Robust flux model predictive control method based on prediction error compensation

Abstract

The application discloses a robust double-vector model predictive permanent magnet synchronous motor flux linkage control method based on prediction error compensation. The model predictive flux linkage control of the permanent magnet synchronous motor is highly dependent on the accuracy of motor parameters, however, the motor parameters are changed under the influence of external factors such as temperature and magnetic saturation, thereby increasing the electromagnetic torque and stator flux linkage ripple and reducing the tracking performance of the control system. In order to reduce the sensitivity of the double-vector model predictive flux linkage control algorithm to the motor parameters, the application respectively establishes the prediction error model and error transmission relationship of each link of delay compensation, flux linkage prediction and optimal voltage vector action time calculation, and establishes an independent error compensation scheme for each link through online error compensation, so as to improve the parameter robustness of the double-vector model predictive flux linkage control algorithm and improve the prediction flux linkage accuracy.

Description

Technical Field

[0001] This invention relates to the field of control technology for permanent magnet synchronous motors, and in particular to a robust dual-vector model predictive control method for flux linkage of permanent magnet synchronous motors based on prediction error compensation. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in many industrial and technological fields, such as electric vehicles, subways, and ship propulsion, due to their significant advantages such as high power density and simple structure. Currently, model predictive flux linkage control (MMC), a control method based on motor models, has been successfully applied in the field of PMSM drives due to its advantages of simple structure, fast dynamic response, and ease of multi-constraint optimization.

[0003] Model predictive flux linkage control (MMCC) is highly dependent on the accuracy of motor parameters. However, these parameters are affected by external factors such as temperature and magnetic saturation, leading to deviations in the prediction results. This, in turn, affects the selection of the optimal voltage vector combination and the inaccurate calculation of the optimal voltage vector's duration, ultimately reducing the performance of the control system. To address the negative impact of parameter perturbations on permanent magnet synchronous motor drive systems, researchers have proposed several effective methods. One approach involves designing a disturbance state observer to observe and compensate for prediction errors and parameter disturbances. However, implementing this observer increases the computational burden on the system. Another approach combines parameter identification algorithms with model predictive control, replacing the original model parameters with the identified system parameters. However, the system's parameter robustness depends entirely on the effectiveness of the identified parameters, resulting in poor disturbance rejection performance.

[0004] To improve the parameter robustness of the dual-vector model predictive flux linkage control algorithm, this invention proposes a robust dual-vector model predictive flux linkage control method for permanent magnet synchronous motors based on prediction error compensation. Prediction error models and error propagation relationships are established for each stage, including delay compensation, flux linkage prediction, and optimal voltage vector action time calculation. Independent error compensation schemes are established for each stage through online error compensation, which can more effectively enhance the system's robustness to parameter mismatch while maintaining high prediction flux linkage accuracy. Summary of the Invention

[0005] The purpose of this invention is to improve the robustness of dual-vector model predictive flux linkage control to parameter mismatch. It proposes a robust dual-vector model predictive flux linkage control method for permanent magnet synchronous motors based on prediction error compensation, thereby improving the prediction flux linkage accuracy of permanent magnet synchronous motor drive systems.

[0006] A robust dual-vector model predictive flux linkage control method for permanent magnet synchronous motors based on prediction error compensation is characterized by establishing prediction error models and error propagation relationships for each stage of delay compensation, flux linkage prediction, and optimal voltage vector action time calculation in order to reduce the sensitivity of the dual-vector model predictive flux linkage control algorithm to motor parameters. The obtained prediction errors are then compensated to each stage to improve the parameter robustness of the dual-vector model predictive flux linkage control algorithm.

[0007] Its specific characteristics are as follows:

[0008] Define L and ψ f These are the actual values ​​of the stator inductance and rotor permanent magnet flux linkage of the permanent magnet synchronous motor, respectively, L0 and ψ. f0 For nominal values, the parameter deviations of stator inductance and rotor permanent magnet flux linkage are ΔL = L0 - L and Δψ, respectively. f =ψ f0 -ψ f The direct axis and quadrature axis of a permanent magnet synchronous motor are represented by the d-axis and q-axis, respectively.

