CN115494722B - Model reference self-adaption method, device, electronic equipment and storage medium - Google Patents
Model reference self-adaption method, device, electronic equipment and storage medium Download PDFInfo
- Publication number
- CN115494722B CN115494722B CN202210993921.7A CN202210993921A CN115494722B CN 115494722 B CN115494722 B CN 115494722B CN 202210993921 A CN202210993921 A CN 202210993921A CN 115494722 B CN115494722 B CN 115494722B
- Authority
- CN
- China
- Prior art keywords
- side winding
- representing
- model
- coordinate system
- determining
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 64
- 238000004804 winding Methods 0.000 claims abstract description 155
- 230000001360 synchronised effect Effects 0.000 claims abstract description 64
- 230000004907 flux Effects 0.000 claims abstract description 48
- 238000013178 mathematical model Methods 0.000 claims abstract description 38
- 230000009466 transformation Effects 0.000 claims abstract description 22
- 230000001131 transforming effect Effects 0.000 claims abstract description 7
- 230000003044 adaptive effect Effects 0.000 claims description 25
- 238000005070 sampling Methods 0.000 claims description 6
- 230000006978 adaptation Effects 0.000 claims description 4
- 238000004590 computer program Methods 0.000 claims description 3
- 238000004364 calculation method Methods 0.000 abstract description 10
- 230000035945 sensitivity Effects 0.000 abstract description 4
- 238000010586 diagram Methods 0.000 description 29
- 238000004891 communication Methods 0.000 description 11
- 238000004088 simulation Methods 0.000 description 11
- 238000013461 design Methods 0.000 description 9
- 230000008859 change Effects 0.000 description 5
- 230000008569 process Effects 0.000 description 5
- 230000000694 effects Effects 0.000 description 4
- 238000007796 conventional method Methods 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 230000010349 pulsation Effects 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 2
- 230000008901 benefit Effects 0.000 description 2
- 230000005540 biological transmission Effects 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 230000000737 periodic effect Effects 0.000 description 2
- 238000012545 processing Methods 0.000 description 2
- 230000003068 static effect Effects 0.000 description 2
- 230000009471 action Effects 0.000 description 1
- 239000003990 capacitor Substances 0.000 description 1
- 230000003750 conditioning effect Effects 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 230000003993 interaction Effects 0.000 description 1
- 238000012821 model calculation Methods 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000004044 response Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B11/00—Automatic controllers
- G05B11/01—Automatic controllers electric
- G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
- G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Automation & Control Theory (AREA)
- Control Of Motors That Do Not Use Commutators (AREA)
- Control Of Ac Motors In General (AREA)
Abstract
The application provides a model reference self-adaption method, a device, electronic equipment and a storage medium. The method comprises the following steps: determining the phase of the power side winding voltage according to the phase-locked loop; determining an adjustable model under a synchronous coordinate system according to the phase and a mathematical model of the brushless doubly-fed motor under the synchronous coordinate system; transforming the coordinate corresponding to the pre-sampled control side winding current into a synchronous coordinate system to determine a reference model; determining a linearization error between the adjustable model and the reference model; determining PI parameters according to the linearization error to obtain estimated rotation speed information, and determining estimated position information according to the estimated rotation speed information; and feeding back the estimated position information to the coordinate transformation corresponding to the control side winding current in a closed loop manner to control the brushless doubly-fed motor. The method reduces the use of a flux linkage observer, improves the calculation method of the error between the adjustable model and the reference model, improves the sensitivity to the angle difference in a larger range, and improves the practicability.
Description
Technical Field
The present disclosure relates to the field of motor control technologies, and in particular, to a model reference adaptive method, apparatus, electronic device, and storage medium.
Background
In the related art, the calculation of an adjustable model in a model reference adaptive system is too complex, a plurality of flux linkage integrals and coordinate transformation are involved, and errors between the reference model and the adjustable model are calculated in the related art, and the errors are insensitive to a large range of angle differences, so that the PI design difficulty is increased. Moreover, the related art requires the use of a flux linkage observer, and the cutoff frequency of the flux linkage observer is not easily designed. Therefore, the related art has the problems of complex calculation, difficult determination of the design parameters of the PI controller, complex motor control and low practicability.
Disclosure of Invention
In view of the foregoing, it is an object of the present application to provide a model reference adaptive method, apparatus, electronic device and storage medium.
In view of the above object, in a first aspect, the present application provides a model reference adaptive method, including:
determining the phase of the power side winding voltage according to the phase-locked loop;
determining an adjustable model under a synchronous coordinate system according to the phase and the mathematical model of the brushless doubly-fed motor under the synchronous coordinate system;
transforming the coordinate corresponding to the pre-sampled control side winding current to the synchronous coordinate system to determine a reference model;
determining a linearization error between the adjustable model and the reference model;
determining PI parameters according to the linearization error to obtain estimated rotation speed information, and determining estimated position information according to the estimated rotation speed information;
and feeding back the estimated position information to the coordinate transformation corresponding to the control side winding current in a closed loop manner so as to control the brushless doubly-fed motor.
In a possible implementation manner, the determining the adjustable model under the synchronous coordinate system according to the mathematical model of the brushless doubly-fed motor under the phase and synchronous coordinate system includes:
performing coordinate transformation on the synchronous coordinate system according to the phase to determine a mathematical model of the brushless doubly-fed motor; wherein the mathematical model is expressed as
Wherein u is 1 Representing the power side winding voltage, R 1 Representing the power side winding resistance, i 1 Represents the power side winding current, ψ 1 Represents the power side winding flux linkage vector, j represents the imaginary unit, ω 1 Represents the angular speed of the voltage of the power grid, R r Representing rotor winding resistance, i r Representing rotor current, ψ r Representing the rotor flux linkage vector, t representing the differential time, p 1 Represents the pole pair number, omega of the power side winding m Indicating the mechanical angular velocity of the rotor, u 2 Represents the control side winding voltage, R 2 Indicating the resistance of the control side winding, i 2 Represents the control side winding current, ψ 2 Representing the control side winding flux linkage vector, p 2 Representing the pole pair number of the control side winding, L 1 Representing the power side winding inductance,L m1 representing the mutual inductance of the power side winding, L r Representing rotor winding inductance, L m2 Indicating the mutual inductance of the control side winding, L 2 Representing the control side winding inductance;
at steady state, the rotor flux linkage in the mathematical model under the synchronous coordinate system is represented by rotor current to determine an adjustable model; wherein the rotor flux linkage is represented as
Where dq represents the d-axis and q-axis in the synchronous coordinate system.
