Sensorless model prediction speed control method for synchronous reluctance motor

Abstract

The invention discloses a sensorless model prediction speed control method for a synchronous reluctance motor. The method comprises the following steps: firstly, establishing a mathematical model of the synchronous reluctance motor; then constructing a model reference adaptive system; an improved adaptive law combining mechanical and electromagnetic models is constructed; and deducing a linearization model, and performing linearization approximation on the IAL-MRAS error system containing a nonlinear feedback link near a working point to obtain the linearization model and a transfer function of the IAL-MRAS error system. And finally, establishing a prediction model to obtain a stator current prediction value and a flux linkage prediction value, and performing switching vector optimization through a cost function. By systematically improving the speed / position estimator, the dynamic performance of sensorless driving of the synchronous reluctance motor is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high-performance synchronous reluctance motor control, and particularly relates to a synchronous reluctance motor sensorless model predictive speed control method. BACKGROUND

[0002] High-performance control of a synchronous reluctance motor (SynRM) cannot be achieved without rotor position information, and accurate rotor absolute position information is also required, but the acquisition of motor rotor position information often requires the installation of a position sensor on the motor side. High-precision position sensors are not only expensive, but also reduce the reliability of the system. If the position sensor can be removed, i.e., sensorless control is performed, the cost of the drive system can be reduced.

[0003] In recent years, model predictive control (MPC) has received extensive attention in the field of motor control as an advanced control strategy. Traditional model predictive control adopts a double-loop structure, and the speed loop parameters need to be adjusted, which increases the complexity of the system. Model predictive direct speed control (MPDSC) is adopted, which eliminates the speed loop and adopts a single-loop control structure, improving the dynamic response speed of the system. At the same time, single-shot prediction only pursues the minimum error at the next moment, which is easy to cause overshoot and oscillation due to short-term optimization. Two-shot prediction can simulate the behavior of the system after two shots, avoid long-term risks through global optimization, achieve smoother and faster speed tracking under high-speed acceleration, load mutation and other conditions, suppress overshoot and oscillation, and make the system more robust.

[0004] Traditional MRAS performs sensorless control based only on an electromagnetic model, and when the motor encounters load fluctuations, its anti-interference ability is insufficient. IAL-MRAS can consider the mechanical factors affecting the speed change and estimate the rotor position and load torque simultaneously through linear ESO, and through the conversion of the nonlinear feedback link into a linear transfer function structure, it solves the problems of parameter tuning difficulty and system analysis complexity, thereby enhancing the robustness of the system. SUMMARY

[0005] The purpose of the present application is to provide a synchronous reluctance motor sensorless model predictive speed control method, which improves the dynamic performance of synchronous reluctance motor sensorless drive by systematically improving the speed / position estimator. This improved adaptive law combines mechanical and electromagnetic models, considers the mechanical factors affecting the speed change, and can estimate the rotor position and load torque simultaneously. In addition, the two-shot predictive model predictive speed control method is adopted, which suppresses overshoot and oscillation through advance prediction, making the system more robust.

[0006] The technical solution adopted in this invention is a sensorless model predictive speed control method for synchronous reluctance motors, which is implemented according to the following steps: Step 1: Establish a mathematical model of the synchronous reluctance motor; Step 2: Construct a model reference adaptive system; Step 3: Construct an improved adaptive law that combines mechanical and electromagnetic models; Step 4: Derive the linearized model. The IAL-MRAS error system containing nonlinear feedback is linearized and approximated near the operating point to obtain its linearized model and transfer function.

[0007] Step 5: Establish a prediction model to obtain the predicted values ​​of stator current and flux linkage, and perform switching vector optimization through a cost function.

[0008] The invention is further characterized in that, Step 1 is implemented in the following steps: The mathematical model of a synchronous reluctance motor in a two-phase rotating coordinate system is as follows: (1) (2) (3) (4) In the formula, R s Indicates stator resistance. 、 express d , q Shaft-stator voltage components, 、 express d , q Shaft stator current components, 、 express d , q Shaft stator flux linkage components, Represents electric angular velocity. 、 express d, q Shaft stator inductance component, Indicates electromagnetic torque. Represents the extreme logarithm. Indicates the load torque. It represents the moment of inertia.

[0009] Step 2 is implemented in the following steps: Step 201: Establish the matrix form of the current differential equation: (5) In the formula, p is the differential operator; Simultaneously define the following matrix , , At this point, equation (5) simplifies to: (6) Estimated speed Compared with actual speed Substituting into (5), we get: (7) In the formula, , ; Step 202: Select the reference model and the adjustable model, taking into account the state matrix. Including the speed estimation equation, equation (7) is selected as the adjustable model for generating the estimated current. The synchronous reluctance motor is used as the reference model, and the actual current is measured by a current sensor. Subtracting equation (6) from equation (7), the stator current error equation is written as: (8) In the formula, , , ; Based on equation (8), a system with the current error as the state variable is designed: (9) In the formula, , It is a linear compensation matrix; Pick 0 <k<1; Step 203: Design an adaptive law based on Popov's superstability theory. This adaptive law calculates the rotor speed based solely on the current error generated by the electromagnetic model, as shown below: (10) in, initial value .

[0010] Step 3 is implemented in the following steps: Step 301: Establish the mechanical model of the linear extended state observer (ESO): (11) In the formula, For speed prediction error, This is the actual electric angular velocity. To estimate the electric angular velocity; , For observer gain; Step 302: Derive the dynamic relationship model between the estimated load torque and the estimated speed: (12) In the formula, To estimate the time derivative of the rotational speed; This formula shows that the load torque is estimated. Compared with the estimated speed There is a definite dynamic coupling relationship between them, which provides a theoretical basis for subsequent sensorless estimation; Step 303: Construct an adaptive load torque law based on current error, and calculate the estimated values ​​of sensorless rotational speed and rotor position: To address the issue of requiring actual electrical angular velocity when observing load torque in a linear ESO, the current error of the electromagnetic model is used to replace the velocity error, utilizing the stator current reference value. With estimated current To determine the error term, construct an adaptive law for load torque: (13) In the formula, , A positive PI parameter For integration, This is the current error term.

[0011] Substituting equation (13) into the speed estimation equation of the linear ESO, we obtain the sensorless electric angular velocity estimate: (14) By integrating the estimated electrical angular velocity, the estimated value of the rotor electrical angle is obtained: (15).

