] In summary, this invention improves the robustness of sensorless model predictive control of permanent magnet synchronous motors, effectively enhancing prediction accuracy and motor control capabilities. Attached Figure Description

[0021] Figure 1 This is a control block diagram of the sensorless model predictive speed control method for permanent magnet synchronous motors in this invention; Figure 2 This is a diagram showing the relationship between the parameter identification, improved SMO, and prediction modules in this invention. Figure 3 This is a basic voltage vector block diagram of the two-level inverter in this invention; Figure 4 This is a block diagram of a two-level voltage source inverter in this invention. Detailed Implementation

[0022] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0023] Example 1 The present invention provides a sensorless model predictive speed control method for permanent magnet synchronous motors, the flowchart of which is shown below. Figure 1 As shown, please follow these steps: Step 1: Based on two-phase rotation dq A coordinate system is used to model the mathematical model of the permanent magnet synchronous motor, resulting in the mathematical model of the permanent magnet synchronous motor. Step 1 is implemented in the following steps: like Figure 4 The diagram shows the circuit of a permanent magnet synchronous motor under the control of a two-level voltage source inverter, in the three-phase stationary state. abc A mathematical model of a surface-mounted permanent magnet synchronous motor (SPMMSM) is established in a coordinate system, under three-phase stationary conditions. abc Coordinate transformation to two-phase rotation in coordinate system d - q coordinate system, obtained d - q The mathematical model in the coordinate system is shown below: Voltage equation: (1) In the formula, , for d shaft and q Shaft-stator voltage components, , for d shaft and q Shaft stator current components, , for d shaft and q Shaft stator flux linkage components, R s For stator resistance, This refers to the rotor angular velocity; The flux linkage equation is: (2) In the formula, For permanent magnet flux linkage, SPMSM quadrature and direct axis inductance ; The torque equation is: (3) In the formula, p It is the extreme logarithm; The equation of motion is: (4) In the formula, For load torque, For rotational inertia, For electromagnetic torque, B The coefficient of viscous friction, This refers to the mechanical angular velocity.

[0024] Step 2: Based on the two-phase rotation of the permanent magnet synchronous motor obtained in Step 1 dq Mathematical models in coordinate systems, Figure 2 In the improved SMO module, an adaptive gain sliding mode observer is built and designed to obtain the estimated back EMF and extract rotor position and speed information. Step 2 is implemented in the following steps: Step 201, considering two-phase rotation d - q The coordinate system observer needs to obtain the rotor position in advance, leading to a circular dependency problem in the sensorless system. Therefore, the mathematical model established in step 1 is transformed to a two-phase stationary state via coordinate transformation. Design a sliding mode observer in a coordinate system, with both phases stationary. Voltage equation in coordinate system: (5) In the formula, , for shaft and Shaft-stator voltage components, , for shaft and Shaft stator current components, and express The extended back electromotive force of the shaft, Rotor position; Convert equation (5) into the form of a current state equation: (6) Design the Sliding Mode Observer (SMO) expression: (7) In the formula, and This represents the estimated current value. and The control input for the sliding mode observer is expressed as: (8) In the formula, hFor sliding mode gain, when the estimated current value is greater than the actual value, the control input of the sliding mode observer is a positive number, and the sign function is selected. This is the switching function; Step 202: Analyze the requirements that the sliding mode gain should meet when the observer is stable. Subtracting equation (6) from equation (7) yields the error equation for the stator current: (9) In the formula, , It is an error in current observation. Sliding mode gain in equation (8) h Regarding current observations and Whether it converges and converges to the actual value and The speed when the sliding mode gain h If the value is too large, the observed values ​​will converge to the actual values ​​quickly, but this will cause the observed values ​​to fluctuate violently and the estimation error will increase. Therefore, it is necessary to select an appropriate sliding mode gain value. Define the sliding surface function. Step 1 , Step 2 Defined sliding surface: (10) For the sliding surface in step 1, select an appropriate sliding gain. h When the observed current and the actual current satisfy the sliding surface equation (10), and the difference between them is 0, then the state... This allows the back electromotive force to be reached and maintained on the sliding surface, thus enabling precise extraction of the back electromotive force. To analyze the stability of the sliding mode observer, the Lyapunov equation is defined: (11) According to the Lyapunov stability principle, when the Lyapunov equations satisfy... When the system is asymptotically stable, taking the derivative of equation (11) gives: (12) For SMO to be stable and convergent, according to equation (12), the following must be satisfied: (13) Based on equation (13), the sliding mode gain requirement is derived and simplified to obtain: (14) At this point, the system state reaches the sliding surface, and the current observation error is 0. Therefore, equation (9) can be written as: (15) According to equation (8), we have: (16) Step 203: This invention applies the super-twisting algorithm to the sensorless control of SMOs to construct a second-order sliding mode observer. As long as the sliding mode gain is set higher than the estimation error of the back electromotive force, the sliding mode gain is small, thereby reducing chattering. The sliding mode observer designed using this method is more suitable for practical applications because it does not require the derivative values ​​of state variables, and its finite-time convergence is more accurate.

