CONTROL METHOD OF DUAL THREE-PHASE PERMANENT MAGNET SYNCHRONOUS MOTOR BY ALTERNATELY PERFORMING SAMPLING AND CONTROL PROCEDURES

Abstract

The present invention discloses a control method of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures, which belongs to the field of power generation, power transformation or power distribution technologies. Sampling instants, vector loading instants, and reference value tracking instants of two sets of windings alternate in two halves of a sampling period, and the equivalent sampling frequency of the motor drive system is doubled and the digital delay and the predictive horizon are halved without changing the sampling frequency of a single set of three-phase windings. In addition, by means of a two-layer MPC strategy, a deficient-rank problem is settled that the controlled dimensionality of the system is reduced to two dimensions but the motor control objective is still four dimensions caused by the method with controlling a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures. According to the control method of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures provided in the present invention, the steady-state and dynamic control performance of a motor drive system for a dual three-phase permanent magnet synchronous motor is effectively improved, and computation burden of the control algorithm is reduced.

Claims

1. A control method of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures, comprising: sampling phase currents of a second set of windings at an instant kT.sub.s, sampling phase currents of a first set of windings and loading control vectors of the second set of windings at an instant (k+1/2)T.sub.s, loading control vectors of the first set of windings and completing tracking of reference values of currents by the second set of windings at an instant (k+1)T.sub.s, completing tracking of reference values of currents at an instant (k+3/2)T.sub.s by the first set of windings, using a two-layer MPC strategy with an objective that d-axis total current is equally divided for d-axis currents of two sets of windings, q-axis total current is equally divided for q-axis currents of the two sets of windings, and the d-axis total current and the q-axis total current follow the reference values, to determine a reference value of the d-axis current and a reference value of the q-axis current of each set of windings, selecting candidate vectors that do not cause switch transitions between P level and N level under a constraint of the reference values of the d-axis and q-axis currents, and calculating cost functions for the evaluation of candidate vectors to obtain the candidate vector with the smallest cost function as a final loaded vector, wherein k is a positive integer, and T.sub.s is the switching period.

2. The control method of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures according to claim 1, wherein a method with selecting candidate vectors that do not cause switch transitions between P level and N level under a constraint of the reference value of the d-axis and q-axis current is: deleting candidate vectors unable to be extrapolated when there exists at least one candidate vector, during extrapolation of which all the controlled variables are within the ranges of error bounds, and using average switching frequency calculated according to an extrapolation result as a cost function; and using a weighting factor-based cost function where the absolue control errors of the controlled variables are summarized with corresponding weighting factors when all candidate vectors are unable to be extrapolated.

3. The control method of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures according to claim 1, wherein a method with selecting candidate vectors that do not cause switch transitions between P level and N level is: calculating d-axis and q-axis reference voltages of one set of windings according to the reference values of the d-axis and q-axis currents of the two sets of windings, performing polar coordinate transformation on the d-axis and q-axis reference voltages of the set of windings, and selecting vectors in a triangular sector in which the reference voltage vector of the inverter corresponding to the set of windings is located as candidatevectors according to a result of the polar coordinate transformation, wherein when at least one candidate vector does not cause switch transitions between P level and N level, all candidate vectors that do not cause switch transitions between P level and N level are determined to be the final candidate vectors, and when candidate vectors in triangular sectors cause switch transitions between P level and N level, the triangular sector is expanded to a hexagonal sector, vectors located in both the triangular sector and the hexagonal sector in which a reference voltage vector of the inverter corresponding to the set of windings are excluded, and the remaining vectors in the hexagonal area are candidate vectors, determine candidate vectors that do not cause switch transitions between P level and N level as the final candidate vectors.

4. The control method of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures according to claim 1, wherein reference voltages with the objective that the d-axis total current is equally divided for the d-axis currents of two sets of windings and the q-axis total current is equally divided for the q-axis currents of the two sets of windings are: $\{\begin{array}{c}{u}_{d1}^{*}=R_s{i}_{d1}\left(k+1\right)+L_d\left(i_{d1}^{*}-i_{d1}\left(k+1\right)\right)/\left(T_s/2\right)-\omega \left(k\right)L_{qm}{i}_{q2}\left(k+1\right)+\\ L_{dm}\left(i_{d{2}^{*}}-i_{d2}\left(k+1\right)\right)/\left(T_{s}l2\right)-\omega \left(k\right)L_q{i}_{q1}\left(k+1\right)\\ u_{q1}^{*}=R_s{i}_{q1}\left(k+1\right)+L_q\left(i_{q1}^{*}-i_{q1}\left(k+1\right)\right)/\left(T_s/2\right)+\omega \left(k\right)L_{dm}{i}_{d2}\left(k+1\right)+\\ L_{qm}\left(i_{q{2}^{*}}-i_{q2}\left(k+1\right)\right)/\left(T_s/2\right)+\omega \left(k\right)L_d{i}_{d1}\left(k+1\right)+\omega \left(k\right){\psi }_f\\ u_{d2}^{*}=R_s{i}_{d2}\left(k+1\right)+L_d\left(i_{d2}^{*}-i_{d2}\left(k+1\right)\right)/\left(T_s/2\right)-\omega \left(k\right)L_{qm}{i}_{q1}\left(k+1\right)+\\ L_{dm}\left(i_{d1}^{*}-i_{d1}\left(k+1\right)\right)/\left(T_s/2\right)-\omega \left(k\right)L_q{i}_{q2}\left(k+1\right)\\ u_{q2}^{*}=R_s{i}_{q2}\left(k+1\right)+L_q\left(i_{q2}^{*}-i_{q2}\left(k+1\right)\right)/\left(T_s/2\right)+\omega \left(k\right)L_{dm}{i}_{d1}\left(k+1\right)+\\ L_{qm}\left(i_{q1}^{*}-i_{q1}\left(k+1\right)\right)/\left(T_s/2\right)+\omega \left(k\right)L_d{i}_{d2}\left(k+1\right)+\omega \left(k\right){\psi }_f\end{array},$ wherein u.sub.d1*, u.sub.q1*, u.sub.d2*, and u.sub.q2* are respectively d-axis reference voltages and q-axis reference voltages of the two sets of windings, i.sub.d1*=i.sub.d2*=(1/2)i.sub.d*, i.sub.q1*=i.sub.q2*=(1/2)i.sub.q*, i.sub.d1*, i.sub.q1*, i.sub.d2*, and i.sub.q2* are d-axis reference currents and q-axis reference currents of the two sets of windings, respectively, i.sub.d* and i.sub.q* are d-axis total reference current and q-axis total reference current, respectively, i.sub.d1(k+1), i.sub.q1(k+1), i.sub.d2(k+1), and i.sub.q2(k+1) are the d-axis currents and the q-axis currents of the two sets of windings at an instant (k+1)T.sub.s, respectively, L.sub.d and L.sub.q are d-axis inductance and q-axis inductance, respectively, R.sub.s is stator resistance, L.sub.dm and L.sub.qm are d-axis mutual inductance and q-axis mutual inductance, respectively, ω(k) is an electric angular speed at an instant kT.sub.s, and ψ.sub.f is a permanent magnet flux linkage.