[0012] Step 4 is implemented in the following steps: Step 401: Define the input and output of the linearized error system: The actual electric angular velocity As input, estimate the electric angular velocity. As output, load torque A linearized error system is constructed as the perturbation signal. Here, the variable y represents the velocity estimation error. The function reflects the coupling relationship between current error and speed error; Step 402: Derive the transition transfer function : The transition transfer function G(s) describes the velocity estimation error. The relationship between the variable y and the electromagnetic model state-space matrix of the synchronous reluctance motor is derived from the following: (16) In the formula, Stator current estimation error vector , , for dq shaft current estimate; State matrix of the electromagnetic model of synchronous reluctance motor , Stator resistance; For the characteristic matrix, For the Laplace operator; Through algebraic operations, Simplified to two-term second-order transfer functions (17) In the formula, It is the connection speed estimation error. The transition function with respect to current error; Step 403, Linearization of the equations of motion: Performing a Laplace transform on equation (4) yields the linear transfer function of torque and velocity: (18) This formula incorporates electromagnetic torque With load torque Actual electric angular velocity Related, among which This is the inertial torque term; Step 404: Construct a linearized model: a. Substitute the torque and speed relationship Substituting equation (18) into equations (13) and (14), we obtain the linearized model of IAL-MRAS, estimating the electric angular velocity and load torque as follows: (19) In the formula, the open-loop transfer function , This is the equivalent moment of inertia used in IAL-MRAS; b. Steady-state performance analysis According to the final value theorem, take equation (19) as follows: ,get: (20) From the above equation, it can be seen that even if the equivalent moment of inertia in the improved adaptive law is improved... With actual moment of inertia Different, estimating velocity in steady state Still converges to the actual speed Estimate load torque Converging to actual load torque At the same time At that time, the system dynamic error is only related to the load torque. The system exhibits optimal dynamic performance when the changes are related to the changes in the parameters.

[0013] Step 5 is implemented in the following steps: Step 501: Based on the mathematical model of the synchronous reluctance motor in the two-phase stationary coordinate system, estimate the load torque and speed using MRAS; Step 502: Based on the forward Euler discretization formula, obtain d shaft and q Predicted shaft current values: By discretizing equation (5), the predicted value for the first beat is obtained as follows: (twenty one) In the formula, express Moment d Predicted shaft current value express Moment q Predicted shaft current value for time d Measured value of shaft current, for time q Measured value of shaft current, for Rotational speed measurement value at any time for time d Shaft stator voltage value, for time q Shaft stator voltage values; Using a two-phase prediction strategy, the second-phase current prediction is derived based on the first-phase current prediction: (twenty two) In the formula, since the optimal switching vector predicted in two cycles is actually taken as the switching vector after two cycles, therefore Moment dq The shaft and stator voltage values ​​are respectively equal to time dq Shaft stator voltage values; Step 503: Establish the relationship between stator voltage and switching vector. a. First, convert the three-phase voltage to a Clarke transform. αβ Voltage: , (twenty three) b. Then, through the inverse Park transformation... αβ Voltage converted to dq Voltage: , (twenty four) c. Finally, perform the switching state and three-phase voltage conversion: (25) d. In summary: (26) Step 504: Establish a speed prediction model; Step 505: Design the cost function based on the velocity error; Step 506: Solve for the reference torque; Step 507: Solve for the q-axis reference current and finally design the cost function.

[0014] Step 504 is implemented in the following steps: Using the forward Euler discretization formula (4), the rotational speed prediction model is obtained: First prediction: (27) Second shot prediction: (28) In the formula, for The measured value of the mechanical rotation speed at any given time. express The predicted mechanical angular velocity at time i = 1, 2. express The measured value of the electromagnetic torque at time t. This represents the measured load torque value at time k. express The predicted value of the electromagnetic torque at time t. This represents the predicted load torque value at time k+1.

[0015] Also taking load torque into account It usually exhibits slow variability, so in a short period of time It can be considered a constant; the conversion relationship between mechanical angular velocity and electrical angular velocity is as follows: , The sampling period is generally taken as... for .

[0016] Step 505 is implemented in the following steps: The control objective is defined as minimizing speed error and torque error. Weighting factors are used to balance the priorities of the two, and the cost function is expressed as follows: First prediction: (29) Second shot prediction: (30) In the formula, express The reference value of the mechanical angular velocity at time k is equal in magnitude to the reference values ​​at times k and k+1. As the weight of the speed error, This is the weight of the torque error.

[0017] Step 506 shall be implemented in accordance with the following steps: Differentiating equation (29) yields: (31) Discretizing the above equation, we can obtain the reference torque at time k as follows: (32) Similarly, the reference torque at time k+1 can be obtained as follows: (33) Step 507 is implemented in the following steps: Considering that the torque of the synchronous reluctance motor is determined by... and A joint decision, and It is usually set as a constant, so it is defined as follows: (34) (35) In the formula, The torque constant can be calculated using the following formula: (36) Final cost function design: First, the stator flux linkage of the synchronous reluctance motor It can be calculated using the following formula: (37) Effective magnetic flux The definition is as follows: (38) The effective flux linkage at time k+2 is obtained from equation (38): (39) The final cost function is designed to select the optimal switching vector, with the goal of minimizing current and flux linkage errors while satisfying current constraints. Predictive control iterates through all eight switching vectors, calculates the cost function value for each vector, and selects the vector with the minimum cost as the control output for the next cycle.

[0018] (40) In the formula, This is a current constraint term; if the predicted current exceeds the maximum value of the stator current... If the cost function is infinite, then the switch vector should be excluded. To accurately calculate the stator current value after two cycles, the Lagrange extrapolation method can be used for the following calculation: (41).

[0019] The beneficial effects of this invention are that the sensorless model predictive speed control method for synchronous reluctance motors provides a series of advantages to address the technical challenges in synchronous reluctance motor control. This method, by introducing model predictive speed control and the IAL-MARS model, effectively improves the dynamic performance and disturbance rejection capability of the motor, making the control strategy more flexible and robust.