In a possible implementation manner, the performing coordinate transformation on the synchronous coordinate system according to the phase to determine a mathematical model of the brushless doubly-fed motor further includes:
representing the rotor current by the power side winding voltage and the power side winding current; wherein the rotor current is expressed as
Determining an estimated control side winding current in a synchronous coordinate system according to the mathematical model, the rotor flux linkage and the rotor current, and determining the estimated control side winding current as the adjustable model; the adjustable model is expressed as
In one possible implementation, the linearization error is calculated by:
wherein,represents a cross product, +..
In one possible implementation manner, the determining PI parameters according to the linearization error to obtain estimated rotation speed information, and determining estimated position information according to the estimated rotation speed information includes:
determining PI controller parameters based on the linearization error to determine estimated rotational speed information
-converting said estimated rotational speed informationIntegrating to determine estimated position information +.>
In a second aspect, the present application provides a model reference adaptive device comprising:
a first determination module configured to determine a phase of the power side winding voltage from the phase locked loop;
a second determination module configured to determine an adjustable model in a synchronous coordinate system from the phase and a mathematical model of the brushless doubly-fed motor in the synchronous coordinate system;
a third determining module configured to transform coordinates corresponding to the control-side winding current acquired by pre-sampling to the synchronous coordinate system to determine a reference model;
a fourth determination module configured to determine a linearization error between the tunable model and the reference model;
a fifth determining module configured to determine PI parameters from the linearization error to obtain estimated rotational speed information, and to determine estimated position information from the estimated rotational speed information;
a control module configured to feed back the estimated position information in a closed loop to a coordinate transformation corresponding to the control side winding current to control the brushless doubly-fed motor.
In one possible implementation, the second determining module is further configured to:
performing coordinate transformation on the synchronous coordinate system according to the phase to determine a mathematical model of the brushless doubly-fed motor; wherein the mathematical model is expressed as
Wherein u is 1 Representing the power side winding voltage, R 1 Representing the power side winding resistance, i 1 Represents the power side winding current, ψ 1 Represents the power side winding flux linkage vector, j represents the imaginary unit, ω 1 Represents the angular speed of the voltage of the power grid, R r Representing rotor winding resistance, i r Representing rotor current, ψ r Representing the rotor flux linkage vector, t representing the differential time, p 1 Represents the pole pair number, omega of the power side winding m Indicating the mechanical angular velocity of the rotor, u 2 Represents the control side winding voltage, R 2 Indicating the resistance of the control side winding, i 2 Represents the control side winding current, ψ 2 Representing the control side winding flux linkage vector, p 2 Representing the pole pair number of the control side winding, L 1 Representing the inductance of the power side winding, L m1 Representing the mutual inductance of the power side winding, L r Representing rotor winding inductance, L m2 Indicating the mutual inductance of the control side winding, L 2 Representing the control side winding inductance;
at steady state, the rotor flux linkage in the mathematical model under the synchronous coordinate system is represented by rotor current to determine an adjustable model; wherein the rotor flux linkage is represented as
Where dq represents the d-axis and q-axis in the synchronous coordinate system.
In one possible implementation, the fifth determining module is further configured to:
determining PI controller parameters based on the linearization error to determine estimated rotational speed information
-converting said estimated rotational speed informationIntegrating to determine estimated position information +.>
In a third aspect, the present application provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the model reference adaptation method according to the first aspect when executing the program.
In a fourth aspect, the present application provides a non-transitory computer readable storage medium storing computer instructions for causing a computer to perform the model reference adaptation method of the first aspect.
From the above, it can be seen that the model reference adaptive method, apparatus, electronic device and storage medium provided by the present application determine the phase of the power side winding voltage according to the phase-locked loop; determining an adjustable model under a synchronous coordinate system according to the phase and the mathematical model of the brushless doubly-fed motor under the synchronous coordinate system; transforming the coordinate corresponding to the pre-sampled control side winding current to the synchronous coordinate system to determine a reference model; determining a linearization error between the adjustable model and the reference model; determining PI parameters according to the linearization error to obtain estimated rotation speed information, and determining estimated position information according to the estimated rotation speed information; and feeding back the estimated position information to the coordinate transformation corresponding to the control side winding current in a closed loop manner so as to control the brushless doubly-fed motor. By converting the adjustable model and the reference model into the synchronous coordinate system and omitting the dynamic process, the use of a flux linkage observer is reduced, the whole control method is simpler, the calculation method of the error between the adjustable model and the reference model is improved, the linear error between the adjustable model and the reference model is calculated, the sensitivity to the angle difference in a larger range is improved, the parameter design of the PI controller is simplified, the calculation amount of the whole motor control method is reduced, the method is simple and convenient, and the practicability is improved.
Drawings
In order to more clearly illustrate the technical solutions of the present application or related art, the drawings that are required to be used in the description of the embodiments or related art will be briefly described below, and it is apparent that the drawings in the following description are only embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort to those of ordinary skill in the art.
Fig. 1 shows an exemplary structural schematic diagram of a brushless doubly-fed motor speed regulation control system provided in an embodiment of the present application.
