# A Review of Levitation Control Methods for Low- and Medium-Speed Maglev Systems

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## Abstract

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## 1. Introduction

- (1)
- The magnetic levitation system modeling for levitation control is reviewed in detail, including the modeling based on dynamic equations and data. Specific problems in modeling, such as the coupling of two levitation points and electromagnet-guideway coupling, are also discussed.
- (2)
- The advantages and disadvantages of levitation control techniques and uncertainty factors in the control system are analyzed.
- (3)
- Recent studies on the effect of levitation control on the guideway vibration and fault-tolerant control design are also summarized.

## 2. History Background of the EMS-Type Maglev Train System

## 3. EMS-Type Maglev Train System and Modeling

#### 3.1. Overview of EMS-Type Maglev Train System

- Linear motors are used in the traction system of the EMS-type maglev trains: long-stator linear synchronous motor (LSM) and short-stator linear-induced motors (LIM) are commonly selected depending on the speed requirements of the train.
- The bogie system serves as a crucial component for mounting the levitation system and guiding the electromagnets and traction motors in maglev trains.
- The braking system ensures the safe operation of maglev trains; braking systems can be divided into common, fast, emergency, and holding brake methods.
- The levitation and guidance mechanisms are achieved using electromagnets installed on the levitation bogie and an F-type rail. The electromagnets are energized to attract the F-type rail to levitate the vehicle. Precise control of the current in the electromagnets ensures that the train remains stably suspended within a dynamic stability range, which is typically 8–12 mm.
- The difference in the supporting and guidance functions between the maglev train system and the conventional rail transport system results in a difference in the guideway design. The construction cost of the rail-bridge system exceeds 60–70% of the total initial investment in a maglev train. For EMS-type maglev trains, the guideway structures can be divided into three types: steel sleeper-based rail structures, direct-connected rail structures without sleepers, and integral bed rail structures.

#### 3.2. The Modelling of EMS-Type Maglev Train System

#### 3.2.1. Dynamic Equations-Based Modeling

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- Single-point levitation system modeling

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- Multi-point levitation system modeling

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- Electromagnet-guideway coupling system modeling

- ▪
- Vehicle–guideway coupling system modeling

#### 3.2.2. Data-Driven-Based Modeling

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- Interactive learning method

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- Takagi–Sugeno fuzzy model

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- Neural network-based model

