Positioning and Velocity Measurement Methods and Systems for High-Speed Maglev Vehicles
By setting up an antenna unit on the high-speed maglev vehicle and using the transmitting and receiving antennas to generate induced electromotive force, the problem of DC component in the signal of the rotary transformer in the linear motor is solved, and orthogonal signal processing without DC component is realized, enabling accurate positioning and speed measurement of the high-speed maglev vehicle.
Patent Information
- Application Number
- CN202310763766.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-06-27
- Publication Date
- 2026-03-06
- Estimated Expiration
- 2043-06-27
AI Technical Summary
In existing technologies, the use of rotary transformers in linear motors presents the problem of DC signal components, which leads to difficulties in positioning and speed measurement.
An antenna unit is installed on a high-speed maglev vehicle. An induced electromotive force is generated by a transmitting antenna and a receiving antenna. The relative position information is determined by the induced electromotive force. Low-pass filtering and digital processing are used to obtain orthogonal signals without DC components, so as to realize positioning and speed measurement.
The DC component in the signal was effectively removed, relative position information was obtained, and accurate positioning and speed measurement of the high-speed maglev vehicle were achieved.
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Figure CN119190140B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of magnetic levitation traction control technology, and in particular to a method and system for positioning, speed measurement and position identification of a high-speed magnetic levitation vehicle. Background Technology
[0002] Vehicle-mounted zero-flux positioning and speed measurement borrows design principles from rotary transformers. A rotary transformer is a position sensor whose output voltage varies with the rotor angle. The rotor winding is an excitation winding, and the excitation signal on it is obtained through brushes or magnetic field coupling of the stator. Two-phase stator windings are placed orthogonally to each other to generate sine and cosine signals. When the excitation winding is energized with an AC voltage of a certain frequency, the voltage amplitude of the output winding has a sine and cosine function relationship with the rotor angle. Based on the principle of rotary transformers, the vehicle-mounted zero-flux positioning and speed measurement scheme unfolds the rotary transformer rotary motor into a linear motor, considers the spatial position to set two sets of orthogonal signals, and uses existing zero-flux coils to obtain the angle, thereby achieving the function of relative positioning.
[0003] For permanent magnet synchronous rotating motors, a rotary transformer is often used for position identification. It passes a high-frequency signal through the excitation winding to obtain orthogonal sine and cosine signals, thereby obtaining angle information.
[0004] Rotary transformers are mainly used in rotary motors. There is no corresponding method for applying them to linear motors. Furthermore, since there is no iron core in linear motors, the received signal will have a DC component. Summary of the Invention
[0005] This invention provides a method and system for positioning, speed measurement, and location identification of a high-speed maglev vehicle, which can solve the technical problems in the prior art.
[0006] This invention provides a method for positioning, speed measurement, and position identification of a high-speed magnetic levitation vehicle, wherein the method includes:
[0007] An antenna unit is installed on a high-speed magnetic levitation vehicle, the antenna unit including a transmitting antenna and a receiving antenna;
[0008] A high-frequency current is passed through the transmitting antenna to generate a magnetic field. As the vehicle moves, an induced current is generated in the levitation coil on the same side as the transmitting antenna. The induced current flows through the hinge line into the levitation coil on the opposite side, which is on the same side as the receiving antenna, thereby generating an induced electromotive force in the receiving antenna.
[0009] The relative position information of the high-speed maglev vehicle is determined based on the generated induced electromotive force.
[0010] Preferably, the transmitting antenna includes a first transmitting antenna and a second transmitting antenna, and the receiving antenna includes a first receiving antenna and a second receiving antenna corresponding to the first transmitting antenna, as well as a third receiving antenna and a fourth receiving antenna corresponding to the second transmitting antenna. The first receiving antenna and the second receiving antenna are 180 degrees apart in spatial position, the third receiving antenna and the fourth receiving antenna are 180 degrees apart in spatial position, and the first receiving antenna and the third receiving antenna are 90 degrees apart in spatial position.