[0025] The super-twisting algorithm addresses the discontinuous parts of the sliding mode switching term. Integral calculations were performed, improving the system's dynamic performance and providing continuity. The trajectory within the second-order sliding mode control surface hovers around the origin, with the basic form as follows: (17) In the formula, For system state variables, For the first i The error between the actual and estimated values ​​of each state variable Indicates the first i The perturbation of each state variable k i It is the first i The sliding mode gain of each state variable, and k i >0; In the above formula, "." represents the derivative of the variable, and the same applies below; Combining equations (7) and (17), the sliding mode observer based on the super-twistin algorithm is designed as follows: (18) In the formula, h 1 and h 2 is the sliding mode gain; Combining equations (17) and (18), the disturbance coefficient is designed as follows: (19) Subtracting equation (6) from equation (18) yields the current error equation: (20) In the formula, , It is an error in current observation; When the sliding mode observer system reaches stability, i.e., the estimation error reaches... At this point, the estimated value is approximately the actual value, and the estimated back electromotive force is obtained according to equation (20): (twenty one) Step 204: Introduce a linear correction term for the observation error to improve the observer's performance, enabling the system to handle linearly growing disturbances. Compare equation (17) with the addition of the correction term. and The specific structure is as follows: (twenty two) In the formula, h 1 ，h 2 ，h 3 ，h 4 represents the sliding mode gain, where the perturbation coefficient must satisfy the following formula: (twenty three) In the formula, the parameters Used to adjust the proportion of each part, requiring ; for Combining equations (22) and (18), the SMO based on the linear super-twisting algorithm with added correction terms is obtained as follows: (twenty four) At this point, subtracting equation (6) from equation (24) yields the current error equation: (25) In the formula, Let be the disturbance quantity, represented by the linear component of the disturbance and other small disturbances. The sum of these is: (26) The estimated back electromotive force is obtained from equation (25): (27) Step 205: Traditional fixed-gain SMOs struggle to simultaneously achieve convergence speed and chatter suppression. This invention employs adaptive gain, which automatically adjusts the gain according to operating conditions. Based on step 204, a time-varying gain is designed. The specific structure of the SMO is improved according to equation (24): (28) The adaptive gain design is as follows: (29) In the formula, As the integration factor, the initial gain is set to a small positive number, always satisfying... Therefore, the back electromotive force of the adaptive gain SMO is estimated by equation (28). , Similarly; (30) Step 206: The sliding mode observer used in this invention places the high-frequency switching part in the integrator to achieve the correction effect. Therefore, it is not necessary to filter out the high-frequency signal through a low-pass filter, thus avoiding the phase delay caused by the low-pass filter. Based on the calculations in step 205... and The position and angle information of the rotor are calculated using the arctangent function. Then, the angular velocity is obtained by differentiating the angle. ,Right now: (31) (32).

