A method and simulation device for modeling magnetic levitation using a double system

Abstract

The application relates to the field of simulation, in particular to a method for modeling a magnetic suspension object by using a double system and a simulation device. The model data generation module comprises a dynamic model and a control model, the model data generation module realizes data model code generation and downloads to an embedded development board for real-time simulation operation, the model data generation module transmits characteristic parameters to the embedded development board before simulation, the characteristic parameters include the mass of the magnetic suspension object, the coil resistance, the coil inductance, the magnetic force-current coefficient, the magnetic force-position coefficient, the initial position of the magnetic suspension object, and real-time coil voltage parameters are continuously given; the embedded development board receives the displacement of the magnetic suspension object, the coil current and the coil voltage in real time by running the method for modeling the magnetic suspension object by using the double system, calculates the displacement of the magnetic suspension object and the coil current at the next moment, feeds back the calculated displacement of the magnetic suspension object and the coil current at the next moment to a simulation platform, and the simulation platform performs simulation display. The application can more directly observe the relationship between the current and the position information.

Description

Technical Field

[0001] This invention relates to the field of simulation, and in particular to a method and simulation device for modeling magnetically suspended objects using a dual-system approach. Background Technology

[0002] Magnetic suspension is an organic combination of multiple fields and technologies such as electromagnetics, control theory, and computer control. It is also an unstable and strongly nonlinear system. Therefore, magnetic suspension system is a relatively ideal experimental project in control theory research. In teaching experiments, it is necessary to develop a simple magnetic suspension simulation system to facilitate understanding.

[0003] With the development of magnetic levitation technology, it is being applied in more and more fields, such as vehicle flywheel batteries, submarine vibration reduction and noise reduction, and wind power generation. The foundations of the magnetic bearings used in these applications are also in motion. The connection between the magnetic levitation object and the ground is usually non-rigid, and their movements are coupled and mutually influential, thus forming a magnetic levitation object-foundation coupled system in terms of structure and dynamics. Therefore, the simulation system of magnetic levitation objects is generally very complex. For example, the Chinese invention patent "A Modeling Method and System for Magnetic Levitation Bearings under Multi-parameter Uncertainty" (application number 202011637726.8) has too many parameters and involves many complex external factors, which actually reduces the understanding of the magnetic levitation phenomenon. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method and simulation device for modeling magnetically suspended objects using a dual-system approach. This invention divides the system into two systems, which are analyzed together through electromagnetic forces. A simple mathematical model can simulate the position of the magnetically suspended object. This invention requires less input information and allows for a more intuitive observation of the relationship between current and position information.

[0005] The technical solution of this invention is: a method for modeling magnetically suspended objects using a dual-system approach, characterized by the following steps:

[0006] Step 1: Establish the mathematical model of the electrical subsystem; assuming the resistance and inductance values ​​are constant, according to Kirchhoff's laws, the circuit relationship on the coil is as follows:

[0007]

[0008] Where u(t) represents the change in voltage across the electromagnetic coil, L and R represent the inductance and resistance of the electromagnetic coil, i represents the change in current flowing through the coil, and I and U represent the operating current and operating voltage of the coil when the magnetic suspension is stable at the operating point.

[0009] Step 2: Establish the mathematical model of the magneto-mechanical subsystem; the controlled object, the magnetically suspended object, is only subject to the electromagnetic attraction F and its own gravity mg during the suspension process; the dynamic equation of the magnetically suspended object in the vertical direction is as follows:

[0010]

[0011] Where m represents the mass of the magnetic suspension, f(t) is the attractive force of the electromagnetic coil, and x(t) is the displacement of the magnetic suspension;

[0012] Step 3: Merge the two systems using electromagnetic attraction.

