A model predictive control method for permanent magnet synchronous motor

Abstract

The present invention discloses a model predictive control method for a permanent magnet synchronous motor. In a speed loop, a discrete and linearized state space model of a permanent magnet synchronous motor is established based on a speed equation of the permanent magnet synchronous motor. A load torque observer is introduced into the speed loop, and the speed after observation is compensated for the speed of the current prediction cycle. At the same time, the load torque is used as a variable in the state space to improve the algorithm's ability to resist external disturbances. In a current loop, a discrete and linearized state space model of a permanent magnet synchronous motor is established based on the current equation of the permanent magnet synchronous motor. At the same time, an extended state observer is introduced into the current loop, and the current after observation is compensated for the current value of the current prediction cycle, thereby improving the algorithm's ability to resist internal disturbances. The state space models of the speed loop and the current loop are improved using Laguerre polynomials, and the control quantity is parameterized, thereby reducing the time for obtaining the optimal control, reducing the amount of calculation, and improving the system response.

Description

Technical Field

[0001] The present invention relates to the field of permanent magnet synchronous motor drive control, and in particular to a permanent magnet synchronous motor model predictive control method. Background Art

[0002] With the emergence of high-energy permanent magnet materials, permanent magnet motors have become increasingly attractive. Permanent magnet synchronous motors do not require excitation current, have a simple structure and high reliability, and have been widely used in various fields. Vector control using PI regulation is the most widely used permanent magnet synchronous motor control method, but due to the strong coupling of permanent magnet synchronous motors and their sensitivity to internal and external disturbances, traditional FOC control algorithms are difficult to meet motor control requirements. Therefore, more advanced motor control algorithms have emerged, such as fuzzy control, sliding mode control, and model predictive control.

[0003] Model predictive control is a relatively new control method for permanent magnet synchronous motors. Based on the system model, the state and control variables of the current cycle of the system are used to predict the output of the next cycle and the control variables are rolled over in a loop. It usually includes three parts: prediction model, rolling optimization and feedback correction. According to the prediction model, it can be divided into step response, transfer function and state control model. The principle of the permanent magnet synchronous motor model predictive control method based on the state space model is: first establish the state space model of the motor, and then select the appropriate value function to obtain the optimal control variables for each cycle.

[0004] Both the finite set model prediction and the continuous set model prediction control algorithms establish prediction models based on the mathematical equations of permanent magnet synchronous motors. In order to reduce the impact of internal and external load disturbances on the prediction model, methods such as q-axis current approximation, observer, and prediction error compensation are introduced on the basis of the prediction model. At the same time, in order to solve the problem of large amount of calculation in the model prediction algorithm, a variety of algorithms are also used in the finite set model prediction control to reduce the amount of calculation, such as reducing the selection of switch states and reducing the design of weight coefficients. In the continuous set model prediction control, the optimal control solution is completed offline and stored in a table, and only the optimization of the table is realized online.

[0005] Therefore, a motor model predictive control method is needed that can reduce the amount of calculation for finding the optimal control and improve the system response. Summary of the invention

[0006] 1. Technical problems to be solved:

[0007] In view of the above technical problems, the present invention provides a permanent magnet synchronous motor model predictive control method. The method introduces the Laguerre function based on the mathematical model of the permanent magnet synchronous motor, and represents the control variables using a series of Laguerre polynomials, thereby reducing the amount of calculation for finding the optimal control and improving the system response.

[0008] 2. Technical solution:

[0009] A permanent magnet synchronous motor model predictive control method, characterized in that it includes the following steps:

[0010] Step 1: Establish the PMSM mathematical model in the dq rotating coordinate system and preset the motor running speed;

[0011] Step 2: LMPC-LB speed loop control; Based on the speed equation of the permanent magnet synchronous motor, a discrete and linearized permanent magnet synchronous motor state space model is established, with the speed and external load at each sampling moment as state variables, the q-axis current as the input control variable of the state space, and the speed as the output variable of the state space; the value of the state variable load at the current moment is obtained by the load observer, and the value of the state variable speed at the current moment is compensated by the speed value observed by the load observer; the increment of the control variable iq is expressed by Laguerre polynomials; the prediction process is based on the state space model and according to the value of the system variable at the current moment, and the optimal control variable at the next moment is obtained by minimizing the value function, thereby realizing the control of the speed loop.