[0009] Given the motor parameters as nominal values, the estimation expression for the delay compensation stage is:

[0010]

[0011] In the formula, and They are (k+1)T respectively s The motor parameters at any given time are estimated values ​​of the stator flux linkages along the d-axis and q-axis under nominal conditions; ψ d (k) and ψ q (k) represents kT s Estimated values ​​of stator flux linkage along the d-axis and q-axis at time T1; k and kT respectively s First optimal voltage vector within time moment Second optimal voltage vector Duration of action; and The first optimal voltage vector is the one with the nominal values ​​of the motor parameters. The slopes of the stator d-axis and q-axis flux linkage changes; and The second optimal voltage vectors are the nominal values ​​of the motor parameters. The slopes of the stator d-axis and q-axis flux linkage changes are expressed as follows:

[0012]

[0013] In the formula, u di (k) and u qi(k) represent the first optimal voltage vector. d-axis and q-axis components; u dj (k) and u qj (k) represent the second optimal voltage vector. The d-axis and q-axis components; R is the stator resistance; ω e Electric angular velocity;

[0014] The stator flux prediction error caused by parameter mismatch in the delay compensation stage is:

[0015]

[0016] In the formula, and They are (k+1)T respectively s The prediction error of the d-axis and q-axis stator flux linkage in the time delay compensation stage;

[0017] Given that the motor parameters are at their nominal values, the estimation expression for the flux linkage prediction component is:

[0018]

[0019] In the formula, (k+1)T s The six effective voltage vectors output by the inverter at any given time are u m (m=1, 2, 3, 4, 5, 6), u d (k+1) and u q (k+1) represent the effective voltage vector u m The d-axis and q-axis components; and They are (k+2)T respectively s Time u m Predicted values ​​of d-axis and q-axis stator flux linkages when the motor parameters are at their nominal values ​​under action;

[0020] The stator flux prediction error caused by parameter mismatch is:

[0021]

[0022] In the formula, ψ d (k+1) and ψ q (k+1) represents (k+1)T s Estimated values ​​of stator flux linkage on the d-axis and q-axis, taking into account delay compensation at all times; and They are (k+2)T respectively s The prediction errors of the stator flux linkage in the d-axis and q-axis of the flux linkage prediction stage at time;

[0023] Let (k+1)T sThe first optimal voltage vector applied at time 1 Second optimal voltage vector The duration of action is T1 k+1 and The slopes of the stator d-axis and q-axis flux linkage changes can be expressed as:

[0024]

[0025] In the formula, and These are the first optimal voltage vectors when the motor parameters are at their nominal values. The slopes of the flux linkage changes along the d-axis and q-axis; and These are the second optimal voltage vectors when the motor parameters are at their nominal values. The slopes of the flux linkage changes along the d-axis and q-axis; u di (k+1) and u qi (k+1) represent the first optimal voltage vector. d-axis and q-axis components; u dj (k+1) and u qj (k+1) represent the second optimal voltage vector. The d-axis and q-axis components;

[0026] The stator flux prediction error caused by parameter mismatch in the optimal voltage vector action time estimation stage is:

[0027]

[0028] In the formula, and They are (k+2)T respectively s The prediction errors of the d-axis and q-axis stator flux linkage in the optimal voltage vector action time estimation stage; where,

[0029]

[0030] In the formula, and The first optimal voltage vector is respectively The slopes of the flux linkage changes along the d-axis and q-axis; and The second optimal voltage vectors are respectively The slopes of the flux linkage changes along the d-axis and q-axis;

[0031] Ignoring the smaller first optimal voltage vector in equations (2) and (3) Second optimal voltage vector After the action time term, the prediction error of the delay compensation stage, expressed as equation (4), is approximately:

[0032]

[0033] Ignoring the smaller optimal voltage vector action time term in equation (6), the prediction error of the flux linkage prediction stage is approximately expressed as:

[0034]

[0035] The estimated prediction error is compensated for in the flux linkage prediction stage to obtain the following result.