#### 3.2.3. Summary of Models

## 4. Maglev System Control Methods

#### 4.1. Linear Control Methods on Maglev Levitation Systems

#### 4.1.1. PID Control Algorithms

#### 4.1.2. Linear Quadratic Regulator Algorithms

#### 4.1.3. H_{2} and H_{∞} Control

#### 4.1.4. Fractional Order Control

#### 4.1.5. Basic State Feedback Control

#### 4.1.6. Feedback Linearization Control Algorithms

#### 4.2. Nonlinear Control Methods on Maglev Levitation Systems

#### 4.2.1. Nonlinear PID Control Algorithms

#### 4.2.2. State Feedback Control Algorithms

#### 4.2.3. Adaptive Control Algorithms

#### 4.2.4. Robust Control Algorithms

#### 4.2.5. Sliding Mode Control Algorithms

#### 4.2.6. Backstepping Control

#### 4.3. Artificial Intelligent Control Methods on Maglev Levitation Systems

#### 4.3.1. Fuzzy Logic Control Algorithms

#### 4.3.2. Conventional Neural Network Algorithms

#### 4.3.3. Deep Learning Algorithms

#### 4.4. Control Item Design and Uncertainty Factors

#### 4.5. Summary

#### 4.5.1. Linear Control Methods

- The PID control algorithm is easy to apply, and the choice of the three coefficients is of great importance for designing the proper PID controller. However, there are two disadvantages in PID: (1) compared with other controllers, such as the LQR controller, the PID controller exhibits larger peak overshoot and settling time, and (2) the disturbance cannot be ignored in real applications. Real-time changes in the three coefficients are required to adapt to different scenarios. Therefore, the fuzzy logic and IMC methods have been used in PID control to better tune the coefficients in the PID controller.
- The LQR controller assumes that all state variables are accessible for feedback. However, in a maglev system, it is widely recognized that the velocity of the air gap cannot be directly measured, and the presence of disturbances significantly influences the system’s behavior. Thus, the state estimation and DOBC can be combined to improve the performance of the LQR controller.
- ${H}_{2}$ and ${H}_{\mathrm{\infty}}$ control algorithms use the ${H}_{2}$ and ${H}_{\mathrm{\infty}}$ norms, which are two popular measures in optimal control theory for control design and are robust when there are disturbances.
- The fractional order control algorithm is normally combined with other methods, such as PID and sliding mode control, by introducing additional fractional order parameters in the control design. With additional parameters, the traditional controllers show better performance in terms of robustness and disturbance rejection.
- The basic state feedback control algorithm uses the state variables of the system for control design. The state variables of the controller must be carefully selected to improve the accuracy and robustness of the controller, and the state observer or model predictive method can be combined to obtain sufficient state variables for controller design.

#### 4.5.2. Nonlinear Control Methods

- The PID control algorithm applied to nonlinear system control must be carefully designed. For example, it is necessary to change the conventional transfer function into an exponential function to increase the stiffness of the system when it is apart from the operating point or combine it with other methods, such as TMD, to decrease the system vibration and PSO to optimize the coefficients of the PID.
- The state feedback control algorithm can address the time delay of the system and real-time disturbances, such as nonlinear and periodic bounded disturbances and uncertainties. It can combine with an optimal method, such as PSO, to improve the controller parameters.
- The adaptive control algorithm shows great potential in enhancing the performance of control systems, particularly when handling uncertainties caused by factors such as degradation and modeling inaccuracies. In addition to directly applying adaptive control algorithms to maglev levitation systems, model-assisted/reference-adaptive control algorithms are implemented.
- A robust control algorithm can address the uncertain part of the system and develop an effective design method that considers uncertainty information. The robust controller can also be combined with a disturbance observer to increase robustness to disturbances.
- SMC is a type of nonlinear control algorithm widely employed in the field of nonlinear control due to its straightforward physical implementation, rapid response, and robustness. Modifications can be made to the SMC for various purposes. For example, the designed GFTISMC improves the global fast response speed of the maglev system and reduces the steady-state error. The nonsingular robust SMC reduces the upper bound of the uncertainty and interference of the SMC. The SMC can also combine with other control algorithms or optimization algorithms, such as the fuzzy logic control method and PSO method.
- The backstepping control algorithm is typically adopted to decouple nonlinearities and eliminate uncertainties. It can be combined with SMC to reduce the chattering of the SMC and improve the dynamic response of the system.

#### 4.5.3. Artificial Intelligent Control Methods

- The fuzzy logic control algorithm can use expert knowledge to obtain the output control signal, which has better control performance than the PID controller and can be directly applied to nonlinear systems. However, traditional fuzzy logic controllers are designed based on human operator experience and cannot linguistically determine the exact action for the output. The T–S fuzzy control method was proposed as a mathematical tool to overcome this problem. In addition, optimization methods such as PSO can be combined to better tune the parameters of the controller. It can also combine the ${\mathcal{l}}_{2}-{\mathcal{l}}_{\mathrm{\infty}}$ control to ensure that the controlled output is less than a prescribed level and PID to optimally adjust the coefficients and restrain the coupled vibration of the vehicle and guideway.
- The conventional neural network algorithm can address complex nonlinear problems that have the characteristics of approximation of nonlinear functions, a simple structure, and fast convergence. This solution can effectively improve the control performance against large uncertainties in the system. In maglev levitation control, conventional neural network algorithms are commonly used as controllers to output the control item or optimize the parameters of other controllers, such as PID and state feedback controllers.
- The deep learning algorithm places emphasis on designing and evaluating training algorithms and model architectures for contemporary neural networks. These networks can better represent the intricate features of complex problems. Although few studies have investigated deep-learning-based maglev levitation control, the application of DBN and DRL has demonstrated the robustness and effectiveness of the deep-learning algorithm in the maglev levitation area.