Fig. 2 shows an exemplary flowchart of a model reference adaptive method according to an embodiment of the present application.
Fig. 3 shows a schematic view of a motor control structure frame in an embodiment according to the application.
FIG. 4 shows a schematic diagram of steady-state experimental results of robust predictive control at rotational speed of 350rpm in accordance with an embodiment of the present application.
Fig. 5 shows a schematic diagram of steady-state experimental results of robust predictive control at rotational speed 600rpm according to an embodiment of the present application.
Fig. 6 shows a schematic diagram of steady state estimation error experimental results at a rotational speed of 350rpm for robust predictive control in accordance with an embodiment of the present application.
Fig. 7 shows a schematic diagram of steady state estimation error experimental results at a rotational speed of 580rpm for robust predictive control in accordance with an embodiment of the present application.
Fig. 8 shows experimental waveforms for robust predictive control under control side winding inductance variation in a controller in accordance with an embodiment of the present application.
Fig. 9 shows a schematic diagram of experimental estimation error experimental results of robust predictive control under control side winding mutual inductance variation in a controller according to an embodiment of the present application.
Fig. 10 is a schematic diagram showing experimental results of simulation waveforms under actual control side winding mutual inductance variation in a robust predictive control according to an embodiment of the present application.
Fig. 11 shows a schematic diagram of experimental results of simulation estimation errors under actual control side winding mutual inductance variation in a robust predictive control according to an embodiment of the present application.
Fig. 12 shows a schematic diagram of dynamic experimental results of robust predictive control under a power step in accordance with an embodiment of the present application.
Fig. 13 shows a schematic diagram of the experimental results of the dynamic estimation error under power step for robust predictive control in accordance with an embodiment of the present application.
Fig. 14 shows a schematic diagram of experimental results of dynamic experimental results of robust predictive control under rotational speed variation according to an embodiment of the present application.
Fig. 15 illustrates dynamic estimation errors under rotational speed variation for robust predictive control in accordance with an embodiment of the present application.
Fig. 16 shows an exemplary structural schematic diagram of a model reference adaptive device according to an embodiment of the present application.
Fig. 17 shows an exemplary structural schematic diagram of an electronic device according to an embodiment of the present application.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the present application more apparent, the present application will be further described in detail below with reference to the accompanying drawings.
It should be noted that unless otherwise defined, technical or scientific terms used in the embodiments of the present application should be given the ordinary meaning as understood by one of ordinary skill in the art to which the present application belongs. The terms "first," "second," and the like, as used in embodiments of the present application, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. The word "comprising" or "comprises", and the like, means that elements or items preceding the word are included in the element or item listed after the word and equivalents thereof, but does not exclude other elements or items. The terms "connected" or "connected," and the like, are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", etc. are used merely to indicate relative positional relationships, which may also be changed when the absolute position of the object to be described is changed.
As described in the background section, in the related art, the model reference adaptive system is configured to observe a reference model (without position information) and an adjustable model (with position information) of the same variable, and then the difference between the two models is used to obtain the rotation speed and the position through an adaptive law, so that the principle is simple, and the structure is accurate, and is more studied and applied in the transmission system. However, the adjustable model calculation of the conventional method is too complex, and involves multiple flux linkage integrals and coordinate transformation. The error between the reference model and the adjustable model is calculated using conventional methods, and is insensitive to a large range of angle differences, which also increases the difficulty of PI design. Moreover, the conventional method requires the use of a flux linkage observer, and the cut-off frequency of the flux linkage observer is not easy to design.
The inventor found through research that in a related art, in order to reduce the use of a flux linkage observer, a brushless doubly-fed motor model reference adaptive method without the flux linkage observer is proposed, but there is a certain error in position estimation. In another related art, the PI design is simplified based on linearization errors. However, none of these methods simplifies the calculation of the adjustable model and is relatively complex.
That is, the related art cannot satisfy the following simultaneously: 1) The adjustable model is easy to calculate; 2) Errors are sensitive to large range angle differences; 3) The PI controller is simple in design; 4) Reducing the use of flux linkage observers.
As such, the model reference adaptive method, device, electronic equipment and storage medium provided by the application determine the phase of the power side winding voltage according to the phase-locked loop; determining an adjustable model under a synchronous coordinate system according to the phase and the mathematical model of the brushless doubly-fed motor under the synchronous coordinate system; transforming the coordinate corresponding to the pre-sampled control side winding current to the synchronous coordinate system to determine a reference model; determining a linearization error between the adjustable model and the reference model; determining PI parameters according to the linearization error to obtain estimated rotation speed information, and determining estimated position information according to the estimated rotation speed information; and feeding back the estimated position information to the coordinate transformation corresponding to the control side winding current in a closed loop manner so as to control the brushless doubly-fed motor. By converting the adjustable model and the reference model into the synchronous coordinate system and omitting the dynamic process, the use of a flux linkage observer is reduced, the whole control method is simpler, the calculation method of the error between the adjustable model and the reference model is improved, the linear error between the adjustable model and the reference model is calculated, the sensitivity to the angle difference in a larger range is improved, the parameter design of the PI controller is simplified, the calculation amount of the whole motor control method is reduced, the method is simple and convenient, and the practicability is improved.
The model reference adaptive method provided by the embodiment of the application is specifically described by a specific embodiment.
Fig. 1 shows an exemplary structural schematic diagram of a brushless doubly-fed motor speed regulation control system provided in an embodiment of the present application.
Referring to fig. 1, fig. 1 is a hardware circuit structure diagram of the present invention, which includes a three-phase voltage source, a brushless doubly-fed motor, a three-phase two-level inverter, a dc side capacitor, a voltage and current sampling circuit, a dsace real-time simulation system, and a driving circuit. The voltage and current sampling circuit respectively acquires direct-current side voltage, power side a, b and c three-phase voltage, control side a, b and c three-phase voltage, power side a, b two-phase current and control side a, b two-phase current by using a voltage Hall sensor and a current Hall sensor, and sampling signals enter a dSPACE real-time simulation system after passing through a signal conditioning circuit and are converted into digital signals. The dSPACE real-time simulation system completes the operation of the method provided by the invention, outputs six paths of switching pulses, and then obtains the final driving signals of six switching tubes of the inverter after passing through the driving circuit.