[0036]

[0037] In the formula, ψ dp (k+2) and ψ qp (k+2) represents (k+2)T s Time u m Predicted values ​​of stator flux linkages along the d-axis and q-axis under the action; and They are (k+2)T respectively s Predicted values ​​of stator flux linkage on the d-axis and q-axis after error compensation in the flux linkage prediction process;

[0038] Ignoring the smaller optimal voltage vector action time terms in equations (7) and (8), the prediction error of the optimal voltage vector action time calculation stage, expressed in equation (9), is approximately:

[0039]

[0040] By compensating the estimated prediction error into the calculation of the optimal voltage vector action time, we can obtain...

[0041]

[0042] In the formula, ψ d (k+2) and ψ q (k+2) represents (k+2)T s Predicted values ​​of stator flux linkage along the d-axis and q-axis at time t; and They are (k+2)T respectively s Predicted values ​​of stator flux linkage on the d-axis and q-axis after error compensation in the calculation of the optimal voltage vector action time.

[0043] By calculating formulas (10) to (14), the prediction error compensation of the dual-vector model predictive flux control algorithm can be realized, thereby improving the prediction flux accuracy when the motor parameters are mismatched. Attached Figure Description

[0044] Figure 1 This is a block diagram of a robust two-vector model predictive flux linkage control system based on prediction error compensation. Detailed Implementation

[0045] The embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0046] The robust dual-vector model predictive flux linkage control method based on prediction error compensation proposed in this invention is implemented on the hardware foundation of a typical surface-mounted permanent magnet synchronous motor digital control drive system. The most basic hardware includes a permanent magnet synchronous motor, a digital signal processor, an absolute position encoder, a contactless Hall current sensor, an inverter, and a DC power supply. The system control algorithm is implemented in the digital signal processor. The overall system block diagram of this invention is shown below. Figure 1 As shown. This invention relies on discrete algorithms and is implemented using a digital signal processor.

[0047] The relationship between the axes in the control system is defined as follows: the axis of the A-phase winding in the ABC three-phase stator coordinate system coincides with the α-axis in the αβ two-phase stationary coordinate system. The rotor position electrical angle θ is defined as the direct axis (d-axis) in the dq synchronous rotating coordinate system oriented by the permanent magnet magnetic field of the permanent magnet rotor coincides with the axis of the A-phase winding. e The starting point.

[0048] First, assume that the three-phase windings of the permanent magnet synchronous motor are perfectly symmetrical, and neglect eddy current losses and hysteresis losses. Then, use a non-contact Hall current sensor to monitor the three-phase stator current i of the permanent magnet synchronous motor. A i B and i C Measurements are performed on the three-phase stator current i by a digital signal processor. A i B and i C Sampling. Then, the sampled three-phase stator current i... A i B and i C The α-axis current i in the αβ two-phase stationary coordinate system is obtained by Clark transformation. α and β-axis current i β Its coordinate transformation expression is:

[0049]

[0050] Then, consider the α-axis current i in the αβ two-phase stationary coordinate system. α and β-axis current i β The direct-axis current i in the dq synchronous rotating coordinate system oriented by the permanent magnet magnetic field of the permanent magnet rotor is obtained by the Park transformation. d and cross-axis current i q Its coordinate transformation expression is:

[0051]

[0052] The voltage equation and flux linkage equation for a surface-mounted permanent magnet synchronous motor are as follows:

[0053]

[0054] In the formula, u d and u q These are the d-axis and q-axis components of the stator voltage, respectively; i d and i q These are the d-axis and q-axis components of the stator current, respectively; ψ d and ψ q ψ represents the d-axis and q-axis components of the stator flux linkage, respectively; R is the stator resistance; L is the motor synchronous inductance; ψ f For rotor permanent magnet flux linkage; ω e θ is the electric angular velocity; e denoted as the rotor position electrical angle; p is the differential operator.

