Permanent magnet motor system strong disturbance rejection predictive control method

Abstract

The application discloses a strong anti-interference prediction control method for a permanent magnet motor system, and comprises the following steps: S1, according to a voltage increment model used by GPCC, an improved strategy of replacing fixed parameters in the model with controllable variables is proposed; S2, based on parameterless regulation and control of GPCC and model adaptive updating requirements, a controllable variable updating strategy aiming at reducing prediction current error is proposed; and S3, according to the SMO design principle and taking into account a certain anti-interference ability, the controllable variable updating strategy is corrected. The application can eliminate the dependence of GPCC on model parameters, realize parameterless control, and improve the anti-interference ability of the control system without affecting the dynamic performance.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet motors, and in particular to a strong anti-disturbance predictive control method for a permanent magnet motor system. Background Art

[0002] Compared to traditional model predictive control, generalized predictive current control (GPCC) uses precomputed output variable expressions to adjust control actions, reducing the burden of online computation and addressing long-term prediction issues. Furthermore, GPCC uses a voltage increment model to implement permanent magnet synchronous motor (PMSM) current control, effectively avoiding bias errors caused by parameter mismatch or dead-zone voltage.

[0003] However, the voltage increment model is obtained by performing a difference operation on the models of adjacent cycles, in which the DC component is offset and the weight of the current differential term is amplified. When the coefficient of this term, i.e., the inductance mismatch, is present, it will seriously affect the dynamic tracking performance and steady-state oscillation amplitude of the control system.

[0004] At the same time, the incremental model's ability to replace the initial model relies on the assumption that the speed remains constant between successive cycles. However, the accuracy of the position encoder can be affected by factors such as mounting location and signal processing. Furthermore, when load disturbances are large, the low filter bandwidth of the measured speed fails to capture high-frequency fluctuations in the actual speed. Using fixed inductance parameters in the incremental model results in large model errors and poor rejection of measurement noise and load disturbances. Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a strong anti-disturbance predictive control method for a permanent magnet motor system, to realize parameter-free control of GPCC, and to enable it to have a certain anti-disturbance capability without affecting its dynamic tracking performance.

[0006] Technical solution: A method for strong anti-disturbance predictive control of a permanent magnet motor system, comprising the following steps:

[0007] S1, according to the voltage increment model in GPCC, the fixed parameters in the voltage increment model are replaced by controllable variables to obtain a parameter-free voltage model; then the output variable Δu is pre-calculated by the set cost function. dq Expressions of

[0008] S2, based on GPCC's parameter-free control and model adaptive update requirements, updates the controllable variables with the goal of reducing the predicted current error;

[0009] S3, modify the update strategy of controllable variables.

[0010] Furthermore, in step S1, fixed parameters in the voltage increment model are replaced by controllable variables, which is implemented as follows:

[0011] Assuming the interior permanent magnet synchronous motor is an ideal motor, based on the forward Euler method, its discrete voltage model in the dq coordinate system is obtained:

[0012]

[0013] Where, the subscripts d and q represent the d-axis and q-axis parameters respectively; the superscript k represents the value of the corresponding parameter at the kth sampling moment; R represents the stator resistance; L d , L q 、u d 、u q 、i d and i q Respectively represent d-axis inductance, q-axis inductance, d-axis stator voltage, q-axis stator voltage, d-axis current, q-axis current; ψ f represents the permanent magnet flux; ω e is the electrical angular velocity; T s Indicates the sampling time;

[0014] Ignoring the speed change between adjacent cycles, subtracting the above equation from the equation at time k-1, we get the PMSM discrete voltage increment model:

[0015]

[0016] In the formula, the variable marked with "Δ" represents its corresponding increment;

[0017] Replacing the coefficients of the current differential term with the controllable variables and discarding the remaining terms, we obtain the non-parameterized voltage increment model:

[0018]

[0019] Where, α d , α q are the controlled variables of dq axis respectively;

[0020] According to the implementation conditions of GPCC, the above parameter-free model is rewritten into the following form:

[0021]

[0022] In the formula, variables with superscript “^” represent their predicted values; bold variables represent their two-dimensional vector form, such as i dq k =[i d k ;i q k ]; I is the second-order identity matrix; A m 、Bm 、C m and X m Represents the selected corresponding matrix;

