Permanent magnet synchronous motor two-step model prediction control method for predefined switch switching

Abstract

The invention relates to the technical field of motor control, in particular to a permanent magnet synchronous motor two-step model prediction control method for predefined switch switching, which comprises the following steps of: 1, constructing a mathematical model of a surface-mounted permanent magnet synchronous motor in a d-q rotating coordinate system; 2, constructing a current prediction module according to the mathematical model of the surface-mounted permanent magnet synchronous motor; 3, obtaining a reference voltage through a reference voltage calculation module based on I (k + 1); 4, obtaining a first-step voltage vector selection table through the reference voltage Uref; 5, obtaining a second-step voltage vector selection table through the first-step possible optimal voltage vector set U1; 6, calculating the predicted current of the first step in the future through a first-step predicted current module; step 7, calculating the predicted current of the second step in the future through a second-step predicted current module; and step 8, calculating an output optimal voltage vector through a cost function module. According to the invention, the steady-state performance of the system can be improved while the calculation burden and switching frequency of the system are reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and particularly relates to a two-step model predictive control method for a permanent magnet synchronous motor with predefined switch switching. Background Art

[0002] Permanent magnet synchronous motors have outstanding advantages in terms of power density, efficiency, dynamic performance, and compactness. They are the preferred solution for modern high-performance drive systems and are widely used in industries, new energy vehicles, home appliances, and other fields. For motors that have been designed, an effective solution to improve system performance is to use high-performance control strategies. Currently, commonly used control strategies include direct torque control, field-oriented control, and model predictive control. Among them, model predictive control has been widely studied and applied due to its fast dynamic response, multi-input multi-output method, and easy addition of constraints. The development of electronic technology has further promoted its replacement of direct torque control and field-oriented control as a new popular control solution in the industry.

[0003] Existing traditional model predictive control schemes applied to three-phase permanent magnet synchronous motors have a single output voltage vector, a high computational complexity for iterative calculation using a cost function, and a high switching frequency without modulation technology. In view of this, the concept of multi-step length is introduced to obtain the optimal solution within a long prediction time domain, effectively improving the steady-state performance and reducing the switching frequency. However, the optimization complexity increases exponentially with the increase in the number of prediction steps, restricting its further application in practical fields.

[0004] Therefore, it is necessary to introduce an innovative control strategy to effectively balance the computational burden, steady-state performance, and switching frequency of model predictive control, which is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0005] The purpose of the present invention is to solve the deficiencies in the prior art and propose a two-step model predictive control method for a permanent magnet synchronous motor with predefined switch switching to improve the steady-state performance of the system while reducing the system computational burden and switching frequency.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A two-step model predictive control method for a permanent magnet synchronous motor with predefined switch switching includes the following steps:

[0008] Step 1: Construct a mathematical model of a surface-mounted permanent magnet synchronous motor in the d-q rotating coordinate system:

[0009]

[0010] Wherein u d and u qare the d-axis and q-axis components of the voltage U, respectively, i d and i q are the d-axis and q-axis components of the current I, respectively, and R, L, λ pm represent resistance, inductance, and permanent magnet flux linkage, respectively, and n p is the number of pole pairs of the motor, and ω represents the mechanical angular velocity;

[0011] Step 2: Construct a current prediction module based on the mathematical model of the surface-mounted permanent magnet synchronous motor:

[0012] Discretize Equation (1) according to the Euler equation to obtain the predicted current value at the next moment:

[0013] I(k + 1) = A1I + B1U + C1 (2)

[0014] In the formula

[0015]

[0016] i d (k + 1) and i q (k + 1) represent the d-axis and q-axis components of the current value I(k + 1) at the next moment, respectively, and T s = 0.00005 s represents the control period; the voltage U and current I therein are measured from the three-phase voltage u abc = [u a u b u c T The three-phase current i abc = [i a i b i c T are obtained through the 2r / 3s coordinate transformation, ω is obtained by taking the derivative of the motor angle measured by the encoder, and the derivation of the abc coordinate system transformed into the dq coordinate system by the 2r / 3s coordinate transformation matrix is as follows:

[0017]

[0018] Step 3: Obtain the reference voltage based on I(k + 1) through the reference voltage calculation module:

[0019] U ref = A2I ref + B2I(k + 1) + C2 (4)

[0020] In the formula I ref = [i d ref i q ref ​​​T is the reference current, i d ref = 0 is the given d-axis reference current, i q ref is the given reference speed ω ref Subtract the q-axis reference current obtained by ω via the PI controller. U ref = [u d ref u q ref T is the reference voltage, u d ref , u q ref are the d-axis and q-axis components of the reference voltage respectively, and θ is the motor angle;

[0021] Step 4: Obtain the first-step voltage vector selection table via the reference voltage U ref ;

[0022] Step 5: Obtain the second-step voltage vector selection table via the first-step possible optimal voltage vector set U1;

[0023] Step 6: Calculate the predicted current of the first step in the future via the first-step predicted current module;

[0024] Step 7: Calculate the predicted current of the second step in the future via the second-step predicted current module;

[0025] Step 8: Calculate the optimal voltage vector of the output via the cost function module;

[0026] Step 9: Convert the optimal voltage vector u opt into a switching signal to directly drive the motor;

[0027] Step 10: Finally, output the switching signal to the inverter to drive the permanent magnet synchronous motor to run.

[0028] Preferably, in Step 4, the specific steps are as follows:

[0029] According to the reference voltage U ref in the Figure 2 shown inverter voltage vector space, the first-step possible optimal voltage vector set U1 of the next step length can be quickly selected. First, transform U ref to the αβ coordinate system:

[0030]

[0031] where U αβ ref = [u α ref u β ​ref T Reference voltage represented in the αβ coordinate system, u α ref , u β ref are the α-axis and β-axis components of the reference voltage respectively, θ is the motor angle, based on U αβ ref Determine the sector based on the position in the αβ coordinate system:

[0032] θ u = arctan(u β ref / u α ref ) (6)

[0033] θ u is the position angle of U αβ ref in the αβ coordinate system, and the determination method is as shown in the first-step voltage vector selection table.

[0034] Preferably, in step 5, the specific steps are as follows:

[0035] Use a predefined switching method to determine the first-step possible optimal voltage vector set U1. To reduce switching and thus lower the switching frequency, after obtaining the first-step possible optimal voltage vector set U1, limit the switching to once or not at all.

[0036] Preferably, in step 6, the specific steps are as follows:

[0037] I(k + 2) = A1I(k + 1) + B1U1 dq + C1 (7)

[0038] In the formula

[0039]

[0040] I(k + 2) is the predicted current value of the future first step considering delay compensation, i d (k + 2) and i q (k + 2) represent the d-axis and q-axis components of I(k + 2) respectively, I(k + 1) is the current value at the next moment output by the current prediction model, U1 dq is transformed from the voltage vector in the first-step possible optimal voltage vector set U1 output by the first-step voltage vector selection table, and the transformation formula is as follows:

[0041]

[0042] ​θ is the angle of the permanent magnet synchronous motor obtained through the encoder. In the first step, there are two voltage vectors in the set U1 of the possible optimal voltage vectors, which means that these two voltage vectors need to be substituted into Equation (7) one by one to obtain two predicted current values for the first step in the future for the cost function to select the optimal one.