[0055] The corresponding state equations are obtained from equations (17) and (18).

[0056]

[0057] Using sampling period T s Applying a first-order forward Euler approximation to equation (19), the predicted flux linkage model for the permanent magnet synchronous motor is as follows:

[0058]

[0059] In the formula, ψ d (k+1) and ψ q (k+1) represents (k+1)T s Estimates of stator flux linkages on the d-axis and q-axis, taking into account delay compensation at all times; ψ d (k) and ψ q (k) represents kT s Estimated values ​​of stator flux linkage along the d-axis and q-axis at time T1; k and kT respectively s First optimal voltage vector within time moment Second optimal voltage vector Duration of action; and The first optimal voltage vector is respectively The slopes of the stator d-axis and q-axis flux linkage changes; and The second optimal voltage vectors are respectively The slopes of the stator d-axis and q-axis flux linkage changes are expressed as:

[0060]

[0061] In the formula, u di (k) and u qi (k) represent the first optimal voltage vector. d-axis and q-axis components; u dj (k) and u qj (k) represent the second optimal voltage vector. The d-axis and q-axis components.

[0062] Because digital control systems involve hold and calculation stages, a time delay exists, which degrades the system's control performance. Therefore, in kT s The timing should first be based on (k-1)T s The first and second optimal voltage vectors obtained at time (k+1)T are estimated to obtain (k+1)T. s The flux linkage at time k is further obtained as (k+2)T. s Predictive flux at time

[0063]

[0064] in

[0065]

[0066] In the formula, (k+1)T s The six effective voltage vectors output by the inverter at any given time are u m (m=1, 2, 3, 4, 5, 6), u d (k+1) and u q (k+1) represent the effective voltage vector u m d-axis and q-axis components; ψ dp (k+2) and ψ qp (k+2) represents (k+2)T s Time u m Predicted values ​​of stator flux linkages along the d-axis and q-axis under the action.

[0067] Let (k+1)T s The first optimal voltage vector applied at time 1 Second optimal voltage vector The duration of action is T1 k+1 and The slopes of the stator d-axis and q-axis flux linkage changes can be expressed as:

[0068]

[0069] (k+2)T s The predicted value of the stator flux linkage at time t is

[0070]

[0071] In the formula, ψ d (k+2) and ψ q (k+2) represents (k+2)T s Predicted values ​​of stator flux linkage along the d-axis and q-axis at time t; and The first optimal voltage vector is respectively The slopes of the flux linkage changes along the d-axis and q-axis; and The second optimal voltage vectors are respectively The slopes of the flux linkage changes along the d-axis and q-axis; u di (k+1) and u qi (k+1) represent the first optimal voltage vector. d-axis and q-axis components; u dj (k+1) and u qj (k+1) represent the second optimal voltage vector. The d-axis and q-axis components.

[0072] According to the principle of no beat time, let Solving equation (26) yields the first optimal voltage vector. Second optimal voltage vector Duration T1 k+1 and

[0073] As can be seen from equations (20) to (26) above, the model predicts flux linkage control, which is highly dependent on the motor parameters L, R, and ψ. f The accuracy of the prediction is affected by external factors such as temperature and magnetic saturation, which can cause deviations in the prediction results and consequently affect the selection of the optimal voltage vector combination and the calculation of the optimal voltage vector's duration. Considering that resistance changes do not significantly affect the steady-state control performance of the predicted flux linkage, this invention mainly focuses on L and ψ. f The impact of parameter mismatch on system control performance is analyzed.

[0074] Define L and ψ f These are the actual values ​​of the stator inductance and rotor permanent magnet flux linkage of the permanent magnet synchronous motor, respectively, L0 and ψ. f0 For nominal values, the parameter deviations of stator inductance and rotor permanent magnet flux linkage are ΔL=L0-L and Δψ, respectively. f =ψ f0 -ψ f .

