S S symmetry Article A New Strategy for Improving the Tracking Performance of Magnetic Levitation System in Maglev Train Mingda Zhai , Zhiqiang Long * and Xiaolong Li College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China * Correspondence: [email protected] Received: 18 July 2019; Accepted: 13 August 2019; Published: 16 August 2019 Abstract: The maglev train is a whole new method of transportation without wheels, consisting of 20 groups of symmetry suspension units. The magnetic levitation system plays a major role in suspending the maglev train stably and following the track quickly with the desired gap. However, vertical track irregularity in the maglev train line has a dreadful effect on the tracking performance of the magnetic levitation system. The investigations carried out by our team have revealed that the fluctuation of the suspension gap becomes more and more serious with increases in running speed. In this paper, a mathematical model with consideration of vertical track irregularity is established. In order to overcome and suppress the fluctuation of the suspension gap, we propose a new strategy which includes installing an accelerometer on the electromagnet to address this problem. This strategy has already been successfully implemented and applied to the suspension controller for a magnetic levitation system in the Changsha maglev express. Real operation data indicates the tracking performance of the magnetic levitation system was obviously improved. Keywords: maglev train; symmetry; magnetic levitation system; vertical track irregularity; tracking performance; strategy 1. Introduction In 1814, the first steam locomotive was invented by George Stephenson, renowned as the “Father of Railways”. The Stockton and Darlington Railway was opened to carry passengers in 1825. Rail transport was one of the most important technological inventions of the industrial revolution. Ever since then, the wheel of time has never stopped. Time goes by as fast as a high-speed train, and we have already entered into an age without wheels. The maglev train is a whole new method of transportation without wheels. Plenty of scholars and engineers in Japan, the United States, China and South Korea are carrying out research in related fields and have already achieved many successes [1–3]. It is well known that the Shanghai high-speed maglev train went into operation in 2002. The Incheon airport maglev line of South Korea officially began to carry passengers on 3 February 2016. A superconducting maglev train with a high speed of 603 km/h will come out in 2027. As shown in Figure1, the Changsha maglev express is the first domestic medium-low speed maglev line in China and completely owns the proprietary intellectual property rights. This line stretches over 18.55 km and started trial operations on 6 May 2016. Beijing’s 1st maglev Line S1 is the second domestic medium-low speed maglev line in China and began operating on 31 December 2017. The Qingyuan maglev travel line is under construction, and will go into operation on September 2019. In recent years, the maglev train increasingly began to receive considerable attention and has become an active traffic field. Symmetry 2019, 11, 1053; doi:10.3390/sym11081053 www.mdpi.com/journal/symmetry Symmetry 2019, 11, 1053 2 of 18 Symmetry 2019, 11, x FOR PEER REVIEW 2 of 19 Figure 1. A photograph of the medium-low speed maglev train in Changsha. Compared with conventional railway systems, the medium-low speed maglev train makes full use of electromagnetic electromagnetic force force to to achieve achieve active active suspen suspensionsion and and runs runs the the train train using using a linear a linear motor. motor. It completelyIt completely abandons abandons the the wheel-rail wheel-rail relationship relationship and and achieves achieves non-contact non-contact motion, motion, which which not not only eliminates friction to reduce noise and vibration, but also allows the maglev train to travel through buildings on viaducts smoothly and quietly. What’s more, there are zero emissions to the atmosphere during running. Therefore, Therefore, the the maglev maglev train train is is sa safe,fe, sound, sound, low-carbon low-carbon and and environmentally environmentally friendly. friendly. This paper isis concernedconcerned chiefly chiefly with with the the study study of of the the magnetic magnetic levitation levitation system system in ain medium-low a medium- lowspeed speed maglev maglev train. train. The The magnetic magnetic levitation levitation system system plays plays a major a major role inrole suspending in suspending the maglev the maglev train trainstably stably and following and following the track the quickly. track quickly. Most scholars Most scholars concentrate concentrate on the research on the onresearch the levitation on the levitationcontrol algorithm control underalgorithm the conditionsunder the ofconditions a straight of track. a straight However, track. vertical However, track irregularityvertical track in irregularitythe maglev trainin the line maglev has a banefultrain line influence has a onba theneful tracking influence performance. on the tracking Unfortunately, performance. many Unfortunately,experts are not concernedmany experts about are this not issue. concerned In order about to address this issue. this issue,In order the to mathematical address this model issue, with the mathematicalconsideration ofmodel vertical with track consideration irregularity of is vertical established track in irregularity this paper. Foris established the benefit in of this improving paper. For the thetracking benefit performance, of improving we proposethe tracking a new performance, strategy of installing we propose an accelerometer a new strate ongy the of electromagnetinstalling an accelerometerto address this on problem. the electromagnet to address this problem. 2. Nominal Nominal Controller of Magnetic Levitation System Magnets of the same same polarity polarity repel repel each each other, other, whil whilee those those of of different different polarity polarity attract attract each each other. other. The medium-low speed maglev train takes advantageadvantage of the attraction between the electromagnet and the F-type F-type track track to to realize realize suspension suspension at at a adefin defineded height. height. A Acomplete complete magl maglevev train train has has 20 20sets sets of electromagnets,of electromagnets, installed installed on on the the bottom bottom of of the the ca carriage.rriage. When When the the current current is is switched switched on, upward electromagnetic force is generated. The F-type track wi willll suck up the base of the vehicle, and the base and the carriagecarriage areare connectedconnected by by air air springs. springs. Thus, Thus, the th magleve maglev train train is ableis able to suspendto suspend itself itself in thein the air, air,against against gravity. gravity. The interactionThe interaction between between electromagnetic electromagnetic force and force gravity and gravity will always will keepalways a dynamic keep a dynamicbalance, levitatingbalance, levitating the maglev the train maglev above train the rail.above No the matter rail. howNo matter the speed how and the railway speed lineand changes,railway linethe gapchanges, between the thegap trackbetween and the the track electromagnet and the electromagnet has to remain has unchanged to remain under unchanged the action under of the actionsuspension of the controller suspension for controller the magnetic for the levitation magnetic system. levitation system. As shown in Figure 22,, thethe magneticmagnetic levitationlevitation controlcontrol systemsystem consists of a suspension controller, a gap sensorsensor andand anan actuator, actuator, which which is is the the electromagnet. electromagnet. The The gap gap sensor sensor measures measures the the gap gap between between the theelectromagnet electromagnet and theand F-type the F-type track constantly.track constantly. The suspension The suspension controller controller calculates calculates the control the quantity control quantityaccording according to the measured to the measured gap signal gap to adjustsignal theto ad currentjust the of current the electromagnet of the electromagnet in real time. in Whenreal time. the Whencurrent the varies, current the intensityvaries, the of theintensity closed-loop of the magneticclosed-loop field magnetic established field between established the electromagnet between the electromagnetand the F-type trackand the will changeF-type accordingly.track will change The electromagnetic accordingly. forceThe electromagnetic will consequently force vary will and consequentlymake the electromagnet vary and make fall or the float electromagnet to levitate the fall maglev or float train to levitate in the target the maglev gap. train in the target gap. Symmetry 2019, 11, x FOR PEER REVIEW 3 of 19 Symmetry 2019, 11, 1053 3 of 18 Symmetry 2019, 11, x FOR PEER REVIEW 3 of 19 Figure 2. The structure of the magnetic levitation system in the medium-low speed maglev train. Figure 2. TheThe structure structure of the magnetic levitation syst systemem in the medium-low speed maglev train. Because of the symmetry of the magnetic levitation system in medium-low speed maglev trains, the mathematical model of single magnetic levitation system is easily established. If all factors are Because of the symmetry of the the magnetic magnetic levitati levitationon system