A high-speed maglev system fault injection method based on a semi-physical simulation system

Abstract

The application provides a high-speed maglev system fault injection method based on a semi-physical simulation system, and the method comprises the following steps: a train simulated by a simulation platform runs according to a target running curve based on a traction control instruction, and simulation running starts; a system fault type to be injected is determined, and the determined system fault type is injected into a traction control system or the simulation platform, so that the high-speed maglev system fails; in the case that the system fault type is a communication fault, an optical fiber, a network cable or a power supply is disconnected, so that the communication fault is injected; in the case that the system fault type is a ground running equipment running fault, any one or more parameters are changed, so that the ground running equipment running fault is injected; in the case that the system fault type is a ground running equipment action execution fault, a state feedback signal is forcibly converted, so that the ground running equipment action execution fault is injected.

Description

Technical Field

[0001] This invention relates to the field of ultra-high-speed maglev traction control technology, and in particular to a fault injection method for high-speed maglev systems based on a hardware-in-the-loop simulation system. Background Technology

[0002] Against the backdrop of the current development of ultra-high-speed maglev trains, which can operate at speeds exceeding 1000 km / h, they have attracted widespread attention both domestically and internationally.

[0003] When the high-speed maglev train runs on the track, the ground traction converter equipment supplies power to the stator section of the linear motor and generates a traveling wave magnetic field, which drives the train. The traction control system adjusts the converter output voltage according to the current operating status of the train, and the switch controller controls the opening and closing of the trackside switching stations along the line according to the current position of the train and the step-changing strategy. It also controls the frequency, phase, and amplitude of the current output to the stator section of the linear motor, so that the train runs along the planned trajectory.

[0004] When a vehicle is operating on the line, in addition to normal operating conditions, there are also fault operating conditions. During the early design phase, the control system analyzed and studied several fault scenarios based on the system architecture and designed the action logic adopted by the control system under these scenarios. During the hardware-in-the-loop simulation system integration and testing, corresponding faults were injected to achieve functional testing of the control system under fault conditions.

[0005] Currently, the main type of fault injection is communication fault, and the fault types are relatively simple. Summary of the Invention

[0006] This invention provides a fault injection method for high-speed maglev systems based on a hardware-in-the-loop simulation system, which can solve the technical problem that the fault injection types in the prior art are relatively limited.

[0007] This invention provides a fault injection method for a high-speed maglev system based on a hardware-in-the-loop simulation system. The high-speed maglev system includes a traction control system, a positioning and speed measurement system, an operation control system, and a simulation platform. The simulation platform is used to simulate ground operating equipment, which includes a traction converter, a traction power supply network, a trackside switching station, and a train. The method includes:

[0008] The positioning and speed measurement system sends the train's position and speed information to the traction control system and the operation control system, respectively. The operation control system obtains operation control commands based on the train's position and speed information and sends them to the traction control system. The traction control system obtains traction control commands based on the train's position and speed information and the operation control commands and sends them to the simulation platform. The train simulated by the simulation platform runs according to the target running curve based on the traction control commands, and the simulation operation begins.

[0009] The system fault types to be injected are determined and then injected into the traction control system or simulation platform to cause a fault in the high-speed maglev system. These fault types include communication faults, ground operating equipment malfunctions, and ground operating equipment execution failures. Communication faults include communication failures between various controllers within the traction control system, between the traction control system and the ground operating equipment, between the traction control system and the positioning and speed measurement system, and between the operation control system and the ground operating equipment. Ground operating equipment malfunctions include abnormal states of the ground operating equipment during operation. Ground operating equipment execution failures include instances where various systems within the high-speed maglev system fail to execute corresponding actions according to traction control commands and fail to report their respective statuses.

[0010] In the event of a communication failure, the communication failure can be injected by disconnecting any one or more optical fibers or network cables between the controllers within the traction control system, or by disconnecting any one or more optical fibers or network cables between the traction control system and the ground operating equipment, the traction control system or the positioning and speed measurement system, or by disconnecting any one or more power supplies corresponding to the controllers within the traction control system.

[0011] When the system fault type is a ground operating equipment malfunction, change any one or more parameters of the current loop, such as resistance, inductance, capacitance, train operating attitude, train speed and position, traction converter output voltage and current, or linear motor back EMF, to inject the ground operating equipment malfunction.

[0012] In the case of a system fault type of ground operating equipment execution failure, the state feedback signal sent by the simulation platform to the traction control system is forcibly converted by setting normally closed / normally open feedback contacts, so as to realize the injection of ground operating equipment execution failure.