[0023] Then, the prediction model for the next N steps is derived from the iterative relationship:

[0024]

[0025] Combine the multi-step predicted current Y with the command current Y * The difference between the two values ​​is calculated and the voltage increment ΔU is constrained. The cost function is as follows:

[0026]

[0027] Where G is the weight coefficient of the voltage increment, which is used to adjust the degree of constraint on voltage change. The corresponding expression is G = diag[G1 G 2… G N ] T , G k =I×g / G_step n-1 , n=1, 2, 3, ..., N, where the value of g needs to be adjusted according to the actual control effect; the value of G_step should be less than 1 so that the constraint on the voltage increment is strengthened as the number of prediction steps increases;

[0028] After solving, the expression of GPCC output ΔU is obtained:

[0029]

[0030] Among them, Y, F, Ω, and ΔU represent the selected corresponding matrices.

[0031] Furthermore, in step S2, the controllable variable is updated in real time to α d and α q Without considering measurement noise and nonlinear disturbance, the predicted current error at time k is used to be equivalent to the model error at time k, and it is fully compensated to the predicted current equation at time k+1, and α is obtained. d and α q The predicted value of and the expression for the predicted current at time k+1.

[0032] Furthermore, in step S3, based on the design principle of SMO, d and α q The update strategy is modified; the current prediction error is defined as a sliding mode function, and the exponential approach rate method is used to obtain the α based on SMO d Prediction value expression:

[0033]

[0034] In the formula, variables with superscript “^” represent their predicted values; k represents the sliding mode function; sgn represents the sign function; q and c are the exponential gain and sign function gain of SMO respectively;

[0035] After SMO output limiting, variable weight filtering is introduced:

[0036]

[0037]

[0038] In the formula, the variables with superscript “'” represent their filtered values; |s k |Represents k The absolute value of; β is the filter coefficient;

[0039] Therefore, after correction, α d The expressions for the predicted value and the predicted current at time k+1 are as follows:

[0040]

[0041] Where s k represents the sliding mode function; sgn represents the sign function; q and c are the exponential gain and sign function gain of SMO, respectively.

[0042] Compared with the prior art, the present invention has the following significant effects:

[0043] 1. Based on the traditional GPCC, this invention uses a parameter-free model with controllable variables to replace the traditional voltage increment model. Since the proposed model only contains current differential terms, it effectively avoids the coupling relationship between the d and q axes of the voltage model, simplifies the mathematical model of the system, and has almost no impact on the control performance.

[0044] 2. In the parameter-free model proposed in the present invention, since each equation contains only one controllable variable and no other parameter information is required, the lack-rank problem of multivariate prediction can be avoided and the complexity of variable prediction can be reduced;

[0045] 3. The PF-GPCC strategy of the present invention updates the controllable variables in real time through SMO, which can significantly improve the parameter robustness and anti-disturbance capability of GPCC without affecting the dynamic performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 The overall structural diagram of PF-GPCC based on SMO is shown in the figure.

[0047] Figure 2(a) is the acceleration and deceleration test result of the traditional GPCC with measured parameters under no-load condition.

[0048] (b) is L under no-load q *(given)=1.5L q (Measured) acceleration and deceleration test results of traditional GPCC,

[0049] (c) is L under no-load q *(given)=0.5L q (Measured) acceleration and deceleration test results of traditional GPCC,

[0050] (d) Acceleration and deceleration test results of the proposed SMO-based PF-GPCC under no-load conditions.

[0051] Figure 3 (a) is the load-reduction test result of the traditional GPCC using measurement parameters.

[0052] (b) The load-addition and load-reduction test results of the proposed SMO-based PF-GPCC. DETAILED DESCRIPTION

[0053] The present invention will be described in further detail below with reference to the accompanying drawings and specific implementations.

[0054] like Figure 1 The flowchart of the strong parameter robustness auto-disturbance rejection predictive control method for the permanent magnet motor system in this example is shown. The proposed parameter-free voltage model is used to realize multi-step current prediction, and then the output variable Δu is pre-calculated by the set cost function. dq In the corresponding PF-GPCC module in the figure, this expression, as well as the input current sampling and reference value, will be used to control the system action. dq Through the integrator with a limiting link, u can be obtained dq , and then through the "1.5ω e T s The 2r / 2s coordinate transformation of position angle delay compensation can obtain the reference input signal u of SVPWM αβ At the same time, for the controllable variable α in the non-parameterized voltage model dq The prediction will be achieved through the proposed cascade of SMO (Sliding Mode Observer), limiting and variable weight filtering.