5. The control method of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures according to claim 4, wherein the current reference values of the first set of windings with an objective that the d-axis total current and the q-axis total current follow the reference values are: $\{\begin{array}{c}{i}_{d1}\left(k+3/2\right)=(L_d{i}_{d2}\left(k+1\right)+L_{dm}{i}_{d1}\left(k+1\right)-L_d{i}_d^{*}+u_{d2}{T}_s/2-R_s{T}_s{i}_{d2}\left(k+1\right)/2+\\ \omega \left(k\right)L_q{T}_s{i}_{q2}\left(k+1\right)/2+\omega \left(k\right)L_{qm}{T}_s{i}_{q1}\left(k+1\right)/2)/\left(L_{dm}-L_d\right)\\ i_{q1}\left(k+3/2\right)=(L_{qm}{i}_{q1}\left(k+1\right)+L_q{i}_{q2}\left(k+1\right)-T_s\omega \left(k\right){\psi }_f/2-L_q{i}_q^{*}-R_s{T}_s{i}_{q2}\left(k+1\right)/2-\\ \omega \left(k\right)L_d{T}_s{i}_{d2}\left(k+1\right)/2-\omega \left(k\right)L_{dm}{T}_s{i}_{d1}\left(k+1\right)/2+u_{q2}{T}_s/2)/\left(L_{qm}-L_q\right)\end{array},$ and expressions of the current reference values of the second set of windings with the objective that the d-axis total current and the q-axis total current follow the reference values are: $\{\begin{array}{c}{i}_{d2}\left(k+1\right)=(L_d{i}_{d1}\left(k+1/2\right)+L_{dm}{i}_{d2}\left(k+1/2\right)-L_d{i}_d+u_{d1}{T}_s/2-R_s{T}_s{i}_{d1}\left(k+1/2\right)/2+\\ \omega \left(k\right)L_q{T}_s{i}_{q1}\left(k+1/2\right)/2+\omega \left(k\right)L_{qm}{T}_s{i}_{q2}\left(k+1/2\right)/2)/\left(L_{dm}-L_d\right)\\ i_{q2}\left(k+1\right)=(L_q{i}_{q1}\left(k+1/2\right)+L_{qm}{i}_{q2}\left(k+1/2\right)-T_s\omega \left(k\right){\psi }_f/2-L_q{i}_q-R_s{T}_s{i}_{q1}\left(k+1/2\right)/2-\\ \omega \left(k\right)L_d{T}_s{i}_{d1}\left(k+1/2\right)/2-\omega \left(k\right)L_{dm}{T}_s{i}_{d2}\left(k+1/2\right)/2+u_{q1}{T}_s/2)/\left(L_{qm}-L_q\right)\end{array},$ wherein i.sub.d1(k+3/2) and i.sub.q1(k+312) are the d-axis and q-axis currents of the first set of windings at an instant (k+3/2)T.sub.s, respectively, and i.sub.d2(k+1) and i.sub.q2(k+1) are the d-axis and q-axis currents of the second set of windings at an instant (k+1)T.sub.s, respectively.

6. The control method of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures according to claim 2, wherein the expression of calculating the switching frequency is g.sub.1=n.sub.s/N, g.sub.1 is the switching frequency, n.sub.s is the number of commutations defined for each vector candidate, N is the extrapolation length, $n_s=\underset{x}{.Math.}\left[S_x\left(k+1\right)-S_x\left(k\right)\right],$ S.sub.x(k+1) and S.sub.x(k) are switch functions of phase x at the instant (k+1)T.sub.s and the instant kT.sub.s, respectively, x=a, b, c, d, e, f and $S_x=\{\begin{array}{cc}1& \mathrm{nthe}x\mathrm{phase}\mathrm{outputs}P\mathrm{level}\\ 0& \mathrm{nthe}x\mathrm{phase}\mathrm{outputs}O\mathrm{level}\\ -1& \mathrm{nthe}x\mathrm{phase}\mathrm{outputs}P\mathrm{level}\end{array}.$

7. The control method of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures according to claim 2, wherein the expression of weighting factor-based cost function where the absolue control errors of the controlled variables are summarized with corresponding weighting factors is: $g_2=\underset{x}{.Math.}{\lambda }_x{g}_x,$ g.sub.x is an absolute value of the control error of variable x, λ.sub.x is the weight coefficient of g.sub.x, $g_x=\{\begin{array}{cc}x\left(k+2\right)-x_{\max },& x\left(k+2\right)>x_{\max }\\ x_{\min }-x\left(k+2\right),& x\left(k+2\right)<x_{\min }\\ 0,& x_{\min }\le x\left(k+2\right)\le x_{\max }\end{array},$ x(k+2) is the predicted value of the controlled variable x at an instant (k+2)T.sub.s, x.sub.min and x.sub.max are the allowable minimum and maximum value of the variable x, respectively, x.sub.max=x.sub.ref+Δx, x.sub.min=x.sub.ref−Δx, Δx is the allowable absolute error of the variable x, and x.sub.ref is the reference value of the variable x; i.sub.d1 and i.sub.q1 are respectively the d-axis current and the q-axis current of the first set of windings, i.sub.d2 and i.sub.q2 are respectively the d-axis current and the q-axis current of the second set of windings, and V.sub.n is a DC-link mid-point voltage of the inverter; during the sampling and control procedure of the first set of windings, x∈{i.sub.d1, i.sub.q1, V.sub.n}, during the sampling and control procedure of the second set of windings, x∈{i.sub.d2, i.sub.q2, V.sub.n}.