[0043] Preferably, in step 7, the specific steps are as follows:

[0044] Calculate the predicted current for the second step in the future according to the voltage vectors in the voltage vector selection table for the second step as follows:

[0045] I(k + 3) = A1I(k + 2) + B1U2 dq + C1 (9)

[0046] In the formula

[0047]

[0048] I(k + 3) is the predicted current value for the second step in the future. i d (k + 3) and i q (k + 3) respectively represent the d-axis and q-axis components of I(k + 3). I(k + 2) is the predicted current value for the first step in the future output by the first-step predicted current module. U2 dq is transformed from the voltage vector in the set U2 of the possible optimal voltage vectors for the second step output by the voltage vector selection table for the second step. The transformation formula is as follows:

[0049]

[0050] Preferably, in step 8, the specific steps are as follows:

[0051] Establish a cost function module to evaluate I(k + 2) = [i d (k + 2) i q (k + 2)] T and I(k + 3) = [i d (k + 3) i q (k + 3)] T , and the expression of the cost function is as follows:

[0052]

[0053] i d ref is the given d-axis reference current, i q ref is the given reference speed ω refSubtract the q-axis reference current obtained by ω through the PI controller, obtain the combination of the first-step optimal voltage vector and the second-step optimal voltage vector that minimizes the cost function through Equation (11), and finally output the optimal voltage vector u to the inverter according to the principle of multi-step model predictive control rolling optimization opt Is the first-step optimal voltage vector for minimizing the cost function.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] 1. By predefining the switch switching within the next two steps, the present invention can avoid the cost function of the multi-step model predictive control from simultaneously including the current tracking term and the switch limit term, reducing the complexity of the control strategy and simultaneously reducing the switching frequency of the system.

[0056] 2. Based on the reference voltage, the present invention selects the voltage vectors that may be applied in the first step and predefines the switch switching to select the voltage vectors in the second step based on this. Substituting the formed voltage vector sequence into the cost function effectively reduces the computational burden of the traditional multi-step model predictive control, from the original 64 iterative calculations to 11 calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Is the flow block diagram of the present invention;

[0058] Figure 2 Is the space distribution diagram of the inverter voltage vectors in the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0059] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings, so that those skilled in the art can better understand the advantages and features of the present invention, and thus make a clearer definition of the protection scope of the present invention. The embodiments described in the present invention are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative work fall within the protection scope of the present invention.

[0060] A two-step model predictive control method for a permanent magnet synchronous motor with predefined switch switching includes the following steps:

[0061] Step 1: Construct the mathematical model of the surface-mounted permanent magnet synchronous motor in the d-q rotating coordinate system:

[0062]

[0063] In the formula u d And u q Are the d-axis and q-axis components of the voltage U respectively, id and i q are the d-axis and q-axis components of the current I, respectively, and R, L, λ pm represent resistance, inductance, and permanent magnet flux linkage respectively, and n p is the number of pole pairs of the motor, and ω represents the mechanical angular velocity;

[0064] Step 2: Construct a current prediction module based on the mathematical model of the surface-mounted permanent magnet synchronous motor:

[0065] Discretize Equation (1) according to the Euler equation to obtain the predicted current value at the next moment:

[0066] I(k + 1) = A1I + B1U + C1 (2)

[0067] In the formula

[0068]

[0069] i d (k + 1) and i q (k + 1) represent the d-axis and q-axis components of the current value I(k + 1) at the next moment respectively, and T s = 0.00005 s represents the control period; the voltage U and current I therein are measured from the three-phase voltage u abc = [u a u b u c T The three-phase current i abc = [i a i b i c T is obtained through the 2r / 3s coordinate transformation. ω is obtained by taking the derivative of the motor angle measured by the encoder. The derivation of the abc coordinate system changing to the dq coordinate system through the 2r / 3s coordinate transformation matrix is as follows:

[0070]

[0071] Step 3: Obtain the reference voltage based on I(k + 1) via the reference voltage calculation module:

[0072] U ref = A2I ref + B2I(k + 1) + C2 (4)

[0073] In the formula I ref = [i d ref i q ref T is the reference current, i​​​d ref = 0 is the given d-axis reference current, i q ref is the given reference speed ω ref subtracted by the q-axis reference current obtained by ω via the PI controller. U ref = [u d ref u q ref T is the reference voltage, u d ref , u q ref are the d-axis and q-axis components of the reference voltage respectively, and θ is the motor angle;