[0011] Preferably, determining the relative positional relationship of the high-speed maglev vehicle based on the generated induced electromotive force includes:
[0012] Subtract the induced electromotive force y1 generated by the first receiving antenna from the induced electromotive force y2 generated by the second receiving antenna to obtain the AC amplitude signal y1-2 without DC component;
[0013] Subtract the induced electromotive force y3 generated by the third receiving antenna from the induced electromotive force y4 generated by the fourth receiving antenna to obtain the AC amplitude signal y3-4 without DC component;
[0014] Low-pass filtering is performed on AC amplitude signals y1-2 and y3-4 without DC components to obtain mutually orthogonal high-frequency sine signals y1-2_lpf and high-frequency cosine signals y3-4_lpf.
[0015] The relative position of the high-speed maglev vehicle is obtained by digitally processing the high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf.
[0016] Preferably, the AC amplitude signals y1-2 and y3-4 without DC components are represented by the following formulas:
[0017]
[0018] Where c is the signal amplitude after subtraction, θ is the angle signal containing relative position information, and ω is the angular frequency of the high-frequency signal.
[0019] Preferably, the high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf are represented by the following formulas:
[0020]
[0021] Where d is the signal amplitude after low-pass filtering.
[0022] Preferably, digital processing of the high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf to obtain the relative position of the high-speed maglev vehicle includes:
[0023] The relative position of the high-speed maglev vehicle is obtained by performing arctangent calculations on the high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf.
[0024] This invention provides a positioning and velocity measurement system for a high-speed maglev vehicle, wherein the system includes:
[0025] An antenna unit is installed on a high-speed magnetic levitation vehicle, and the antenna unit includes a transmitting antenna and a receiving antenna.
[0026] An inverter is used to pass a high-frequency current through the transmitting antenna to generate a magnetic field. As the vehicle moves, an induced current is generated in the levitation coil on the same side as the transmitting antenna. The induced current flows through the hinge line into the levitation coil on the opposite side, which is on the same side as the receiving antenna, thereby generating an induced electromotive force in the levitation coil on the opposite side in the receiving antenna.
[0027] A positioning device is used to determine the relative position information of a high-speed maglev vehicle based on the generated induced electromotive force.
[0028] Preferably, the transmitting antenna includes a first transmitting antenna and a second transmitting antenna, and the receiving antenna includes a first receiving antenna and a second receiving antenna corresponding to the first transmitting antenna, as well as a third receiving antenna and a fourth receiving antenna corresponding to the second transmitting antenna. The first receiving antenna and the second receiving antenna are 180 degrees apart in spatial position, the third receiving antenna and the fourth receiving antenna are 180 degrees apart in spatial position, and the first receiving antenna and the third receiving antenna are 90 degrees apart in spatial position.
[0029] The above technical solution allows for the coupling of a transmitting antenna with a levitation coil, enabling the sensing of voltage signals that change with position in the receiving antenna. This voltage signal can then be used to extract angles, ultimately achieving positioning and speed measurement for high-speed maglev vehicles. Attached Figure Description
[0030] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.
[0031] Figure 1An antenna element arrangement diagram according to an embodiment of the present invention is shown;
[0032] Figure 2A-2C A schematic diagram of receiving antenna data processing according to an embodiment of the present invention is shown;
[0033] Figures 3A-3C A schematic diagram of angle processing according to an embodiment of the present invention is shown. Detailed Implementation
[0034] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0035] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0036] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.
[0037] This invention provides a method for positioning, speed measurement, and location identification of a high-speed maglev vehicle, wherein the method includes:
[0038] An antenna unit is installed on a high-speed magnetic levitation vehicle, the antenna unit including a transmitting antenna and a receiving antenna;
[0039] A high-frequency current is passed through the transmitting antenna to generate a magnetic field. As the vehicle moves (advances), an induced current is generated in the levitation coil (e.g., a zero-flux coil) on the same side as the transmitting antenna. The induced current flows through the hinge line into the levitation coil on the opposite side, which is on the same side as the receiving antenna, thereby generating an induced electromotive force in the receiving antenna.
[0040] The relative position information of the high-speed maglev vehicle is determined based on the generated induced electromotive force.
[0041] For example, as the coupling area with the zero flux coil changes, the amplitude of the induced electromotive force in the receiving antenna changes periodically. By acquiring the effective signal in the amplitude, the relative position information of the aircraft can be obtained.