[0020] Traditional model-based speed control prediction, using a single-step prediction approach, only aims to minimize the error at the next moment, which is prone to overshoot, oscillation, or constraint violation due to the pursuit of "short-term optimality." This invention's two-step prediction framework simultaneously simulates the system behavior in the next two steps, taking into account both current and subsequent state errors. Through global optimization, it avoids long-term risks and achieves smoother and faster speed tracking under conditions such as high-speed acceleration and sudden load changes, suppressing overshoot and oscillation. Simultaneously, the extended prediction horizon makes the system more robust to model uncertainties, parameter changes, and computational delays, maintaining stable performance even when parameters have errors or the algorithm has lag.

[0021] IAL-MRAS combines mechanical and electromagnetic models, taking into account mechanical factors affecting speed changes. This overcomes the limitations of traditional MRAS, which relies solely on electromagnetic models, improving the anti-interference capability and system stability of synchronous reluctance motors. It can simultaneously estimate rotor position and load torque. Furthermore, by transforming the nonlinear feedback loop into a linear transfer function structure, it solves the problems of difficult parameter tuning and complex system analysis, thereby enhancing the system's robustness.

[0022] In summary, this invention provides a novel method for controlling synchronous reluctance motors by introducing model predictive speed control and the IAL-MRAS model. This method offers significant advantages in improving control accuracy, enhancing robustness, and refining dynamic response. These technological improvements enable synchronous reluctance motors to have a wider range of applications, especially in cost-sensitive and performance-critical scenarios. Attached Figure Description

[0023] Figure 1 This is a block diagram of the sensorless model predictive speed control method for synchronous reluctance motors according to the present invention; Figure 2 This is a model reference adaptive principle block diagram of the improved adaptive law in this invention; Figure 3 This is the basic voltage vector block diagram of the two-level voltage source inverter in this invention; Figure 4 This is a block diagram of a two-level voltage source inverter in this invention. Detailed Implementation

[0024] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0025] The synchronous reluctance motor control method proposed in this invention achieves high-performance control of the synchronous reluctance motor by combining model predictive speed control technology and IAL-MRAS. This method first establishes a mathematical model of the synchronous reluctance motor based on its two-phase rotating coordinate system, encompassing both the electrical and mechanical characteristics of the motor. By introducing load torque characteristics into the adaptive law, the motor's anti-interference capability is improved.

[0026] The improved model reference adaptive system is the core of this invention. It considers the mechanical factors affecting speed changes, improves the anti-interference capability and system stability of the synchronous reluctance motor, and can simultaneously estimate rotor position and load torque. Furthermore, by transforming the nonlinear feedback loop into a linear transfer function structure, the problems of difficult parameter tuning and complex system analysis are solved, thereby enhancing the system's robustness.

[0027] The method of this invention improves the control accuracy and stability of synchronous reluctance motors while enhancing their anti-interference capabilities, thus showing broad application prospects. This method is particularly suitable for cost-sensitive and performance-critical applications. By combining model reference adaptation with model predictive speed control, this invention provides a novel approach to improve the control performance of synchronous reluctance motors, enabling them to achieve superior performance in a wider range of applications.

[0028] Example 1 The sensorless model predictive speed control method for synchronous reluctance motors of the present invention is illustrated in the flowchart below. Figure 1As shown, please follow these steps: Step 1: Establish a mathematical model of the synchronous reluctance motor based on a two-phase rotating coordinate system; Step 1 is implemented in the following steps: Figure 4 For the circuit of a synchronous reluctance motor under the control of a two-level voltage source inverter, the mathematical model of the synchronous reluctance motor in a two-phase rotating coordinate system is as follows: (1) (2) (3) (4) In the formula, R s Indicates stator resistance. 、 express d , q Shaft-stator voltage components, 、 express d , q Shaft stator current components, 、 express d , q Shaft stator flux linkage components, Represents electric angular velocity. 、 express d, q Shaft stator inductance component, Indicates electromagnetic torque. Represents the extreme logarithm. Indicates the load torque. It represents the moment of inertia.

[0029] Step 2: Construct a Model Reference Adaptive System (MRAS), and use the error signals obtained from the reference model and the adjustable model to adaptively adjust and obtain the rotor position estimate. Step 2 is implemented in the following steps: Step 201: Establish the matrix form of the current differential equation: (5) In the formula, p is the differential operator; Simultaneously define the following matrix , , At this point, equation (5) simplifies to: (6) Estimated speed Compared with actual speed Substituting into (5), we get: (7) In the formula, , ; Step 202: Select the reference model and the adjustable model, taking into account the state matrix. Including the speed estimation equation, equation (7) is selected as the adjustable model for generating the estimated current. The synchronous reluctance motor is used as the reference model, and the actual current is measured by a current sensor. Subtracting equation (6) from equation (7), the stator current error equation is written as: (8) In the formula, , , ; Based on equation (8), a system with the current error as the state variable is designed: (9) In the formula, , It is a linear compensation matrix; Because SynRM has a significant salient pole effect, d Tiny fluctuations in shaft current can be amplified by rotational speed errors, thus generating noise. Therefore, a diagonal matrix adjustment is chosen. dq Weighting of shaft errors, optimizing error convergence speed, reducing noise, and taking... 0 <k<1; Step 203: Design an adaptive law based on Popov's superstability theory. In traditional MRAS speed estimators, the PI controller is often used as the adaptive law. This adaptive law calculates the rotor speed based solely on the current error generated by the electromagnetic model, as shown below: (10) in, initial value .

[0030] Step 3: Construct an improved adaptive law that combines mechanical and electromagnetic models, while also considering mechanical factors that affect speed changes, which can estimate rotor position and load torque through linear ESO. Step 3 is implemented in the following steps: Step 301: Establish the mechanical model of the linear extended state observer (ESO): (11) In the formula, For speed prediction error, This is the actual electric angular velocity. To estimate the electric angular velocity; , For observer gain; Step 302: Derive the dynamic relationship model between the estimated load torque and the estimated speed: (12) In the formula, To estimate the time derivative of the rotational speed; This formula shows that the load torque is estimated. Compared with the estimated speed There is a definite dynamic coupling relationship between them, which provides a theoretical basis for subsequent sensorless estimation; Step 303: Construct an adaptive load torque law based on current error, and calculate the estimated values ​​of sensorless rotational speed and rotor position: To address the issue of requiring actual electrical angular velocity when observing load torque in a linear ESO, the current error of the electromagnetic model is used to replace the velocity error, utilizing the stator current reference value. With estimated current To determine the error term, construct an adaptive law for load torque: (13) In the formula, , A positive PI parameter For integration, This is the current error term.