Fig. 2 shows an exemplary flowchart of a model reference adaptive method according to an embodiment of the present application.
Referring to fig. 2, a model reference adaptive method provided in an embodiment of the present application specifically includes the following steps:
s202: the phase of the power side winding voltage is determined from the phase locked loop.
S204: and determining an adjustable model under the synchronous coordinate system according to the phase and the mathematical model of the brushless doubly-fed motor under the synchronous coordinate system.
S206: and transforming the coordinate corresponding to the pre-sampled control side winding current into the synchronous coordinate system to determine a reference model.
S208: a linearization error between the tunable model and the reference model is determined.
S210: and determining PI parameters according to the linearization errors to obtain estimated rotating speed information, and determining estimated position information according to the estimated rotating speed information.
S212: and feeding back the estimated position information to the coordinate transformation corresponding to the control side winding current in a closed loop manner so as to control the brushless doubly-fed motor.
Fig. 3 shows a schematic view of a motor control structure frame in an embodiment according to the application.
Referring to fig. 2 and 3, a coordinate transformation may be performed on the synchronous coordinate system according to the phase to determine a mathematical model of the brushless doubly-fed motor; wherein the mathematical model is expressed as
Wherein u is 1 Representing the power side winding voltage, R 1 Representing the power side winding resistance, i 1 Represents the power side winding current, ψ 1 Represents the power side winding flux linkage vector, j represents the imaginary unit, ω 1 Represents the angular speed of the voltage of the power grid, R r Representing rotor winding resistance, i r Representing rotor current, ψ r Representing the rotor flux linkage vector, t representing the differential time, p 1 Represents the pole pair number, omega of the power side winding m Indicating the mechanical angular velocity of the rotor, u 2 Represents the control side winding voltage, R 2 Indicating the resistance of the control side winding, i 2 Represents the control side winding current, ψ 2 Representing the control side winding flux linkage vector, p 2 Representing the pole pair number of the control side winding, L 1 Representing the inductance of the power side winding, L m1 Representing the mutual inductance of the power side winding, L r Representing rotor winding inductance, L m2 Indicating the mutual inductance of the control side winding, L 2 Representing the control side winding inductance;
to simplify the tunable model, the dynamic process may be omitted. At steady state, the rotor flux linkage in the mathematical model under the synchronous coordinate system is represented by rotor current to determine an adjustable model; wherein the rotor flux linkage is represented as
Where dq represents the d-axis and q-axis in the synchronous coordinate system.
Because the denominator of the above formula is large, the rotor flux linkage can be considered to be approximately equal to 0. Similarly, rotor current i rdq Can use the power side winding voltage u 1dq And current i 1dq The representation is:
obtaining estimated control side winding current under synchronous coordinate system from mathematical model of brushless doubly-fed motor under synchronous coordinate system and the two formulasThe method is an adjustable model:
in some embodiments, based on the adjustable model and the reference model, the linearization error ζ between the two can be calculated as follows:
wherein,represents a cross product, +..
In some embodiments, the PI controller parameters are designed to obtain an estimated speed based on the obtained linearization error ζIntegrating the estimated rotational speed to obtain estimated position information +.>Closed loop feedback of estimated position information to sampled control side winding current i 2 Is used for the coordinate transformation of the (c).
The effectiveness of the method can be obtained through simulation and experimental results. All simulations and experiments substituted the estimated position and rotational speed closed loop into robust predictive control based on the extended state observer.
FIG. 4 shows a schematic diagram of steady-state experimental results of robust predictive control at rotational speed of 350rpm in accordance with an embodiment of the present application.
Fig. 5 shows a schematic diagram of steady-state experimental results of robust predictive control at rotational speed 600rpm according to an embodiment of the present application.
Referring to fig. 4 and 5, the active power reference values are-350W, and the reactive power reference values are 0Var. The waveforms are active power, reactive power, power side three-phase current and control side three-phase current in sequence from top to bottom. It can be found from the comparison of fig. 3 and fig. 4 that the actual active power value and the actual reactive power value of the two methods can both track the upper reference value, and the fluctuation is small, which indicates that good control effect can be obtained at different rotation speeds.
Fig. 6 shows a schematic diagram of steady state estimation error experimental results at a rotational speed of 350rpm for robust predictive control in accordance with an embodiment of the present application.
Fig. 7 shows a schematic diagram of steady state estimation error experimental results at a rotational speed of 580rpm for robust predictive control in accordance with an embodiment of the present application.
Referring to fig. 6 and 7, waveforms from top to bottom are rotor speed, rotor position, estimated speed error, and estimated position error, respectively. As can be seen from a comparison of fig. 5 and 6, there is a periodic fluctuation in the rotational speed and position of the two methods, the frequency of occurrence of the pulsation is related to the rotational speed, and when the rotational speed is 350rpm, the observed pulsation occurs approximately every 0.17s (60/350); when the rotation speed was 600rpm, the interval time was 0.1s.
Fig. 8 shows experimental waveforms for robust predictive control under control side winding inductance variation in a controller in accordance with an embodiment of the present application.
Fig. 9 shows a schematic diagram of experimental estimation error experimental results of robust predictive control under control side winding mutual inductance variation in a controller according to an embodiment of the present application.
Fig. 10 is a schematic diagram showing experimental results of simulation waveforms under actual control side winding mutual inductance variation in a robust predictive control according to an embodiment of the present application.
Fig. 11 shows a schematic diagram of experimental results of simulation estimation errors under actual control side winding mutual inductance variation in a robust predictive control according to an embodiment of the present application.