[0026] Step 3, in Figure 2 In the parameter identification module, the multi-new information extended Kalman filter method based on the forgetting factor least squares method is used to identify the permanent magnet flux linkage parameters. The forgetting factor least squares method is used to optimize the identification process of the permanent magnet flux linkage by the new information extended Kalman filter, thereby achieving more accurate tracking of the permanent magnet flux linkage. Step 3 is implemented in the following steps: Step 301: The essence of the least squares method is to obtain unknown data based on known data. Assume... and Given two sets of data matrices, we have n Group data input, with the following formula: (33) In the formula, For the input observation matrix, Let be the matrix of parameters to be observed. To output the observation matrix; make Substituting the parameter matrix estimate into equation (33) yields the fitted output observation matrix: The residual is defined as: The residuals are used to evaluate whether the estimated matrix of the observed parameters is close to the true matrix of the observed parameters. The analytical solution of the parameter matrix estimate obtained by the least squares method is: (34) The solution to the observation parameter matrix obtained from equation (34) is: (35) The least squares method minimizes the sum of squares of the residuals, enabling the algorithm to converge quickly. Step 302: Recursive Least Squares (RLS) avoids redundant calculations in traditional least squares methods. k Time data correction k-For data at time 1, the recursive least squares method can be expressed as: (36) In the formula, for k Time-based RLS estimation of the observation parameter matrix; for k- Estimate the observation parameter matrix at time 1; for k Time correction value; The recursive expression for RLS is: (37) In the formula, P ( k ) is the RLS covariance matrix. K ( k ) is the RLS gain matrix. I It is the identity matrix; Step 303: The permanent magnet synchronous motor rotates in two phases. d - q In the coordinate system, neglecting the inductor voltage drop in steady state, the voltage equation simplifies to: (38) According to equation (38), let the input matrix Parameter matrix to be identified Output matrix ; Based on the RLS in step 302, a forgetting factor is introduced into the data before the current time step. To obtain a better solution, smaller weights are assigned. Based on equation (37), the expression for the Forgetting Factor Recursive Least Squares (FFRLS) method is: (39) In the formula, P ( k ) is the FFRLS covariance matrix. K ( k ) is the FFRLS gain matrix. I For identity matrix, forgetting factor Take a value between 0 and 1, and let the initial state be... , ,in To ensure large real numbers, For sufficiently small real numbers; In summary, the inductance is obtained L Estimate the predicted value; Step 304: The motor model itself is a nonlinear, multivariable system, making it difficult to solve the problem of motor parameter identification using traditional Kalman filtering methods. Extended Kalman Filtering (EKF) can simultaneously identify the parameters and states of a nonlinear system, effectively handle state parameter estimation and data correction, fully consider the influence of system noise and measurement noise, and also has filtering capabilities.

[0027] The state equations and measurement equations of a Kalman filter system in a linear system are expressed as follows: (40) In the formula, A ( t )for n × n The state transition matrix, x ( t )for n dimensional state vector, Differentiate the state vector. B ( t )for n × r The control matrix, u ( t )for r × n Dimensional control input vector, m ( t )for n Dimensional process noise, y ( t )for m 3D measurement vector, C ( t )for m × n The measurement transformation matrix, v ( t )for m Measurement noise, with a mean of zero and a variance of . R ( k Its value has no effect on the system noise in the state equation; Equation (40) represents the state equation and measurement equation of a continuous nonlinear system, and a Taylor series expansion is performed: (41) In the formula, , State estimate x The function, for x The estimated value, u As the system input, equation (41) is expressed in the form of an estimate as follows: (42) Ignore the higher-order terms in equation (41) and And by subtracting from equation (42), we get: (43) In the formula, Indicates the difference. F ( t )and H ( t The Jacobian matrix of partial derivative terms is defined as follows: (44) The state equation and measurement equation obtained after discretizing equation (43) are as follows: (45) Among them, when sampling time T s When the value is sufficiently small, the nonlinear system is transformed into a linear system, and the state transition matrix is... and measurement matrix Represented as: (46) When the system is running, In order to be in k The best result obtained from parameter estimation at any given time is set as the optimal estimate; if at this time, using... k Before and k Estimate from the measurement of time achievable , is defined as the posterior estimate; conversely, if using k Before that time, it did not include k The time can be estimated to get The posterior estimate is defined as the prior estimate. Since the posterior estimate contains more estimation information, it is closer to the true value than the prior estimate.