## 5. Maglev Train Controller in Other Situations

#### 5.1. Vehicle–Guideway Vibration Suppression Control Design

#### 5.2. Redundancy and Fault-Tolerant Design

#### 5.3. Summary

## 6. Discussion

- (1)
- Linear control methods: The maglev levitation systems are first linearized using Taylor expansion or feedback linearization methods. The linear control methods can normally be classified into state feedback methods and optimal control methods based on the principle of control. To achieve better control performance, the conventional linear control methods are combined with other methods, such as fuzzy logic and IMC.
- (2)
- Nonlinear control methods: Compared with linear control methods, nonlinear control methods can be directly applied to the maglev levitation models. Nonlinear control methods, such as robust control and adaptive control, show great potential in enhancing the performance of control systems, especially in handling uncertainties caused by factors such as degradation and modeling inaccuracies.
- (3)
- Artificial intelligence control methods: Artificial intelligence control methods can handle the complex nonlinear problem of maglev levitation systems. In particular, deep learning control algorithms, such as deep reinforcement learning, can simultaneously achieve the advantage of model-based control and data-driven control.

## 7. Conclusions and Prospects

#### 7.1. Theoretical and Practical Implications

#### 7.2. Future Prospects

- (1)
- Maglev trains and advanced control methods can contribute to the development of sustainable and innovative transportation infrastructure.
- (2)
- Maglev trains can enhance accessibility, reduce dependence on fossil fuel-based transportation, and promote sustainable urban mobility. The use of efficient control methods can improve the safety of the maglev trains, as well as contribute to the development of sustainable cities and communities.
- (3)
- Maglev trains are energy-efficient and have low carbon emissions. Thus, energy consumption can be optimized, further reducing greenhouse gas emissions and supporting climate action initiatives.
- (4)
- The development and implementation of maglev train control methods require collaboration and partnerships between governments, research institutes, and industry stakeholders. Such collaboration can foster knowledge sharing, technology transfer, and capacity building, contributing to the achievement of SDGs.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**Flowchart of the maglev train system modeling: (

**a**) Data acquisition from real model, (

**b**) System modeling.

**Figure 4.**Configuration of a single EMS system module [15].

**Figure 6.**Schematic of the maglev electromagnet-guideway coupling system [50].

**Figure 10.**Schematic diagram of state motion process [18].

**Figure 11.**Schematic of fuzzy logic control [106]. (

**a**) Type-1 fuzzy logic control; (

**b**) type-2 fuzzy logic control.

**Figure 12.**Structure of the DBN [120].

**Figure 13.**Network structure in the deep deterministic policy gradient (DDPG) algorithm [27].

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**MDPI and ACS Style**

Zhu, Q.; Wang, S.-M.; Ni, Y.-Q.
A Review of Levitation Control Methods for Low- and Medium-Speed Maglev Systems. *Buildings* **2024**, *14*, 837.
https://doi.org/10.3390/buildings14030837

**AMA Style**

Zhu Q, Wang S-M, Ni Y-Q.
A Review of Levitation Control Methods for Low- and Medium-Speed Maglev Systems. *Buildings*. 2024; 14(3):837.
https://doi.org/10.3390/buildings14030837

**Chicago/Turabian Style**

Zhu, Qi, Su-Mei Wang, and Yi-Qing Ni.
2024. "A Review of Levitation Control Methods for Low- and Medium-Speed Maglev Systems" *Buildings* 14, no. 3: 837.
https://doi.org/10.3390/buildings14030837