[0074] Step 4: Obtain the first-step voltage vector selection table via the reference voltage U ref ;

[0075] Specifically, in Step 4, the specific steps are as follows:

[0076] According to the reference voltage U ref in the Figure 2 shown inverter voltage vector space, the first-step possible optimal voltage vector set U1 for the next step can be quickly selected. First, transform U ref to the αβ coordinate system:

[0077]

[0078] where U αβ ref = [u α ref u β ref T represents the reference voltage in the αβ coordinate system, u α ref , u β ref are the α-axis and β-axis components of the reference voltage respectively, and θ is the motor angle. Determine the sector according to the position of U αβ ref in the αβ coordinate system:

[0079] θ u = arctan(u β ref / u α ref )(6)

[0080] θ u is U αβ ref ​​The position angle in the αβ coordinate system is judged by the method shown in the first-step voltage vector selection table.

[0081] Table 1 First-step voltage vector selection table

[0082]

[0083] Step 5: Obtain the second-step voltage vector selection table via the first-step possible optimal voltage vector set U1;

[0084] Specifically, in Step 5, the specific steps are as follows:

[0085] Here, a predefined switching method is used to determine the first-step possible optimal voltage vector set U1. To reduce switching to lower the switching frequency, after obtaining the first-step possible optimal voltage vector set U1, the switching is restricted to once or not at all. The second-step possible optimal voltage vector set U2 is selected as shown in the following table:

[0086] Table 2 Second-step voltage vector selection table

[0087]

[0088]

[0089] Step 6: Calculate the predicted current of the first step in the future via the first-step predicted current module;

[0090] Specifically, in Step 6, the specific steps are as follows:

[0091] I(k + 2) = A1I(k + 1) + B1U1 dq + C1 (7)

[0092] In the formula

[0093]

[0094] I(k + 2) is the predicted current value of the first step in the future considering delay compensation, i d (k + 2) and i q (k + 2) respectively represent the d-axis and q-axis components of I(k + 2), I(k + 1) is the current value at the next moment output by the current prediction model, and U1 dq is transformed from the voltage vector in the first-step possible optimal voltage vector set U1 output by the first-step voltage vector selection table, and the transformation formula is as follows:

[0095]

[0096] θ is the angle of the permanent magnet synchronous motor obtained through the encoder. In the first step, there are two voltage vectors in the possible optimal voltage vector set U1, which means that these two voltage vectors need to be substituted into Equation (7) one by one to obtain two predicted current values for the first step in the future for the cost function to select the best. The amplitude and phase of each voltage vector in U1 are shown in Table 3:

[0097] Table 3 Values of each voltage vector in U1 in the αβ coordinate system

[0098]

[0099]

[0100] Vdc = 311V represents the value of the bus voltage.

[0101] Step 7: Calculate the predicted current for the second step in the future via the second-step predicted current module;

[0102] Specifically, in Step 7, the specific steps are as follows:

[0103] Calculate the predicted current for the second step in the future according to the voltage vectors in the second-step voltage vector selection table as follows:

[0104] I(k + 3) = A1I(k + 2) + B1U2 dq + C1 (9)

[0105] In the formula

[0106]

[0107] I(k + 3) is the predicted current value for the second step in the future, i d (k + 3) and i q (k + 3) respectively represent the d-axis and q-axis components of I(k + 3), I(k + 2) is the predicted current value for the first step in the future output by the first-step predicted current module, and U2 dq is transformed from the voltage vector in the possible optimal voltage vector set U2 of the second step output by the second-step voltage vector selection table. The transformation formula is as follows:

[0108]

[0109] Step 8: Calculate the optimal voltage vector output via the cost function module;

[0110] Specifically, in Step 8, the specific steps are as follows:

[0111] Establish a cost function module to evaluate I(k + 2) = [i d (k + 2) i q (k + 2)]T and I(k + 3) = [i d (k + 3)i q (k + 3)] T , the expression of the cost function is as follows:

[0112]

[0113] i d ref is the given d-axis reference current, i q ref is the given reference speed ω ref minus the q-axis reference current obtained by ω through the PI controller, the combination of the first-step optimal voltage vector and the second-step optimal voltage vector that minimizes the cost function is obtained through Equation (11). According to the principle of multi-step model predictive control rolling optimization, the final optimal voltage vector u output to the inverter opt is the first-step optimal voltage vector that minimizes the cost function.