[0028] The optimal estimate at the previous time step was: (47) Therefore, the five recursive formulas of the EKF algorithm for discrete nonlinear systems are as follows: (1) State prediction The prior estimate is obtained from the posterior estimate at time k-1 and the control input to predict the prior estimate at time k, according to equation (47). (48) (2) Covariance prediction The uncertainty used to calculate the prior state estimate is expressed by combining equation (46) as follows: (49) Among them, due to process noise covariance matrix ,but for The covariance matrix, the covariance of the prior estimation error , The covariance of the state estimation error; (3) Calculate the Kalman gain To weigh the reliability of prior state estimates against observed values, combined with equations (46) and (49), it can be expressed as: (50) In the formula, To measure noise The covariance matrix; (4) Status update use k Time observation value Corrected prior state estimation Combining equations (45), (46), (48), and (50), we obtain k Posterior state estimation at time step: (51) (5) Covariance update The uncertainty used to update the posterior state estimate, combined with the expressions (46), (49), and (50), is as follows: (52) Step 305: Under the current system state estimation and control input conditions, the difference between the actual observation and the predicted observation is defined as new information, reflecting the error between the model prediction and the actual measurement. Ordinary EKF can only use a single new piece of information, while Multi-innovation Extended Kalman Filtering (MIEKF) can use two or more new pieces of information for updates, improving estimation accuracy, reducing noise impact, and enhancing system robustness.

[0029] Define the new information as: (53) In the formula, For the latest information at the current moment, Given the information system from the previous time step, we have: (54) The gain matrix of MIEKF is expressed as: (55) Combining equations (54) and (55), we obtain the posterior optimal estimate. p* The length of new information is represented by an average weighted average. (56) Based on equations (48), (49), (50), (51), (52) obtained in step 304 and equation (56), the five recursive formulas for the discrete nonlinear system MIEKF are as follows: (57) Step 306: When using MIEKF to identify the parameters of the PMSM, it is approximately assumed that the motor speed remains basically unchanged. The state equation of the PMSM is: (58) Discretize equation (58) using the Euler discretization method of the preceding term: (59) The estimated values ​​of the motor parameters, ignoring noise, are as follows: The output equation is: Set the measurement matrix: .

[0030] The state transition matrix, expressed in terms of motor parameters, is as follows: (60) In the formula, and Expressed using motor parameters: (61) During parameter tuning, considering the complexity of parameter identification and the presence of noise interference, the initial values ​​of the covariance matrix, system noise matrix, and measurement noise matrix are tuned using a trial-and-error method. Substituting the parameters from step 306 into the above process in step 3 yields the online [parameters / values]. The parameters are identified, and the identified permanent magnet flux linkage parameters are denoted as follows: .

[0031] Step 4, as follows Figure 2 As shown, the parameter identification of permanent magnet flux linkage is introduced into the motor speed estimation and model prediction module to improve the robustness of the system, and a sliding mode load torque observer is established to estimate the load torque. Step 4 is implemented in the following steps: Step 401: The estimated rotor position obtained in step 3 is as follows: (62) The estimated rotational speed can be obtained by differentiating the rotor position: (63) Step 402: According to equation (4), ignoring the influence of friction, and with p as the differential operator, construct the state equation of PMSM: (64) Based on equation (64), and taking motor speed and load torque as the observation objects, a sliding mode load torque observer is established as follows: (65) in: (66) In the formula, This is an estimated value for the rotor's mechanical angular velocity. k For sliding mode gain, U 0 represents the traditional approximation rate; Define the speed estimation error Subtracting equation (64) from equation (65) yields the sliding mode error equation: (67) The speed estimation error is defined as the sliding surface, i.e. According to sliding mode control theory, when the system enters steady state and slides around the sliding surface, the following condition is met: At this point, the load torque can be estimated as: (68) Considering the discontinuity of the sign function and the presence of high-frequency noise in the load torque observations, which may cause system chattering, a first-order low-pass filter is added. After filtering out higher harmonics, the estimated load torque value is expressed as follows according to equation (68): (69) In the formula, ω c This is the cutoff frequency of the low-pass filter; s For the Laplace operator.

[0032] Step 5: Establish a prediction model based on the mathematical model of the permanent magnet synchronous motor obtained in Step 1. Figure 2 In the prediction module, the updated estimated values ​​of permanent magnet synchronous motor speed, load torque, and current obtained in step 4 are used as inputs to the prediction model to predict the stator current at time k+1 and the speed at time k+2. Delay compensation is taken into account to obtain the predicted values ​​of stator current and speed. Step 5 is implemented in the following steps: Substituting equation (3) into equation (4), and discretizing it using the Euler method of the first term, we introduce the SMO estimate. and identification parameters renew, To predict the step size, the discrete equation of motion is obtained as follows: (70) Discretize equation (1) using the Euler method for the first term, and introduce the estimated and identified parameters to obtain the predicted value of the stator current: (71) According to equation (70), in order to unify the timing of velocity prediction and current prediction, when predicting the current at time k+1, the velocity at time k+2 is predicted, while considering delay compensation, resulting in the prediction model: (72).