8. A system for implementing the control method of a dual three-phase permanent magnet synchronous motor according to claim 1, comprising: a position encoder, mounted on an output shaft of the dual three-phase permanent magnet synchronous motor, and configured to detect the angular position of the motor; a speed calculation module, wherein the input end of the speed calculation module is the angle position, and the speed calculation module is configured to output the rotating speed; a PI controller used in the closed-loop speed control, wherein the input end of the speed PI controller receives the speed and the reference value of the rotating speed, and the speed PI controller is configured to generate the torque reference value according to a difference between the rotating speed and the reference value of the rotating speed; a maximum torque per ampere control module, wherein the input end of the maximum torque per ampere control module receives the reference value of the torque, and the maximum torque per ampere control module is configured to output the reference value of d-axis and q-axis current of the two sets of three-phase windings; a dual synchronous coordinate transformation module, configured to: receive six-phase currents sampled from the dual three-phase permanent magnet synchronous motor, and output the d-axis and q-axis currents of the two sets of windings at an instant kT.sub.s; a current prediction module, wherein the input end of the current prediction module is connected to the output end of the dual synchronous coordinate transformation module, and the current prediction module is configured to predict the d-axis and q-axis currents of the two sets of windings and the DC-link mid-point voltage at an instant (k+1)T.sub.s; a discrete-time motor model-based deadbeat control module, wherein the input end is connected to the output end of the current prediction module, another input end is connected to the output end of the maximum torque per ampere control module, and the discrete-time motor model-based deadbeat control module is configured to calculate and then output d-axis and q-axis reference voltages of the two sets of windings; a polar coordinate transformation module, wherein the input end of the polar coordinate transformation module is connected to the output end of the discrete-time motor model-based deadbeat control module, and the polar coordinate transformation module is configured to perform polar coordinate transformation on the d-axis and q-axis reference voltages of the two sets of three-phase windings and the d-axis reference voltage and the q-axis reference voltage of the second set of windings; and a multi-step MPC module, configured to: sample phase currents of the second set of windings at the instant kT.sub.s, sample phase currents of the first set of windings and load control vectors of the second set of windings at an instant (k+1/2)T.sub.s, load control vectors of the first set of windings and complete tracking of the reference values of the currents by the second set of windings at the instant (k+1)T.sub.s, complete tracking of the reference values of the currents by the first set of windings at an instant (k+3/2)Ts, use a two-layer MPC strategy with an objective that d-axis total current is equally divided for d-axis currents of two sets of windings, q-axis total current is equally divided for q-axis currents of the two sets of windings, and the d-axis total current and the q-axis total current follow the reference values, to determine a reference value of the d-axis current and a reference value of the q-axis current of each set of windings, select candidate vectors that do not cause switch transitions between P level and N level under a constraint of the reference values of the d-axis and q-axis currents, and calculating cost functions for the evaluation of candidate vectors to obtain a candidate vector with the smallest cost function as a final loaded vector

9. The system for implementing the control method of a dual three-phase permanent magnet synchronous motor according to claim 8, wherein the multi-step MPC module stores a computer program, and the program, when being executed by a processor, implements the method with controlling a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] FIG. 1 is a block diagram of multi-step MPC of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures, where 1.1 is a PI controller used in closed-loop speed control, 1.2 is a maximum torque per ampere control module, 1.3 is a discrete-time motor model-based deadbeat control module, 1.4 is a polar coordinate transformation module, 1.5 is a multi-step MPC module, 1.6 is the DC link, 1.7 is a dual three-phase three-level inverter, 1.8 is a dual three-phase permanent magnet synchronous motor, 1.9 is a position encoder, 1.10 is a dual synchronous coordinate transformation module, 1.11 is a current prediction module, and 1.12 is a speed calculation module.

[0021] FIG. 2 is a flowchart of a multi-step MPC method.

[0022] FIG. 3 is a voltage space vector distribution diagram of the first set of three-level inverter in dual three-phase permanent magnet synchronous motor drives and a schematic diagram of candidate vector selection based on the triangular area method, where

[0023] V.sub.ref1 is the reference voltage vector corresponding to the first set of windings.

[0024] FIG. 4 is a voltage space vector distribution diagram of the second set of three-level inverter in dual three-phase permanent magnet synchronous motor drives and a schematic diagram of candidate vector selection based on the triangular area method, where

[0025] V.sub.ref2 is a reference voltage vector corresponding to the second set of windings.

[0026] FIG. 5 is a schematic diagram of the intersectional traversal of candidate vectors of a dual three-phase inverter in conventional synchronous control.

[0027] FIG. 6 is a voltage space vector distribution diagram of the first set of three-level inverter in the dual three-phase permanent magnet synchronous motor drives and a schematic diagram of candidate vector selection based on a hexagonal area method.

[0028] FIG. 7 is the voltage space vector distribution diagram of the second set of three-level inverter in the dual three-phase permanent magnet synchronous motor drives and a schematic diagram of candidate vector selection based on the hexagonal area method.

[0029] FIG. 8 is an example diagram of multi-step MPC of qi-axis current.

[0030] FIG. 9 is a sequence diagram of predictive control of the synchronous predictive control method.

[0031] FIG. 10 is a sequence diagram of predictive control of a control method by alternately performing sampling and control procedures.

[0032] FIG. 11 is experimental waveform diagrams of A-, B-, D-, and E-phase currents of PMSM in a conventional synchronous control method, where i.sub.A, i.sub.B, i.sub.D, and i.sub.E are experimental waveforms of the A-, B-, D-, and E-phase currents of the motor, respectively.

