CN111969900B - NPC three-level BLDC torque ripple minimization control method based on duty ratio modulation - Google Patents
NPC three-level BLDC torque ripple minimization control method based on duty ratio modulation Download PDFInfo
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Abstract
The invention provides a duty ratio modulated NPC three-level BLDC torque ripple minimization control method, which comprises the steps of firstly obtaining three-phase stator current through a current sensor, and obtaining a rotor position angle and an electrical angular velocity through an encoder to calculate three-phase back electromotive force at different rotor positions; then, a dq axis current predicted value at the moment k +1 is obtained through a coordinate change and current prediction model; then, the duty ratio calculation module is used for obtaining the action time of the optimal vector; and finally, outputting a switching state which is favorable for inhibiting the fluctuation of the midpoint potential through midpoint potential balance control to drive the motor. The invention effectively reduces the torque pulsation of the brushless direct current motor through duty ratio modulation, and inhibits the fluctuation of the neutral point potential of the NPC three-level inverter through neutral point potential balance control.
Description
Technical Field
The invention relates to a duty ratio modulated NPC three-level BLDC torque ripple minimization control method, and belongs to the field of motor driving and control.
Background
Brushless direct current (BLDC) motors have the advantages of simple structure, large starting torque, no commutation spark, long service life, etc., and are receiving wide attention in the fields of electric vehicles, aerospace, industrial control, automation, etc. The conventional control method of the brushless direct current motor mainly comprises square wave control, vector control and the like. The square wave control is realized by a Hall position sensor or a position-free control algorithm, and the commutation is carried out once every 60 degrees of electric angle according to the position of the rotor, so that the current waveform similar to the square wave can be obtained, and the method has the advantages of simple control, low requirement on hardware and the like, but has the defects of large torque fluctuation and low efficiency, and is usually applied to occasions with low requirement on the performance of the motor. Vector control is a control strategy of sine wave current, a commutation concept of square wave control does not exist, smaller torque fluctuation and current harmonic waves can be obtained, but complex coordinate transformation is required, and the requirement on hardware is increased. In order to further simplify the control algorithm and improve the dynamic response, the model prediction current control has received extensive attention.
The model prediction current control selects the optimal voltage vector acting on the inverter through the rolling advantage of the cost function, and can avoid the calculation of a complex trigonometric function in vector control. In addition, a current inner loop in vector control is replaced by the current prediction module, the dynamic response of the system can be further improved, and a complicated adjusting process of a current loop PI parameter is avoided. However, in the conventional model prediction current control, only one voltage vector acts in one sampling period, so that it is difficult to ensure that the actual value of the current accurately tracks the change of the reference value of the current, which causes large torque fluctuation and affects the steady-state performance of the system.
Disclosure of Invention
The technical problem is as follows: aiming at the technical problems, the invention provides a duty ratio modulated NPC three-level BLDC torque ripple minimization control method, which can further reduce the torque ripple of the BLDC, improve the dynamic response of a system and ensure the neutral point potential balance of an NPC three-level inverter through a duty ratio control strategy.
The technical scheme is as follows: a duty cycle modulated NPC three level BLDC torque ripple minimization control method, comprising the steps of:
step 1: will give a rotation speed Nr refAnd the actual rotational speed N obtained by the encoderrThe deviation between the q-axis current reference value i is obtained through a PI controller of a rotating speed loopq refAnd giving a d-axis current reference value id ref＝0；
Step 2: obtaining rotor position information theta and electrical angular velocity omega from an encodereAnd calculates the three-phase back electromotive force e of the motor at the moment ka(k)，eb(k) And ec(k) Obtaining the back electromotive force e under the stationary coordinate system at the moment k through Clark transformationα(k)、eβ(k) And obtaining the back electromotive force e under a two-phase rotating coordinate system at the moment k through Park transformationd(k)、eq(k)；
And step 3: three-phase stator current i at moment k is measured through three current sensorsa(k)，ib(k) And ic(k) Obtaining the stator current i under the stationary coordinate system at the moment k through Clark transformationα(k)、iβ(k) Obtaining the stator current i under the two-phase rotating coordinate system at the moment k through Park conversiond(k)、iq(k)；
And 4, step 4: carrying out discretization processing on the current differential equation at the moment k through a first-order Euler function to obtain the stator current i under a two-phase rotating coordinate system at the moment k +1d(k +1) and iq(k+1)；
And 5: obtaining an optimal voltage vector V by rolling optimization of a cost functionoptAnd obtaining the action time t of the optimal vector by a duty ratio modulation method according to the dead-beat control principleopt；
Step 6: and obtaining an optimal switching state which is beneficial to inhibiting the fluctuation of the midpoint potential through a balance control algorithm of the midpoint potential to drive the inverter.