[0033] Step 6: Based on the predicted stator current and rotational speed values ​​obtained in Step 5, design a cost function, add weighting coefficients, and use a rolling solution to find the voltage vector that minimizes the cost function. The spatial voltage vector distribution is as follows: Figure 3 As shown, the optimal control performance of the permanent magnet synchronous motor is achieved.

[0034] The corrected cost function for predictive speed control of the sensorless permanent magnet synchronous motor model constructed in step 6 is as follows: (73) In the formula, and Given a value, the limiting term .

[0035] Weighting factors of the cost function in step 6 and Select the per-unit value based on the given value: (74).

[0036] Example 2 The present invention provides a sensorless model predictive speed control method for permanent magnet synchronous motors, the flowchart of which is shown below. Figure 1 As shown, please follow these steps: Step 1: Based on two-phase rotation dq A coordinate system is used to model the mathematical model of the permanent magnet synchronous motor, resulting in the mathematical model of the permanent magnet synchronous motor. Step 2: Based on the two-phase rotation of the permanent magnet synchronous motor obtained in Step 1 dq Mathematical models in coordinate systems, Figure 2 In the improved SMO module, an adaptive gain sliding mode observer is constructed and designed to obtain the estimated back EMF and extract rotor position and speed information. Step 3, in Figure 2In the parameter identification module, the multi-new information extended Kalman filter method based on the forgetting factor least squares method is used to identify the permanent magnet flux linkage parameters. The forgetting factor least squares method is used to optimize the identification process of the permanent magnet flux linkage by the new information extended Kalman filter, thereby achieving more accurate tracking of the permanent magnet flux linkage. Step 4: Introduce the parameter identification of the permanent magnet flux linkage into the motor speed estimation and model prediction module, such as... Figure 2 As shown, the robustness of the system is improved, and a sliding mode load torque observer is established to estimate the load torque; Step 5: Establish a prediction model based on the mathematical model of the permanent magnet synchronous motor obtained in Step 1. Figure 2 In the prediction module, the updated estimated values ​​of permanent magnet synchronous motor speed, load torque, and current obtained in step 4 are used as inputs to the prediction model to predict the stator current at time k+1 and the speed at time k+2. Delay compensation is considered to obtain the predicted values ​​of stator current and speed. Step 6: Design a cost function based on the predicted stator current and rotational speed values ​​obtained in Step 5, and add weighting coefficients to find... Figure 3 The optimal spatial voltage vector is used to achieve optimal control performance of the permanent magnet synchronous motor.

Claims

1. A sensorless model predictive speed control method for permanent magnet synchronous motors, characterized in that, The specific steps are as follows: Step 1: Model the mathematical model of the permanent magnet synchronous motor to obtain the mathematical model of the permanent magnet synchronous motor; Step 2: Construct and design an adaptive gain sliding mode observer; Step 3: Identify the flux linkage parameters of the permanent magnet using the multi-new information extended Kalman filter method based on the forgetting factor least squares method; Step 4: Introduce the parameter identification of the permanent magnet flux linkage into the motor speed estimation and model prediction module. Step 5: Predict the stator current at time k+1 and the rotational speed at time k+2; Step 6: Design the cost function and add weighting coefficients to achieve the optimal control performance of the permanent magnet synchronous motor.

2. The sensorless model predictive speed control method for permanent magnet synchronous motors according to claim 1, characterized in that, Step 1 is implemented in the following steps: At three-phase rest abc A mathematical model of a surface-mounted permanent magnet synchronous motor (SPMSM) is established in a coordinate system, under three-phase stationary conditions. a- bc Coordinate transformation to two-phase rotation in coordinate system d - q coordinate system, obtained d - q The mathematical model in the coordinate system is shown below: Voltage equation: （1） In the formula, , for d shaft and q Shaft-stator voltage components, , for d shaft and q Shaft stator current components, , for d shaft and q Shaft stator flux linkage components, R s For stator resistance, This refers to the rotor angular velocity; The flux linkage equation is: （2） In the formula, For permanent magnet flux linkage, SPMSM quadrature and direct axis inductance ; The torque equation is: （3） In the formula, p It is the extreme logarithm; The equation of motion is: （4） In the formula, For load torque, For rotational inertia, For electromagnetic torque, B The coefficient of viscous friction, This refers to the mechanical angular velocity.