[0075] Given the motor parameters as nominal values, the estimation expression for the delay compensation stage is:

[0076]

[0077] In the formula, and They are (k+1)T respectively s The motor parameters at any given time are estimated values ​​of the stator flux linkages on the d-axis and q-axis under nominal conditions; and The first optimal voltage vector is the one with the nominal values ​​of the motor parameters. The slopes of the stator d-axis and q-axis flux linkage changes; and The second optimal voltage vectors are the nominal values ​​of the motor parameters. The slopes of the stator d-axis and q-axis flux linkage changes are expressed as follows:

[0078]

[0079] The stator flux prediction error caused by parameter mismatch in the delay compensation stage is:

[0080]

[0081] In the formula, and They are (k+1)T respectively s The prediction error of the stator flux linkage in the d-axis and q-axis of the time delay compensation stage.

[0082] Substituting equations (20) and (27) into equation (30), we can obtain

[0083]

[0084] In the formula,

[0085] As can be seen from equation (31), the predicted flux linkage error of the delay compensation stage is related to kT s The d-axis and q-axis components of the stator flux linkage at any given time are related to the rotational speed and motor parameters. When parameter mismatch occurs, the prediction error generated by the delay compensation stage will be transmitted to the flux linkage prediction stage, and the flux linkage prediction stage itself will also have errors due to parameter mismatch. The estimation expression for the flux linkage prediction stage under the condition that the motor parameters are at nominal values ​​is as follows:

[0086]

[0087] In the formula, (k+1)T s The six effective voltage vectors output by the inverter at any given time are u m (m=1, 2, 3, 4, 5, 6), and They are (k+2)T respectively s Time u m The predicted values ​​of the d-axis and q-axis stator flux linkages when the motor parameters are at their nominal values.

[0088] The stator flux prediction error caused by parameter mismatch is:

[0089]

[0090] In the formula, and They are (k+2)T respectively s The prediction errors of the stator flux linkage along the d-axis and q-axis in the time flux linkage prediction stage.

[0091] Substituting equations (23) and (32) into equation (33), we can obtain

[0092]

[0093] As can be seen from equation (34), the flux prediction error consists of two parts: the error caused by parameter mismatch in this stage and the error transmitted in the delay compensation stage. This affects the evaluation of the cost function and the optimal voltage vector combination cannot be selected for the motor.

[0094] Similarly, when parameters are mismatched, the calculation of the optimal voltage vector action time will itself introduce errors, and it will also be affected by errors transmitted from the flux linkage prediction stage. Let (k+2)T s The first optimal voltage vector applied at time 1 Second optimal voltage vector The slopes of the stator flux linkage changes along the d-axis and q-axis can be expressed as:

[0095]

[0096] In the formula, and These are the first optimal voltage vectors when the motor parameters are at their nominal values. The slopes of the flux linkage changes along the d-axis and q-axis; and These are the second optimal voltage vectors when the motor parameters are at their nominal values. The slopes of the flux linkage changes along the d-axis and q-axis.

[0097] The motor parameters are (k+2)T under the nominal conditions. s The stator flux linkage prediction value at time is

[0098]

[0099] The stator flux prediction error in the optimal voltage vector action time calculation stage caused by parameter mismatch is:

[0100]

[0101] In the formula, and They are (k+2)T respectively s The prediction error of the stator flux linkage along the d-axis and q-axis in the calculation of the optimal voltage vector action time.

[0102] Substituting equations (26) and (37) into equation (38), we get

[0103]

[0104] in

[0105]

[0106] Based on the above, an independent error compensation mechanism is established for each stage. Considering that the sampling period of the model is in the microsecond range, and the corresponding effective voltage vector action time is also in the microsecond range, the first optimal voltage vector with smaller values ​​in equations (28) and (29) is ignored. Second optimal voltage vector After the action time term, the prediction error of the delay compensation stage is approximately expressed as equation (31) as follows:

[0107]

[0108] Ignoring the smaller optimal voltage vector action time term in equation (34), the prediction error of the flux linkage prediction stage is approximately expressed as:

[0109]

[0110] The estimated prediction error is compensated for in the flux linkage prediction stage to obtain the following result.

