Development of new electromagnetic suspension–based high‐speed Maglev vehicles in China: Historical and recent progress in the field of dynamical simulation

High‐speed Maglev is a cutting‐edge technology brought back into the focus of research by plans of the Chinese government for the development of a new 600 km/h Maglev train. A Chinese‐German cooperation with industrial and academic partners has been established to pursue this ambitious goal and bring together experts from multiple disciplines. This contribution presents the joint work and achievements of CRRC Qingdao Sifang, thyssenkrupp Transrapid, CDFEB, and the ITM of the University of Stuttgart, regarding research and development in the field of high‐speed Maglev systems. Furthermore, an overview is given of the historical development of the Transrapid in Germany, the associated development of dynamical simulation models, and recent developments regarding high‐speed Maglev trains in China.

First prototypes of a new vehicle have been presented to the public already. In May 2019, the newly designed vehicle front and mid section prototype was exhibited in Qingdao. In June 2020, a modified mid section prototype, see Figure 6, was successfully running on a test track at Tongji University in Shanghai. On July 20, 2021, a train consisting of five sections, depicted in Figure 7, was F I G U R E 3 Schematic representation of the full section test bench and detailed view of a single levitation frame of a section on the test bench (images from CRRC Qingdao Sifang).

F I G U R E 4 Full section test bench with a mid section test vehicle (image from CRRC Qingdao Sifang).
F I G U R E 5 A 665 m commissioning test line at the National Innovation Center of High Speed Train (image from CRRC Qingdao Sifang).
F I G U R E 6 Test run of a mid section prototype at Tongji University in June 2020 (image from CRRC Qingdao Sifang). Besides the simulation and test platform, a trial production center is established, which is capable to fulfill the requirements for a small batch of trial production for the components and subsystems, including the chips, the traction system, the operation control system, the vehicle, and the infrastructure elements.
After five years of intensive R&D and cooperation with project partners, the key technologies of high-speed Maglev train systems have been fully and deeply investigated. An integrated research, test, and trial production platform has been constructed.
The system integration for traction and running at a low speed has been implemented. The technological capabilities and industrialization of high-speed Maglev systems enable to build a demonstration line of high-speed Maglev transport and will allow one to carry out test runs at a top speed of 600 km/h during the 14th Basically, two different technologies for magnetic levitation exist.
One is the so-called electrodynamic suspension (EDS), based on repulsive magnet forces, the other is electromagnetic suspension (EMS), based on attractive magnet forces. A brief overview of historical developments regarding hardware (vehicles and tracks) and software (numerical simulation models) related to EMS-based Maglev systems is given in the following.

| Development line of the Transrapid
This section is based on the comprehensive overview of historical developments in the area of Maglev vehicles and technology given by Schach et al., 2 Meisinger and Shu, 3  All vehicles up to TR04 from 1973, see Figure 8, were operating with asynchronous short-stator linear motors. The first protoype of a synchronous long-stator linear motor was used in the Henschel- Chinese and German politicians took place. 6 The SMT vehicle, see Transrapid projects all over the world with track lengths ranging from a few dozen kilometers, connecting the city of Munich to the airport, 8,9 up to a few hundred kilometers in China and the United States of America, 10 for example, were discussed. However, none of them was realized and, therefore, the SMT line in Shanghai is the first and until today the only commercial high-speed Maglev transportation system in the world.