Further, in the step 1, an electrical angle θ of the brushless dc motor is obtained from the encoder, and an electrical angular velocity ω is calculated by the formula (1)eThen calculating the actual rotating speed N of the motor according to the formula (2)r(ii) a Then setting the given rotating speed N of the motorr refAnd the actual rotational speed NrDifference e ofnCalculating a q-axis current reference value i according to a formula (3) through a PI controller of a rotating speed ringq ref；
Wherein k ispAnd kiRespectively representing the proportional and integral gains of the rotating speed loop PI controller, and s represents a complex variable.
Further, in the step 2, three-phase back electromotive force e at different rotor positions of the motor at the time k is calculated according to the table 1a(k)，eb(k) And ec(k) (ii) a Then, according to formula (4)The Clark transformation shown obtains the back electromotive force e under the stationary coordinate system at the moment kα(k) And eβ(k) And then obtaining the back electromotive force e under the two-phase rotating coordinate system at the moment k through Park change shown in formula (5)d(k) And eq(k)；
TABLE 1
Wherein the coefficient m is 2npψf，npRepresenting the number of pole pairs, #fRepresenting a permanent magnet flux linkage.
Further, in the step 3, the stator current i in the stationary coordinate system at the time k is calculated by the formula (6)α(k) And iβ(k) (ii) a Calculating the stator current i in the two-phase rotating coordinate system at the k moment of the dq axis by the formula (7)d(k) And iq(k)；
Further, the step 4 comprises the following specific steps: obtaining a stator voltage component u under a two-phase rotating coordinate system at the moment k by a formula (9)d(k) And ud(k) Discretizing the current differential equation shown in the formula (10) through a first-order Euler equation shown in the formula (8) to obtain a k +1 moment current prediction equation shown in the formula (11);
wherein x (k +1) and x (k) represent the states at time k +1 and time k; t issRepresents the sampling period of the system; u shapedcRepresents the bus voltage of the NPC three-level inverter; sx(i) Representing different switching states of the inverter output (i e {1,2, …,27}, S ∈ {1,2, …,27}, S }x(i)∈{-1,0,1}，x∈{a,b,c})；uα(k) And uβ(k) Representing the stator voltage component in the stationary coordinate system at the moment k; r represents a stator resistance of the brushless dc motor; l issRepresenting the stator inductance.
Further, the step 5 comprises the following specific steps: firstly, the value of the cost function g under the action of different vectors is calculated by the formula (12)iAnd calculating the minimum value g of the cost function by the formula (13)opt(ii) a Then obtaining a value satisfying goptVoltage vector V ofoptAnd calculating a voltage vector VoptStator voltage u under two-phase rotating coordinate system at time kd_opt(k) And uq_opt(k) (ii) a Then, according to the q-axis current dead-beat control principle shown in the formula (14), calculating the action time t of the optimal vectoroptIn which S isoptAnd S0Is obtained by the equations (15) and (16)) Obtaining; finally, the optimal vector V in one sampling period is distributedoptHas an action time of toptTorque ripple minimization control of the brushless direct current motor is realized; wherein, when t isopt>TsThen t isopt＝Ts(ii) a When t isopt<0, then topt＝0；
gopt＝min{g1,g2,...,g27},opt∈{1,2,...,27} (13)
S0＝-Riq(k)-ωe(Ldid(k)+ψf) (15)
Sopt＝S0+uq_opt(k) (16)
Wherein the content of the first and second substances,
the d-axis current reference value at the time k +1,
a q-axis current reference value at the moment k + 1; r represents a stator resistance of the brushless dc motor; omegaeIs the electrical angular velocity; psifRepresents a permanent magnet flux linkage; l isdRepresenting d-axis inductance, T, of a brushless DC motorsRepresenting the sampling period.