[0031] Substituting equation (13) into the speed estimation equation of the linear ESO, we obtain the sensorless electric angular velocity estimate: (14) By integrating the estimated electrical angular velocity, the estimated value of the rotor electrical angle is obtained: (15).

[0032] Step 4: Derive the linearized model. The IAL-MRAS error system containing nonlinear feedback is linearized and approximated near the operating point to obtain its linearized model and transfer function.

[0033] Step 4 is implemented in the following steps: Step 401: Define the input and output of the linearized error system: Neither tuning the adaptive law parameters nor further analyzing the system can handle nonlinear feedback channels. Therefore, it is necessary to linearize the error system. Using the linearized model of IAL-MRAS, the system can be analyzed using the transfer function.

[0034] like Figure 2 As shown, the actual electric angular velocity As input, estimate the electric angular velocity. As output, load torque A linearized error system is constructed as the perturbation signal. Here, the variable y represents the velocity estimation error. The function reflects the coupling relationship between current error and speed error; Step 402: Derive the transition transfer function : The transition transfer function G(s) describes the velocity estimation error. The relationship between the variable y and the electromagnetic model state-space matrix of the synchronous reluctance motor is derived from the following: (16) In the formula, Stator current estimation error vector , , for dq shaft current estimate; State matrix of the electromagnetic model of synchronous reluctance motor , Stator resistance; For the characteristic matrix, For the Laplace operator; Through algebraic operations, Simplified to two-term second-order transfer functions (17) In the formula, It is the connection speed estimation error. The transition function with respect to current error; Step 403, Linearization of the equations of motion: Performing a Laplace transform on equation (4) yields the linear transfer function of torque and velocity: (18) This formula incorporates electromagnetic torque With load torque Actual electric angular velocity Related, among which This is the inertial torque term; Step 404: Construct a linearized model: c. Substitute the torque-speed relationship Substituting equation (18) into equations (13) and (14), we obtain the linearized model of IAL-MRAS, estimating the electric angular velocity and load torque as follows: (19) In the formula, the open-loop transfer function , This is the equivalent moment of inertia used in IAL-MRAS; d. Steady-state performance analysis According to the final value theorem, take equation (19) as follows: ,get: (20) From the above equation, it can be seen that even if the equivalent moment of inertia in the improved adaptive law is improved... With actual moment of inertia Different, estimating velocity in steady state Still converges to the actual speed Estimate load torque Converging to actual load torque At the same time At that time, the system dynamic error is only related to the load torque. The system exhibits optimal dynamic performance when the changes are related to the changes in the parameters.

[0035] Step 5: Establish a prediction model to predict the electromagnetic torque and speed at time k+2, obtain the predicted values ​​of stator current and flux linkage, and perform switching vector optimization through a cost function.

[0036] Step 5 is implemented in the following steps: Step 501: Based on the mathematical model of the synchronous reluctance motor in the two-phase stationary coordinate system, estimate the load torque and speed using MRAS; Step 502: Based on the forward Euler discretization formula, obtain d shaft and q Predicted shaft current values: By discretizing equation (5), the predicted value for the first beat is obtained as follows: (twenty one) In the formula, express Moment d Predicted shaft current value express Moment q Predicted shaft current value for time d Measured value of shaft current, for time q Measured value of shaft current, for Rotational speed measurement value at any time for time d Shaft stator voltage value, for time q Shaft stator voltage values; Considering the shortcomings of single-phase prediction in practical digital systems, such as control delay and insufficient disturbance rejection capability, two-phase prediction is adopted as the control strategy. Two-phase prediction can achieve anticipatory suppression and smooth transition when facing various operating conditions, thereby improving the dynamic performance, steady-state accuracy and robustness of the control.

[0037] Based on the first-phase current prediction, the second-phase current prediction is obtained: (twenty two) In the formula, since the optimal switching vector predicted in two cycles is actually taken as the switching vector after two cycles, therefore Moment dq The shaft and stator voltage values ​​are respectively equal to time dq Shaft stator voltage values; Step 503: Establish the relationship between stator voltage and switching vector. a. First, convert the three-phase voltage to a Clarke transform. αβ Voltage: , (twenty three) b. Then, through the inverse Park transformation... αβ Voltage converted to dq Voltage: , (twenty four) c. Finally, perform the switching state and three-phase voltage conversion: (25) d. In summary: (26) Step 504: Establish a speed prediction model; Step 505: Design the cost function based on the velocity error; Step 506: Solve for the reference torque; Step 507: Solve for the q-axis reference current and finally design the cost function.

[0038] 7. The sensorless model predictive speed control method for a synchronous reluctance motor according to claim 6, characterized in that step 504 is specifically implemented according to the following steps: Using the forward Euler discretization formula (4), the rotational speed prediction model is obtained: First prediction: (27) Second shot prediction: (28) In the formula, for The measured value of the mechanical rotation speed at any given time. express The predicted mechanical angular velocity at time i = 1, 2. express The measured value of the electromagnetic torque at time t. This represents the measured load torque value at time k. express The predicted value of the electromagnetic torque at time t. This represents the predicted load torque value at time k+1.

[0039] Also taking load torque into account It usually exhibits slow variability, so in a short period of time It can be considered a constant; the conversion relationship between mechanical angular velocity and electrical angular velocity is as follows: , The sampling period is generally taken as... for .

[0040] 8. The sensorless model predictive speed control method for a synchronous reluctance motor according to claim 7, characterized in that step 505 is specifically implemented according to the following steps: The control objective is defined as minimizing speed error and torque error. Weighting factors are used to balance the priorities of the two, and the cost function is expressed as follows: First prediction: (29) Second shot prediction: (30) In the formula, express The reference value of the mechanical angular velocity at time k is equal in magnitude to the reference values ​​at times k and k+1. As the weight of the speed error, This is the weight of the torque error.