| Historical development of dynamic simulation models
In parallel to the development of the first principle Maglev vehicles realized in hardware during the 1970s, analogue and first digital numeric simulation models of the vehicle and its components were established to support the development process.
Already for the first principle Maglev vehicle Komet, simple mechanical and magnet models supported the control design. 11,12 The involved mechanical rigid body models and linearized magnet models contributed, inter alia, to derive the modular electrical and mechanical structure for magnet suspension known as magnetic wheels 13 which was realized within the vehicles Komet M and TR05. 14 Current EMS-based Maglev vehicles still exploit this modular concept and thus benefit in terms of performance, reliability, and maintenance. This highlights the achievements gained by the early Maglev pioneers under the leadership of Prof.
Dr.-Ing. Eveline Gottzein as well as the successful use of dynamic simulation models for system optimization. In addition, the dynamics of Maglev vehicles on flexible guideways created research interest and simple vehicle models were coupled with Euler-Bernoulli beams to capture the vehicle-track interaction. 15,16 The mechanical models developed motivated even more sophisticated approaches for Maglev vehicle control design. [17][18][19] Along with the analysis of cars and wheel-on-rail systems, the general and standardized methodology for the analysis of vehicle dynamics was developed 20,21 which includes the analysis of Maglev vehicle dynamics due to its modularized fashion originating from a system  The analysis of Maglev vehicle dynamics involves different disciplines including classical vehicle system dynamics, magnet dynamics, Maglev control design, and power electronics. Whereas for magnet dynamics and control design usually self-generated codes are used, standardized software tools for mechanical system modeling, such as the commercial codes SIMPACK 34,35 or ADAMS, 36 are also used for modeling the Maglev vehicle mechanics. Worth mentioning is also the research code NEWEUL 37 and its successor Neweul-M 238 developed at the Institute of Engineering and Computational Mechanics for deriving the symbolical equations of motion for multibody systems and used in numerous studies. 26,28,39 Moreover, also worth mentioning is the software package TR.Mechatron 28 which couples the above mentioned different disciplines based on Matlab/Simulink. Currently, the software package is continually     For the description of the guideway unevenness, the building tolerances given in the Design Principles High-Speed Maglev System (MSB) 51 are used. It is assumed that the irregularities follow a random pattern but are always smaller than the specified tolerances.

| Mathematical guideway model
Therefore, a normal distribution is applied, 39  and gap signals, 39 as was previously done. 52 Such a validated profile of guideway unevenness is used as a reference input for most dynamic analyses in this paper and is called the reference profile REF.
Other unevenness profiles are used for predicting the vehicle dynamics on planned guideways with smaller unevenness amplitudes and longer unevenness wavelengths, suitable for higher vehicle speeds. 53 For more detailed dynamic analyses that consider the bending movement of the girders during the run-on of the bow section of the vehicle, the girders are modeled by the finite element method as described in Section 4.8.

| Vehicle dynamics in the frequency domain
Once the input is defined, simulation models can be used for the analysis and prediction of vehicle dynamics. The models can be developed with different detail levels, according to the questions to be answered. In the following sections, several models will be outlined, ranging from a model describing just one magnet (but this in high detail) to a 3D model describing all mechanical components of a three sections long Maglev vehicle.
According to the international standards for ride comfort evaluation, 54 mainly vibrations up to about 80 Hz are felt by the passengers. The evaluation is less influenced by single events but mostly by vibrations that the passengers are exposed to for a long time. Therefore, a phenomenological model based on statistical data analysis is applied for the prediction of the ride comfort. In contrast to this, the simulation models described in the following sections of this paper are motivated by the representation of physical parts (mechanical, pneumatic, electrical, and magnetic) and the detailed analysis of specific driving situations.
The statistical analysis is based on the assumption that vibrations with small amplitudes occur much more often than vibrations with F I G U R E 11 Schematic illustration of cross-section model (left) and longitudinal-section model (right) from TR.Mechatron. In the sketch of the longitudinal-section model, the magnet forces are depicted by spring-damper elements.
large amplitudes during a typical ride of a high-speed Maglev vehicle.
Therefore, linear methods may be applied and a large set of measured data is transformed into the frequency domain by using Fast Fourier Transform. 39 An input-output behavior model was found that describes the relevant vehicle dynamics properties independent from the vehicle speed in the form of a transfer function in the frequency domain. The so-called Ride Comfort Transfer Function (RCTF) 39 describes the relation between guideway unevenness as input and accelerations close to the passenger seats as output. By using this RCTF, the ride comfort can quickly be predicted for different guideway designs and vehicle speeds higher than what is currently being used. 53 An important aspect is that for evaluations that require Recently, the method was augmented for the calculation of statistical data of the electromagnets, for example, the occurrence of magnet gaps, electrical voltages, and currents during typical rides. 55 For these analyses, the data analytics-based method was applied in combination with the physical simulation models of the electromagnets described in the following sections. between the electric circuits has to be neglected, which exists due to the magnetic network. However, this simplification is reasonable because the coupling is found to be small. 56 The simplified magnet models' dynamics is described by just one ordinary differential to apply the methodology to comparable magnets. Figure 13 summarizes and visualizes the steps of the proposed modeling approach.