[0033] FIG. 12 is experimental waveform diagrams of A-, B-, D-, and E-phase currents of PMSM in the control method by alternately performing sampling and control procedures.

[0034] FIG. 13 is experimental waveform diagrams of DC-link capacitor voltages and mid-point voltage in the conventional synchronous control method.

[0035] FIG. 14 is experimental waveform diagrams of DC-link capacitor voltages and mid-point voltage in the control method by alternately performing sampling and control procedures.

[0036] FIG. 15 shows experimental results of speed and torque waveforms in the conventional synchronous control method.

[0037] FIG. 16 shows experimental results of speed and torque waveforms in the control method by alternately performing sampling and control procedures.

[0038] FIG. 17 shows experimental results of dynamic responses of speed and torque waveforms in the conventional synchronous control method.

[0039] FIG. 18 shows amplified experimental waveforms results of dynamic responses of speed and torque waveforms in the conventional synchronous control method.

[0040] FIG. 19 shows experimental results of dynamic responses of speed and torque waveforms in the control method by alternately performing sampling and control procedures.

[0041] FIG. 20 shows amplified experimental waveforms results of dynamic responses of speed and torque waveforms in the control method by alternately performing sampling and control procedures.

[0042] FIG. 21 shows execution time of procedures obtained through experiments in the conventional synchronous control method and the control method by alternately performing sampling and control procedures.

DETAILED DESCRIPTION

[0043] The inventive concept of the present invention is further described below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are merely used for describing the present invention rather than limiting the scope of the present invention. After reading the present invention, any equivalent modification made by a person skilled in the art shall fall within the scope defined by the appended claims of this application.

[0044] The present invention provides a control method of a dual three-phase permanent magnet synchronous motor by alternately performing sampling and control procedures. To improve the control performance of the motor drive system with low switching frequencies, the present invention doubles the equivalent sampling frequency of the motor drive system by alternately performing sampling and control procedures of the dual three-phase windings and corresponding converters without changing the sampling frequency of a single set of three-phase windings. Therefore, the steady-state and dynamic control performance of the motor drive system with low switching frequencies is improved effectively.

[0045] For a system for controlling a dual three-phase permanent magnet synchronous motor under a low switching frequency condition, the present invention provides a multi-step model predictive control scheme of alternately performing sampling and control procedures. The scheme of the control method by alternately performing sampling and control procedures is shown in FIG. 1. The control system includes a speed PI controller 1.1, a maximum torque per ampere control module 1.2, a discrete-time motor model-based deadbeat control module 1.3, a polar coordinate transformation module 1.4, a multi-step MPC module 1.5, the DC link 1.6, a dual three-phase three-level inverter 1.7, a dual three-phase permanent magnet synchronous motor 1.8, a position encoder 1.9, a dual synchronous coordinate transformation module 1.10, a current prediction module 1.11, and a speed calculation module 1.12. The position encoder 1.9 mounted on an output shaft of the dual three-phase permanent magnet synchronous motor 1.8 is configured to detect an angular position θ.sub.e of the motor. The speed calculation module 1.12 calculates a rotating speed n according to the angular position θ.sub.e, and feeds the difference between the rotating speed n and the reference value n* into the speed PI controller 1.1. The speed PI controller 1.1 generates the torque reference value T.sub.e*. Then the maximum torque per ampere control module 1.2 generates dq-axis reference currents according to the torque reference T.sub.e*. Equal division is performed to obtain reference values i.sub.d1* and i.sub.q1* of dq-axis currents of the first set of windings and reference values i.sub.d2* and i.sub.q2* of dq-axis currents of the second set of windings. Six-phase currents i.sub.A, i.sub.B, i.sub.C, i.sub.D, i.sub.E, and i.sub.F obtained by sampling circuits are processed by the dual synchronous coordinate transformation module 1.10 to obtain dq-axis currents i.sub.d1.sup.k, i.sub.q1.sup.k, i.sub.d2.sup.k, and id of two sets of windings at instant kT.sub.s in the dual synchronous coordinate system. Then the current prediction module 1.11 compensates for the digital delay. Values of dq-axis currents i.sub.d1.sup.k+1, i.sub.q1.sup.k+1, i.sub.d2.sup.k+1 and i.sub.q2.sup.k+1 and DC-link mid-point voltage V.sub.n.sup.k+1 at the next instant (k+1)T.sub.s are predicted. According to the reference values of the currents and predicted values of the currents, the discrete-time motor model-based deadbeat control module 1.3 calculates reference voltages U.sub.d1* and U.sub.q1* of the first set of windings and reference voltages U.sub.d2* and U.sub.q2* of the second set of windings according to the reference values of the currents and predicted values of the currents. The polar coordinate transformation module 1.4 and the multi-step MPC module 1.5 determine the final loaded vector. Consequently, the dual three-phase three-level inverter 1.7 is controlled to implement the control algorithm for the dual three-phase permanent magnet synchronous motor 1.8.

[0046] In a multi-step MPC method by alternately performing sampling and control procedures of the present invention, a specific procedure of determining a loaded the vector by the multi-step model predictive control module is shown in FIG. 2, and includes the following steps.

[0047] Step 2.1: Select, according to results of the polar coordinate transformation of reference voltages U.sub.d1* and U.sub.q1* of the first set of windings and reference voltages U.sub.d2* and U.sub.q2* of the second set of windings, vectors in a triangular sector in which reference voltage vectors of an corresponding inverter are located as candidate vectors.

[0048] Step 2.2: Determine whether there is at least one candidate vector among the candidate vectors selected in step 2.1 that does not cause switch transitions between P level and N level, and if yes, perform step 2.4, or otherwise, perform step 2.3.

[0049] Step 2.3: Expand a selection range from the triangular sector in which the reference voltage vectors are located to a hexagonal sector in which the reference voltage vectors are located, and perform the operation of step 2.4 on the candidate vectors within the hexagonal sector.