[0041] 9. The sensorless model predictive speed control method for a synchronous reluctance motor according to claim 8, characterized in that step 506 is specifically implemented according to the following steps: Differentiating equation (29) yields: (31) Discretizing the above equation, we can obtain the reference torque at time k as follows: (32) Similarly, the reference torque at time k+1 can be obtained as follows: (33) 10. The sensorless model predictive speed control method for a synchronous reluctance motor according to claim 9, characterized in that step 507 is specifically implemented according to the following steps: Considering that the torque of the synchronous reluctance motor is determined by... and A joint decision, and It is usually set as a constant, so it is defined as follows: (34) (35) In the formula, The torque constant can be calculated using the following formula: (36) Final cost function design: First, the stator flux linkage of the synchronous reluctance motor It can be calculated using the following formula: (37) Effective magnetic flux The definition is as follows: (38) The effective flux linkage at time k+2 is obtained from equation (38): (39) Design the final cost function to select the optimal switching vector, with the goal of minimizing current and flux linkage errors while satisfying current constraints. Figure 3 As shown, predictive control iterates through all eight switching vectors, calculates the cost function value corresponding to each vector, and selects the vector with the lowest cost as the control output for the next cycle.

[0042] (40) In the formula, This is a current constraint term; if the predicted current exceeds the maximum value of the stator current... If the cost function is infinite, then the switch vector should be excluded. To accurately calculate the stator current value after two cycles, the Lagrange extrapolation method can be used for the following calculation: (41).

[0043] Example 2 The sensorless model predictive speed control method for synchronous reluctance motors of the present invention is illustrated in the flowchart below. Figure 1As shown, please follow these steps: Step 1: Establish a mathematical model of the synchronous reluctance motor based on a two-phase rotating coordinate system; Step 2: Construct a Model Reference Adaptive System (MRAS), and use the error signals obtained from the reference model and the adjustable model to adaptively adjust and obtain the rotor position estimate. Step 3: Construct an improved adaptive law that combines mechanical and electromagnetic models, while also considering mechanical factors that affect speed changes, which can estimate rotor position and load torque through linear ESO. Step 4: Derive the linearized model. The IAL-MRAS error system containing nonlinear feedback is linearized and approximated near the operating point to obtain its linearized model and transfer function.

[0044] Step 5: Establish a prediction model to predict the electromagnetic torque and speed at time k+2, obtain the predicted values ​​of stator current and flux linkage, and perform switching vector optimization through a cost function.

[0045] Example 3 The sensorless model predictive speed control method for synchronous reluctance motors of the present invention is illustrated in the flowchart below. Figure 1 As shown, please follow these steps: Step 1: Establish a mathematical model of the synchronous reluctance motor based on a two-phase rotating coordinate system; Step 1 is implemented in the following steps: Figure 4 For the circuit of a synchronous reluctance motor under the control of a two-level voltage source inverter, the mathematical model of the synchronous reluctance motor in a two-phase rotating coordinate system is as follows: (1) (2) (3) (4) In the formula, R s Indicates stator resistance. 、 express d , q Shaft-stator voltage components, 、 express d , q Shaft stator current components, 、 express d , q Shaft stator flux linkage components, Represents electric angular velocity. 、 express d, q Shaft stator inductance component, Indicates electromagnetic torque. Represents the extreme logarithm. Indicates the load torque. It represents the moment of inertia.

[0046] Step 2: Construct a Model Reference Adaptive System (MRAS), and use the error signals obtained from the reference model and the adjustable model to adaptively adjust and obtain the rotor position estimate. Step 2 is implemented in the following steps: Step 201: Establish the matrix form of the current differential equation: (5) In the formula, p is the differential operator; Simultaneously define the following matrix , , At this point, equation (5) simplifies to: (6) Estimated speed Compared with actual speed Substituting into (5), we get: (7) In the formula, , ; Step 202: Select the reference model and the adjustable model, taking into account the state matrix. Including the speed estimation equation, equation (7) is selected as the adjustable model for generating the estimated current. The synchronous reluctance motor is used as the reference model, and the actual current is measured by a current sensor. Subtracting equation (6) from equation (7), the stator current error equation is written as: (8) In the formula, , , ; Based on equation (8), a system with the current error as the state variable is designed: (9) In the formula, , It is a linear compensation matrix; Because SynRM has a significant salient pole effect, d Tiny fluctuations in shaft current can be amplified by rotational speed errors, thus generating noise. Therefore, a diagonal matrix adjustment is chosen.dq Weighting of shaft errors, optimizing error convergence speed, reducing noise, and taking... 0 <k<1; Step 203: Design an adaptive law based on Popov's superstability theory. In traditional MRAS speed estimators, the PI controller is often used as the adaptive law. This adaptive law calculates the rotor speed based solely on the current error generated by the electromagnetic model, as shown below: (10) in, initial value .

[0047] Step 3: Construct an improved adaptive law that combines mechanical and electromagnetic models, while also considering mechanical factors that affect speed changes, which can estimate rotor position and load torque through linear ESO. Step 4: Derive the linearized model. The IAL-MRAS error system containing nonlinear feedback is linearized and approximated near the operating point to obtain its linearized model and transfer function.

[0048] Step 5: Establish a prediction model to predict the electromagnetic torque and speed at time k+2, obtain the predicted values ​​of stator current and flux linkage, and perform switching vector optimization through a cost function.

[0049] Example 4 The sensorless model predictive speed control method for synchronous reluctance motors of the present invention is illustrated in the flowchart below. Figure 1 As shown, please follow these steps: Step 1: Establish a mathematical model of the synchronous reluctance motor based on a two-phase rotating coordinate system; Step 1 is implemented in the following steps: Figure 4 For the circuit of a synchronous reluctance motor under the control of a two-level voltage source inverter, the mathematical model of the synchronous reluctance motor in a two-phase rotating coordinate system is as follows: (1) (2) (3) (4) In the formula, R s Indicates stator resistance. 、 express d , q Shaft-stator voltage components, 、 expressd , q Shaft stator current components, 、 express d , q Shaft stator flux linkage components, Represents electric angular velocity. 、 express d, q Shaft stator inductance component, Indicates electromagnetic torque. Represents the extreme logarithm. Indicates the load torque. It represents the moment of inertia.