[0055] Figure 2 This is a comparison chart of the experimental results of acceleration and deceleration under no-load conditions, where Figure 2 (a) is the acceleration and deceleration test result of the traditional GPCC with measured parameters under no-load condition. Figure 2 (b) is L under no-load q *(given)=1.5L q (Measured) acceleration and deceleration test results of traditional GPCC, Figure 2 (c) is L under no-load q *(given)=0.5L q (Measured) acceleration and deceleration test results of traditional GPCC, Figure 2 (d) in Figure 3 is the acceleration and deceleration test results of the proposed SMO-based PF-GPCC under no-load conditions.

[0056] Figure 3 The comparison chart of the experimental results of adding and reducing loads is shown in Figure 2. Figure 3 (a) is the load-reduction test result of the traditional GPCC using measured parameters. Figure 3 (b) in the figure shows the load-and-unload test results of the proposed SMO-based PF-GPCC.

[0057] The active disturbance rejection predictive control method for a permanent magnet motor system with strong parameter robustness specifically comprises the following steps:

[0058] Step 1: Based on the voltage increment model used by GPCC, an improved strategy is proposed to replace the fixed parameters in the model with controllable variables;

[0059] In one embodiment, the above step 1 specifically includes:

[0060] Assuming the interior permanent magnet synchronous motor is an ideal motor, based on the forward Euler method, its discrete voltage model in the dq coordinate system can be obtained:

[0061]

[0062] Where, the subscripts d and q represent the d-axis and q-axis parameters respectively; the superscripts of all expressions about k represent the corresponding sampling moments, for example, i d k Representative i d The value at time k (current sampling time); R represents the stator resistance; L d , L q 、u d 、u q 、i d and i q Represent the dq components of inductance, stator voltage and current respectively; ψ f represents the permanent magnet flux; ω e is the electrical angular velocity; T s Indicates the sampling time.

[0063] Ignoring the speed change between adjacent cycles, the PMSM discrete voltage increment model can be obtained by subtracting the above equation from the equation at time k-1 (the previous sampling time):

[0064]

[0065] In the formula, the variable marked with "Δ" represents its corresponding increment, for example, Δi d k =i d k -i d k-1 .

[0066] The voltage increment model is obtained by performing a difference operation on the models of adjacent cycles, where the DC component is offset and the weight of the current differential term is amplified. At the same time, due to nonlinear perturbations in the control link, such as inverter dead zone, current measurement noise, and speed encoder calculation delay, the ideal voltage model is difficult to equate to actual operating conditions. Therefore, by replacing the coefficient of the current differential term with a controllable variable and discarding the remaining terms, a parameter-free voltage increment model can be obtained:

[0067]

[0068] Where, α d , α q are the controllable variables of the dq axes, respectively, which include the true parameter values ​​in the traditional model and the unknown parts caused by the model error.

[0069] According to the implementation conditions of GPCC, the above parameter-free model is rewritten into the following form:

[0070]

[0071] In the formula, variables with superscript “^” represent their predicted values; bold variables represent their two-dimensional vector form, such as i dq k =[i d k ;i q k ]; I is the second-order identity matrix; A m 、B m 、C m and X m Represents the selected corresponding matrix.

[0072] Then, the prediction model for the next N steps can be derived from the iterative relationship:

[0073]

[0074] Combine the multi-step predicted current Y with the command current Y *The difference between the two and the voltage increment ΔU can be constrained by using the following cost function:

[0075]

[0076] Where G is the weight coefficient of the voltage increment, which is used to adjust the degree of constraint on voltage change. The corresponding expression is G = diag[G1 G 2… G N ] T , G k =I×g / G_step n-1 (n=1,2,3,…,N), where the value of g needs to be adjusted according to the actual control effect; the value of G_step should be less than 1 so that the constraint on the voltage increment is strengthened with the increase of the number of prediction steps.