[0013] Electromagnetic attraction is expressed as:

[0014]

[0015] Where k and x0 are correction parameters for the actual characteristics of the electromagnet, and X represents the position where the magnetic suspension is stable at the operating point;

[0016] For the nonlinear representation of equation (3), we can approximate it using Taylor series:

[0017]

[0018] in,

[0019] k x This is called the magnetic-position coefficient, k i This is called the magnetic force-current coefficient;

[0020] At the equilibrium point (I,X,x0,U), we have

[0021]

[0022] Combining (1) and (4), we get:

[0023]

[0024]

[0025] Step 4: Calculate the transfer functions of the two systems respectively.

[0026] Taking the Laplace transform of equations (6) and (7), we can obtain the transfer functions of the electrical subsystem and the magneto-mechanical subsystem, respectively.

[0027]

[0028]

[0029] Step four: Using the voltage of the coil as the input signal, calculate the displacement information of the output magnetic levitation object.

[0030] The technical solution of this invention is: a simulation device for modeling magnetically suspended objects using a dual-system approach, comprising a host computer and an embedded development board. The host computer includes a simulation platform and a model data generation module. The model data generation module includes a dynamic model and a control model. It generates data model code and downloads it to the embedded development board for real-time simulation. Before simulation, the model data generation module transmits characteristic parameters to the embedded development board, including the mass of the magnetically suspended object, coil resistance, coil inductance, magnetic force-current coefficient, magnetic force-position coefficient, and the initial position of the magnetically suspended object, continuously providing real-time coil voltage parameters. The embedded development board, through the dual-system modeling method, receives the displacement, coil current, and coil voltage of the magnetically suspended object in real time, calculates the displacement and coil current of the magnetically suspended object at the next moment, and feeds back the calculated displacement and coil current of the magnetically suspended object at the next moment to the simulation platform for simulation display.

[0031] According to the simulation device for modeling magnetic suspension objects using a dual system as described above, the feature is that the embedded development board is an F4-Pro embedded development board.

[0032] According to the simulation device for modeling magnetically suspended objects using a dual system as described above, the feature is that the model data generation module is developed using Simulink.

[0033] According to the simulation device for modeling magnetically suspended objects using a dual system as described above, the feature is that the virtual prototype platform uses Unity3D to realize the virtual prototype of the magnetically suspended object.

[0034] According to the simulation device for modeling magnetic suspension objects using a dual system as described above, the simulation platform is used to build a virtual prototype platform. The virtual prototype implementation process is as follows: first, based on the actual magnetic suspension object, three-dimensional models of each component of the virtual prototype are established using Solidworks; then, the three-dimensional model of the magnetic suspension object is imported into the virtual experimental scene constructed by Unity3D; and finally, components are added. Attached Figure Description

[0035] Figure 1 Working principle of magnetic suspension.

[0036] Figure 2 Overall architecture of the virtual experiment system for magnetic suspension objects.

[0037] Figure 3 Virtual prototype of magnetic suspension object. Detailed Implementation

[0038] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0039] like Figure 1 As shown, a method for modeling magnetically suspended objects using a dual-system approach employs an electrical subsystem and a magneto-mechanical subsystem. In this invention, an electric current directly generates a force on the magnetically suspended object through a magnetic field, serving as the link between the subsystems.

[0040] In the modeling process, the magnetic-mechanical subsystem is assumed to have the following characteristics: (1) The iron core is magnetically saturated and there is no hysteresis phenomenon; (2) The magnetic flux of the iron core is infinite; (3) The generated current in the iron core is ignored; (4) The electromagnetic induction coefficient in the coil is constant near the equilibrium point.

[0041] Step 1: Establish a mathematical model of the electrical subsystem.

[0042] In this step, the electromagnet is approximated as a coil consisting of an inductor and a resistor connected in series. Assuming the resistance and inductance are constant, according to Kirchhoff's laws, the circuit relationship on the coil is as follows:

[0043]

[0044] Where u(t) represents the change in voltage across the electromagnetic coil, L and R represent the inductance and resistance of the electromagnetic coil, i represents the change in current flowing through the coil, and I and U represent the operating current and operating voltage of the coil when the magnetic suspension is stable at the operating point (equilibrium point).