[0050] Step 2: Construct a Model Reference Adaptive System (MRAS), and use the error signals obtained from the reference model and the adjustable model to adaptively adjust and obtain the rotor position estimate. Step 2 is implemented in the following steps: Step 201: Establish the matrix form of the current differential equation: (5) In the formula, p is the differential operator; Simultaneously define the following matrix , , At this point, equation (5) simplifies to: (6) Estimated speed Compared with actual speed Substituting into (5), we get: (7) In the formula, , ; Step 202: Select the reference model and the adjustable model, taking into account the state matrix. Including the speed estimation equation, equation (7) is selected as the adjustable model for generating the estimated current. The synchronous reluctance motor is used as the reference model, and the actual current is measured by a current sensor. Subtracting equation (6) from equation (7), the stator current error equation is written as: (8) In the formula, , , ; Based on equation (8), a system with the current error as the state variable is designed: (9) In the formula, , It is a linear compensation matrix; Because SynRM has a significant salient pole effect, d Tiny fluctuations in shaft current can be amplified by rotational speed errors, thus generating noise. Therefore, a diagonal matrix adjustment is chosen. dq Weighting of shaft errors, optimizing error convergence speed, reducing noise, and taking... 0 <k<1; Step 203: Design an adaptive law based on Popov's superstability theory. In traditional MRAS speed estimators, the PI controller is often used as the adaptive law. This adaptive law calculates the rotor speed based solely on the current error generated by the electromagnetic model, as shown below: (10) in, initial value .

[0051] Step 3: Construct an improved adaptive law that combines mechanical and electromagnetic models, while also considering mechanical factors that affect speed changes, which can estimate rotor position and load torque through linear ESO. Step 3 is implemented in the following steps: Step 301: Establish the mechanical model of the linear extended state observer (ESO): (11) In the formula, For speed prediction error, This is the actual electric angular velocity. To estimate the electric angular velocity; , For observer gain; Step 302: Derive the dynamic relationship model between the estimated load torque and the estimated speed: (12) In the formula, To estimate the time derivative of the rotational speed; This formula shows that the load torque is estimated. Compared with the estimated speed There is a definite dynamic coupling relationship between them, which provides a theoretical basis for subsequent sensorless estimation; Step 303: Construct an adaptive load torque law based on current error, and calculate the estimated values ​​of sensorless rotational speed and rotor position: To address the issue of requiring actual electrical angular velocity when observing load torque in a linear ESO, the current error of the electromagnetic model is used to replace the velocity error, utilizing the stator current reference value. With estimated current To determine the error term, construct an adaptive law for load torque: (13) In the formula, , A positive PI parameter For integration, This is the current error term.

[0052] Substituting equation (13) into the speed estimation equation of the linear ESO, we obtain the sensorless electric angular velocity estimate: (14) By integrating the estimated electrical angular velocity, the estimated value of the rotor electrical angle is obtained: (15).

[0053] Step 4: Derive the linearized model. The IAL-MRAS error system containing nonlinear feedback is linearized and approximated near the operating point to obtain its linearized model and transfer function.

[0054] Step 5: Establish a prediction model to predict the electromagnetic torque and speed at time k+2, obtain the predicted values ​​of stator current and flux linkage, and perform switching vector optimization through a cost function.

[0055] Example 5 The sensorless model predictive speed control method for synchronous reluctance motors of the present invention is illustrated in the flowchart below. Figure 1 As shown, please follow these steps: Step 1: Establish a mathematical model of the synchronous reluctance motor based on a two-phase rotating coordinate system; Step 1 is implemented in the following steps: Figure 4 For the circuit of a synchronous reluctance motor under the control of a two-level voltage source inverter, the mathematical model of the synchronous reluctance motor in a two-phase rotating coordinate system is as follows: (1) (2) (3) (4) In the formula, R s Indicates stator resistance. 、 express d , q Shaft-stator voltage components, 、 express d , qShaft stator current components, 、 express d , q Shaft stator flux linkage components, Represents electric angular velocity. 、 express d, q Shaft stator inductance component, Indicates electromagnetic torque. Represents the extreme logarithm. Indicates the load torque. It represents the moment of inertia.

[0056] Step 2: Construct a Model Reference Adaptive System (MRAS), and use the error signals obtained from the reference model and the adjustable model to adaptively adjust and obtain the rotor position estimate. Step 2 is implemented in the following steps: Step 201: Establish the matrix form of the current differential equation: (5) In the formula, p is the differential operator; Simultaneously define the following matrix , , At this point, equation (5) simplifies to: (6) Estimated speed Compared with actual speed Substituting into (5), we get: (7) In the formula, , ; Step 202: Select the reference model and the adjustable model, taking into account the state matrix. Including the speed estimation equation, equation (7) is selected as the adjustable model for generating the estimated current. The synchronous reluctance motor is used as the reference model, and the actual current is measured by a current sensor. Subtracting equation (6) from equation (7), the stator current error equation is written as: (8) In the formula, , , ; Based on equation (8), a system with the current error as the state variable is designed: (9) In the formula, , It is a linear compensation matrix; Because SynRM has a significant salient pole effect, d Tiny fluctuations in shaft current can be amplified by rotational speed errors, thus generating noise. Therefore, a diagonal matrix adjustment is chosen. dq Weighting of shaft errors, optimizing error convergence speed, reducing noise, and taking... 0 <k<1; Step 203: Design an adaptive law based on Popov's superstability theory. In traditional MRAS speed estimators, the PI controller is often used as the adaptive law. This adaptive law calculates the rotor speed based solely on the current error generated by the electromagnetic model, as shown below: (10) in, initial value .

[0057] Step 3: Construct an improved adaptive law that combines mechanical and electromagnetic models, while also considering mechanical factors that affect speed changes, which can estimate rotor position and load torque through linear ESO. Step 3 is implemented in the following steps: Step 301: Establish the mechanical model of the linear extended state observer (ESO): (11) In the formula, For speed prediction error, This is the actual electric angular velocity. To estimate the electric angular velocity; , For observer gain; Step 302: Derive the dynamic relationship model between the estimated load torque and the estimated speed: (12) In the formula, To estimate the time derivative of the rotational speed; This formula shows that the load torque is estimated. Compared with the estimated speed There is a definite dynamic coupling relationship between them, which provides a theoretical basis for subsequent sensorless estimation; Step 303: Construct an adaptive load torque law based on current error, and calculate the estimated values ​​of sensorless rotational speed and rotor position: To address the issue of requiring actual electrical angular velocity when observing load torque in a linear ESO, the current error of the electromagnetic model is used to replace the velocity error, utilizing the stator current reference value. With estimated current To determine the error term, construct an adaptive law for load torque: (13) In the formula, , A positive PI parameter For integration, This is the current error term.