[0042] The above technical solution allows for the coupling of a transmitting antenna with a levitation coil, enabling the sensing of voltage signals that change with position in the receiving antenna. This voltage signal can then be used to extract angles, ultimately achieving positioning and speed measurement for high-speed maglev vehicles.
[0043] In this scenario, a high-speed maglev vehicle could be, for example, a high-speed maglev train, with the antenna unit mounted on the train and the zero-flux coil positioned on the ground. Positioning is achieved by coupling the transmitting and receiving antennas with the zero-flux coil and utilizing changes in the coupling area.
[0044] According to one embodiment of the present invention, such as Figure 1 As shown, the transmitting antenna includes a first transmitting antenna (transmitting antenna 1) and a second transmitting antenna (transmitting antenna 2), and the receiving antenna includes a first receiving antenna (receiving antenna 1) and a second receiving antenna (receiving antenna 2) corresponding to the first transmitting antenna, as well as a third receiving antenna (receiving antenna 3) and a fourth receiving antenna (receiving antenna 4) corresponding to the second transmitting antenna. The first receiving antenna and the second receiving antenna are 180 degrees apart in spatial position, the third receiving antenna and the fourth receiving antenna are 180 degrees apart in spatial position, and the first receiving antenna and the third receiving antenna are 90 degrees apart in spatial position.
[0045] The first transmitting antenna, the first receiving antenna, and the second receiving antenna form the first group of antennas; the second transmitting antenna, the third receiving antenna, and the fourth receiving antenna form the second group of antennas.
[0046] A high-frequency current is passed through the first transmitting antenna to generate a magnetic field, which in turn induces an electromotive force in the first and second receiving antennas. A high-frequency current is passed through the second transmitting antenna to generate a magnetic field, which in turn induces an electromotive force in the third and fourth receiving antennas.
[0047] The induced electromotive force (EMF) of the first receiving antenna, the second receiving antenna, the third receiving antenna, and the fourth receiving antenna are shown in the following formulas:
[0048]
[0049]
[0050] In the formula, y1 is the induced electromotive force of the first receiving antenna, y2 is the induced electromotive force of the second receiving antenna, y3 is the induced electromotive force of the third receiving antenna, y4 is the induced electromotive force of the fourth receiving antenna, a is the amplitude of the induced electromotive force, θ is the angle signal containing position information, b is the DC bias of the induced electromotive force, and ω is the angular frequency of the high-frequency signal.
[0051] According to one embodiment of the present invention, determining the relative positional relationship of a high-speed magnetic levitation vehicle based on the generated induced electromotive force includes:
[0052] Subtract the induced electromotive force y1 generated by the first receiving antenna from the induced electromotive force y2 generated by the second receiving antenna to obtain the AC amplitude signal y1-2 without DC component;
[0053] Subtract the induced electromotive force y3 generated by the third receiving antenna from the induced electromotive force y4 generated by the fourth receiving antenna to obtain the AC amplitude signal y3-4 without DC component;
[0054] Low-pass filtering is performed on AC amplitude signals y1-2 and y3-4 without DC components to obtain mutually orthogonal high-frequency sine signals y1-2_lpf (i.e., the low-pass filtered sine signal) and high-frequency cosine signals y3-4_lpf (i.e., the low-pass filtered cosine signal).
[0055] The relative position of the high-speed maglev vehicle is obtained by digitally processing the high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf.
[0056] In other words, two sets of orthogonal signals are obtained through two sets of antennas, thereby acquiring sine and cosine signals, and further obtaining position information to achieve the function of relative positioning.
[0057] The schematic diagram of the signals from the first receiving antenna and the second receiving antenna is shown below. Figure 2A and 2BAs shown, the signal amplitudes acquired by the first and second receiving antennas exhibit AC components with DC components, and the magnitude of the DC component b is related to the air gap and the motion speed. By subtracting the first receiving antenna from the second receiving antenna, an AC amplitude signal y1-2 (sine wave signal) without DC components can be obtained, as shown below. Figure 2C As shown. Similarly, subtracting the third receiving antenna from the fourth receiving antenna yields the corresponding cosine signal y3-4.