[0012] Step 3: LMPC-ESO current loop control; Based on the current equation of the permanent magnet synchronous motor, a discrete and linearized permanent magnet synchronous motor state space model is established, with the d-axis and q-axis currents at each sampling moment as state variables in the state space, and the d-axis and q-axis voltages as input control variables; the increments of the control variables d-axis voltage ud and q-axis voltage uq are expressed using Laguerre polynomials; an extended state observer is introduced, and the real-time motor currents id and iq observed by the extended state observer are used as the current values ​​at the current moment in the prediction model to participate in the prediction.

[0013] Step 4: Based on the d-axis ud and q-axis voltages uq obtained in step 3, the permanent magnet synchronous motor is controlled accordingly.

[0014] Furthermore, step 2 specifically includes the following steps:

[0015] S21: In the dq rotating coordinate system, the current and speed model of the permanent magnet synchronous motor is established as shown in formula (1):

[0016]

[0017]

[0018]

[0019] (1) In the formula, i d is the d-axis current, i q is the q-axis current, ud is the d-axis voltage, u q is the q-axis voltage, L is the magnetic permeability, P is the number of motor pole pairs, ω m is the mechanical speed, φ f is the magnetic flux, T L is the external load; R s is the resistance, J is the moment of inertia, and B is the damping coefficient;

[0020] After discretizing equation (1), the current and speed discrete models of the permanent magnet synchronous motor are obtained as follows:

[0021]

[0022] (2) Where T is the sampling period, k is the kth sampling time;

[0023] S22: The mechanical speed ω at time k m (k), external load T L (k) as the state variable and the q-axis current as the input control variable to establish the speed loop state space model, as shown in the following equation (3):

[0024]

[0025]

[0026] (3) In the formula, the state variable x(k), the spatial variable y(k) and the control variable u(k) are as follows:

[0027]

[0028]

[0029]

[0030] S23: Establish a load observer, whose algorithm formula is as follows (5):

[0031]

[0032] (5) In the formula, Both represent the state quantity corresponding to the load observer; Replace the corresponding state quantity in formula (4);

[0033] S24: Establishing an incremental expansion model of the speed loop according to the speed loop state space model in S22, specifically including:

[0034]

[0035]

[0036] Then in formula (6)

[0037] C ω1 =[O 1] = [0 01];

[0038] S25 uses the Laguerre function to modify the q-axis current increment in step S24:

[0039]

[0040] S26 uses the set speed value and the current speed value as the value function variable Y, and the q-axis current as the variable U to establish the speed loop value function J ω ;

[0041]

[0042] By minimizing the above cost function, the optimal corresponding control variable Δi for each cycle is solved q ;

[0043] S27 calculates the q-axis current increment Δi according to the above steps. q , that is, the optimal control q-axis current is obtained, as shown in the following formula (9):

[0044] i q (k+1)=i q (k)+Δi q (k+1) (9).

[0045] Furthermore, step three specifically includes the following steps:

[0046] S31: Establish a discrete state space model of the current loop: as shown in equation (10):

[0047]

[0048] (10) In the formula, i d (k),i q (k) are the d-axis and q-axis current values ​​observed by the extended state observer;

[0049] S32: Establish a state space model of the current loop according to the current loop discrete model of S31. The state space model of the current loop is expressed as formula (11):

[0050]

[0051] In formula (11):

[0052]

[0053] S33: In step S32, an extended state observer is introduced into the state space model of the current loop, and the observed current is used as the state variable of the current cycle for prediction; specifically, it is assumed that the changes in resistance, permeance, and flux linkage during the operation of the motor are ΔR s ,ΔL,Δφ f , then the current part of the formula (1) corresponding to the current model of the permanent magnet synchronous motor is transformed into:

[0054]

[0055]

[0056] make:

[0057]

[0058]

[0059] Discretize (12) and change it into:

[0060]

[0061] The general formula of the extended state observer is as follows (14):

[0062] E(k)=Z1(k)-I(k)

[0063] Z1(k+1)=Z1(k)+TZ2(k)+BTU(k)-Tβ1E(k)

[0064] Z2(k+1)=Z2(k)-Tβ2E(k) (14);

[0065] (14) In the formula, Z1 is the observed output i of the extended state observer d ,i q , Z2 is the observation output F of the extended state observer d ,F q ;

[0066] The observed current of the extended state observer is used as the value of the state variable of the current cycle to participate in the prediction, so formula (11) can be transformed into:

[0067]

[0068] S34 establishes the current loop incremental expansion state space model based on the state space model in S32:

[0069]

[0070]

[0071] (16)Where:

[0072]

[0073]

[0074]

[0075] S35: The increment Δu of the control variable u in step S32 is expressed by using the Laguerre function as shown in the following formula (17):

[0076]

[0077] S36: Based on the motor stator current being closer to the preset current vector, the value function is set as follows (18);

[0078]

[0079] S37: Minimize the value function in S36 to find the optimal voltage increment Δu, that is, to obtain the optimal control voltage of the following formula (19):

[0080]

[0081] 3. Beneficial effects:

[0082] (1) The present invention provides a permanent magnet synchronous motor model predictive control method, which introduces the Laguerre function based on the mathematical model of the permanent magnet synchronous motor, and expresses the control variables using a series of Laguerre polynomials, thereby reducing the amount of calculation required to find the optimal control and improving the system response.

