Research on Siding Mode Controller of High-Speed Maglev Train Under Aerodynamic Load

The high-speed maglev train will be subjected to extremely obvious aerodynamic load during operation, it will also be subjected to instantaneous aerodynamic impact load in the case of passing, which will bring extreme challenges to the suspension stability and safe operation of the train. It is necessary to consider the influence of aerodynamic load and shock wave in the design of suspension control algorithm. Traditional proportion integration differentiation (PID) control cannot follow the change of vehicle parameters or external disturbance, which is easy to cause suspension fluctuation and instability. In order to improve the suspension stability and vibration suppression of high-speed maglev train under aerodynamic load and impact, a controller based on sliding mode technique is designed in this paper, and in this controller, the deformation of the primary suspension is introduced to replace the aerodynamic load on the electromagnet. In order to verify the control performance of the designed controller, the dynamic simulation model of train with three vehicles is established, and the dynamic response of the train under the condition of passing in open air is calculated. Compared with the PID controller, it is verified that the sliding mode control (SMC) method proposed in this paper can effectively restrain the electromagnet fluctuation of the train under aerodynamic load.

The speed of the wheel-rail train is increasing gradually in order to meet the needs of people's life, but the increasing of speed will be restricted by the limit of wheel-rail adhesion. The appearance of the maglev train has changed this situation. The maglev train relies on the electromagnetic force between the levitation electromagnet and the track to realize suspension, and uses the guidance electromagnet to achieve the guidance function. Compared with the traditional vehicle, it has the advantages of low energy consumption, low environmental impact, low noise, less maintenance and strong climbing ability.
In recent years, maglev train has made significant progress, and China's maglev system at 600 km/h has been launched on July 20, 2021. Since the aerodynamic load is directly proportional to the square of the speed, the aerodynamic load must increase sharply with the increase of the vehicle speed. Taking the of Shanghai maglev demonstration line as an example, the numerical calculation shows that if the train runs at 600 km/h, the average aerodynamic lift of the tail car can reach 10 tons, and the instantaneous lift can reach 14 tons when the train passing another train. The stable suspension of EMS high speed maglev vehicle is realized by controlled vertical electromagnetic force, such a large aerodynamic lift and impact will have momentous influence on the suspension stability and safety of the train. Kwon et al. [1] performed numerical simulation on the response of maglev vehicle passing through the suspension bridge and was subjected to gusts of wind. The research shows that the ride comfort of the maglev vehicle is reduced due to the low frequency vibration of the vehicle caused by the bridge and turbulence wind. Yau [2] considered the aerodynamic load caused by unstable air flow and calculated the response of the vehicle-guideway coupling system. The results show that the aerodynamic load may cause the significant acceleration amplification of the high-speed maglev vehicle. Wu and Shi [3] completed the numerical analysis of dynamic response of maglev vehicle body under wind field. Simulation of the lateral vibration response of maglev vehicle when it passing in open air has been completed by some Liu and Tian [4]. Takizawa [5] studied the comfort of the MLX01 Maglev train when it passing at 500 km/h. For EMS maglev train, due to the inherent instability of electromagnetic levitation, it is necessary to exert control on the levitation system to maintain stable operation, therefore, the response of EMS maglev train under external disturbance is closely related to the control algorithm. At present, the control algorithm of high-speed maglev train is still based on PID control, which realizes feedback control by calculating the acceleration of electromagnet and the difference between actual gap and rated gap. However, PID control does not involve the parameters of vehicle system and external disturbance. When the train is subjected to the aerodynamic load and impact, the control algorithm does not change with it, which is easy to cause the fluctuation and instability of suspension gap. Common state feedback control is difficult to meet the control requirements, so algorithms such as neural network control, genetic algorithm control and sliding mode control have been used to magnetic levitation system. Among them, sliding mode control is gradually carried into the control of magnetic levitation system because of its strong robustness and anti-disturbance. In recent years, many scholars have applied sliding mode control technology to the levitation control of maglev train.
Molero et al. [6] used the sliding mode control to the magnetic levitation ball to control the position of the nonlinear system composed of the iron ball and the electromagnetic coil. Wang [7] analyzed a single-axis magnetic levitation system and then designed an adaptive sliding mode control which could deal with unknown parameters to complete the guidance and positioning of the system. Bandal et al. [8] designed a sliding mode controller for position control of electromagnet, which based on the concept of proportional integral switching surface, and compared it with the feedback linearization controller. Yang et al. [9] developed a new dynamic sliding surface by combining the disturbance estimation value and its high-order derivative information, and proposed a continuous dynamic sliding mode control (CDSMC) method that can be used in suspension control system. Benomair et al. [10] proposed a fuzzy sliding mode controller (FSMC) which can estimate the unmeasured state using a nonlinear observer. In order to study the influence of air resistance on the dynamic response of maglev train, Gao et al. [11] proposed an operation control method based on sliding mode periodic adaptive learning control (SM-PALC) to reduce the position error and improve the robustness of the control system. Dourla et al. [12] designed a dynamic sliding mode controller by controlling the current through the electromagnetic coil. Chen et al. [13] introduced sliding mode control into the research of flexible track of maglev train, and designed the sliding mode adaptive state feedback controller of maglev system, then compared with PID controller, it is found that the controller can guarantee faster dynamic response and stronger robustness when considering flexible orbit disturbance.
A hybrid flux density observer based on current and voltage feedback is proposed by Xu et al. [14], and an adaptive sliding mode controller is designed to reduce the parameter uncertainty and disturbance upper bound of the sliding mode controller.
Sliding mode control has the characteristic of variable structure, it can force the system to move according to the state trajectory of the predetermined "sliding mode" in the dynamic process according to the current state of the system, to overcome the uncertainty of the system. Because the sliding mode can be designed and is independent of parameters and disturbances, it has the advantages of fast response, insensitivity to parameter changes and disturbances, no need for on-line identification of the system and simple physical implementation. In order to overcome the influence of the aerodynamic load and suppress the vibration of the electromagnet during the running of the train, the sliding mode control technology is adopted in this paper to design the suspension controller of the maglev train. However, due to the fact that the aerodynamic loads on maglev trains cannot be measured and obtained in real time during the operation of trains, how to introduce the influence of aerodynamic disturbances conveniently and effectively, so that the sliding mode controller can change its structure in time when it is subjected to aerodynamic load and impact, no scholar has given a solution at present.
Given that the vibration caused by the aerodynamic load and impact acting on the maglev train body will be transmitted to the electromagnet through the secondary suspension, the maglev frame and the primary suspension, so the fluctuation of primary suspension force can be regarded as the disturbance of aerodynamic load to the electromagnetic suspension system. Therefore, this paper considers the influence of primary suspension force disturbance on a single point  The vertical motion equation of the electromagnet can be written as: The levitation force between the electromagnet and the guide rail is calculated by the classical electromagnetic force formula as follows: In Eq. (2), μ0 is the air permeability, z is the suspension gap, A is the effective area of the electromagnet, N is the turns of the coil, fst (t) and funst (t) represent the balance value and the fluctuation of primary suspension force, respectively.
The maglev train directly adjusts the current in the electromagnet through the suspension control unit. The dynamic equation can be written as follows: The state equation is rewritten as: or Where, = [ Design of sliding mode controller (1) Design of sliding surface The switching function s(x) is designed and the switching surface s(x)=0 is determined to ensure the asymptotic stability and good dynamic characteristics of the dynamic system on the sliding surface.
Define tracking error 0 ,̇0 are the irregularity of the track and its derivative, respectively The switching function of the system is designed as: In order to guarantee the asymptotic stability on the sliding surface of the system, that is ( ) = 0, it is necessary to meet > 0.
(2) Design of sliding mode law The design of sliding mode control law should meet the following requirements: it can make the system state enter the sliding mode state from any initial point, and keep it on the sliding mode surface stably and reliably.
The law of convergence mainly has: constant rate of convergence, exponential rate of convergence and power rate of convergence. The exponential reaching law can effectively reduce buffeting vibration in the form of: According to Eq. (9), we can get: According to Eq. When s is large, the system state can converge to 0 at a large speed. In the exponential approach, the approach velocity approaches 0 from a larger velocity, which not only shortens the approach time, but also decreases the velocity when the moving point reaches the switching surface. In order to further suppress the buffeting vibration of sliding mode control, the saturation function is used to replace the switching function, and the control law is changed as follows: Where sat is a saturation function whose expression is: The control law of the system can ultimately be determined as:  In this paper, the dynamic simulation model of train was established by using multi-body dynamics software. Based on the dynamic model shown in Fig. 2, a simulation model of TR08 single vehicle was established, then the maglev train with three vehicles was formed, which is shown in Fig. 3, and the position of electromagnet on each train is marked in the figure.

Fig. 3 Dynamic model of TR08 maglev train
In this paper, the train was controlled dispersedly, so that the design of the whole vehicle suspension control system could be completed by designing the single electromagnet suspension control system, which could make the control system more simplified. Each suspension electromagnet of TR08 train has 12 coils, six of which share one control unit, and each control unit is independent of each other. This paper used SIMULINK to simulate the control module, based on the sliding mode control technology proposed in this paper, the single channel suspension control scheme is present as follows:   Table 1.       In order to more specifically illustrate the fluctuation of the levitation gap of electromagnet under using three kinds of controller, Fig. 10 -Fig. 12show the levitation gap amplitudes, including all electromagnets of the whole vehicle. It can be seen that under the action of the sliding mode controller designed in this paper, the suspension gap amplitude of the whole train at 300 km/h is less than 0.1 mm, the suspension gap amplitude at 400 km/h is less than 0.2 mm, and the suspension gap amplitude at 500 km/h is less than 2 mm, showing good suspension stability. The amplitude at H1 is 0.01384 mm when the sliding mode control designed in this paper is used, which is reduced by 90.49% compared with PID control and 79.61% compared with using traditional sliding mode controller.
At the position T7 of the last electromagnet of the tail car, the amplitude of the suspension gap is 0.51499 mm under using PID control, and 0.22301 mm when using the traditional sliding mode control. The amplitude of the suspension gap at T7 is 0.03761 mm under using the control proposed in this paper, which is 92.70% less than that of PID control and 83.14% less than that of the traditional sliding mode controller.

Conclusion
In this paper, the influence of aerodynamic load on electromagnet is replaced by the disturbance of primary suspension force, then a sliding mode controller considering the disturbance of primary suspension force is designed. Xiaohui Zeng：Funding acquisition, Supervision.
Bo Yin: Improve data.