[0058] According to one embodiment of the present invention, the AC amplitude signals y1-2 and y3-4 without DC components are represented by the following formulas:
[0059]
[0060] Where c is the signal amplitude after subtraction, θ is the angle signal containing relative position information, and ω is the angular frequency of the high-frequency signal.
[0061] According to an embodiment of the present invention, the high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf are represented by the following formula:
[0062]
[0063] Where d is the signal amplitude after low-pass filtering.
[0064] According to one embodiment of the present invention, digital processing of the high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf to obtain the relative position of the high-speed maglev vehicle includes:
[0065] The relative position of the high-speed maglev vehicle is obtained by performing arctangent calculations on the high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf.
[0066] In other words, the arctangent of a sine signal and a cosine signal can be used to obtain the angle signal θ, such as... Figures 3A-3B As shown, angle information is obtained by utilizing the envelope of a high-frequency sine signal and a high-frequency cosine signal, such as... Figure 3C As shown, this enables the positioning and speed measurement of the aircraft.
[0067] This invention also provides a positioning and velocity measurement system for a high-speed maglev vehicle, wherein the system includes:
[0068] An antenna unit is installed on a high-speed magnetic levitation vehicle, and the antenna unit includes a transmitting antenna and a receiving antenna.
[0069] A power source is used to pass a high-frequency current through the transmitting antenna to generate a magnetic field. As the vehicle moves, an induced current is generated in the levitation coil on the same side as the transmitting antenna. The induced current flows through the hinge line into the levitation coil on the opposite side, which is on the same side as the receiving antenna, thereby generating an induced electromotive force in the levitation coil on the opposite side of the receiving antenna.
[0070] A positioning device is used to determine the relative position information of a high-speed maglev vehicle based on the generated induced electromotive force.
[0071] The above technical solution allows for the installation of an antenna unit on a high-speed maglev vehicle. By coupling the transmitting antenna with the levitation coil, a voltage signal that changes with position can be induced in the receiving antenna. This voltage signal can then be used to extract the angle, ultimately enabling the positioning and speed measurement of the high-speed maglev vehicle.
[0072] According to one embodiment of the present invention, the transmitting antenna includes a first transmitting antenna and a second transmitting antenna, and the receiving antenna includes a first receiving antenna and a second receiving antenna corresponding to the first transmitting antenna, as well as a third receiving antenna and a fourth receiving antenna corresponding to the second transmitting antenna. The first receiving antenna and the second receiving antenna are 180 degrees apart in spatial position, the third receiving antenna and the fourth receiving antenna are 180 degrees apart in spatial position, and the first receiving antenna and the third receiving antenna are 90 degrees apart in spatial position.
[0073] The system described above corresponds to the method described above. For specific examples, please refer to the description of the method above, which will not be repeated here.
[0074] In one example of the present invention, by controlling the inverter to output a 50kHz sinusoidal high-frequency signal to the transmitting antenna, the voltage measured in the receiving antenna through the coupling of the zero-flux coil is also a 50kHz sinusoidal signal.
[0075] Since both the transmitting and receiving antennas are mounted on the high-speed maglev vehicle, while the zero-flux coil is mounted on the ground, as the vehicle moves forward, the coupling area between the receiving antenna and the zero-flux coil changes periodically, and the amplitude of the high-frequency signal obtained in the receiving antenna also changes periodically.
[0076] Therefore, by using two sets of antenna elements, the DC component in the receiving antenna is removed by signal subtraction to obtain high-frequency sine and high-frequency cosine signals, and angle information is obtained through signal processing, thereby realizing the high-speed maglev vehicle positioning and speed measurement function.
[0077] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention; the directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.
[0078] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.
[0079] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.