3. The sensorless model predictive speed control method for permanent magnet synchronous motors according to claim 2, characterized in that, Step 2 is implemented in the following steps: Step 201: Select the mathematical model established in Step 1 and transform it to a two-phase stationary state. Design a sliding mode observer in a coordinate system, with both phases stationary. Voltage equation in coordinate system: （5） In the formula, , for shaft and Shaft-stator voltage components, , for shaft and Shaft stator current components, and express The extended back electromotive force of the shaft, Rotor position; Convert equation (5) into the form of a current state equation: （6） Design the Sliding Mode Observer (SMO) expression: （7） In the formula, and This represents the estimated current value. and The control input for the sliding mode observer is expressed as: （8） In the formula, h For sliding mode gain, when the estimated current value is greater than the actual value, the control input of the sliding mode observer is a positive number, and the sign function is selected. This is the switching function; Step 202: Analyze the requirements that the sliding mode gain should meet when the observer is stable. Subtracting equation (6) from equation (7) yields the error equation for the stator current: （9） In the formula, , It is an error in current observation. Sliding mode gain in equation (8) h Regarding current observations and Whether it converges and converges to the actual value and The velocity is determined by defining the sliding surface function. Steps 1 and 2 define the sliding surface: （10） For the sliding surface in step 1, select an appropriate sliding gain. h When the observed current and the actual current satisfy the sliding surface equation (10), and the difference between them is 0, then the state... It will reach and remain on the sliding surface. To analyze the stability of the sliding observer, the Lyapunov equation is defined: （11） According to the Lyapunov stability principle, when the Lyapunov equations satisfy... When the system is asymptotically stable, taking the derivative of equation (11) gives: （12） For SMO to be stable and convergent, according to equation (12), the following must be satisfied: （13） Based on equation (13), the sliding mode gain requirement is derived and simplified to obtain: （14） At this point, the system state reaches the sliding surface, and the current observation error is 0. Therefore, equation (9) can be written as: （15） According to equation (8), we have: （16） Step 203: The super-twisting algorithm addresses the discontinuous parts in the sliding mode switching term. Integral calculations were performed, and the trajectory within the second-order sliding mode control surface hovers around the origin, with the basic form as follows: （17） In the formula, For system state variables, For the first i The error between the actual and estimated values ​​of each state variable Indicates the first i The perturbation of each state variable k i It is the first i The sliding mode gain of each state variable, and k i >0; In the above formula, "." represents the derivative of the variable, and the same applies below; Combining equations (7) and (17), the sliding mode observer based on the super-twistin algorithm is designed as follows: （18） In the formula, h 1 and h 2 is the sliding mode gain; Combining equations (17) and (18), the disturbance coefficient is designed as follows: （19） Subtracting equation (6) from equation (18) yields the current error equation: （20） In the formula, , It is an error in current observation; When the sliding mode observer system reaches stability, i.e., the estimation error reaches... At this point, the estimated value is approximately the actual value, and the estimated back electromotive force is obtained according to equation (20): （21） Step 204: Introduce a linear correction term for the observation error to improve the observer performance. Compare equation (17) by adding the correction term. and The specific structure is as follows: （22） In the formula, h 1 ，h 2 ，h 3 ，h 4 represents the sliding mode gain, where the perturbation coefficient must satisfy the following formula: （23） In the formula, the parameters Used to adjust the proportion of each part, requiring ; for Combining equations (22) and (18), the SMO based on the linear super-twisting algorithm with added correction terms is obtained as follows: （24） At this point, subtracting equation (6) from equation (24) yields the current error equation: （25） In the formula, Let be the disturbance quantity, represented by the linear component of the disturbance and other small disturbances. The sum of these is: （26） The estimated back electromotive force is obtained from equation (25): （27） Step 205: Traditional fixed-gain SMOs struggle to simultaneously achieve convergence speed and chatter suppression. This invention employs adaptive gain, which automatically adjusts the gain according to operating conditions. Based on step 204, a time-varying gain is designed. The specific structure of the SMO is improved according to equation (24): （28） The adaptive gain design is as follows: （29） In the formula, As the integration factor, the initial gain is set to a small positive number, always satisfying... Therefore, the back electromotive force of the adaptive gain SMO is estimated by equation (28). , Similarly; （30） Step 206: Based on the calculations in step 205 and The position and angle information of the rotor are calculated using the arctangent function. Then, the angular velocity is obtained by differentiating the angle. ,Right now: （31） （32）。 