[0077] After solving, the expression of GPCC output ΔU can be obtained:

[0078]

[0079] Among them, Y, F, Ω, and ΔU represent the selected corresponding matrices.

[0080] Step 2: Based on the parameter-free control of GPCC and the need for model adaptive updating, a controllable variable update strategy is proposed to reduce the predicted current error.

[0081] In one embodiment, the above step 2 specifically includes:

[0082] Since the proposed parameter-free model contains the controllable variable α d and α q In order to enhance its reliability, it is necessary to observe the model error and update the controllable variable α in real time. d and α q Without considering measurement noise and nonlinear disturbance, the predicted current error at time k can be used to equal the model error at time k, and it can be fully compensated into the predicted current equation at time k+1, so α can be obtained. d and α q The predicted value of and the expression for the predicted current at time k+1. Since the models of the d and q axes are the same, only the d axis is used as an example here:

[0083]

[0084] Among them, variables with a superscript “^” represent their predicted values.

[0085] Step 3: According to the SMO design principle and taking into account a certain degree of anti-disturbance ability, the update strategy of the controllable variables is modified.

[0086] In one example, step 3 specifically includes:

[0087] α in the voltage increment model d and α q The update of α needs to consider the influence of measurement noise and nonlinear disturbance. The use of a high-bandwidth full compensation strategy will lead to a significant decrease in the anti-disturbance ability of the control system and make it difficult to operate stably. The design principle of SMO can be combined to d and α q The update strategy is used to correct the current prediction error. By defining the current prediction error as a sliding mode function and using the exponential approach method, we can obtain the α based on SMO. d Prediction value expression:

[0088]

[0089] Where s k represents the sliding mode function; sgn represents the sign function; q and c are the exponential gain and sign function gain of SMO, respectively.

[0090] In order to further improve the control system's suppression effect on high-frequency disturbances, it is necessary to reduce the compensation bandwidth of the prediction error and take into account the Δu at time k. d As a divisor, a smaller value will affect α d The stability of the prediction results can be determined by SMO output limiting (0.2×~5×T S / L d ), variable weight filtering is introduced:

[0091]

[0092] In the formula, the variables with superscript “'” represent their filtered values; |s k |Represents k The absolute value of β is the filter coefficient, which increases with the increase of the current prediction error, not only meeting the α d The filtering requirements of the prediction results are eliminated, and the SMO is able to track and compensate the prediction current error in a timely manner.

[0093] Therefore, after correction, α d The expressions for the predicted value and the predicted current at time k+1 are as follows:

[0094]

[0095] In order to achieve the asymptotic stability of SMO, the following sliding mode conditions need to be met:

[0096]

[0097] Since the constraint on the voltage increment in the cost function will continue to increase with the increase in the number of prediction steps, the voltage increment has a tendency to decay in the recovery phase after the sudden change in the working condition. The polynomial on the left side of the above sliding mode condition is less than zero and will leave a certain margin. Further combined with the polynomial on the right side, q can be set to 1 and c to 0.01.

[0098] Figure 2 The comparison of acceleration and deceleration experiments between traditional GPCC and PF-GPCC under no-load conditions under the condition of weak constraint of cost function on voltage increment is given. Figure 2 From (a) and (d) in Figure 1, we can see that both GPCC and PF-GPCC using measurement parameters can quickly track the current command and have good steady-state performance under no-load conditions. Figure 2 From (b) in the figure, it can be seen that when the q-axis given inductance of the traditional GPCC is large, the q-axis current will oscillate significantly. Figure 2 As shown in (c), the dynamic tracking performance of the q-axis current of the traditional GPCC is poor when the q-axis given inductance is small.

[0099] Figure 3 The comparison of load increase and decrease experiments between traditional GPCC and PF-GPCC at constant speed under the condition of weak constraint of cost function on voltage increment is given. Figure 3 From (a) in Figure 1, we can see that the traditional GPCC using measured parameters has good dynamic tracking performance, but it cannot operate stably under full load. Figure 3 As shown in (b), PF-GPCC still has good anti-disturbance capability under full load conditions and retains the fast dynamic response characteristics of GPCC.