[0013] Preferably, the parameters for operational faults in the injected ground-based equipment are obtained using the following formula:

[0014]

[0015] U=U1sin(ω1t+φ1)+U2sin(ω2t+φ2)+...+U n sin(ω n t+φ n )

[0016] E = f(v,s) x ,s y ,s z ,θ x ,θ y ,θ z )

[0017] I = f(U,E,v,s) x ,s y ,s z ,θ x ,θ y ,θ z ,R,L,C)

[0018] F xyz =f(v,s) x ,s y ,s z ,θ x ,θ y ,θ z ,E,I)

[0019] In the formula, I represents the output current of the traction converter, I1, I2, ..., I... n These are the fundamental current, the second harmonic current, ..., the nth harmonic current, ω1, ω2, ..., ωn, respectively. n These represent the fundamental frequency, the second harmonic frequency, ..., the nth harmonic frequency of the current and voltage, respectively. These represent the current phases corresponding to the fundamental wave, the second harmonic, ..., the nth harmonic, respectively. t represents time, and U is the output voltage of the traction converter. U1, U2, ..., U... n These represent the fundamental voltage, the voltage of the second harmonic, ..., the voltage of the nth harmonic, φ1, φ2, ..., φ... n Let f(v,s) represent the voltage phases corresponding to the fundamental wave, the second harmonic, ..., the nth harmonic, respectively; E is the back electromotive force of the linear motor; and f(v,s) is the voltage phase corresponding to the nth harmonic. x ,s y ,s z ,θ x ,θ y ,θ z ) represents the back electromotive force function of the motor, v represents the train speed, and s represents the speed of the train. x ,s y ,s z θ represents the displacement of the train in the three directions of propulsion, levitation, and guidance, respectively. x ,θ y ,θ z Let f(U,E,v,s) represent the deflection angles of the train in the propulsion, levitation, and guidance directions, respectively. x ,s y ,s z ,θ x ,θ y ,θ z(R, L, C) is the current calculation function, where R, L, and C are the resistance, inductance, and capacitance parameters corresponding to the current loop, respectively, and F... xyz Let f(v,s) be the force exerted on the train in the three directions of propulsion, levitation, and guidance. x ,s y ,s z ,θ x ,θ y ,θ z ,E,I) is the electromagnetic force calculation function.

[0020] By applying the technical solution of this invention, different fault injection methods can be designed according to the fault type in a hardware-in-the-loop simulation platform to achieve thorough testing of the control system. After the train starts running, the traction control system pulls the train along the planned curve. During this process, actual operational faults that may occur are injected to simulate system fault scenarios. In this scenario, the traction control system needs to identify the fault type and take corresponding actions according to the designed fault handling measures to minimize the impact of the fault point on the entire system, thereby realizing the fault handling and protection functions of the traction control system. This invention can be applied to the traction control system of maglev transportation. Attached Figure Description

[0021] 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.

[0022] Figure 1 A flowchart of a fault injection method for a high-speed maglev system based on a hardware-in-the-loop simulation system, according to an embodiment of the present invention, is shown.

[0023] Figure 2 A diagram illustrating the operational architecture of a high-speed maglev system based on a hardware-in-the-loop simulation system, according to an embodiment of the present invention, is shown. Detailed Implementation

[0024] 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.

[0025] 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.

[0026] 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.

[0027] like Figure 1 and Figure 2 As shown, this invention provides a fault injection method for a high-speed maglev system based on a hardware-in-the-loop simulation system. The high-speed maglev system includes a traction control system, a positioning and speed measurement system, an operation control system, and a simulation platform. The simulation platform simulates ground-based operating equipment, including a traction converter, a traction power supply network, a trackside switching station, and a train. The method includes:

[0028] The positioning and speed measurement system sends the train's position and speed information to the traction control system and the operation control system, respectively. The operation control system obtains operation control commands based on the train's position and speed information and sends them to the traction control system. The traction control system obtains traction control commands based on the train's position and speed information and the operation control commands and sends them to the simulation platform. The train simulated by the simulation platform runs according to the target running curve based on the traction control commands, and the simulation operation begins.

[0029] The system fault types to be injected are determined and then injected into the traction control system or simulation platform to cause a fault in the high-speed maglev system. The system fault types include communication faults, ground operation equipment operation faults, and ground operation equipment execution action faults.