[0114] Step 9: The optimal voltage vector u is converted into a switching signal through the switch lookup table opt to directly drive the motor; the optimal voltage vector u opt The switching signal table corresponding to the possible voltage vectors that may be applied is shown in Table 4:

[0115] Table 4 Switch Lookup Table

[0116]

[0117] Step 10: The final switching signal is output to the inverter to drive the permanent magnet synchronous motor to run.

[0118] In summary, the present invention calculates the first possible optimal voltage vector set U1 through the reference voltage, and determines the second possible optimal voltage vector set U2 through the predefined switch switching. This solution only needs to calculate the reference voltage once, and only needs to perform iterative calculations 10 times in the cost function, and only needs to calculate 11 times in total, which is far less than the 64 times required by the traditional two-step long prediction control, greatly reducing the computational burden of the system. In addition, the principle of the predefined switch switching is that the switching between the second-step voltage vector and the first-step voltage vector is only 0 times or 1 time, greatly reducing the switching frequency of the system, and thus improving the system efficiency.

[0119] The descriptions and practices disclosed in the present invention are easy to think and understand for those of ordinary skill in the art. Without departing from the principles of the present invention, several improvements and refinements can also be made. Therefore, the modifications or improvements made without departing from the spirit of the present invention should also be regarded as within the protection scope of the present invention.

Claims

1. A two-step model predictive control method for a permanent magnet synchronous motor with predefined switch switching, characterized in that It includes the following steps: Step 1: Construct the mathematical model of the surface-mounted permanent magnet synchronous motor in the d-q rotating coordinate system: where u d and u q are the d-axis and q-axis components of the voltage U respectively, and i d and i q are the d-axis and q-axis components of the current I respectively. R, L, and λ pm represent resistance, inductance, and permanent magnet flux linkage respectively, n p is the number of pole pairs of the motor, and ω represents the mechanical angular velocity; Step 2: Construct a current prediction module based on the mathematical model of the surface-mounted permanent magnet synchronous motor: Discretize Equation (1) according to the Euler equation to obtain the predicted current value at the next moment: I(k + 1) = A1I + B1U + C1 (2) In the formula i d (k + 1) and i q (k + 1) respectively represent the d-axis and q-axis components of the current value I(k + 1) at the next moment, T s = 0.00005 s represents the control period; the voltage U and current I are respectively measured by a voltage sensor and a current sensor for the three-phase voltage u of the motor abc = [u a u b u c T The three-phase current i abc = [i a i b i c T Obtained through the 2r / 3s coordinate transformation, ω is obtained by taking the derivative of the motor angle measured by the encoder. The derivation of the abc coordinate system being transformed into the dq coordinate system by the 2r / 3s coordinate transformation matrix is as follows:​​ Step 3: Obtain the reference voltage via the reference voltage calculation module based on I(k + 1): U ref = A2I ref + B2I(k + 1)+ C2(4) where I ref = [i d ref i q ref T is the reference current, i d ref = 0 is the given d-axis reference current, i q ref is the given reference speed ω ref minus the q-axis reference current obtained by ω through the PI controller, U ref = [u d ref u q ref T is the reference voltage, u d ref , u q ref are the d-axis and q-axis components of the reference voltage respectively, and θ is the motor angle;​​ Step 4: Obtain the first-step voltage vector selection table via the reference voltage U ref ​ Step 5: Obtain the voltage vector selection table in the second step via the first-step possible optimal voltage vector set U1; Step 6: Calculate the predicted current in the first step in the future via the first-step predicted current module; Step 7: Calculate the predicted current in the second step in the future via the second-step predicted current module; Step 8: Calculate the optimal voltage vector output via the cost function module; Step 9: Find the optimal voltage vector u through the switching lookup table opt Convert it into a switching signal to directly drive the motor; Step 10: Finally, output the switching signal to the inverter to drive the permanent magnet synchronous motor to operate.