[0100] The above merely describes a preferred embodiment of the present invention. A person skilled in the art will readily appreciate other advantages and variations based on the above embodiment. Therefore, the present invention is not limited to the above embodiment, which serves only as an example to provide a detailed, illustrative description of one form of the present invention. Any common changes and substitutions made by a person skilled in the art within the scope of the present invention's technical solution, without departing from the spirit of the present invention, should be included within the scope of protection of the present invention.

Claims

1. A strong anti-disturbance predictive control method for a permanent magnet motor system, characterized in that: The steps are as follows: S1, according to the voltage increment model in GPCC, the fixed parameters in the voltage increment model are replaced by controllable variables to obtain a parameter-free voltage model; then the output variable Δu is pre-calculated by the set cost function. dq Expressions of S2, based on GPCC's parameter-free control and model adaptive update requirements, updates the controllable variables with the goal of reducing the predicted current error; S3, modify the update strategy of the controllable variables; In step S1, the fixed parameters in the voltage increment model are replaced by controllable variables, which is implemented as follows: Assuming the interior permanent magnet synchronous motor is an ideal motor, based on the forward Euler method, its discrete voltage model in the dq coordinate system is obtained: Where, the subscripts d and q represent the d-axis and q-axis parameters respectively; the superscript k represents the value of the corresponding parameter at the kth sampling moment; R represents the stator resistance; L d 、L q 、u d 、u q 、i d and i q Respectively represent d-axis inductance, q-axis inductance, d-axis stator voltage, q-axis stator voltage, d-axis current, q-axis current; ψ f represents the permanent magnet flux; ω e is the electrical angular velocity; T s Indicates the sampling time; Ignoring the speed change between adjacent cycles, subtracting the above equation from the equation at time k-1, we get the PMSM discrete voltage increment model: In the formula, the variable marked with "Δ" represents its corresponding increment; Replacing the coefficients of the current differential term with the controllable variables and discarding the remaining terms, we obtain the non-parameterized voltage increment model: Where, α d , α q are the controlled variables of dq axis respectively; According to the implementation conditions of GPCC, the above parameter-free model is rewritten into the following form: In the formula, variables with superscript "^" represent their predicted values; The bold variables represent their two-dimensional vector form; among them, i dq k =[i d k ;i q k ]; I is the second-order identity matrix; A m 、B m 、C m and X m Represents the selected corresponding matrix; Then, the prediction model for the next N steps is derived from the iterative relationship: Combine the multi-step predicted current Y with the command current Y * The difference between the two values ​​is calculated and the voltage increment ΔU is constrained. The cost function is as follows: Where G is the weight coefficient of the voltage increment, which is used to adjust the degree of constraint on voltage change. The corresponding expression is G = diag[G1 G 2… G N ] T , G k =I×g / G_step n-1 , n=1,2,3,. .. , N, where the value of g needs to be adjusted according to the actual control effect; the value of G_step should be less than 1, so that the constraint on the voltage increment is strengthened as the number of prediction steps increases; After solving, the expression of GPCC output ΔU is obtained: Among them, Y, F, Ω, and ΔU represent the selected corresponding matrices.

2. The method for strong anti-disturbance predictive control of a permanent magnet motor system according to claim 1, characterized in that: In step S2, the controllable variable is updated in real time to α d and α q Without considering measurement noise and nonlinear disturbance, the predicted current error at time k is used to be equivalent to the model error at time k, and it is fully compensated to the predicted current equation at time k+1, and α is obtained. d and α q The predicted value of and the expression for the predicted current at time k+1.

3. The method for strong anti-disturbance predictive control of a permanent magnet motor system according to claim 2, characterized in that: In step S3, combining the design principles of SMO, d and α q Modify the update strategy; The current prediction error is defined as a sliding mode function, and the exponential approach method is used to obtain the α based on SMO. d Prediction value expression: In the formula, variables with superscript "^" represent their predicted values; s k represents the sliding mode function; sgn represents the sign function; q and c are the exponential gain and sign function gain of SMO respectively; After SMO output limiting, variable weight filtering is introduced: In the formula, the variables with superscript "'" represent their filtered values; |s k |Represents k The absolute value of; β is the filter coefficient; Therefore, after correction, α d The expressions for the predicted value and the predicted current at time k+1 are as follows: Where s k represents the sliding mode function; sgn represents the sign function; q and c are the exponential gain and sign function gain of SMO, respectively.

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