[0045] Step 2: Establish a mathematical model of the magneto-mechanical subsystem.

[0046] This invention ignores other disturbing forces acting on the magnetically suspended object. Therefore, the controlled magnetically suspended object is only subject to the electromagnetic attraction F and its own gravity mg during levitation. The dynamic equation of the magnetically suspended object in the vertical direction can be described as follows:

[0047]

[0048] Where m represents the mass of the magnetic suspension, f(t) is the attractive force of the electromagnetic coil, and x(t) is the displacement of the magnetic suspension relative to the operating point (equilibrium point).

[0049] Step 3: Merge the two systems using electromagnetic attraction.

[0050] Under the above assumptions, according to the laws governing electromagnetism, electromagnetic attraction can be expressed as:

[0051]

[0052] Where k and x0 are correction parameters for the actual characteristics of the electromagnet, and the corresponding parameter values ​​can be obtained by experimental identification. X represents the position of the magnetic suspension at the working point (equilibrium point).

[0053] For the nonlinear representation of equation (3), we can approximate it using Taylor series:

[0054]

[0055] in,

[0056] k x This is called the magnetic-position coefficient, k i It is called the magnetic force-current coefficient.

[0057] At the equilibrium point (I,X,x0,U), we have

[0058]

[0059] Since RI = U, combining (1) and (4), we can obtain

[0060]

[0061]

[0062] Step 4: Calculate the transfer functions of the two systems respectively.

[0063] Taking the Laplace transform of equations (6) and (7), we can obtain the transfer functions of the electrical subsystem and the magneto-mechanical subsystem, respectively.

[0064]

[0065]

[0066] Step four: Using the coil voltage as the input signal, calculate the output signals as the displacement of the magnetic suspension and the coil current, thereby simulating the position of the magnetic suspension. The position display shows the position change caused by voltage variations. This invention requires the initial position of the magnetic suspension to be provided during calculation; the initial position can be selected from the operating point (equilibrium point).

[0067] like Figure 2As shown, this invention also discloses a simulation device for modeling magnetically suspended objects using a dual-system approach, including a host computer and an embedded development board. The embedded development board of this invention can be an F4-Pro embedded development board, supporting 100M Ethernet, CAN, USART, and other communications, and featuring PWM output, encoder output, switch input, and multiple AD acquisition channels. The host computer of this invention includes a simulation platform and a model data generation module. The model data generation module includes a dynamic model and a control model, and can be developed using Simulink. The data model code is generated and downloaded to the embedded development board for real-time simulation. The simulation platform is used to build a virtual prototype platform, which can use Unity3D to implement a virtual prototype of the magnetically suspended object. The virtual prototype implementation process can be as follows: First, using an actual magnetically suspended object as a prototype, three-dimensional models of each component of the virtual prototype are built using Solidworks. Then, the three-dimensional model of the magnetically suspended object is imported into the virtual experimental scene constructed by Unity3D. Finally, components such as physical materials, colliders, and sounds are added. To use decoration tools to render the experimental table with lighting, making the scene more realistic and intuitive...

[0068] The model data generation module of this invention transmits characteristic parameters and control parameters to the embedded development board before simulation. Characteristic parameters include the mass of the magnetic levitation object, coil resistance, coil inductance, magnetic force-current coefficient, magnetic force-position coefficient, etc., and continuously provides real-time coil voltage parameters. Control parameters include the proportional coefficient, integral coefficient, derivative coefficient, filter coefficient, and magnetic levitation object position setpoint of the inner and outer loop magnetic levitation object position controllers, etc. If no control parameters are available, only characteristic parameters can be used. The embedded development board receives information such as the displacement, coil current, and coil voltage of the magnetic levitation object in real time by running the magnetic levitation object modeling method, calculates the displacement and coil current of the magnetic levitation object at the next moment, and feeds back the calculated displacement and coil current of the magnetic levitation object at the next moment to the simulation platform. The simulation platform then performs simulation display, such as... Figure 3 As shown.