In order to verify the parameter robustness of the control side winding current based optimization model reference adaptive method, fig. 8, 9 and 10 and 11 show experimental and simulation results of changing the control side winding mutual inductance parameters, respectively. In fig. 8, 9, the motor parameter in the controller is periodically stepped. Fig. 9 shows that at the instant of the parameter change, both the estimated rotational speed and the position show some degree of step, but the estimated rotational speed can converge quickly, and the magnitude of the position step is relatively small, and it can be seen from fig. 8 that the parameter change has little effect on the control effect. As can be seen from fig. 10, when the actual motor parameters are changed in the simulation, the system operation state is changed, and it takes a while to be stabilized again. As can be seen from fig. 11, the stabilized power can accurately track the reference value and the rotational speed estimation is accurate. Therefore, robust predictive control based on an optimization model reference adaptive method still has stronger parameter robustness.
Fig. 12 shows a schematic diagram of dynamic experimental results of robust predictive control under a power step in accordance with an embodiment of the present application.
Fig. 13 shows a schematic diagram of the experimental results of the dynamic estimation error under power step for robust predictive control in accordance with an embodiment of the present application.
Referring to the observed error in fig. 13, it can be seen that a large error occurs in the rotational speed at the instant of the power step, and the position observation error becomes around 0.1rad. Over time, the observed rotational speed quickly converges to an actual value, while the position error remains at about 0.1rad. As can be seen from fig. 12, the response time of the power step slows down due to the time required for convergence, but eventually the power reference can be stably tracked.
Fig. 14 shows a schematic diagram of experimental results of dynamic experimental results of robust predictive control under rotational speed variation according to an embodiment of the present application.
Fig. 15 illustrates dynamic estimation errors under rotational speed variation for robust predictive control in accordance with an embodiment of the present application.
Referring to fig. 14 and 15, it can be seen from fig. 14 and 15 that the power tracking effect is still good for the rotational speed change, where the observed convergence speed is faster than the rotational speed change. However, in the position-free control method based on the rotation speed observer, larger periodic pulsation still occurs in the estimated rotation speed.
From the above, it can be seen that the model reference adaptive method, apparatus, electronic device and storage medium provided by the present application determine the phase of the power side winding voltage according to the phase-locked loop; determining an adjustable model under a synchronous coordinate system according to the phase and the mathematical model of the brushless doubly-fed motor under the synchronous coordinate system; transforming the coordinate corresponding to the pre-sampled control side winding current to the synchronous coordinate system to determine a reference model; determining a linearization error between the adjustable model and the reference model; determining PI parameters according to the linearization error to obtain estimated rotation speed information, and determining estimated position information according to the estimated rotation speed information; and feeding back the estimated position information to the coordinate transformation corresponding to the control side winding current in a closed loop manner so as to control the brushless doubly-fed motor. By converting the adjustable model and the reference model into the synchronous coordinate system and omitting the dynamic process, the use of a flux linkage observer is reduced, the whole control method is simpler, the calculation method of the error between the adjustable model and the reference model is improved, the linear error between the adjustable model and the reference model is calculated, the sensitivity to the angle difference in a larger range is improved, the parameter design of the PI controller is simplified, the calculation amount of the whole motor control method is reduced, the method is simple and convenient, and the practicability is improved.
It should be noted that, the method of the embodiments of the present application may be performed by a single device, for example, a computer or a server. The method of the embodiment can also be applied to a distributed scene, and is completed by mutually matching a plurality of devices. In the case of such a distributed scenario, one of the devices may perform only one or more steps of the methods of embodiments of the present application, and the devices may interact with each other to complete the methods.
It should be noted that some embodiments of the present application are described above. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims may be performed in a different order than in the embodiments described above and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.
Fig. 16 shows an exemplary structural schematic diagram of a model reference adaptive device according to an embodiment of the present application.
Based on the same inventive concept, the application also provides a model reference self-adaptive device corresponding to the method of any embodiment.
Referring to fig. 16, the model reference adaptation apparatus includes: the device comprises a first determining module, a second determining module, a third determining module, a fourth determining module, a fifth determining module and a control module; wherein,
a first determination module configured to determine a phase of the power side winding voltage from the phase locked loop;
a second determination module configured to determine an adjustable model in a synchronous coordinate system from the phase and a mathematical model of the brushless doubly-fed motor in the synchronous coordinate system;
a third determining module configured to transform coordinates corresponding to the control-side winding current acquired by pre-sampling to the synchronous coordinate system to determine a reference model;
a fourth determination module configured to determine a linearization error between the tunable model and the reference model;
a fifth determining module configured to determine PI parameters from the linearization error to obtain estimated rotational speed information, and to determine estimated position information from the estimated rotational speed information;
a control module configured to feed back the estimated position information in a closed loop to a coordinate transformation corresponding to the control side winding current to control the brushless doubly-fed motor.
In one possible implementation, the second determining module is further configured to:
performing coordinate transformation on the synchronous coordinate system according to the phase to determine a mathematical model of the brushless doubly-fed motor; wherein the mathematical model is expressed as
Wherein u is 1 Representing the power side winding voltage, R 1 Representing power side winding resistance，i 1 Represents the power side winding current, ψ 1 Represents the power side winding flux linkage vector, j represents the imaginary unit, ω 1 Represents the angular speed of the voltage of the power grid, R r Representing rotor winding resistance, i r Representing rotor current, ψ r Representing the rotor flux linkage vector, t representing the differential time, p 1 Represents the pole pair number, omega of the power side winding m Indicating the mechanical angular velocity of the rotor, u 2 Represents the control side winding voltage, R 2 Indicating the resistance of the control side winding, i 2 Represents the control side winding current, ψ 2 Representing the control side winding flux linkage vector, p 2 Representing the pole pair number of the control side winding, L 1 Representing the inductance of the power side winding, L m1 Representing the mutual inductance of the power side winding, L r Representing rotor winding inductance, L m2 Indicating the mutual inductance of the control side winding, L 2 Representing the control side winding inductance;
at steady state, the rotor flux linkage in the mathematical model under the synchronous coordinate system is represented by rotor current to determine an adjustable model; wherein the rotor flux linkage is represented as
Where dq represents the d-axis and q-axis in the synchronous coordinate system.