2. The two-step long model predictive control method for a permanent magnet synchronous motor with predefined switch switching according to claim 1, characterized in that In Step 4, the specific steps are as follows: According to the reference voltage U ref For the rapid selection of the next step size of the inverter voltage vector space under the reference voltage U, the first step may be the optimal voltage vector set U1. First, transform U ref to the αβ coordinate system: where U αβ ref = [u α ref u β ref T represents the reference voltage in the αβ coordinate system, u α ref , u β ref are the α-axis and β-axis components of the reference voltage respectively, θ is the motor angle, and the sector is judged according to the position of U αβ ref in the αβ coordinate system:​ θ u = arctan(u β ref / u α ref ) (6) θ u is U αβ ref The position angle in the αβ coordinate system, and the determination method is as shown in the first-step voltage vector selection table.

3. A two-step long model predictive control method for a permanent magnet synchronous motor with predefined switch switching, characterized in that In Step 5, the specific steps are as follows: Use the predefined switching method to determine the first-step possible optimal voltage vector set U1. To reduce switching to lower the switching frequency, after obtaining the first-step possible optimal voltage vector set U1, limit the switching to once or not at all.

4. A two-step model predictive control method for a permanent magnet synchronous motor with predefined switch switching, characterized in that In Step 6, the specific steps are as follows: I(k + 2)=A1I(k + 1)+B1U1 dq +C1 (7) In the formula I(k + 2) is the predicted current value of the first step in the future considering delay compensation, i d (k + 2) and i q (k + 2) represent the d-axis and q-axis components of I(k + 2) respectively. I(k + 1) is the current value at the next moment output by the current prediction model. U1 dq is transformed from the voltage vector in the set U1 of the first possible optimal voltage vectors output by the first-step voltage vector selection table. The transformation formula is as follows: θ is the angle of the permanent magnet synchronous motor obtained through the encoder. There are two voltage vectors in the first-step possible optimal voltage vector set U1, which means that these two voltage vectors need to be substituted into Equation (7) one by one to obtain two predicted current values in the first step in the future for the cost function to select the better one.

5. A two-step long model predictive control method for a permanent magnet synchronous motor with predefined switch switching, characterized in that, In Step 7, the specific steps are as follows: Calculate the predicted current in the second step in the future according to the voltage vectors in the second-step voltage vector selection table as follows: I(k + 3)=A1I(k + 2)+B1U2 dq +C1 (9) In the formula I(k + 3) is the predicted current value for the second step in the future, i d (k + 3) and i q (k + 3) represent the d-axis and q-axis components of I(k + 3) respectively. I(k + 2) is the predicted current value for the first step in the future output by the first-step prediction current module. U2 dq is transformed from the voltage vector in the set of second-step possible optimal voltage vectors U2 output by the second-step voltage vector selection table. The transformation formula is as follows:

6. A two-step long model predictive control method for a permanent magnet synchronous motor with predefined switch switching, characterized in that, In Step 8, the specific steps are as follows: Build a cost function module to evaluate I(k+2) = [i d (k+2)i q (k+2)] T and I(k+3) = [i d (k+3)i q (k+3)] T , and the expression of the cost function is as follows: i d ref is the given d-axis reference current, i q ref is the given reference speed ω ref subtracts the q-axis reference current obtained by ω through the PI controller, obtains the combination of the first-step optimal voltage vector and the second-step optimal voltage vector that minimizes the cost function via Equation (11), and finally outputs the optimal voltage vector u to the inverter according to the principle of multi-step model predictive control rolling optimization opt is the first-step optimal voltage vector that minimizes the cost function.

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