| Modeling and simulation of electromagnet test bench
To use simulation models for predicting the system behavior, it is important that the simulation model accurately represents the actual condition or at least to be aware of the operation range that can be predicted accurately. Moreover, simulation models usually rely on surrogate parameters which need to be calibrated by measurements.
The validation and calibration of simulation models involve these two aspects precisely. However, validating simulation models is usually challenging and needs the coordinated work of experts in simulation and measurements.
Validating simulation models or their submodules, respectively, in a clearly defined environment and based on systems of manageable representing the actual conditions. The work establishes the connection between simulation models and the test bench visualized in Figure 13. A photo of the considered electromagnet test bench is shown in Figure 2. The test bench is designed for testing different magnet types, including guidance and levitation magnets. A guideway mockup closes the magnets' flux paths to induce the magnet force and is moved by synchronized hydraulic cylinders in the vertical direction. Figure 14 shows a schematic sketch of the test bench and illustrates its principal structure.   The mechanics model represents one-eighth of a Transrapid's crosssection and is modeled as a rigid multibody system using Neweul-M 2 .
The multibody system comprises, among others, two secondary air springs that couple the car body with the levitation frame, see

| Interaction of a Maglev vehicle with a single elastic guideway element
A perfectly rigid guideway would be ideal for the passengers' ride comfort and the magnet control system of a Maglev vehicle. For an elevated, pillared guideway as it is realized at the Transrapid line in Shanghai, however, the individual guideway elements cannot be manufactured perfectly rigid. The stiffer a guideway element has to be, the more expensive and resource-intensive its manufacturing process is. It is, therefore, necessary to find a tradeoff between a lightweight guideway on the one hand, to satisfy financial and environmental aspects, and a guideway with high stiffness on the other hand, to achieve stability and passenger ride comfort of the overall system.
Existing models in the TR.Mechatron package did not consider the elasticity of guideways dynamically. Instead, the bending of the girders is taken into account as static guideway disturbance. 39 However, this approximation is not necessarily valid for all magnets guideway bending. Simulations are performed using either a coarse distribution with two magnet forces per magnet or a fine distribution with twelve magnet forces per magnet, that is, one magnet force at each magnet pole, as illustrated in Figure 23. The corresponding magnet models, 56 see Section 4.4, were developed in this joint project as well. Note that both magnet model variants, the one with the coarse distribution just like the one with the fine distribution, include the same important physical effects like saturation and eddy currents. Therefore, the considered magnet models are almost equal in capturing the physical details, and only the magnet force discretization is less detailed in one of the two considered cases.
The simulation results show that the coarse spatial discretization with a single concentrated substitute magnet force per half magnet sufficiently approximates the fine discretization with one force per pole when mechanical vehicle and guideway dynamics are in focus.
However, the magnet model computing this single force must provide a sufficiently accurate representation of the magnet dynamics. The used magnet model 56 proves to fulfill this requirement. This is a highly welcome result since the simplified magnet model providing forces with a coarse discretization has significantly shorter computation times than the detailed model with a fine discretization. It is about 100 times faster. In summary, the efficient simplified magnet model with one force per half magnet can be used for transient vehicleguideway dynamics simulations as long as the simplified magnet model captures the magnet's physics sufficiently accurately.