In one possible implementation, the second determining module is further configured to:
representing the rotor current by the power side winding voltage and the power side winding current; wherein the rotor current is expressed as
Determining an estimated control side winding current in a synchronous coordinate system according to the mathematical model, the rotor flux linkage and the rotor current, and determining the estimated control side winding current as the adjustable model; the adjustable model is expressed as
In one possible implementation, the linearization error is calculated by:
wherein,represents a cross product, +..
In one possible implementation, the fifth determining module is further configured to:
determining PI controller parameters based on the linearization error to determine estimated rotational speed information
-converting said estimated rotational speed informationIntegrating to determine estimated position information +.>
For convenience of description, the above devices are described as being functionally divided into various modules, respectively. Of course, the functions of each module may be implemented in the same piece or pieces of software and/or hardware when implementing the present application.
The device of the foregoing embodiment is configured to implement the corresponding model reference adaptive method in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiment, which is not described herein.
Fig. 17 shows an exemplary structural schematic diagram of an electronic device according to an embodiment of the present application.
Based on the same inventive concept, the application also provides an electronic device corresponding to the method of any embodiment, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the model reference adaptive method of any embodiment when executing the program. Fig. 17 shows a more specific hardware architecture of an electronic device according to this embodiment, where the device may include: processor 1710, memory 1720, input/output interface 1730, communication interface 1740, and bus 1750. Wherein processor 1710, memory 1720, input/output interface 1730, and communication interface 1740 enable communication connection among each other within the device via bus 1750.
The processor 1710 may be implemented by a general purpose CPU (Central Processing Unit ), microprocessor, application specific integrated circuit (Application Specific Integrated Circuit, ASIC), or one or more integrated circuits, etc. for executing relevant programs to implement the technical solutions provided in the embodiments of the present disclosure.
Memory 1720 may be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory ), a static storage device, a dynamic storage device, or the like. Memory 1720 may store an operating system and other application programs, and when the embodiments of the present disclosure are implemented in software or firmware, the relevant program code is stored in memory 1720 and executed by processor 1710 as called for.
The input/output interface 1730 is used to connect with an input/output module to implement information input and output. The input/output module may be configured as a component in a device (not shown in the figure) or may be external to the device to provide corresponding functionality. Wherein the input devices may include a keyboard, mouse, touch screen, microphone, various types of sensors, etc., and the output devices may include a display, speaker, vibrator, indicator lights, etc.
Communication interface 1740 is for connecting communication modules (not shown) to enable communication interactions of the present device with other devices. The communication module may implement communication through a wired manner (such as USB, network cable, etc.), or may implement communication through a wireless manner (such as mobile network, WIFI, bluetooth, etc.).
Bus 1750 comprises a path for transferring information between components of the device (e.g., processor 1710, memory 1720, input/output interface 1730, and communication interface 1740).
It is noted that although the above-described devices illustrate only processor 1710, memory 1720, input/output interface 1730, communication interface 1740, and bus 1750, in an implementation, the device may include other components necessary to achieve proper operation. Furthermore, it will be understood by those skilled in the art that the above-described apparatus may include only the components necessary to implement the embodiments of the present description, and not all the components shown in the drawings.
The electronic device of the foregoing embodiment is configured to implement the corresponding model reference adaptive method in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiment, which is not described herein.
Based on the same inventive concept, corresponding to any of the above embodiments of the method, the present application further provides a non-transitory computer readable storage medium storing computer instructions for causing the computer to perform the model reference adaptive method as described in any of the above embodiments.
The computer readable media of the present embodiments, including both permanent and non-permanent, removable and non-removable media, may be used to implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of storage media for a computer include, but are not limited to, phase change memory (PRAM), static Random Access Memory (SRAM), dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), read Only Memory (ROM), electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium, which can be used to store information that can be accessed by a computing device.
The storage medium of the foregoing embodiments stores computer instructions for causing the computer to perform the model reference adaptive method according to any of the foregoing embodiments, and has the advantages of the corresponding method embodiments, which are not described herein.
Those of ordinary skill in the art will appreciate that: the discussion of any of the embodiments above is merely exemplary and is not intended to suggest that the scope of the application (including the claims) is limited to these examples; the technical features of the above embodiments or in the different embodiments may also be combined within the idea of the present application, the steps may be implemented in any order, and there are many other variations of the different aspects of the embodiments of the present application as described above, which are not provided in detail for the sake of brevity.
Additionally, well-known power/ground connections to Integrated Circuit (IC) chips and other components may or may not be shown within the provided figures, in order to simplify the illustration and discussion, and so as not to obscure the embodiments of the present application. Furthermore, the devices may be shown in block diagram form in order to avoid obscuring the embodiments of the present application, and this also takes into account the fact that specifics with respect to implementation of such block diagram devices are highly dependent upon the platform on which the embodiments of the present application are to be implemented (i.e., such specifics should be well within purview of one skilled in the art). Where specific details (e.g., circuits) are set forth in order to describe example embodiments of the application, it should be apparent to one skilled in the art that embodiments of the application can be practiced without, or with variation of, these specific details. Accordingly, the description is to be regarded as illustrative in nature and not as restrictive.
While the present application has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations of those embodiments will be apparent to those skilled in the art in light of the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may use the embodiments discussed.