[0111]

[0112] In the formula, and They are (k+2)T respectively s The predicted values ​​of the stator flux linkage on the d-axis and q-axis after error compensation in the flux linkage prediction process.

[0113] Ignoring the smaller optimal voltage vector action time terms in equations (35) and (36), the prediction error of the optimal voltage vector action time calculation stage, equation (39), is approximately expressed as:

[0114]

[0115] Compensating for the prediction error obtained from the above estimation in the calculation of the optimal voltage vector action time yields the following result:

[0116]

[0117] In the formula, and They are (k+2)T respectively s The predicted values ​​of the d-axis and q-axis stator flux linkage after error compensation in the calculation of the optimal voltage vector action time. Based on the deadbeat principle, let... Solving equation (44) yields the first optimal voltage vector considering parameter mismatch. Second optimal voltage vector Duration T1 k+1 and

[0118] By calculating formulas (40) to (44), the prediction error compensation of the dual-vector model predictive flux control algorithm can be realized, thereby improving the prediction flux accuracy when the motor parameters are mismatched.

[0119] This invention proposes a robust dual-vector model predictive flux linkage control method for permanent magnet synchronous motors (PMSMs) based on prediction error compensation. By investigating the performance degradation of dual-vector model predictive flux linkage control algorithms caused by motor parameter mismatch, prediction error models and error propagation relationships are established for each stage: delay compensation, flux linkage prediction, and optimal voltage vector action time calculation. Independent error compensation schemes are also established for each stage. Compared to traditional dual-vector model predictive flux linkage control algorithms, this method enhances robustness to parameter mismatch and improves the prediction flux linkage accuracy of the PMSM control system.