Further, the step 6 includes the following specific steps: first, the optimum voltage vector V is judgedoptWhether the vector is a small vector or not, if not, the neutral point potential balance control is not carried out; if VoptIf the vector is small, the voltage of the lower voltage-dividing capacitor u is measured by a voltage sensorC2And upper voltage dividing capacitor voltage uC1Then, the midpoint potential u is calculated by the formula (18)0And calculating the midpoint current i by the formula (19)npIn which three-phase currents i flow into the machinea，ib，icIs positive; if inp*u0>If 0 is true, V continues to be usedoptAs output vector for controlling the inverter, otherwise, V is usedoptAs an output vector;
u0＝uC2-uC1 (18)
wherein S isx(opt) is VoptThe corresponding switch state.
Has the advantages that: the invention relates to a brushless direct current motor driven by a three-level inverter based on Neutral-point-clamped (NPC). And obtaining a current predicted value at the next moment by discretizing a current differential equation by a first-order Euler equation, constructing a cost function taking the stator current as a control variable on the basis of the principle that the current tracking error is minimum, and obtaining a basic voltage vector which meets the minimum cost function as an optimal vector. Furthermore, the duty ratio modulation is used for distributing the action time of the optimal vector and the zero vector in one sampling period, so that the torque ripple can be effectively reduced, and the steady-state performance of the BLDC system is improved. Meanwhile, the control of the midpoint potential balance is only realized by the characteristic that the redundant small vectors have opposite effects on the midpoint potential.
Drawings
FIG. 1 is a control schematic provided by the present invention;
FIG. 2 is a control flow diagram provided by the present invention;
fig. 3 is a steady state simulation diagram of duty cycle modulated NPC three-level BLDC torque ripple minimization control, fig. 3(a) is a conventional BLDC model predicted current control steady state waveform, and 3(b) is a BLDC steady state waveform provided by the present invention.
FIG. 4 is a graph of a dynamic simulation of duty-modulated NPC three-level BLDC torque ripple minimization control, FIG. 4(a) is a dynamic performance simulation under abrupt rotation speed conditions, and FIG. 4(b) is a dynamic performance simulation under abrupt load conditions;
fig. 5 is a simulation diagram of midpoint potential balance for a duty cycle modulated NPC three-level BLDC torque ripple minimization control.
Detailed Description
The present invention will be described in further detail below by way of examples with reference to the accompanying drawings, which are illustrative of the present invention and are not to be construed as limiting the present invention.
A duty-cycle modulated NPC three-level BLDC torque ripple minimization control schematic is shown in fig. 1, and includes a rotation speed loop PI controller module 1, a minimization cost function module 2, a duty-cycle modulation module 3, a midpoint potential balancing module 4, an NPC three-level inverter module 5, a brushless dc motor module 6, an encoder module 8, a coordinate transformation module 8, and a current prediction module 9.
As shown in fig. 2, the method comprises the following steps:
step 1: obtaining the electrical angle theta of the brushless DC motor from the encoder, and calculating the electrical angular velocity omega by the formula (1)eThen calculating the actual rotating speed N of the motor according to the formula (2)r(ii) a Then setting the given rotating speed N of the motorr refAnd the actual rotating speed N of the motor in the formula (2)rDifference e ofnCalculating a q-axis current reference value i according to a formula (3) through a PI controller of a rotating speed ringq ref；
Wherein k ispAnd kiRespectively representing the proportional and integral of a speed loop PI controllerThe gain, s, represents a complex variable.
Step 2: the method for acquiring the dq axis counter electromotive force comprises the following steps:
first, an electrical angle θ of the brushless dc motor is obtained from an encoder and an electrical angular velocity ω of the brushless dc motor is obtained by formula (1)e(ii) a Secondly, three-phase back electromotive force e of the motor at different rotor positions at the moment k is calculated according to the table 1a(k)，eb(k) And ec(k) (ii) a Then, the back electromotive force e of the α β axis in the stationary coordinate system at the time k is obtained according to the Clark transformation shown in formula (4)α(k) And eβ(k) And then obtaining the back electromotive force e of the dq axis under the two-phase rotating coordinate system at the time k through Park change shown in formula (5)d(k) And eq(k)；
TABLE 1 counter electromotive force at different rotor positions
| Rotor position | ea(k) | eb(k) | ec(k) |
| 0～π/3 | m*ωe | -m*ωe | m*ωe*(-θ/(π/6)+1) |
| π/3～2π/3 | m*ωe | m*ωe*((θ-π/3)/(π/6)-1) | -m*ωe |
| 2π/3～π | m*ωe*((2π/3-θ)/(π/6)+1) | m*ωe | -m*ωe |
| π～4π/3 | -m*ωe | m*ωe | m*ωe*((θ-π)/(π/6)-1) |
| 4π/3～5π/3 | -m*ωe | m*ωe*((4π/3-θ)/(π/6)+1) | m*ωe |
| 5π/3～2π | m*ωe*((θ-5π/3)/(π/6)-1) | -m*ωe | m*ωe |
Wherein the coefficient m is 2npψf，npRepresenting the number of pole pairs, #fRepresenting a permanent magnet flux linkage.