The present embodiments are intended to embrace all such alternatives, modifications and variances which fall within the broad scope of the appended claims. Accordingly, any omissions, modifications, equivalents, improvements and/or the like which are within the spirit and principles of the embodiments are intended to be included within the scope of the present application.
Claims (7)
1. A model reference adaptive method, applied to a brushless doubly-fed motor, comprising:
determining the phase of the power side winding voltage according to the phase-locked loop;
determining an adjustable model under a synchronous coordinate system according to the phase and the mathematical model of the brushless doubly-fed motor under the synchronous coordinate system; the determining an adjustable model under a synchronous coordinate system according to the phase and the mathematical model of the brushless doubly-fed motor under the synchronous coordinate system comprises the following steps:
performing coordinate transformation on the synchronous coordinate system according to the phase to determine a mathematical model of the brushless doubly-fed motor; wherein the mathematical model is expressed as
Wherein u is 1 Representing the power side winding voltage, R 1 Representing the power side winding resistance, i 1 Represents the power side winding current, ψ 1 Represents the power side winding flux linkage vector, j represents the imaginary unit, ω 1 Represents the angular speed of the voltage of the power grid, R r Representing rotor winding resistance, i r Representing rotor current, ψ r Representing the rotor flux linkage vector, t representing the differential time, p 1 Represents the pole pair number, omega of the power side winding m Indicating the mechanical angular velocity of the rotor, u 2 Represents the control side winding voltage, R 2 Indicating the resistance of the control side winding, i 2 Represents the control side winding current, ψ 2 Representing the control side winding flux linkage vector, p 2 The control side winding pole pair number is shown,L 1 representing the inductance of the power side winding, L m1 Representing the mutual inductance of the power side winding, L r Representing rotor winding inductance, L m2 Indicating the mutual inductance of the control side winding, L 2 Representing the control side winding inductance;
at steady state, the rotor flux linkage in the mathematical model under the synchronous coordinate system is represented by rotor current to determine an adjustable model; wherein the rotor flux linkage is represented as
Wherein dq represents d-axis and q-axis in the synchronous coordinate system;
the coordinate transformation is performed on the synchronous coordinate system according to the phase to determine a mathematical model of the brushless doubly-fed motor, and then the method further comprises:
representing the rotor current by the power side winding voltage and the power side winding current; wherein the rotor current is expressed as
Determining an estimated control side winding current in a synchronous coordinate system according to the mathematical model, the rotor flux linkage and the rotor current, and determining the estimated control side winding current as the adjustable model; the adjustable model is expressed as
Transforming the coordinate corresponding to the pre-sampled control side winding current to the synchronous coordinate system to determine a reference model;
determining a linearization error between the adjustable model and the reference model;
determining PI parameters according to the linearization error to obtain estimated rotation speed information, and determining estimated position information according to the estimated rotation speed information;
and feeding back the estimated position information to the coordinate transformation corresponding to the control side winding current in a closed loop manner so as to control the brushless doubly-fed motor.
2. The method of claim 1, wherein the linearization error is calculated by:
wherein,represents cross-multiplication, represents dot-multiplication.
3. The method of claim 1, wherein determining PI parameters based on the linearization error to obtain estimated rotational speed information and determining estimated position information based on the estimated rotational speed information comprises:
determining PI controller parameters based on the linearization error to determine estimated rotational speed information
-converting said estimated rotational speed informationIntegrating to determine estimated position information +.>
4. A model reference adaptation device, comprising:
a first determination module configured to determine a phase of the power side winding voltage from the phase locked loop;
a second determining module configured to determine an adjustable model in a synchronous coordinate system from the phase and a mathematical model of the brushless doubly-fed motor in the synchronous coordinate system; the second determination module is further configured to:
performing coordinate transformation on the synchronous coordinate system according to the phase to determine a mathematical model of the brushless doubly-fed motor; wherein the mathematical model is expressed as
Wherein u is 1 Representing the power side winding voltage, R 1 Representing the power side winding resistance, i 1 Represents the power side winding current, ψ 1 Represents the power side winding flux linkage vector, j represents the imaginary unit, ω 1 Represents the angular speed of the voltage of the power grid, R r Representing rotor winding resistance, i r Representing rotor current, ψ r Representing the rotor flux linkage vector, t representing the differential time, p 1 Represents the pole pair number, omega of the power side winding m Indicating the mechanical angular velocity of the rotor, u 2 Represents the control side winding voltage, R 2 Indicating the resistance of the control side winding, i 2 Represents the control side winding current, ψ 2 Representing the control side winding flux linkage vector, p 2 Representing the pole pair number of the control side winding, L 1 Representing the inductance of the power side winding, L m1 Representing the mutual inductance of the power side winding, L r Representing rotor winding inductance, L m2 Indicating the mutual inductance of the control side winding, L 2 Representing the control side winding inductance;
at steady state, the rotor flux linkage in the mathematical model under the synchronous coordinate system is represented by rotor current to determine an adjustable model; wherein the rotor flux linkage is represented as
Wherein dq represents d-axis and q-axis in the synchronous coordinate system;
the coordinate transformation is performed on the synchronous coordinate system according to the phase to determine a mathematical model of the brushless doubly-fed motor, and then the method further comprises:
representing the rotor current by the power side winding voltage and the power side winding current; wherein the rotor current is expressed as
Determining an estimated control side winding current in a synchronous coordinate system according to the mathematical model, the rotor flux linkage and the rotor current, and determining the estimated control side winding current as the adjustable model; the adjustable model is expressed as
A third determining module configured to transform coordinates corresponding to the control-side winding current acquired by pre-sampling to the synchronous coordinate system to determine a reference model;
a fourth determination module configured to determine a linearization error between the tunable model and the reference model;
a fifth determining module configured to determine PI parameters from the linearization error to obtain estimated rotational speed information, and to determine estimated position information from the estimated rotational speed information;
a control module configured to feed back the estimated position information in a closed loop to a coordinate transformation corresponding to the control side winding current to control the brushless doubly-fed motor.