[0030] Communication failures include communication failures between various controllers within the traction control system, between the traction control system and ground operating equipment, between the traction control system and the positioning and speed measurement system, and between the operation control system and the traction control system. Communication failures within the traction control system mainly involve communication failures between different controllers, resulting in the inability to transmit real-time operating data normally, thus hindering closed-loop control and fault protection functions. Communication failures between the traction control system and ground operating equipment mainly involve malfunctions in the communication between the commands issued by the traction control system and the status feedback from the ground operating equipment, leading to unstable system operation.

[0031] Ground operation equipment malfunctions include abnormal states that occur during operation; communication failures between the traction control system, the positioning and speed measurement system, and the operation control system can cause the traction control system to be unable to receive positioning and speed measurement information and operation control commands, thus preventing it from operating according to the planned operation curve.

[0032] Faults in ground-based operating equipment include various systems in the high-speed maglev system failing to execute corresponding actions and report their respective statuses according to traction control commands; for example, trackside switch stations failing to open / close normally, traction converters failing to output voltage pulses according to commands, and traction converters operating in abnormal modes. These will also directly affect train operation.

[0033] In the event of a communication failure, the communication failure can be injected by disconnecting any one or more optical fibers or network cables between the controllers within the traction control system, or by disconnecting any one or more optical fibers or network cables between the traction control system and the ground operating equipment, the traction control system or the positioning and speed measurement system, or by disconnecting any one or more power supplies corresponding to the controllers within the traction control system.

[0034] When the system fault type is a ground operating equipment malfunction, change any one or more parameters of the current loop, such as resistance, inductance, capacitance, train operating attitude, train speed and position, traction converter output voltage and current, or linear motor back EMF, to inject the ground operating equipment malfunction.

[0035] In the case of a system fault type of ground operating equipment execution failure, the state feedback signal sent by the simulation platform to the traction control system is forcibly converted by setting normally closed / normally open feedback contacts, so as to realize the injection of ground operating equipment execution failure.

[0036] This invention, within a hardware-in-the-loop simulation platform, allows for the design of different fault injection methods based on fault type, enabling thorough testing of the control system. After the train begins operation, the traction control system pulls the train along a planned curve. During this process, potentially occurring operational faults are injected to simulate system failure scenarios. In these scenarios, the traction control system needs to identify the fault type and take corresponding actions according to the designed fault handling measures to minimize the impact of the fault point on the entire system, thus realizing the fault handling and protection functions of the traction control system. This invention can be applied to maglev transportation traction control systems.

[0037] According to one embodiment of the present invention, the parameters for operational faults of ground-based operating equipment are obtained by the following formula:

[0038]

[0039] U=U1sin(ω1t+φ1)+U2sin(ω2t+φ2)+...+U n sin(ω n t+φ n )

[0040] E = f(v,s) x ,s y ,s z ,θ x ,θ y ,θ z )

[0041] I = f(U,E,v,s) x ,s y ,s z ,θ x ,θ y ,θ z ,R,L,C)

[0042] F xyz =f(v,s) x ,s y ,s z ,θx ,θ y ,θ z ,E,I)

[0043] In the formula, I represents the output current of the traction converter, I1, I2, ..., I... n These are the fundamental current, the second harmonic current, ..., the nth harmonic current, ω1, ω2, ..., ωn, respectively. n These represent the fundamental frequency, the second harmonic frequency, ..., the nth harmonic frequency of the current and voltage, respectively. These represent the current phases corresponding to the fundamental wave, the second harmonic, ..., the nth harmonic, respectively. t represents time, and U is the output voltage of the traction converter. U1, U2, ..., U... n These represent the fundamental voltage, the voltage of the second harmonic, ..., the voltage of the nth harmonic, φ1, φ2, ..., φ... n Let f(v,s) represent the voltage phases corresponding to the fundamental wave, the second harmonic, ..., the nth harmonic, respectively; E is the back electromotive force of the linear motor; and f(v,s) is the voltage phase corresponding to the nth harmonic. x ,s y ,s z ,θ x ,θ y ,θ z ) represents the back electromotive force function of the motor, v represents the train speed, and s represents the speed of the train. x ,s y ,s z θ represents the displacement of the train in the three directions of propulsion, levitation, and guidance, respectively. x ,θ y ,θ z Let f(U,E,v,s) represent the deflection angles of the train in the propulsion, levitation, and guidance directions, respectively. x ,s y ,s z ,θ x ,θ y ,θ z (R, L, C) is the current calculation function, where R, L, and C are the resistance, inductance, and capacitance parameters corresponding to the current loop, respectively, and F... xyz Let f(v,s) be the force exerted on the train in the three directions of propulsion, levitation, and guidance. x ,s y ,s z ,θ x ,θ y ,θ z ,E,I) is the electromagnetic force calculation function.