[0083] (2) The present invention provides a permanent magnet synchronous motor model predictive control method. In order to improve the ability to resist external load disturbances, a load observer is used in the speed loop to observe the external load at any time and add it to the state space model.

[0084] (3) The present invention provides a permanent magnet synchronous motor model predictive control method, which uses an extended state observer in the current loop to compensate the current loop in order to improve the ability to resist internal disturbances. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is a control block diagram of the present invention. DETAILED DESCRIPTION

[0086] The present invention will be described in detail below with reference to the accompanying drawings.

[0087] As attached Figure 1As shown, a permanent magnet synchronous motor model predictive control method is characterized by comprising the following steps:

[0088] Step 1: Establish the PMSM mathematical model in the dq rotating coordinate system and preset the motor running speed;

[0089] Step 2: LMPC-LB speed loop control; Based on the speed equation of the permanent magnet synchronous motor, a discrete and linearized permanent magnet synchronous motor state space model is established, with the speed and external load at each sampling moment as state variables, the q-axis current as the input control variable of the state space, and the speed as the output variable of the state space; the value of the state variable load at the current moment is obtained by the load observer, and the value of the state variable speed at the current moment is compensated by the speed value observed by the load observer; the increment of the control variable iq is expressed by Laguerre polynomials; the prediction process is based on the state space model and according to the value of the system variable at the current moment, and the optimal control variable at the next moment is obtained by minimizing the value function, thereby realizing the control of the speed loop.

[0090] Step 3: LMPC-ESO current loop control; Based on the current equation of the permanent magnet synchronous motor, a discrete and linearized permanent magnet synchronous motor state space model is established, with the d-axis and q-axis currents at each sampling moment as state variables in the state space, and the d-axis and q-axis voltages as input control variables; the increments of the control variables d-axis voltage ud and q-axis voltage uq are expressed using Laguerre polynomials; an extended state observer is introduced, and the real-time motor currents id and iq observed by the extended state observer are used as the current values ​​at the current moment in the prediction model to participate in the prediction.

[0091] Step 4: Based on the d-axis ud and q-axis voltages uq obtained in step 3, the permanent magnet synchronous motor is controlled accordingly.

[0092] Furthermore, step 2 specifically includes the following steps:

[0093] S21: In the dq rotating coordinate system, the current and speed model of the permanent magnet synchronous motor is established as shown in formula (1):

[0094]

[0095]

[0096]

[0097] (1) In the formula, i d is the d-axis current, i q is the q-axis current, u d is the d-axis voltage, u q is the q-axis voltage, L is the magnetic permeability, P is the number of motor pole pairs, ωm is the mechanical speed, φ f is the magnetic flux, T L is the external load; R s is the resistance, J is the moment of inertia, and B is the damping coefficient;

[0098] After discretizing equation (1), the current and speed discrete models of the permanent magnet synchronous motor are obtained as follows:

[0099]

[0100] (2) Where T is the sampling period, k is the kth sampling time;

[0101] S22: The mechanical speed ω at time k m (k), external load T L (k) as the state variable and the q-axis current as the input control variable to establish the speed loop state space model, as shown in the following equation (3):

[0102]

[0103]

[0104] (3) In the formula, the state variable x(k), the spatial variable y(k) and the control variable u(k) are as follows:

[0105]

[0106]

[0107]

[0108] S23: Establish a load observer, whose algorithm formula is as follows (5):

[0109]

[0110] (5) In the formula, Both represent the state quantity corresponding to the load observer; Replace the corresponding state quantity in formula (4);

[0111] S24: Establishing an incremental expansion model of the speed loop according to the speed loop state space model in S22, specifically including:

[0112]

[0113]

[0114] Then in formula (6)

[0115] C ω1 =[O 1] = [0 01];

[0116] S25 uses the Laguerre function to modify the q-axis current increment in step S24:

[0117]

[0118] S26 uses the set speed value and the current speed value as the value function variable Y, and the q-axis current as the variable U to establish the speed loop value function J ω ;

[0119]

[0120] By minimizing the above cost function, the optimal corresponding control variable Δi for each cycle is solved q ;

[0121] S27 calculates the q-axis current increment Δi according to the above steps. q , that is, the optimal control q-axis current is obtained, as shown in the following formula (9):

[0122] i q (k+1)=i q (k)+Δi q (k+1) (9).