[0120] The above embodiments illustrate and describe the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments are merely illustrative. Therefore, any omissions, modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A robust dual vector model predictive permanent magnet synchronous motor flux linkage control method based on prediction error compensation, characterized in that, In order to reduce the sensitivity of the double vector model flux linkage prediction control algorithm to motor parameters, the prediction error models and error transfer relationships of the delay compensation, flux linkage prediction and optimal voltage vector action time calculation links are established respectively, and the obtained prediction errors are compensated into the links respectively to improve the parameter robustness of the double vector model flux linkage prediction control algorithm; The specific features are as follows: L and ψ f respectively are the actual values of the stator inductance and rotor permanent magnet flux linkage of the permanent magnet synchronous motor, L0and ψ f0 are the nominal values, the parameter deviations of the stator inductance and rotor permanent magnet flux linkage are ΔL = L0- L and Δψ f = ψ f0 - ψ f respectively, the direct axis and quadrature axis of the permanent magnet synchronous motor are denoted by d-axis and q-axis respectively; Under the condition of motor parameters being nominal values, the estimation expression of the delay compensation link is wherein and are (k+1)T s are the estimated values of the d-axis and q-axis stator fluxes at the time instant when the motor parameters are nominal; ψ d (k) and ψ q (k) are the estimated values of the d-axis and q-axis stator fluxes at the time instant kT s ; and are the action times of the first optimal voltage vector s and the second optimal voltage vector at the time instant kT ; and are the d-axis and q-axis stator flux variation slopes of the first optimal voltage vector when the motor parameters are nominal; and are the d-axis and q-axis stator flux variation slopes of the second optimal voltage vector when the motor parameters are nominal, and are expressed as wherein u di (k) and u qi (k) are the d- and q-axis components of the first optimal voltage vector respectively; u dj (k) and u qj (k) are the d- and q-axis components of the second optimal voltage vector respectively; R is the stator resistance; and ω e is the electrical angular velocity. The stator flux linkage prediction error of the delay compensation link caused by parameter mismatch is wherein and are the predicted errors of the d-axis and q-axis stator fluxes of the time delay compensation block respectively s are the predicted errors of the d-axis and q-axis stator fluxes of the time delay compensation block respectively Under the condition of motor parameters being nominal values, the estimation expression of the flux linkage prediction link is In the formula, (k+1)T s The six effective voltage vectors output by the inverter at any given time are u m (m=1, 2, 3, 4, 5, 6), u d (k+1) and u q (k+1) represent the effective voltage vector u m The d-axis and q-axis components; and They are (k+2)T respectively s Time u m Predicted values ​​of d-axis and q-axis stator flux linkages when the motor parameters are at their nominal values ​​under action; The stator flux linkage prediction error of the flux linkage prediction link caused by parameter mismatch is where ψ d (k+1) and ψ q (k+1) are the prediction errors of the d-axis and q-axis stator flux linkage at the (k+2)T s instant, respectively, taking into account the delay compensation of the estimated values of the d-axis and q-axis stator flux linkage; and are the prediction errors of the d-axis and q-axis stator flux linkage at the (k+2)T s instant, respectively, of the flux linkage prediction block. Let (k+1)T s the first optimal voltage vector applied at time instant and the second optimal voltage vector have an action time of and The stator d-axis and q-axis flux linkage variation slopes can be expressed as wherein and are the d-axis and q-axis flux linkage variation slopes of the first optimal voltage vector when the motor parameters are nominal values, respectively; and are the d-axis and q-axis flux linkage variation slopes of the second optimal voltage vector when the motor parameters are nominal values, respectively; di u qi (k+1) are the d-axis and q-axis components of the first optimal voltage vector , respectively; dj u qj (k+1) are the d-axis and q-axis components of the second optimal voltage vector , respectively; The stator flux linkage prediction error of the optimal voltage vector action time calculation link caused by parameter mismatch is wherein and are the prediction errors of the d-axis and q-axis stator fluxes of the time-optimal voltage vector action time calculation block, respectively; wherein s are the prediction errors of the d-axis and q-axis stator fluxes of the time-optimal voltage vector action time calculation block, respectively; wherein wherein and are the d-axis and q-axis flux linkage variation slopes of the first optimal voltage vector respectively; and are the d-axis and q-axis flux linkage variation slopes of the second optimal voltage vector respectively; Neglecting the first optimal voltage vector with a small value in equations (2) and (3) and the second optimal voltage vector After the action time term, the delay compensation element prediction error equation (4) is approximately expressed as After the optimal voltage vector action time term with small value in equation (6) is ignored, the prediction error of the flux linkage prediction link is approximately expressed as After the optimal voltage vector action time terms with small value in equations (7) and (8) are ignored, the prediction error of the optimal voltage vector action time calculation link is approximately expressed as where ψ dp (k+2) and ψ qp (k+2) are the predicted values of the d-axis and q-axis stator fluxes at the time instant (k+2)T s (k+2)T m (k+2)T and (k+2)T s (k+2)T After the optimal voltage vector action time terms with small value in equations (7) and (8) are ignored, the prediction error of the optimal voltage vector action time calculation link is approximately expressed as After the optimal voltage vector action time terms with small value in equations (7) and (8) are ignored, the prediction error of the optimal voltage vector action time calculation link is approximately expressed as wherein ψ d (k+2) and ψ q (k+2) are the predicted values of the d-axis and q-axis stator flux linkage at the (k+2)T s (k+2) time instant, respectively; and (k+2) are the predicted values of the d-axis and q-axis stator flux linkage at the (k+2)T s (k+2) time instant, respectively, after error compensation of the time calculation element of the optimal voltage vector; The prediction error compensation of the double vector model flux linkage prediction control algorithm can be realized by calculating equations (10)-(14), so as to improve the prediction flux linkage accuracy when the motor parameters are mismatched.

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