[0069] This invention reduces the difficulty of system design by independently analyzing and modeling two systems and combining the analysis data of the two systems through electromagnetic force. It enables the position parameters and current parameters of this invention to clearly show their relationship with the change in voltage. The different waveforms of the voltage change can be displayed, allowing for intuitive viewing of the changes in relevant data on the simulation system, which facilitates the understanding of relevant system knowledge.

Claims

1. A method for modeling magnetically suspended objects using a dual-system approach, characterized in that: Includes the following steps: Step 1: Establish the mathematical model of the electrical subsystem; assuming the resistance and inductance values ​​are constant, according to Kirchhoff's laws, the circuit relationship on the coil is as follows: （1） in, It represents the change in voltage across the electromagnetic coil. , This represents the inductance and resistance of an electromagnetic coil. This represents the change in current flowing through the coil. This indicates the operating current and operating voltage of the coil when the magnetic levitation object is stable at the operating point; Step two: Establish a mathematical model of the magneto-mechanical subsystem; the controlled magnetically suspended object is only subject to electromagnetic attraction and its own gravity during the levitation process. The dynamic equation of the magnetically suspended object in the vertical direction is as follows: （2） in, Indicates the mass of the magnetic levitation object. It is electromagnetic attraction. It is the displacement of the magnetically suspended object; Step 3: Merge the two systems using electromagnetic attraction. Electromagnetic attraction is expressed as: （3） in, , These are correction parameters for the actual characteristics of the electromagnet. This indicates the position where the magnetic levitation object is stable at the operating point; For the nonlinear representation of equation (3), we can approximate it using Taylor series: （4） in, ; Called the magnetic-position coefficient, This is called the magnetic force-current coefficient; At the equilibrium point There is （5） Combining (1) and (4), we get: （6） （7） Step 4: Calculate the transfer functions of the two systems respectively. Taking the Laplace transform of equations (6) and (7), we can obtain the transfer functions of the electrical subsystem and the magneto-mechanical subsystem, respectively. （8） （9） Step four: Using the voltage of the coil as the input signal, calculate the displacement information of the output magnetic levitation object.

2. A simulation device for modeling magnetically suspended objects using a dual-system architecture, comprising a host computer and an embedded development board, wherein the host computer includes a simulation platform and a model data generation module, characterized in that: The model data generation module includes a dynamic model and a control model. This module generates the data model code and downloads it to the embedded development board for real-time simulation. Before simulation, the module transmits characteristic parameters to the embedded development board, including the mass of the magnetic suspension, coil resistance, coil inductance, magnetic force-current coefficient, magnetic force-position coefficient, and the initial position of the magnetic suspension. It also continuously provides real-time coil voltage parameters. The embedded development board uses a dual-system approach to model the magnetic suspension, receiving the displacement, coil current, and coil voltage of the magnetic suspension in real time. It then calculates the displacement and coil current of the magnetic suspension at the next moment and feeds these calculations back to the simulation platform for display. This dual-system approach to modeling the magnetic suspension is as described in claim 1.

3. The simulation device for modeling magnetically suspended objects using a dual-system approach according to claim 2, characterized in that: The embedded development board used is the F4-Pro embedded development board.

4. The simulation device for modeling magnetically suspended objects using a dual-system approach according to claim 2, characterized in that: The model data generation module was developed using Simulink.

5. The simulation device for modeling magnetically suspended objects using a dual-system approach according to claim 2, characterized in that: The virtual prototyping platform uses Unity3D to create a virtual prototype of the magnetic levitation object.

6. The simulation device for modeling magnetically suspended objects using a dual-system approach according to claim 2, characterized in that: The simulation platform is used to build a virtual prototype platform. The virtual prototype implementation process is as follows: First, based on the actual magnetic suspension object, a three-dimensional model of each component of the virtual prototype is built using Solidworks. Then, the three-dimensional model of the magnetic suspension object is imported into the virtual experimental scene built by Unity3D. Finally, components are added.

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