[0044] Where, f(v,s) x ,s y ,s z,θ x ,θ y ,θ z () for v,s x ,s y ,s z ,θ x ,θ y ,θ z The function f(U,E,v,s) x ,s y ,s z ,θ x ,θ y ,θ z R, L, C) is related to U, E, v, s x ,s y ,s z ,θ x ,θ y ,θ z A function in R, L, C, f(v,s) x ,s y ,s z ,θ x ,θ y ,θ z E,I) is about v,s x ,s y ,s z ,θ x ,θ y ,θ z Functions of E and I.

[0045] As can be seen from the above formulas, the train's speed changes continuously during operation, and the corresponding current and voltage fundamental frequencies also change, classifying it as a frequency conversion system. In the system circuit, the traction control system controls the output voltage of the traction converter, thereby generating current. The magnitude of the current is related to the system circuit parameters and the motor's back electromotive force (EMF). The interaction between the motor's back EMF and the current directly affects the train's running attitude, and changes in the running attitude, in turn, affect the motor's back EMF, thus influencing the current. Therefore, high-speed maglev systems exhibit complexity and strong coupling.

[0046] In the simulation of ground-based equipment operation failures, this invention performs mathematical modeling of the aforementioned equipment. By changing the system circuit parameters, train running attitude parameters, traction converter output voltage and current, train speed and position, and linear motor back electromotive force at a certain moment, the above values ​​are artificially changed, causing the system to change from normal operating conditions to fault operating conditions. The invention also uses a real-time simulation platform to simulate and calculate the system's transient response and steady-state values.

[0047] According to one embodiment of the present invention, due to the complexity, frequency conversion, and strong coupling of the high-speed maglev system during operation, the data obtained by the traction control system in real time mainly includes the real-time operation data of the train and the voltage and current data output by the traction converter. Therefore, it is necessary to extract and analyze the feature values ​​of the real-time data during this process, and further determine the system operating status and analyze the fault type in combination with the characteristics of high-speed maglev. For different fault levels, derated operation or shutdown is adopted to realize the fault protection function of the maglev system.

[0048] To gain a further understanding of the present invention, the fault injection method for high-speed maglev systems based on a hardware-in-the-loop simulation system will be described in detail below.

[0049] In this embodiment, the fault injection method for a high-speed maglev system based on a hardware-in-the-loop simulation system specifically includes the following steps:

[0050] Step 1: Connect communication signals between system controllers. Connect the communication interfaces between the controllers of each system, and between the controllers and interface modules. After the connection is completed, check the communication. Only after verifying and testing the communication protocol can subsequent tests be carried out.

[0051] Step 2: System control function test. After verifying that the communication signals are correct, conduct control function tests to observe whether each controller can perform the test according to the design process, whether it responds normally to communication control signals, and whether it provides feedback on controller status information.

[0052] Step 3: Power on each system power device. Only after powering on and running the system and checking that it is normal and without faults can the test continue.

[0053] Step 4: The system integration test begins. According to the test procedure, each system controller issues instructions and reports its own operating status. Each device receives the control instructions and executes the corresponding actions to carry out the target test.

[0054] Step 5: During the test, inject the corresponding fault and observe the operating status of each device in the system.

[0055] Step 6: Determine the test results. After the test, determine the operating data of each controller and simulation system to see if the test was successful.

[0056] Step 7: The experiment ends. Collect and store the experimental data for subsequent data analysis. Power off the system.

[0057] In summary, this invention provides a fault injection method for high-speed maglev systems based on a hardware-in-the-loop simulation system. Within the hardware-in-the-loop simulation platform, different fault injection methods can be designed according to the fault type to achieve thorough testing of the control system. After the train begins operation, the traction control system pulls the train along a planned curve. During this process, actual operational faults that may occur are injected to simulate system fault scenarios. In this scenario, the traction control system needs to identify the fault type and take corresponding actions according to the designed fault handling measures to minimize the impact of the fault point on the entire system, thus realizing the fault handling and protection functions of the traction control system. This invention can be applied to maglev transportation traction control systems.