4. The sensorless model predictive speed control method for permanent magnet synchronous motors according to claim 3, characterized in that, Step 3 is implemented in the following steps: Step 301: The essence of the least squares method is to obtain unknown data based on known data. Assume... and Given two sets of data matrices, we have n Group data input, with the following formula: （33） In the formula, For the input observation matrix, Let be the matrix of parameters to be observed. To output the observation matrix; make Substituting the parameter matrix estimate into equation (33) yields the fitted output observation matrix: The residual is defined as: The residuals are used to evaluate whether the estimated matrix of the observed parameters is close to the true matrix of the observed parameters. The analytical solution of the parameter matrix estimate obtained by the least squares method is: （34） The solution to the observation parameter matrix obtained from equation (34) is: （35） The least squares method minimizes the sum of squares of the residuals, enabling the algorithm to converge quickly. Step 302: Recursive Least Squares (RLS) avoids redundant calculations in traditional least squares methods. k Time data correction k- For data at time 1, the recursive least squares method can be expressed as: （36） In the formula, for k Time-based RLS estimation of the observation parameter matrix; for k- Estimate the observation parameter matrix at time 1; for k Time correction value; The recursive expression for RLS is: （37） In the formula, P ( k ) is the RLS covariance matrix. K ( k ) is the RLS gain matrix. I It is the identity matrix; Step 303: The permanent magnet synchronous motor rotates in two phases. d - q In the coordinate system, neglecting the inductor voltage drop in steady state, the voltage equation simplifies to: （38） According to equation (38), let the input matrix Parameter matrix to be identified Output matrix ; Based on the RLS in step 302, a forgetting factor is introduced into the data before the current time step. According to equation (37), the recursive least squares (FFRLS) expression with forgetting factor is obtained as follows: （39） In the formula, P ( k ) is the FFRLS covariance matrix. K ( k ) is the FFRLS gain matrix. I For identity matrix, forgetting factor Take a value between 0 and 1, and let the initial state be... , ,in To ensure large real numbers, For sufficiently small real numbers; In summary, the inductance is obtained L Estimate the predicted value; Step 304: The state equations and measurement equations of the Kalman filter system under linear system conditions are expressed as follows: （40） In the formula, A ( t )for n × n The state transition matrix, x ( t )for n dimensional state vector, Differentiate the state vector. B ( t )for n × r The control matrix, u ( t )for r × n Dimensional control input vector, m ( t )for n Dimensional process noise, y ( t )for m 3D measurement vector, C ( t )for m × n The measurement transformation matrix, v ( t )for m Measurement noise, with a mean of zero and a variance of . R ( k Its value has no effect on the system noise in the state equation; Equation (40) represents the state equation and measurement equation of a continuous nonlinear system, and a Taylor series expansion is performed: （41） In the formula, , State estimate x The function, for x The estimated value, u As the system input, equation (41) is expressed in the form of an estimate as follows: （42） Ignore the higher-order terms in equation (41) and And by subtracting from equation (42), we get: （43） In the formula, Indicates the difference. F ( t )and H ( t The Jacobian matrix of partial derivative terms is defined as follows: （44） The state equation and measurement equation obtained after discretizing equation (43) are as follows: （45） Among them, when sampling time T s When the value is sufficiently small, the nonlinear system is transformed into a linear system, and the state transition matrix is... and measurement matrix Represented as: （46） When the system is running, In order to be in k The best result obtained from parameter estimation at any given time is set as the optimal estimate; if at this time, using... k Before and k Estimate from the measurement of time have to , is defined as the posterior estimate; conversely, if using k Before that time, it did not include k The time can be estimated to get , defined as the prior estimate, and the optimal estimate at the previous time step: （47） Therefore, the five recursive formulas of the EKF algorithm for discrete nonlinear systems are as follows: (1) State prediction The prior estimate is obtained from the posterior estimate at time k-1 and the control input to predict the prior estimate at time k, according to equation (47). （48） (2) Covariance prediction The uncertainty used to calculate the prior state estimate is expressed by combining equation (46) as follows: （49） Among them, due to process noise covariance matrix ,but for The covariance matrix, the covariance of the prior estimation error , The covariance of the state estimation error; (3) Calculate the Kalman gain To weigh the reliability of prior state estimates against observed values, combined with equations (46) and (49), it can be expressed as: （50） In the formula, To measure noise The covariance matrix; (4) Status update use k Time observation value Corrected prior state estimation Combining equations (45), (46), (48), and (50), we obtain k Posterior state estimation at time step: （51） (5) Covariance update The uncertainty used to update the posterior state estimate, combined with the expressions (46), (49), and (50), is as follows: （52） Step 305: Define the new information as: （53） In the formula, For the latest information at the current moment, Given the information system from the previous time step, we have: （54） The gain matrix of MIEKF is expressed as: （55） Combining equations (54) and (55), we obtain the posterior optimal estimate. p* The length of new information is represented by an average weighted average. （56） Based on equations (48), (49), (50), (51), (52) obtained in step 304 and equation (56), the five recursive formulas for the discrete nonlinear system MIEKF are as follows: （57） Step 306: When using MIEKF to identify the parameters of the PMSM, it is approximately assumed that the motor speed remains basically unchanged. The state equation of the PMSM is: （58） Discretize equation (58) using the Euler discretization method of the preceding term: （59） The estimated values ​​of the motor parameters, ignoring noise, are as follows: The output equation is: Set the measurement matrix: The state transition matrix, expressed in terms of motor parameters, is as follows: （60） In the formula, and Expressed using motor parameters: （61） During parameter tuning, considering the complexity of parameter identification and the presence of noise interference, the initial values ​​of the covariance matrix, system noise matrix, and measurement noise matrix are tuned using a trial-and-error method. Substituting the parameters from step 306 into the above process in step 3 yields the online [parameters / values]. The parameters are identified, and the identified permanent magnet flux linkage parameters are denoted as follows: .