[0058] Substituting equation (13) into the speed estimation equation of the linear ESO, we obtain the sensorless electric angular velocity estimate: (14) By integrating the estimated electrical angular velocity, the estimated value of the rotor electrical angle is obtained: (15).

[0059] Step 4: Derive the linearized model. The IAL-MRAS error system containing nonlinear feedback is linearized and approximated near the operating point to obtain its linearized model and transfer function.

[0060] Step 4 is implemented in the following steps: Step 401: Define the input and output of the linearized error system: Neither tuning the adaptive law parameters nor further analyzing the system can handle nonlinear feedback channels. Therefore, it is necessary to linearize the error system. Using the linearized model of IAL-MRAS, the system can be analyzed using the transfer function.

[0061] like Figure 2 As shown, the actual electric angular velocity As input, estimate the electric angular velocity. As output, load torque A linearized error system is constructed as the perturbation signal. Here, the variable y represents the velocity estimation error. The function reflects the coupling relationship between current error and speed error; Step 402: Derive the transition transfer function : The transition transfer function G(s) describes the velocity estimation error. The relationship between the variable y and the electromagnetic model state-space matrix of the synchronous reluctance motor is derived from the following: (16) In the formula, Stator current estimation error vector , , for dq shaft current estimate; State matrix of the electromagnetic model of synchronous reluctance motor , Stator resistance; For the characteristic matrix, For the Laplace operator; Through algebraic operations, Simplified to two-term second-order transfer functions (17) In the formula, It is the connection speed estimation error. The transition function with respect to current error; Step 403, Linearization of the equations of motion: Performing a Laplace transform on equation (4) yields the linear transfer function of torque and velocity: (18) This formula incorporates electromagnetic torque With load torque Actual electric angular velocity Related, among which This is the inertial torque term; Step 404: Construct a linearized model: e. Substitute the torque and speed relationship Substituting equation (18) into equations (13) and (14), we obtain the linearized model of IAL-MRAS, estimating the electric angular velocity and load torque as follows: (19) In the formula, the open-loop transfer function , This is the equivalent moment of inertia used in IAL-MRAS; f. Steady-state performance analysis According to the final value theorem, take equation (19) as follows: ,get: (20) From the above equation, it can be seen that even if the equivalent moment of inertia in the improved adaptive law is improved... With actual moment of inertia Different, estimating velocity in steady state Still converges to the actual speed Estimate load torque Converging to actual load torque At the same time At that time, the system dynamic error is only related to the load torque. The system exhibits optimal dynamic performance when the changes are related to the changes in the parameters.

[0062] Step 5: Establish a prediction model to predict the electromagnetic torque and speed at time k+2, obtain the predicted values ​​of stator current and flux linkage, and perform switching vector optimization through a cost function.

Claims

1. A sensorless model predictive speed control method for synchronous reluctance motors, characterized in that, The specific steps are as follows: Step 1: Establish a mathematical model of the synchronous reluctance motor; Step 2: Construct a model reference adaptive system; Step 3: Construct an improved adaptive law that combines mechanical and electromagnetic models; Step 4: Derive the linearized model. The IAL-MRAS error system containing nonlinear feedback is linearized and approximated near the operating point to obtain its linearized model and transfer function. Step 5: Establish a prediction model to obtain the predicted values ​​of stator current and flux linkage, and perform switching vector optimization through a cost function.

2. The sensorless model predictive speed control method for synchronous reluctance motors according to claim 1, characterized in that, Step 1 is implemented in the following steps: The mathematical model of a synchronous reluctance motor in a two-phase rotating coordinate system is as follows: （1） （2） （3） （4） In the formula, R s Indicates stator resistance. 、 express d , q Shaft-stator voltage components, 、 express d , q Shaft stator current components, 、 express d , q Shaft stator flux linkage components, Represents electric angular velocity. 、 express d, q Shaft stator inductance component, Indicates electromagnetic torque. Represents the extreme logarithm. Indicates the load torque. It represents the moment of inertia.

3. The sensorless model predictive speed control method for synchronous reluctance motors according to claim 2, characterized in that, Step 2 is implemented in the following steps: Step 201: Establish the matrix form of the current differential equation: （5） In the formula, p is the differential operator; Simultaneously define the following matrix , , At this point, equation (5) simplifies to: （6） Estimated speed Compared with actual speed Substituting into (5), we get: （7） In the formula, , ; Step 202: Select the reference model and the adjustable model, taking into account the state matrix. Including the speed estimation equation, equation (7) is selected as the adjustable model for generating the estimated current. The synchronous reluctance motor is used as the reference model, and the actual current is measured by a current sensor. Subtracting equation (6) from equation (7), the stator current error equation is written as: （8） In the formula, , , ; Based on equation (8), a system with the current error as the state variable is designed: （9） In the formula, , It is a linear compensation matrix; Pick 0 <k<1; Step 203: Design an adaptive law based on Popov's superstability theory. This adaptive law calculates the rotor speed based solely on the current error generated by the electromagnetic model, as shown below: （10） in, initial value .