[0050] Step 2.4: Directly disqualify candidate vectors that cause switch transitions between P level and N level, and retain other candidate vectors.

[0051] Step 2.5: Control the dual three-phase three-level inverter 1.7 based on the candidate vectors determined in step 2.4, acquire six-phase currents at present an instant, and then obtain the dq-axis current values of i.sub.d1.sup.k, i.sub.q1.sup.k, i.sub.d2.sup.k and i.sub.q2.sup.k. and predict the values of controlled variables at the next instant, and obtain values of i.sub.d1.sup.k+1, i.sub.q1.sup.k+1, i.sub.d2.sup.k+1, i.sub.q2.sup.k+1 and V.sub.n.sup.k+1.

[0052] Step 2.6: Subsequently determine whether there is a candidate vector under the effect of which the predicted values of controlled variables i.sub.d1, i.sub.q1, i.sub.d2, i.sub.q2, and V.sub.n at the next instant are all within the error bounds, that is, determine whether there exists an extrapolatable candidate vector, and if yes, perform step 2.7, or otherwise, perform step 2.9.

[0053] Step 2.7: Delete candidate vectors unable to be extrapolated, and perform linear extrapolation on the remaining candidate vectors.

[0054] Step 2.8: Calculate a switching frequency based on extrapolation results, evaluate the candidate vectors by using the calculated switching frequency as a cost function, and perform step 2.10.

[0055] Step 2.9: Evaluate the candidate vectors by using a weighting factor-based cost function where the absolue control errors of the controlled variables are summarized with corresponding weighting factors, and perform step 2.10.

[0056] Step 2.10: Obtain a final loaded vector based on the result of step 2.8 or step 2.9. A candidate vector selection based on the triangular area method in the present invention is described in FIG. 3 and FIG. 4. Each leg of the three-level inverter can generate three voltage levels of U.sub.dc/2, 0, −U.sub.dc/2, which is represented by symbols P, O, and N respectively. V.sub.ref1 and V.sub.ref2 are reference voltage vectors of the first set of windings and the second set of windings, respectively. A triangular area in which V.sub.ref1 is located includes four vectors: PON, PNN, POO, and ONN. A triangular area in which V.sub.ref1 is located includes four vectors: ONN, POO, PNN, and PNO. A selection process of the above candidate vectors corresponds to that in step 2.1.

[0057] The process of intersectional traversal of candidate vectors of the dual three-phase inverter in conventional synchronous control in comparison with the present invention is shown in FIG. 5. Starting from step 2.1, the first set of windings has four options. For each option, the second set of windings has four corresponding options. Therefore, the conventional synchronous control method finally obtains 16 combinations of candidate vectors: {PNN, POO}, {PNN, ONN}, {PNN, PNO}, {PNN, PNN}, {POO, POO}, {POO, ONN}, {POO, PNO}, {POO, PNN}, {ONN, POO}, {ONN, ONN}, {ONN, PNO}, {ONN, PNN}, {PON, POO}, {PON, ONN}, {PON, PNO}, and {PON, PNN}.

[0058] A candidate vector selection based on the hexagonal area method in the present invention is described in FIG. 6 and FIG. 7. V.sub.ref1 and V.sub.ref2 are the reference voltage vectors of the first set of windings and the second set of windings, respectively. Considering that the precondition of using the hexagonal area method is that the triangular area method does not satisfy the condition, vectors located in both the hexagonal area and triangular area should be excluded, and only vectors that are only in the hexagonal area but are not in the triangular area should be retained. For example, when V.sub.ref1 and V.sub.ref2 are located at positions shown in FIG. 6 and FIG. 7, respectively, vectors in the hexagonal area in which V.sub.ref1 is located are PPO, OON, OOO, POP, ONO, PNO, PON, PNN, POO, and ONN. The candidate vectors PON, PNN, POO, and ONN in the triangular area are excluded. Consequently, the final candidate vectors determined by using the hexagonal area method are a total of 6 vectors PPO, OON, OOO, POP, ONO, and PNO. Vectors in the hexagonal area in which V.sub.ref2 is located are a total of 10 vectors PPO, OON, PON, OOO, POP, ONO, ONN, POO, PNN, and PNO. The candidate vectors ONN, POO, PNN, and PNO in the triangular area in which V.sub.ref2 is located are excluded. Consequently, the final candidate vectors determined by using the hexagonal area method are a total of 6 vectors PPO, OON, PON, OOO, POP, and ONO.

[0059] The evaluation method with a candidate vector based on an extrapolation method in the present invention is described in FIG. 8. The predicted and extrapolated trajectories of vectors VC.sub.3, VC.sub.1, VC.sub.2, and VC.sub.4 are shown in the four trajectories in FIG. 8. Solid line parts are predicted trajectories based on the discrete-time model. Dashed line parts are linearly extrapolated trajectories. If the predicted value of the variable is within the hysteresis bound, the trajectory extrapolation is able to be conducted to find the length to hit the error bounds, which is defined as the length of extrapolation. For example, extrapolation length of VC.sub.3, VC.sub.1, VC.sub.2, and VC.sub.4 with respect to qi-axis current in FIG. 8 are 1, 2, 3, and 4 respectively. To ensure that all controlled variables are within error ranges, for each candidate vector, the smallest value among the extrapolation length of all the controlled variables is selected as a final extrapolation length N for an entire extrapolation process when the candidate vector is used to perform a control procedure. To introduce an evaluation indicator of the switching frequency, the number of commutations is defined for each vector candidate as follows.