[0123] Furthermore, step three specifically includes the following steps:

[0124] S31: Establish a discrete state space model of the current loop: as shown in equation (10):

[0125]

[0126] (10) In the formula, i d (k),i q (k) are the d-axis and q-axis current values ​​observed by the extended state observer;

[0127] S32: Establish a state space model of the current loop according to the current loop discrete model of S31. The state space model of the current loop is expressed as formula (11):

[0128]

[0129] In formula (11):

[0130]

[0131] S33: In step S32, an extended state observer is introduced into the state space model of the current loop, and the observed current is used as the state variable of the current cycle for prediction; specifically, it is assumed that the changes in resistance, permeance, and flux linkage during the operation of the motor are ΔR s ,ΔL,Δφ f , then the current part of the formula (1) corresponding to the current model of the permanent magnet synchronous motor is transformed into:

[0132]

[0133]

[0134] make:

[0135]

[0136]

[0137] Discretize (12) and change it into:

[0138]

[0139] The general formula of the extended state observer is as follows (14):

[0140] E(k)=Z1(k)-I(k)

[0141] Z1(k+1)=Z1(k)+TZ2(k)+BTU(k)-Tβ1E(k)

[0142] Z2(k+1)=Z2(k)-Tβ2E(k) (14);

[0143] (14) In the formula, Z1 is the observed output i of the extended state observer d ,i q , Z2 is the observation output F of the extended state observer d ,F q ;

[0144] The observed current of the extended state observer is used as the value of the state variable of the current cycle to participate in the prediction, so formula (11) can be transformed into:

[0145]

[0146] S34 establishes the current loop incremental expansion state space model based on the state space model in S32:

[0147]

[0148]

[0149] (16)Where:

[0150]

[0151]

[0152]

[0153] S35: The increment Δu of the control variable u in step S32 is expressed by using the Laguerre function as shown in the following formula (17):

[0154]

[0155] S36: Based on the motor stator current being closer to the preset current vector, the value function is set as follows (18);

[0156]

[0157] S37: Minimize the value function in S36 to find the optimal voltage increment Δu, that is, to obtain the optimal control voltage of the following formula (19):

[0158] Specific embodiment:

[0160] A control block diagram of a permanent magnet synchronous motor model predictive control algorithm is shown in Figure 1 As shown in Figure 1, a dual-loop control method of speed loop and current loop is adopted. In the speed loop, the observed output of the load observer at time k is ω(k), T L (k) is used as the current cycle state variable of the prediction model to participate in the prediction. Then, the speed given ω* and speed ω(k) are substituted into the cost function of the speed loop LMPC-LB algorithm to find the optimal control variable increment Δi q (k), and finally through Δi q (k) and the current i of the previous cycle q (k-1) Get the q-axis current given i of the current loop q *. In the current loop, the q-axis current is given by i q * Obtained from the speed loop, the d-axis current is given by i d * = 0. The observation output of the expanded observer at time k As the current cycle state variable of the current loop prediction model, the d-axis current is given as i d *、q-axis current given i q *、Current current d axis q-axis current Substitute it into the cost function of the current loop LMPC-ESO controller to find the optimal d-axis voltage increment Δu d (k) and q-axis voltage increment Δu q (k), and finally through Δu d (k),Δu q (k) and the voltage u of the previous cycle d (k-1),u q (k-1) Obtain the voltage required for the permanent magnet synchronous motor to operate and participate in motor control.

[0161] Although the present invention has been disclosed as above in terms of preferred embodiments, they are not intended to limit the present invention. Anyone skilled in the art can make various changes or modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection defined by the claims of this application.