And step 3: the method for acquiring the dq axis stator current at the k moment comprises the following steps:
firstly, three-phase stator current i at time k is acquired through three current sensorsa(k)，ib(k) And ic(k) (ii) a Then, the current component i of the α β axis is calculated by Clark transformation of formula (6)α(k) And iβ(k) (ii) a Finally, calculating the stator current component i at the k moment of the dq axis by using Park transformation of formula (7)d(k) And iq(k)；
And 4, step 4: stator current i of dq axis at time k +1d(k +1) and iqThe calculation method of (k +1) is as follows:
first, a stator voltage component u in a two-phase rotational coordinate system at time k is obtained by equation (9)d(k) And ud(k) Then, the current differential equation shown in equation (10) is discretized by a first-order euler equation shown in equation (8) to obtain a current prediction equation at the time k +1 shown in equation (11).
Wherein x (k +1) and x (k) represent the states at time k +1 and time k; t issRepresents the sampling period of the system; u shapedcRepresents the bus voltage of the NPC three-level inverter; sx(i) Representing different switching states of the inverter output (i e {1,2, …,27}, S ∈ {1,2, …,27}, S }x(i)∈{-1,0,1}，x∈{a,b,c})；uα(k) And uβ(k) A stator voltage component representing the α β axis at time k; u. ofd(k) And ud(k) A stator voltage component representing the dq axis at time k; t issRepresents the sampling period of the system; r represents a stator resistance of the brushless dc motor; l issRepresenting the stator inductance.
And 5: obtaining an optimal voltage vector V by rolling optimization of a cost functionoptAnd obtaining the action time t of the optimal vector by a duty ratio modulation method according to the dead-beat control principleoptThe method comprises the following steps:
firstly, the value of the cost function g under the action of different vectors is calculated by the formula (12)iAnd calculating the minimum value g of the cost function by the formula (13)opt(ii) a Then obtaining a value satisfying goptVoltage vector V ofoptAnd calculating the voltage vector V in combination with equation (10)optDq-axis stator voltage u at time kd_opt(k) And uq_opt(k) (ii) a Then, according to the q-axis current dead-beat control principle shown in the formula (14), calculating the action time t of the optimal vectoroptIn which S isoptAnd S0Can be obtained by the equations (15) and (16). Finally, the optimal vector V in one sampling period is distributedoptHas an action time of toptTo realize the torque ripple minimization control of the brushless DC motor, the action time of the zero vector is Ts-topt. In particular, when topt>TsThen t isopt＝Ts(ii) a When t isopt<0, then topt＝0。
gopt＝min{g1,g2,...,g27},opt∈{1,2,...,27} (13)
S0＝-Riq(k)-ωe(Ldid(k)+ψf) (15)
Sopt＝S0+uq_opt(k) (16)
Wherein the content of the first and second substances,
the d-axis current reference value at the time k + 1,
a q-axis current reference value at the moment k + 1; l isdRepresenting the d-axis inductance of the brushless dc motor.
Step 6: the method for acquiring the optimal switch state beneficial to inhibiting the midpoint potential fluctuation through the midpoint potential balance control algorithm comprises the following steps:
first, the optimum voltage vector V obtained in step 5 is judgedoptWhether the vector is a small vector or not, if not, the neutral point potential balance control is not carried out; if VoptIf the vector is small, the voltage of the lower voltage-dividing capacitor u is measured by a voltage sensorC2And upper voltage dividing capacitor voltage uC1Then, the midpoint potential u is calculated by the formula (18)0And calculating the midpoint current i by the formula (19)npIn which three-phase currents i flow into the machinea，ib，icIs positive; if inp*u0>If 0 is true, V continues to be usedoptAs output vector for controlling the inverter, otherwise, V is usedoptAs an output vector.
u0＝uC2-uC1 (18)
Wherein S isx(opt) is VoptThe corresponding switch state.