[00001]$\begin{array}{cc}{n}_s=\underset{x}{.Math.}\left[S_x\left(k+1\right)-S_x\left(k\right)\right],x=a,b,c,d,e,f,& \left(1\right)\end{array}$

[0060] where T.sub.s is the sampling period, a script (k) denotes variable values sampled at the instant kT.sub.s, and S.sub.x is a switch function, which is defined as:

[00002]$\begin{array}{cc}{S}_x=\{\begin{array}{cc}1& \mathrm{The}\mathrm{phase}\mathrm{outputs}aP\mathrm{level}\\ 0& \mathrm{The}\mathrm{phase}\mathrm{outputs}\mathrm{anOlevel}x\in \left\{a,b,c,d,e,f\right\}\\ -1& \mathrm{The}\mathrm{phase}\mathrm{outputs}\mathrm{an}N\mathrm{level}\end{array}.& \left(2\right)\end{array}$

[0061] Obviously, when a total extrapolation length is larger and the number of commutations is smaller, a control performance is better and the switching frequency is smaller. Therefore, the cost function is defined as:

[00003]$\begin{array}{cc}{g}_1=\frac{n_s}{N}.& \left(3\right)\end{array}$

Equation (3) is the cost function in step 2.8. The candidate vector with the smallest value of the cost function is selected as the final loaded vector.

[0062] The weighting factor-based cost function where the absolue control errors of the controlled variables are summarized with corresponding weighting factors is shown in Equation (4):

[00004]$$\begin{gathered} \begin{array}{cc}{g}_2=\underset{x}{.Math.}{\lambda }_x{g}_x,x\in \left\{i_{d1},i_{q1},i_{d2},i_{q2},V_n\right\} \\ {g}_x=\{\begin{array}{cc}x\left(k+2\right)-x_{\max },& x\left(k+2\right)>x_{\max }\\ x_{\min }-x\left(k+2\right),& x\left(k+2\right)<x_{\min }\\ 0,& x_{\min }\le x\left(k+2\right)\le x_{\max }\end{array},& \left(4\right)\end{array} \end{gathered}$$

where λ.sub.x is a weight coefficient of a variable x, xm,n and xmax are the allowable minimum and maximum value of the variable x, respectively. Subsequently, it gets x.sub.min=x.sub.ref−Δx, x.sub.max=x.sub.ref+Δx. Δx is an allowable absolute error between a predicted value and a reference value of the variable x at a moment (k+2)T.sub.s, and x.sub.ref is the reference value of the variable x. During the sampling and control procedure of the first set of windings, x∈{i.sub.d1, i.sub.q1, V.sub.n}. During sampling and control procedure of the second set of windings, x∈{i.sub.d2, i.sub.q2, V.sub.n}. Equation (4) is the cost function in step 2.9. The candidate vector with the smallest value of the cost function is selected as the final loaded vector.

[0063] A sequence diagram of the control method by alternately performing sampling and control procedures for the dual three-phase windings in the present invention is shown in FIG. 9 and FIG. 10. FIG. 9 is a sequence diagram of the synchronous predictive control. Sampling points on the time line of winding 1 and winding 2 represent sampling instants of winding 1 and winding 2 with a synchronous control sequence. Loading points on the time line of winding 1 and winding 2 represent vector loading instants of winding 1 and winding 2 with the synchronous control sequence. Reference tracking points on the time line of the winding 1 and winding 2 are target instants at which currents of winding 1 and winding 2 are expected to follow reference values with the synchronous control sequence. The delay time between a sampling instant and a vector loading instant with the synchronous control sequence is one sampling period. FIG. 10 is a sequence diagram of a control method by alternately performing sampling and control procedures. Sampling points on the time line of winding 1 winding 2 are sampling instants of winding 1 and winding 2 under the sequence of the control method by alternately performing sampling and control procedures. Loading points on the time line of winding 1 and winding 2 are vector loading instants of winding 1 and winding 2 under the sequence of the control method by alternately performing sampling and control procedures. Reference tracking points on the time line of winding 1 and winding 2 are target instants at which the currents of winding 1 and winding 2 are expected to follow reference currents under the sequence of the control method by alternately performing sampling and control procedures. A delay time between sampling and vector loading instants under the sequence of the control method by alternately performing sampling and control procedures is half the sampling period. As shown in FIG. 9, a control strategy in which sampling instants, vector loading instants, and reference tracking instants of the dual windings are simultaneous is called synchronous control. The control strategy in which sampling instants, vector loading instants, the reference tracking instants are interleaved by half of the sampling period is called a control method by alternately performing sampling and control procedures. In the synchronous control, in both sets of windings, sampling is performed at an instant kT.sub.s, new switching vectors are loaded at the instant (k+1)T.sub.s, and the objective is to track the reference values at the instant (k+2)T.sub.s. However, in the control method by alternately performing sampling and control procedures, in the first set of windings, sampling is performed at an instant (k+1/2)T.sub.s, new vectors are loaded at the instant (k+1)T.sub.s, and the objective is to track the reference values at an instant (k+3/2)T.sub.s. In the second set of windings, sampling is performed at the instant kT.sub.s, new vectors are loaded at the instant (k+1/2)T.sub.s, and the objective is to track the reference values at the instant (k+1)T.sub.s. Therefore, the sampling, the loading, and the reference tracking instants of the two sets of windings are staggered by half of the sampling period.

[0064] A two-layer MPC strategy in the present invention is shown in Equations (5), (6), (7), and (8). First-layer MPC is embedded in a procedure of selecting candidate vectors based on a deadbeat control. With the objective that d.sub.1q.sub.1-axis currents and d.sub.2q.sub.2-axis currents track the equally divided reference currents, the reference vector is calculated as shown in Equation (5):