Claims

1. A permanent magnet synchronous motor model predictive control method, characterized in that: The following steps are involved: Step 1: Establish the PMSM mathematical model in the dq rotating coordinate system and preset the motor running speed; Step 2: LMPC-LB speed loop control: Based on the speed equation of the permanent magnet synchronous motor, a discrete and linearized permanent magnet synchronous motor state space model is established, with the speed and external load at each sampling moment as state variables, the q-axis current as the input control variable of the state space, and the speed as the output variable of the state space; The current value of the state variable load is obtained by the load observer, and the current value of the state variable speed is compensated by the speed value observed by the load observer; the control variable i q The increment is expressed by Laguerre polynomials. The prediction process is based on the state space model and the value of the system variable at the current moment. The optimal control variable at the next moment is obtained by minimizing the value function, thereby realizing the control of the speed loop. Step 3: LMPC-ESO current loop control; Based on the current equation of the permanent magnet synchronous motor, a discrete and linearized permanent magnet synchronous motor state space model is established. The d-axis and q-axis currents at each sampling moment are used as state variables in the state space, and the d-axis and q-axis voltages are used as input control variables; the control variable d-axis voltage u d and q-axis voltage u q The increment is expressed by Laguerre polynomials; an extended state observer is introduced to convert the real-time motor current i observed by the extended state observer into d ,i q As the current value at the current moment in the prediction model, it participates in the prediction; Step 4: Based on the d-axis u obtained in step 3 d and q-axis voltage u q , and control the permanent magnet synchronous motor accordingly; Step 2 specifically includes the following steps: S21: In the dq rotating coordinate system, the current and speed model of the permanent magnet synchronous motor is established as shown in formula (1): (1) In the formula, i d is the d-axis current, i q for q Shaft current, u d is the d-axis voltage, u q for q Shaft voltage, L is magnetic permeability, P is the number of motor pole pairs, ω m is the mechanical speed, f f is the magnetic flux, T L is the external load; R s is the resistance, J is the moment of inertia, and D is the damping coefficient; After discretizing equation (1), the current and speed discrete models of the permanent magnet synchronous motor are obtained as follows: (2) Where T is the sampling period, k is the kth sampling time; S22: The mechanical speed ω at time k m (k), external load T L (k) as the state variable and the q-axis current as the input control variable to establish the speed loop state space model, as shown in the following equation (3): (3) In the formula, the state variable x(k), the spatial variable y(k) and the control variable u(k) are as follows: S23: Establish a load observer, whose algorithm formula is as follows (5): (5) In the formula, in is the speed observation value of the load observer, is the load torque observation value of the observer; Replace the corresponding state quantity in formula (4); S24: Establishing an incremental expansion model of the speed loop according to the speed loop state space model in S22, specifically including: Then in formula (6) C ω1 =[O 1]=[0 0 1]; S25 uses the Laguerre function to modify the q-axis current increment in step S24, namely: Where k+i is the i-th sampling time starting from k, c j are the Laguerre polynomial coefficients, l j (k) is the Laguerre polynomial function, N is the number of terms in the Laguerre polynomial; S26 uses the set speed value and the current speed value as the value function variable Y, and the q-axis current as the variable U to establish the speed loop value function J ω ; By minimizing the above value function, the optimal corresponding control variable △i for each cycle is solved q ; S27 is based on the q-axis current increment △i obtained in the above steps. q , that is, the optimal control q-axis current is obtained, as shown in the following formula (9): i q (k+1)=i q (k)+△i q (k+1) (9); Step three specifically includes the following steps: S31: Establish a current loop discrete state space model: as shown in the following equation (10): (10) In the formula, i d (k),i q (k) are the d-axis and q-axis current values ​​observed by the extended state observer; S32: Establish a state space model of the current loop according to the current loop discrete model of S31. The state space model of the current loop is expressed as formula (11): In formula (11): S33: In step S32, an extended state observer is introduced into the state space model of the current loop, and the observed current is used as the state variable of the current cycle for prediction; specifically, it is assumed that the changes in resistance, permeance, and flux linkage during the operation of the motor are △R s ,△L,△f f , then the current part of the formula (1) corresponding to the current model of the permanent magnet synchronous motor is transformed into: make: Discretize (12) and change it into: The general formula of the extended state observer is as follows (14): (14) In the formula, Z1 is the observed output i of the extended state observer d ,i q , Z2 is the observation output F of the extended state observer d ,F q ; The observed current of the extended state observer is used as the value of the state variable of the current cycle to participate in the prediction, so formula (11) can be transformed into: S34 establishes the current loop incremental expansion state space model based on the state space model in S32: (16)Where: S35: The increment Δu of the control variable u in step S32 is expressed by using the Laguerre function as shown in the following formula (17): S36: Based on the motor stator current being closer to the preset current vector, the value function is set as follows (18): S37: Minimize the value function in S36 to find the optimal voltage increment △u, that is, to obtain the optimal control voltage of the following formula (19):

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