The method firstly obtains the three-phase current i of the stator at the moment kx(k) And three-phase back electromotive force ex(k) (x ═ a, b, c), rotor electrical angle θ, electrical angular velocity ωeGiven speed Nr refAnd permanent magnet flux linkage psif(ii) a Then obtaining a reference value i of q-axis current at the moment of k +1 through a rotating speed loop PI controllerq ref(k +1) and given id ref(k +1) ═ 0; then, a current prediction module calculates a dq axis current prediction value i at the moment of k +1q(k +1) and id(k + 1); selecting a cost function g through rolling optimization of the cost functioniMinimum fundamental voltage vector Vopt(ii) a Then, calculating and distributing the action time of the optimal vector and the zero vector through a duty ratio modulation module; and finally, obtaining the switching state of the driving inverter through a midpoint potential balance control module.
The steady-state performance result of the NPC three-level BLDC torque ripple minimization is shown in fig. 3, and it can be seen that compared with the conventional MPCC algorithm shown in fig. 3(a), the proposed invention can more effectively reduce the torque ripple and current harmonic content of the BLDC and ensure a smooth rotation speed. Fig. 4 is a simulation result of dynamic performance of a sudden change speed and a sudden change load in the NPC three-level BLDC torque ripple minimization control method, and it can be seen that the control algorithm provided by the present invention can ensure a fast dynamic response of the BLDC. Fig. 5 shows the midpoint potential balance simulation result, and it can be seen that the inventive algorithm can well suppress the fluctuation of the midpoint potential.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (4)
1. A duty cycle modulated NPC three level BLDC torque ripple minimization control method, comprising the steps of:
step 1: will give a rotation speed Nr refAnd the actual rotational speed N obtained by the encoderrThe deviation between the q-axis current reference value i is obtained through a PI controller of a rotating speed loopq refAnd giving a d-axis current reference value id ref＝0；
Step 2: obtaining rotor position information theta and electrical angular velocity omega from an encodereAnd calculates the three-phase back electromotive force e of the motor at the moment ka(k)，eb(k) And ec(k) Obtaining the back electromotive force e under the stationary coordinate system at the moment k through Clark transformationα(k)、eβ(k) And obtaining the back electromotive force e under a two-phase rotating coordinate system at the moment k through Park transformationd(k)、eq(k)；
And step 3: three-phase stator current i at moment k is measured through three current sensorsa(k)，ib(k) And ic(k) Obtaining the stator current i under the stationary coordinate system at the moment k through Clark transformationα(k)、iβ(k) Obtaining the stator current i under the two-phase rotating coordinate system at the moment k through Park conversiond(k)、iq(k)；
And 4, step 4: carrying out discretization processing on the current differential equation at the moment k through a first-order Euler function to obtain the stator current i under a two-phase rotating coordinate system at the moment k +1d(k +1) and iq(k+1)；
And 5: obtaining an optimal voltage vector V by rolling optimization of a cost functionoptAnd obtaining the action time t of the optimal vector by a duty ratio modulation method according to the dead-beat control principleopt；
Step 6: obtaining an optimal switching state beneficial to inhibiting the fluctuation of the midpoint potential through a balance control algorithm of the midpoint potential to drive the inverter;
the step 4 comprises the following specific steps: obtaining a stator voltage component u under a two-phase rotating coordinate system at the moment k by a formula (9)d(k) And ud(k) Discretizing the current differential equation shown in the formula (10) through a first-order Euler equation shown in the formula (8) to obtain a k +1 moment current prediction equation shown in the formula (11);
wherein x (k +1) and x (k) represent the states at time k +1 and time k; t issRepresents the sampling period of the system; u shapedcRepresents the bus voltage of the NPC three-level inverter; sx(i) Representing different switching states of the inverter output, i ∈ {1,2, …,27}, Sx(i)∈{-1,0,1}，x∈{a,b,c}；uα(k) And uβ(k) Representing the stator voltage component in the stationary coordinate system at the moment k; r represents a stator resistance of the brushless dc motor; l issRepresenting the stator inductance;