| 3D model of a Transrapid section
On the basis of a comprehensive student thesis, 63 the Institute of Engineering and Computational Mechanics has developed a 3D dynamic mechatronic simulation model representing one section of a Transrapid Maglev vehicle. 65 The model roughly represents a system comparable to the mid section prototype, which successfully ran in 2020 on a test track at Tongji University in Shanghai, see Figure 6.

| 3D model of a three-sections vehicle
To calculate the loads in the mechanical parts of the vehicle and to investigate the motion of the mechanical linkages and the vehicle claddings for gauge analyses, a 3D model that contains the mechanical parts of the vehicle in much more detail was developed.
To this end, the software SIMPACK was used, because its extensive library of mechanical elements allows a quick construction of the detailed mechanical linkage between magnets, levitation frames, air spring rockers, and car body. A full three-sections vehicle model was developed using this method, which includes, among others, the force transmission by the relatively stiff coupling between the Transrapid's vehicle sections. • Joining the SIMPACK simulation for the mechanical part with the MATLAB/Simulink simulation of the control and the electromagnetic part as described in Section 4.4, using a co-simulation approach. While this method requires a significant computational effort, it allows one to compute results for the detailed mechanical setup simultaneously with the electric states of the magnets. 34

| Studies on MPC
In addition to the progress made in modeling and simulation of Maglev vehicles described above, the project partners deal with the advanced control methodology MPC. 66,67 MPC is a model-based control technique in which the control input is computed by solving an underlying optimization problem, or more precisely, a so-called optimal control problem (OCP). The OCP involves an objective function to adjust the control goals or performance over a prediction horizon, respectively. The OCP is subject to system dynamics formulated as constraints to predict the system behavior based on a mathematical model. Further, it is possible to immediately consider constraints of the control input and system state within the control design. The resulting control input, which is applied to the system, is obtained by solving the OCP at each time step in a receding horizon fashion, meaning that the prediction horizon is shifted in each step.
At present, the investigations are not directly aimed at using such a control concept within the vehicle, instead to push this forward-looking control methodology and contribute to high-end research projects.
Although there has been made significant progress in MPC research and development in recent years, for example, in real-time optimization and implementation, 68,69 the gap between theory and practice is not entirely closed. The application of MPC is still challenging because the problem usually has to be solved for each system individually, and the design is often very challenging. Real-time capability, validation, certification, or maintenance still need to be solved.
In this context, the Maglev vehicle's magnet control systems represent a versatile benchmark system characterized, for example, by its fast dynamics, system constraints, interdisciplinary nature combining mechanics and electromagnetics, or unstable open-loop dynamics, which is worth considering in detail. Through such a system-specific and practical perspective, it is possible to push the practical research forward and gain more insight into the MPC challenges. In this field, progress is made on controlling a nonlinear system with the number of measured outputs greater than the number of inputs with an MPC-based controller in an offset-free fashion. 60 The study's 60 research question is raised by the magnet control system with its three measured outputs, air gap, acceleration, and current and only one control input, the applied magnet's voltage.
The simplified current-based magnet model, resulting from the modeling approach outlined in Section 4.4, is also successfully used for this study. Further, the magnet control system motivates research questions on safeguarding embedded MPC implementation of safetycritical systems. In this context, a control system architecture involving a sophisticated classification function is proposed to decide whether the current system state is dependable or whether it is necessary to activate an external safety system. 70 The study 70 considers normal constrained embedded hardware, that is, numerical computing devices with limited memory and computing capacity.
Moreover, the variability of an MPC-based control concept allows predicting possible performance improvements by considering guideway disturbance estimates directly in the control design, 62 which constitutes a performance limit for other control techniques since MPC operates in an optimal fashion. In addition, the proposed offsetfree MPC scheme 60 is successfully implemented in different vehicle models, including the lateral cross-section model mentioned in Section 4.6, the 2D longitudinal-section model sketched in Section 4.9, or the 3D model described in Section 4.11.

CONFLICT OF INTEREST STATEMENT
The authors declare no conflict of interest.

DATA AVAILABILITY STATEMENT
Data sharing is not applicable to this article as no new data were created or analyzed in this study.