5. The sensorless model predictive speed control method for permanent magnet synchronous motors according to claim 4, characterized in that, Step 4 is implemented in the following steps: Step 401: The estimated rotor position obtained in step 3 is as follows: （62） The estimated rotational speed can be obtained by differentiating the rotor position: （63） Step 402: According to equation (4), ignoring the influence of friction, and with p as the differential operator, construct the state equation of PMSM: （64） Based on equation (64), and taking motor speed and load torque as the observation objects, a sliding mode load torque observer is established as follows: （65） in: （66） In the formula, This is an estimated value for the rotor's mechanical angular velocity. k For sliding mode gain, U 0 represents the traditional approximation rate; Define the speed estimation error Subtracting equation (64) from equation (65) yields the sliding mode error equation: （67） The speed estimation error is defined as the sliding surface, i.e. According to sliding mode control theory, when the system enters steady state and slides around the sliding surface, the following condition is met: At this point, the load torque can be estimated as: （68） Considering the discontinuity of the sign function and the presence of high-frequency noise in the load torque observations, which may cause system chattering, a first-order low-pass filter is added. After filtering out higher harmonics, the estimated load torque value is expressed as follows according to equation (68): （69） In the formula, ω c This is the cutoff frequency of the low-pass filter; s For the Laplace operator.

6. The sensorless model predictive speed control method for permanent magnet synchronous motors according to claim 5, characterized in that, Step 5 is implemented in the following steps: Substituting equation (3) into equation (4), and discretizing it using the Euler method of the first term, we introduce the SMO estimate. and identification parameters renew, To predict the step size, the discrete equation of motion is obtained as follows: （70） Discretize equation (1) using the Euler method for the first term, and introduce the estimated and identified parameters to obtain the predicted value of the stator current: （71） According to equation (70), in order to unify the timing of velocity prediction and current prediction, when predicting the current at time k+1, the velocity at time k+2 is predicted, while considering delay compensation, resulting in the prediction model: （72）。 7. The sensorless model predictive speed control method for permanent magnet synchronous motors according to claim 6, characterized in that, The correction cost function for predicting speed control using the sensorless model of the permanent magnet synchronous motor in step 6 is as follows: （73） In the formula, and Given a value, the limiting term .

8. The sensorless model predictive speed control method for permanent magnet synchronous motors according to claim 7, characterized in that, The weighting factor of the cost function in step 6 and Select the per-unit value based on the given value: （74）。

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