the step 5 comprises the following specific steps: firstly, the value of the cost function g under the action of different vectors is calculated by the formula (12)iAnd calculating the minimum value g of the cost function by the formula (13)opt(ii) a Then obtaining a value satisfying goptVoltage vector V ofoptAnd calculating a voltage vector VoptStator voltage u under two-phase rotating coordinate system at time kd_opt(k) And uq_opt(k) (ii) a Then, according to the q-axis current dead-beat control principle shown in the formula (14), calculating the action time t of the optimal vectoroptIn which S isoptAnd S0Is obtained by the formulas (15) and (16); finally, the optimal vector V in one sampling period is distributedoptHas an action time of toptTo implement brushless DC motorsTorque ripple minimization control; wherein, when t isopt>TsThen t isopt＝Ts(ii) a When t isopt<0, then topt＝0；
gopt＝min{g1,g2,...,g27},opt∈{1,2,...,27} (13)
S0＝-Riq(k)-ωe(Ldid(k)+ψf) (15)
Sopt＝S0+uq_opt(k) (16)
Wherein the content of the first and second substances,
the d-axis current reference value at the time k +1,
a q-axis current reference value at the moment k + 1; r represents a stator resistance of the brushless dc motor; omegaeIs the electrical angular velocity; psifRepresents a permanent magnet flux linkage; l isdRepresenting d-axis inductance, T, of a brushless DC motorsRepresents a sampling period;
the step 6 comprises the following specific steps: first, the optimum voltage vector V is judgedoptWhether the vector is a small vector or not, if not, the neutral point potential balance control is not carried out; if VoptIf the vector is small, the voltage of the lower voltage-dividing capacitor u is measured by a voltage sensorC2And upper voltage dividing capacitor voltage uC1Then, the midpoint potential u is calculated by the formula (18)0And calculating the midpoint current i by the formula (19)npIn which three-phase currents i flow into the machinea，ib，icIs positive; if inp*u0>If 0 is true, V continues to be usedoptAs output vector for controlling the inverter, otherwise, V is usedoptAs an output vector;
u0＝uC2-uC1 (18)
wherein S isx(opt) is VoptThe corresponding switch state.
2. The duty-cycle modulated NPC three-level BLDC torque ripple minimization control method as claimed in claim 1, wherein in step 1, the electrical angle θ of the brushless dc motor is obtained from the encoder, and the electrical angular velocity ω is calculated by formula (1)eThen calculating the actual rotating speed N of the motor according to the formula (2)r(ii) a Then setting the given rotating speed N of the motorr refAnd the actual rotational speed NrDifference e ofnCalculating a q-axis current reference value i according to a formula (3) through a PI controller of a rotating speed ringq ref；
Wherein k ispAnd kiRespectively representing the proportional and integral gains of the rotating speed loop PI controller, and s represents a complex variable.
3. The duty cycle modulated NPC three-level BLDC torque ripple minimization control method of claim 1, wherein in step 2, the three-phase back electromotive force e at different rotor positions of the motor at time k is calculated according to table 1a(k)，eb(k) And ec(k) (ii) a Then, the back electromotive force e under the stationary coordinate system at the time k is obtained according to Clark transformation shown in formula (4)α(k) And eβ(k) And then obtaining the back electromotive force e under the two-phase rotating coordinate system at the moment k through Park change shown in formula (5)d(k) And eq(k)；
TABLE 1
Wherein the coefficient m is 2npψf，npRepresenting the number of pole pairs, #fRepresenting a permanent magnet flux linkage.
4. The duty-cycle modulated NPC three-level BLDC torque ripple minimization control method as claimed in claim 1, wherein in step 3, the stator current i in the stationary coordinate system at the time k is calculated by formula (6)α(k) And iβ(k) (ii) a Calculating the stator current i in the two-phase rotating coordinate system at the k moment of the dq axis by the formula (7)d(k) And iq(k)；
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Application publication date: 20201120 Assignee: Nantong Mizhu Intelligent Technology Co.,Ltd. Assignor: NANTONG University Contract record no.: X2023980052245 Denomination of invention: A duty cycle modulated NPC three-level BLDC torque ripple minimization control method Granted publication date: 20220211 License type: Common License Record date: 20231214 |