[0080] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for positioning, velocity measurement and position identification of a high-speed maglev vehicle, characterized in that, The method comprises: An antenna unit is arranged on the high-speed maglev vehicle, and the antenna unit comprises a transmitting antenna and a receiving antenna; A high-frequency current is passed through the transmitting antenna to generate a magnetic field, and as the vehicle runs, an induced current is generated in a levitation coil on the same side of the transmitting antenna, the induced current flows into a levitation coil on the opposite side of the receiving antenna through a hinge wire, so that the levitation coil on the opposite side generates an induced electromotive force in the receiving antenna; The relative position information of the high-speed maglev vehicle is determined according to the generated induced electromotive force; The transmitting antenna comprises a first transmitting antenna and a second transmitting antenna, the receiving antenna comprises a first receiving antenna corresponding to the first transmitting antenna, a second receiving antenna, a third receiving antenna corresponding to the second transmitting antenna, and a fourth receiving antenna, the first receiving antenna and the second receiving antenna are 180 degrees apart in spatial position, the third receiving antenna and the fourth receiving antenna are 180 degrees apart in spatial position, and the first receiving antenna and the third receiving antenna are 90 degrees apart in spatial position; Determining the relative position relationship of the high-speed maglev vehicle according to the generated induced electromotive force comprises: The induced electromotive force y1 generated by the first receiving antenna is subtracted from the induced electromotive force y2 generated by the second receiving antenna to obtain an alternating current amplitude signal y1-2 without a direct current component; The induced electromotive force y3 generated by the third receiving antenna is subtracted from the induced electromotive force y4 generated by the fourth receiving antenna to obtain an alternating current amplitude signal y3-4 without a direct current component; The alternating current amplitude signal y1-2 without a direct current component and the alternating current amplitude signal y3-4 without a direct current component are low-pass filtered to obtain a high-frequency sine signal y1-2_lpf and a high-frequency cosine signal y3-4_lpf which are orthogonal to each other; The high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf are digitally processed to obtain the relative position of the high-speed maglev vehicle.
2. The method of claim 1, wherein, The alternating current amplitude signal y1-2 without a direct current component and the alternating current amplitude signal y3-4 without a direct current component are represented by the following formula: Wherein, c is the signal amplitude after subtraction, θ is an angle signal containing relative position information, and ω is the angular frequency of the high-frequency signal.
3. The method of claim 2, wherein, The high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf are represented by the following formula: Wherein, d is the signal amplitude after low-pass filtering.
4. The method of claim 3, wherein, The high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf are digitally processed to obtain the relative position of the high-speed maglev vehicle, which comprises: The high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf are calculated by arctangent to obtain the relative position of the high-speed maglev vehicle.
5. A high speed maglev vehicle positioning and velocity measurement location recognition system characterized by, The system comprises: An antenna unit is arranged on the high-speed maglev vehicle, and the antenna unit comprises a transmitting antenna and a receiving antenna; An inverter is used to pass high-frequency current into the transmitting antenna to generate a magnetic field, and as the vehicle runs, an induced current is generated in the levitation coil on the same side as the transmitting antenna, and the induced current flows through the hinge line into the levitation coil on the opposite side as the receiving antenna, so that the levitation coil on the opposite side generates an induced electromotive force in the receiving antenna; A positioning device is used to determine the relative position information of the high-speed magnetic levitation vehicle according to the generated induced electromotive force; The transmitting antenna includes a first transmitting antenna and a second transmitting antenna, and the receiving antenna includes a first receiving antenna corresponding to the first transmitting antenna, a second receiving antenna, a third receiving antenna corresponding to the second transmitting antenna, and a fourth receiving antenna, the first receiving antenna and the second receiving antenna are 180 degrees apart in spatial position, the third receiving antenna and the fourth receiving antenna are 180 degrees apart in spatial position, and the first receiving antenna and the third receiving antenna are 90 degrees apart in spatial position; Determining the relative position relationship of the high-speed magnetic levitation vehicle according to the generated induced electromotive force includes: Subtracting the induced electromotive force y2 generated by the second receiving antenna from the induced electromotive force y1 generated by the first receiving antenna to obtain an alternating current amplitude signal y1-2 without direct current component; Subtracting the induced electromotive force y4 generated by the fourth receiving antenna from the induced electromotive force y3 generated by the third receiving antenna to obtain an alternating current amplitude signal y3-4 without direct current component; Low-pass filtering the alternating current amplitude signal y1-2 without direct current component and the alternating current amplitude signal y3-4 without direct current component to obtain high-frequency sine signal y1-2_lpf and high-frequency cosine signal y3-4_lpf which are orthogonal to each other; Digitally processing the high-frequency sine signal y1-2_lpf and the high-frequency cosine signal y3-4_lpf to obtain the relative position of the high-speed magnetic levitation vehicle.
Citation Information
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