[00005]$\begin{array}{cc}\{\begin{array}{c}{u}_{d1}^{*}=R_s{i}_{d1}\left(k+1\right)+L_d\left(i_{d1}^{*}-i_{d1}\left(k+1\right)\right)/\left(T_s/2\right)-\omega \left(k\right)L_{\mathrm{qm}}{i}_{q2}\left(k+1\right)+\\ L_{\mathrm{dm}}\left(i_{d2}^{*}-i_{d2}\left(k+1\right)\right)/\left(T_s/2\right)-\omega \left(k\right)L_q{i}_{q1}\left(k+1\right)\\ u_{q1}^{*}=R_s{i}_{q1}\left(k+1\right)+L_q\left(i_{q1}^{*}-i_{q1}\left(k+1\right)\right)/\left(T_s/2\right)+\omega \left(k\right)L_{dm}{i}_{d2}\left(k+1\right)+\\ L_{qm}\left(i_{q2}^{*}-i_{q2}\left(k+1\right)\right)/\left(T_s/2\right)+\omega \left(k\right)L_d{i}_{d1}\left(k+1\right)+\omega \left(k\right){\psi }_f\\ u_{d2}^{*}=R_s{i}_{d2}\left(k+1\right)+L_d\left(i_{d2}^{*}-i_{d2}\left(k+1\right)\right)/\left(T_s/2\right)-\omega \left(k\right)L_{qm}{i}_{q1}\left(k+1\right)+\\ L_{dm}\left(i_{d1}^{*}-i_{d1}\left(k+1\right)\right)/\left(T_s/2\right)-\omega \left(k\right)L_q{i}_{q2}\left(k+1\right)\\ u_{q2}^{*}=R_s{i}_{q2}\left(k+1\right)+L_q\left(i_{q2}^{*}-i_{q2}\left(k+1\right)\right)/\left(T_s/2\right)+\omega \left(k\right)L_{dm}{i}_{d1}\left(k+1\right)+\\ L_{qm}\left(i_{q1}^{*}-i_{q1}\left(k+1\right)\right)/\left(T_s/2\right)+\omega \left(k\right)L_d{i}_{d2}\left(k+1\right)+\omega \left(k\right){\psi }_f\end{array},& \left(5\right)\end{array}$

where i.sub.d1*=i.sub.d2*=(1/2)id*, i.sub.q1*=i.sub.q2*=(1/2)i.sub.q*, L.sub.d and L.sub.q are d-axis inductance and q-axis inductance, respectively, u.sub.d1*, u.sub.q1*, u.sub.q2*, and u.sub.q2* are dq-axis reference voltages of the two sets of windings, respectively, R.sub.s is a stator resistance, i.sub.d1, i.sub.q1, i.sub.d2, and i.sub.q2 are dq-axis currents of the two sets of windings, respectively, L.sub.dm and L.sub.qm are d-axis mutual inductance and q-axis mutual inductance, respectively, ω is an electric angular speed, and ψ.sub.f is a permanent magnet flux linkage. The objective of the second-layer MPC is to make d-axis total current and q-axis total current of the dual windings follow corresponding reference values obtained by the maximum torque per ampere control module. The sampling instant of winding 1 shown in FIG. 10 is used as an example. The switching state of the second inverter remains unchanged between the sampling instant and a reference tracking instant of winding 1. Therefore, dq-axis voltages u.sub.d2 and u.sub.q2 of winding 2 remain unchanged. According to a discrete-time model of the motor, state variables of the motor have the following constraint conditions between the sampling instant and the reference tracking instant of winding 1:

[00006]$\begin{array}{cc}\{\begin{array}{c}{u}_{d2}=R_s{i}_{d2}\left(k+1\right)+L_d\left(i_{d2}\left(k+3/2\right)-i_{d2}\left(k+1\right)\right)/\left(T_{s}l2\right)+L_{dm}(i_{d1}\left(k+3/2\right)-\\ i_{d1}\left(k+1\right))/\left(T_s/2\right)-\omega \left(k\right)L_q{i}_{q2}\left(k+1\right)-\omega \left(k\right)L_{qm}{i}_{q1}\left(k+1\right)\\ u_{q2}=R_s{i}_{q2}\left(k+1\right)+L_q\left(i_{q2}\left(k+3/2\right)-i_{q2}\left(k+1\right)\right)/\left(T_s/2\right)+L_{qm}(i_{q1}\left(k+3/2\right)-\\ i_{q1}\left(k+1\right))/\left(T_s/2\right)+\omega \left(k\right)L_d{i}_{d2}\left(k+1\right)+\omega \left(k\right){\psi }_f+\omega \left(k\right)L_{dm}{i}_{d1}\left(k+1\right)\end{array}.& \left(6\right)\end{array}$

On the other hand, expressions of the objective of the second-layer MPC are:

[00007]$\begin{array}{cc}\{\begin{array}{c}{i}_{d1}\left(k+3/2\right)+i_{d2}\left(k+3/2\right)=i_d^{*}\\ i_{q1}\left(k+3/2\right)+i_{q2}\left(k+3/2\right)=i_q^{*}\end{array}.& \left(7\right)\end{array}$

According to Equations (6) and (7), reference values of d.sub.1q.sub.1-axis currents of winding 1 are solved as shown in Equation (8):

[00008]$\begin{array}{cc}\{\begin{array}{c}{i}_{d1}\left(k+3/2\right)=(L_d{i}_{d2}\left(k+1\right)+L_{dm}{i}_{d1}\left(k+1\right)-L_d{i}_d^{*}+u_{d2}{T}_s/2-R_s{T}_s{i}_{d2}\left(k+1\right)/2+\\ \omega \left(k\right)L_q{T}_s{i}_{q2}\left(k+1\right)/2+\omega \left(k\right)L_{qm}{T}_s{i}_{q1}\left(k+1\right)/2)/\left(L_{dm}-L_d\right)\\ i_{q1}\left(k+3/2\right)=(L_{qm}{i}_{q1}\left(k+1\right)+L_q{i}_{q2}\left(k+1\right)-T_s\omega \left(k\right){\psi }_f/2-L_q{i}_q^{*}-R_s{T}_s{i}_{q2}\left(k+1\right)/2-\\ \omega \left(k\right)L_d{T}_s{i}_{d2}\left(k+1\right)/2-\omega \left(k\right)L_{dm}{T}_s{i}_{d1}\left(k+1\right)/2+u_{q2}{T}_s/2)/\left(L_{qm}-L_q\right)\end{array}.& \left(8\right)\end{array}$

[0065] The reference currents shown in Equation (8) are the reference currents in step 2.8 and step 2.9. Similarly, during sampling and control of the second set of windings, reference values of d.sub.2q.sub.2-axis currents of the winding 2 are calculated as follows:

[00009]$\begin{array}{cc}\{\begin{array}{c}{i}_{d2}\left(k+1\right)=(L_d{i}_{d1}\left(k+1/2\right)+L_{dm}{i}_{d2}\left(k+1/2\right)-L_d{i}_d^{*}+u_{d1}{T}_s/2-R_s{T}_s{i}_{d1}\left(k+1/2\right)/2+\\ \omega \left(k\right)L_q{T}_s{i}_{q1}\left(k+1/2\right)/2+a)\left(k\right)L_{qm}{T}_s{i}_{q2}\left(k+1/2\right)/2)/\left(L_{dm}-L_d\right)\\ i_{q2}\left(k+1\right)=(L_q{i}_{q1}\left(k+1/2\right)+L_{qm}{i}_{q2}\left(k+1/2\right)-T_s\omega \left(k\right){\psi }_f/2-L_q{i}_q^{*}-R_s{T}_s{i}_{q1}\left(k+1/2\right)/2-\\ \omega \left(k\right)L_d{T}_s{i}_{d1}\left(k+1/2\right)/2-\omega )\left(k\right)L_{dm}{T}_s{i}_{d2}\left(k+1/2\right)/2+u_{q1}{T}_s/2)/\left(L_{qm}-L_q\right)\end{array}.& \left(9\right)\end{array}$

[0066] It should be noted that in the control method by alternately performing sampling and control procedures, since a switching state of one inverter remains unchanged, the dimensionality of the system is reduced from four dimensions to two dimensions. The state variable dimensionality related to the motor is also reduced from four dimensions to two dimensions. In the present invention, three variables, that is, the dq-axis currents of the sampled windings and DC-link mid-point voltage, are selected as the controlled variables of the control method by alternately performing sampling and control procedures.

[0067] Verification results of experiments of the present invention are shown in FIG. 11 to FIG. 21. The experiments are carried out based on a laboratory prototype of the neutral point clamped three-level inverter-fed dual three-phase PMSM drive. The control algorithm is implemented by the DSP TI-TMS320F28346. The control signals for power devices are generated by FPGA Xilinx-Spartan6 XC6SLX25 through a driving circuit. A permanent magnet synchronous generator with the external resistors working as the load is mechanically coupled to the dual three-phase motor. The used parameters of the dual three-phase motor are as follows: The number of pole pairs is 4. The q-axis inductance is 13 mH. The d-axis inductance is 10 mH. The leakage inductance is 5 mH. The permanent magnet flux linkage is 0.08 Wb. The stator resistance is 0.225 a The DC-link capacitance is 4000 g. The sampling frequency of a single set of windings is 7.5 kHz.

[0068] Experimental results of the control method by alternately performing sampling and control procedures provided in the present invention under the steady state condition are shown in FIG. 11 to FIG. 16, including waveforms of stator currents, waveforms of capacitor voltages, mid-point voltage fluctuation, and waveforms of speed and torque in the conventional synchronous control method and the control method by alternately performing sampling and control procedures. Compared with synchronous control, when the control method by alternately performing sampling and control procedures is used, the current total harmonic distortion (THD) is reduced from 19.36% to 9.20%, the switching frequency is reduced from 724 Hz to 489 Hz, as shown in FIG. 11 and FIG. 12. The mid-point voltage fluctuation range is reduced from 1.6 V to 1.3 V, as shown in FIG. 13 and FIG. 14. u.sub.C1 and u.sub.C2 are the upper and lower DC-link capacitor voltages respectively. The torque ripple is reduced from 1.21 Nm to 0.76 Nm, as shown in FIG. 15 and FIG. 16. n.sub.ref is the reference speed, and n is the sampled speed. Te represents the torque of the motor. According to the comparison results in FIG. 11 to FIG. 16, the control method by alternately performing sampling and control procedures improves the steady-state control performance of the dual three-phase PMSM drive system.

[0069] Experimental results of the control method by alternately performing sampling and control procedures provided in the present invention at dynamic operations are shown in FIG. 17 to FIG. 20, including waveforms of speed and torque in the conventional synchronous control method and the control method by alternately performing sampling and control procedures. T.sub.e_ref is torque reference. Compared with synchronous control, when the control method by alternately performing sampling and control procedures is used, the rise delay of the torque is reduced from 133 μs to 67 μs, and the response time of the torque is reduced from 2200 μs to 1800 μs, as shown in FIG. 18 and FIG. 20. According to comparison results in FIG. 17 to FIG. 20, the control method by alternately performing sampling and control procedures effectively improves the dynamic control performance of the dual three-phase PMSM drive system.

[0070] Experimental results in reducing control algorithm complexity of the control method by alternately performing sampling and control procedures provided in the present invention are shown in FIG. 21. The whole execution time includes an analog-to-digital conversion procedure, a delay compensation procedure, an MPC algorithm procedure, and a vector loading procedure in the conventional synchronous control and the control method by alternately performing sampling and control procedures. In the conventional synchronous control, the execution time of the analog-to-digital conversion procedure is 11.24 μs, the execution time of the delay compensation procedure is 6.62 μs, the execution time of the MPC procedure is 95.69 μs, and the execution time of the vector loading procedure is 3.01 μs. In the control method by alternately performing sampling and control procedures, the execution time of the analog-to-digital conversion procedure is 11.24 μs, the execution time of the delay compensation procedure is 6.62 μs, the execution time of the MPC procedure is 20.28 μs, and the execution time of the vector loading procedure is 3.01 μs. During each sampling period, the four procedures are performed twice. The conventional synchronous control and the control method by alternately performing sampling and control procedures have the same execution time of the analog-to-digital conversion procedure, the delay compensation procedure, and the vector loading procedure. However, because the control method by alternately performing sampling and control procedures reduces the dimensionality of the system, the execution time of the MPC algorithm procedure is significantly less than that in the conventional synchronous control. Therefore, during the sampling period of a single set of windings, although analog-to-digital conversion, delay compensation, and vector loading procedures are performed twice in the control method by alternately performing sampling and control procedures, the total execution time of the procedures is still less than that in the conventional synchronous control. According to the comparison results in FIG. 21, it can be concluded that the multi-step MPC scheme with alternately performing sampling and control procedures effectively reduces the computation burden of the algorithm.