[0058] The parts of this invention not described in detail are techniques known to those skilled in the art.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] 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 fault injection method for a high-speed maglev system based on a hardware-in-the-loop simulation system, characterized in that, The high-speed maglev system includes a traction control system, a positioning and speed measurement system, an operation control system, and a simulation platform; the simulation platform is used to simulate ground operating equipment, which includes a traction converter, a traction power supply network, a trackside switching station, and a train; the method includes: The positioning and speed measurement system sends the train's position and speed information to the traction control system and the operation control system, respectively. The operation control system obtains operation control commands based on the train's position and speed information and sends them to the traction control system. The traction control system obtains traction control commands based on the train's position and speed information and the operation control commands and sends them to the simulation platform. The train simulated by the simulation platform runs according to the target running curve based on the traction control commands, and the simulation operation begins. The system fault types to be injected are determined and then injected into the traction control system or simulation platform to cause a fault in the high-speed maglev system. These fault types include communication faults, ground operating equipment malfunctions, and ground operating equipment execution failures. Communication faults include communication failures between various controllers within the traction control system, between the traction control system and the ground operating equipment, between the traction control system and the positioning and speed measurement system, and between the operation control system and the ground operating equipment. Ground operating equipment malfunctions include abnormal states of the ground operating equipment during operation. Ground operating equipment execution failures include instances where various systems within the high-speed maglev system fail to execute corresponding actions according to traction control commands and fail to report their respective statuses. In the event of a communication failure, the communication failure can be injected by disconnecting any one or more optical fibers or network cables between the controllers within the traction control system, or by disconnecting any one or more optical fibers or network cables between the traction control system and the ground operating equipment, the traction control system or the positioning and speed measurement system, or by disconnecting any one or more power supplies corresponding to the controllers within the traction control system. When the system fault type is a ground operating equipment malfunction, change any one or more parameters of the current loop, such as resistance, inductance, capacitance, train operating attitude, train speed and position, traction converter output voltage and current, or linear motor back EMF, to inject the ground operating equipment malfunction. In the case of a system fault type of ground operating equipment execution failure, the state feedback signal sent by the simulation platform to the traction control system is forcibly converted by setting normally closed / normally open feedback contacts, so as to realize the injection of ground operating equipment execution failure.

2. The method according to claim 1, characterized in that, The parameters for injecting faults into ground-based operating equipment are obtained using the following formula: U=U1sin(ω1t+φ1)+U2sin(ω2t+φ2)+...+U n sin(ω n t+φ n ) E=f(v,s x ,s y ,s z ,i x ,i y ,i z ) I=f(U,E,v,s x ,s y ,s z ,i x ,i y ,i z ,R,L,C) F xyz =f(v,s x ,s y ,s z ,i x ,i y ,i z ,E,I) In the formula, I represents the output current of the traction converter, I1, I2, ..., I... n These are the fundamental current, the second harmonic current, ..., the nth harmonic current, ω1, ω2, ..., ωn, respectively. n These represent the fundamental frequency, the second harmonic frequency, ..., the nth harmonic frequency of the current and voltage, respectively. These represent the current phases corresponding to the fundamental wave, the second harmonic, ..., the nth harmonic, respectively. t represents time, and U is the output voltage of the traction converter. U1, U2, ..., U... n These represent the fundamental voltage, the voltage of the second harmonic, ..., the voltage of the nth harmonic, φ1, φ2, ..., φ... n Let f(v,s) represent the voltage phases corresponding to the fundamental wave, the second harmonic, ..., the nth harmonic, respectively; E is the back electromotive force of the linear motor; and f(v,s) is the voltage phase corresponding to the nth harmonic. x ,s y ,s z ,θ x ,θ y ,θ z ) represents the back electromotive force function of the motor, v represents the train speed, and s represents the speed of the train. x ,s y ,s z θ represents the displacement of the train in the three directions of propulsion, levitation, and guidance, respectively. x ,θ y ,θ z Let f(U,E,v,s) represent the deflection angles of the train in the propulsion, levitation, and guidance directions, respectively. x ,s y ,s z ,θ x ,θ y ,θ z (R, L, C) is the current calculation function, where R, L, and C are the resistance, inductance, and capacitance parameters corresponding to the current loop, respectively, and F... xyz Let f(v,s) be the force exerted on the train in the three directions of propulsion, levitation, and guidance. x ,s y ,s z ,θ x ,θ y ,θ z ,E,I) is the electromagnetic force calculation function.

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