4. The sensorless model predictive speed control method for synchronous reluctance motors according to claim 3, characterized in that, Step 3 is implemented in the following steps: Step 301: Establish the mechanical model of the linear extended state observer (ESO): （11） In the formula, For speed prediction error, This is the actual electric angular velocity. To estimate the electric angular velocity; , For observer gain; Step 302: Derive the dynamic relationship model between the estimated load torque and the estimated speed: （12） In the formula, To estimate the time derivative of the rotational speed; This formula shows that the load torque is estimated. Compared with the estimated speed There is a definite dynamic coupling relationship between them, which provides a theoretical basis for subsequent sensorless estimation; Step 303: Construct an adaptive load torque law based on current error, and calculate the estimated values ​​of sensorless rotational speed and rotor position: To address the issue of requiring actual electrical angular velocity when observing load torque in a linear ESO, the current error of the electromagnetic model is used to replace the velocity error, utilizing the stator current reference value. With estimated current To determine the error term, construct an adaptive law for load torque: （13） In the formula, , A positive PI parameter For integration, This is the current error term; Substituting equation (13) into the speed estimation equation of the linear ESO, we obtain the sensorless electric angular velocity estimate: （14） By integrating the estimated electrical angular velocity, the estimated value of the rotor electrical angle is obtained: （15）。 5. The sensorless model predictive speed control method for synchronous reluctance motors according to claim 4, characterized in that, Step 4 is implemented in the following steps: Step 401: Define the input and output of the linearized error system: The actual electric angular velocity As input, estimate the electric angular velocity. As output, load torque As a perturbation signal, a linearized error system is constructed, where the variable y is the velocity estimation error. The function reflects the coupling relationship between current error and speed error; Step 402: Derive the transition transfer function : The transition transfer function G(s) describes the velocity estimation error. The relationship between the variable y and the electromagnetic model state-space matrix of the synchronous reluctance motor is derived from the following: （16） In the formula, Stator current estimation error vector , , for dq shaft current estimate; State matrix of the electromagnetic model of synchronous reluctance motor , Stator resistance; For the characteristic matrix, For the Laplace operator; Through algebraic operations, Simplified to two-term second-order transfer functions （17） In the formula, It is the connection speed estimation error. The transition function with respect to current error; Step 403, Linearization of the equations of motion: Performing a Laplace transform on equation (4) yields the linear transfer function of torque and velocity: （18） This formula incorporates electromagnetic torque With load torque Actual electric angular velocity Related, among which This is the inertial torque term; Step 404: Construct a linearized model: g. Substitute the torque and speed relationship Substituting equation (18) into equations (13) and (14), we obtain the linearized model of IAL-MRAS, estimating the electric angular velocity and load torque as follows: （19） In the formula, the open-loop transfer function , This is the equivalent moment of inertia used in IAL-MRAS; h. Steady-state performance analysis According to the final value theorem, take equation (19) as follows: ,get: （20） From the above equation, it can be seen that even if the equivalent moment of inertia in the improved adaptive law is improved... With actual moment of inertia Different, estimating velocity in steady state Still converges to the actual speed Estimate load torque Converging to actual load torque At the same time At that time, the system dynamic error is only related to the load torque. The system exhibits optimal dynamic performance when the changes are related to the changes in the parameters.

6. The sensorless model predictive speed control method for a synchronous reluctance motor according to claim 5, characterized in that, Step 5 is implemented in the following steps: Step 501: Based on the mathematical model of the synchronous reluctance motor in the two-phase stationary coordinate system, estimate the load torque and speed using MRAS; Step 502: Based on the forward Euler discretization formula, obtain d shaft and q Predicted shaft current values: By discretizing equation (5), the predicted value for the first beat is obtained as follows: （21） In the formula, express Moment d Predicted shaft current value express Moment q Predicted shaft current value for time d Measured value of shaft current, for time q Measured value of shaft current, for Rotational speed measurement value at any time for time d Shaft stator voltage value, for time q Shaft stator voltage values; Using a two-phase prediction strategy, the second-phase current prediction is derived based on the first-phase current prediction: （22） In the formula, since the optimal switching vector predicted in two cycles is actually taken as the switching vector after two cycles, therefore Moment dq The shaft and stator voltage values ​​are respectively equal to time dq Shaft stator voltage values; Step 503: Establish the relationship between stator voltage and switching vector. a. First, convert the three-phase voltage to a Clarke transform. αβ Voltage: ， （23） b. Then, through the inverse Park transformation... αβ Voltage converted to dq Voltage: ， （24） c. Finally, perform the switching state and three-phase voltage conversion: （25） d. In summary: （26） Step 504: Establish a speed prediction model; Step 505: Design the cost function based on the velocity error; Step 506: Solve for the reference torque; Step 507: Solve for the q-axis reference current and finally design the cost function.

7. The sensorless model predictive speed control method for a synchronous reluctance motor according to claim 6, characterized in that, Step 504 is implemented in the following steps: Using the forward Euler discretization formula (4), the rotational speed prediction model is obtained: First prediction: （27） Second shot prediction: （28） In the formula, for The measured value of the mechanical rotation speed at any given time. express The predicted mechanical angular velocity at time i = 1, 2. express The measured value of the electromagnetic torque at time t. This represents the measured load torque value at time k. express The predicted value of the electromagnetic torque at time t. This represents the predicted load torque value at time k+1; Also taking load torque into account It usually exhibits slow variability, so in a short period of time It can be considered a constant; the conversion relationship between mechanical angular velocity and electrical angular velocity is as follows: , The sampling period is generally taken as... for .

8. The sensorless model predictive speed control method for a synchronous reluctance motor according to claim 7, characterized in that, Step 505 is implemented in the following steps: The control objective is defined as minimizing speed error and torque error. Weighting factors are used to balance the priorities of the two, and the cost function is expressed as follows: First prediction: （29） Second shot prediction: （30） In the formula, express The reference value of the mechanical angular velocity at time k is equal in magnitude to the reference values ​​at times k and k+1. As the weight of the speed error, This is the weight of the torque error.

9. The sensorless model predictive speed control method for a synchronous reluctance motor according to claim 8, characterized in that, Step 506 is implemented in the following steps: Differentiating equation (29) yields: （31） Discretizing the above equation, we can obtain the reference torque at time k as follows: （32） Similarly, the reference torque at time k+1 can be obtained as follows: （33）。 10. The sensorless model predictive speed control method for a synchronous reluctance motor according to claim 9, characterized in that, Step 507 is implemented in the following steps: Considering that the torque of the synchronous reluctance motor is determined by... and A joint decision, and It is usually set as a constant, so it is defined as follows: （34） （35） In the formula, The torque constant can be calculated using the following formula: （36） Final cost function design: First, the stator flux linkage of the synchronous reluctance motor It can be calculated using the following formula: （37） Effective magnetic flux The definition is as follows: （38） The effective flux linkage at time k+2 is obtained from equation (38): （39） The final cost function is designed to select the optimal switching vector. The goal is to minimize the current and flux linkage errors and satisfy the current constraint. Predictive control calculates the cost function value for each of the eight switching vectors and selects the vector with the minimum cost as the control output for the next cycle. （40） In the formula, This is a current constraint term; if the predicted current exceeds the maximum value of the stator current... If the cost function is infinite, then the switch vector should be excluded. To accurately calculate the stator current value after two cycles, the Lagrange extrapolation method can be used for the following calculation: （41）。

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