5. The apparatus of claim 4, wherein the fifth determination module is further configured to:
determining PI controller parameters based on the linearization error to determine estimated rotational speed information
-converting said estimated rotational speed informationIntegrating to determine estimated position information +.>
6. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the method of any one of claims 1 to 3 when the program is executed by the processor.
7. A non-transitory computer readable storage medium storing computer instructions for causing the computer to implement the method of any one of claims 1 to 3.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210993921.7A CN115494722B (en) | 2022-08-18 | 2022-08-18 | Model reference self-adaption method, device, electronic equipment and storage medium |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210993921.7A CN115494722B (en) | 2022-08-18 | 2022-08-18 | Model reference self-adaption method, device, electronic equipment and storage medium |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115494722A CN115494722A (en) | 2022-12-20 |
| CN115494722B true CN115494722B (en) | 2024-03-12 |
Family
ID=84466958
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210993921.7A Active CN115494722B (en) | 2022-08-18 | 2022-08-18 | Model reference self-adaption method, device, electronic equipment and storage medium |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115494722B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2619899A2 (en) * | 2010-09-20 | 2013-07-31 | Robert Bosch GmbH | Method and device for the sensorless determination of a rotor position of an electric motor |
| CN106411205A (en) * | 2016-09-05 | 2017-02-15 | 华中科技大学 | Rotating speed identification method and system of brushless doubly-fed motor |
| CN107069808A (en) * | 2017-03-28 | 2017-08-18 | 中国电力科学研究院 | A kind of new energy power station model error localization method and device |
| CN111965969A (en) * | 2020-08-19 | 2020-11-20 | 华侨大学 | Double closed-loop anti-interference PID control method and system for speed and position of direct current motor |
| CN113556069A (en) * | 2021-07-23 | 2021-10-26 | 哈尔滨理工大学 | Terminal sliding mode flux linkage observation method of brushless doubly-fed motor |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6784634B2 (en) * | 2001-09-14 | 2004-08-31 | Edwin A. Sweo | Brushless doubly-fed induction machine control |
-
2022
- 2022-08-18 CN CN202210993921.7A patent/CN115494722B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2619899A2 (en) * | 2010-09-20 | 2013-07-31 | Robert Bosch GmbH | Method and device for the sensorless determination of a rotor position of an electric motor |
| CN106411205A (en) * | 2016-09-05 | 2017-02-15 | 华中科技大学 | Rotating speed identification method and system of brushless doubly-fed motor |
| CN107069808A (en) * | 2017-03-28 | 2017-08-18 | 中国电力科学研究院 | A kind of new energy power station model error localization method and device |
| CN111965969A (en) * | 2020-08-19 | 2020-11-20 | 华侨大学 | Double closed-loop anti-interference PID control method and system for speed and position of direct current motor |
| CN113556069A (en) * | 2021-07-23 | 2021-10-26 | 哈尔滨理工大学 | Terminal sliding mode flux linkage observation method of brushless doubly-fed motor |
Non-Patent Citations (1)
| Title |
|---|
| 基于模型参考自适应的无刷双馈电机独立发电***转速辨识方法;马骁;陈宇;苏婧媛;康勇;;中国电机工程学报(第17期);294-303 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN115494722A (en) | 2022-12-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111969914B (en) | Dead beat current prediction control method and equipment for permanent magnet synchronous motor and storage medium | |
| CN114598206A (en) | Design method of permanent magnet synchronous motor wide-speed-domain rotor position observer | |
| CN110807168B (en) | Method and device for estimating sub-synchronous oscillation mode of grid-connected converter | |
| CN114865934A (en) | Grid-connected inverter control method, device and equipment and computer medium | |
| CN112332736B (en) | Asynchronous motor dead beat prediction current control method and device based on current difference | |
| CN115494722B (en) | Model reference self-adaption method, device, electronic equipment and storage medium | |
| CN110557069A (en) | rotor operation parameter estimation method, motor control system and active disturbance rejection controller | |
| CN111162717A (en) | Method and device for detecting initial position angle of permanent magnet synchronous motor rotor and storage medium | |
| CN113552452B (en) | Permanent magnet motor turn-to-turn short circuit residual insulation monitoring method and device and storage medium | |
| CN113746391A (en) | Control method and device for permanent magnet synchronous motor, electronic equipment and storage medium | |
| CN114584026A (en) | Method for optimizing parameter robustness of permanent magnet synchronous motor and related equipment | |
| JP2008219982A (en) | Method and program for estimating position of synchronous motor | |
| CN115360954A (en) | Robust prediction control method of brushless doubly-fed machine and related equipment | |
| CN113904607B (en) | Predictive current control method for permanent magnet synchronous motor and related equipment | |
| Abdelrahem et al. | Improved Direct-Model Predictive Control with a Simple Disturbance Observer for DFIGs | |
| CN107733310B (en) | Speed-sensor-free control method suitable for large-torque starting of asynchronous motor | |
| CN114977941B (en) | Inertia identification method, device and medium for alternating current servo system | |
| CN115765562B (en) | Model-free prediction current control method and device for permanent magnet synchronous motor | |
| CN115714559A (en) | Control method and system for identifying writing error of initial angle of permanent magnet synchronous motor for vehicle | |
| CN116365950A (en) | PMSM high-frequency injection rotor position estimation method without low-pass filtering | |
| CN111711388B (en) | Model-free prediction control method and device for double-fed motor and electronic equipment | |
| CN115864927A (en) | Control method and system for motor rotating speed control response | |
| WO2023124921A1 (en) | Torque estimation method and apparatus for permanent magnet synchronous motor, and device and storage medium | |
| CN117713628A (en) | Motor control method, motor control device, medium and electronic equipment | |
| Nguyen et al. | Numerical approach for estimation of the rotor speed of the asynchronous machine |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |