energies

Article Development of the Reduced-Scale Vehicle Model for the Dynamic Characteristic Analysis of the

Jinho Lee 1, Wonhee You 1 , Jungyoul Lim 1 , Kwan-Sup Lee 1 and Jae-Yong Lim 2,*

1 New Transportation Innovative Research Center, Korea Railroad Research Institute, Uiwang 16105, Korea; [email protected] (J.L.); [email protected] (W.Y.); [email protected] (J.L.); [email protected] (K.-S.L.) 2 Department of Safety Engineering, Seoul National University of Science and Technology, Seoul 01811, Korea * Correspondence: [email protected]

Abstract: This study addresses the Hyperloop characterized by a capsule-type vehicle, supercon- ducting electrodynamic suspension (SC-EDS) levitation, and driving in a near-vacuum tube. Because the Hyperloop is different from conventional transportation, various considerations are required in the vehicle-design stage. Particularly, pre-investigation of the vehicle dynamic characteristics is essential because of the close relationship among the vehicle design parameters, such as size, weight, and suspensions. Accordingly, a 1/10 scale Hyperloop vehicle system model, enabling the analysis of dynamic motions in the vertical and lateral directions, was developed. The reduced-scale model is composed of bogies operated by Stewart platforms, secondary suspension units, and a car body. To realize the bogie motion, an operation algorithm reflecting the external disturbance, SC-EDS levitation, and interaction between the bogie and car body, was applied to the Stewart platform. Flexible rubber springs were used in the secondary suspension unit to enable dynamic characteristic analysis of the vertical and lateral motion. Results of the verification tests were compared with simu-  lation results to examine the fitness of the developed model. The results showed that the developed  reduced-scale model could successfully represent the complete dynamic characteristics, owing to the Citation: Lee, J.; You, W.; Lim, J.; Lee, enhanced precision of the Stewart platform and the secondary suspension allowing biaxial motions. K.-S.; Lim, J.-Y. Development of the Reduced-Scale Vehicle Model for the Keywords: Hyperloop; superconducting electrodynamic suspension (SC-EDS); dynamic characteris- Dynamic Characteristic Analysis of tics; reduced-scale vehicle the Hyperloop. Energies 2021, 14, 3883. https://doi.org/10.3390/en14133883

Academic Editor: João Pombo 1. Introduction Since the concept of the Hyperloop with a 1200 km/h speed was introduced by Elon Received: 10 May 2021 Musk [1], interest in the development of the Hyperloop has been growing. The characteris- Accepted: 25 June 2021 Published: 28 June 2021 tics and the performance of the Hyperloop was analyzed comparing existing transportation systems [2,3]. Research on the station design [4] and the safety management [5] were also

Publisher’s Note: MDPI stays neutral conducted. In [6], the Hyperloop potential was comprehensively assessed by using the with regard to jurisdictional claims in consolidated relevant data sources. In commercial sides, the development of the Hyperloop published maps and institutional affil- vehicle and infrastructure have been under way [7,8]. There are several unique features of iations. the Hyperloop that facilitate achieving such a subsonic driving speed: a near-vacuum tube, electrodynamic suspension (EDS) levitation, linear motor propulsion, and a capsule-type vehicle. Although certainly beyond imagination, the selection of a near-vacuum tube as the driving environment can reduce the air resistance dramatically [9,10]. EDS levitation in the systems can achieve stable levitation without control, eliminating unnecessary driving Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. friction [11,12]. The linear motor for propulsion is one of the key elements that utilizes high- This article is an open access article capacity power from the stator installed in the tube guideway. The lightweight capsule-type distributed under the terms and vehicle plays a significant role in relieving not only the burdens in the propulsion force, conditions of the Creative Commons but also that in the tube infrastructure construction. Attribution (CC BY) license (https:// Various considerations are required, particularly in the design stage, because the creativecommons.org/licenses/by/ abovementioned features of the Hyperloop are rather different from those of the existing 4.0/). wheel–rail-type . In particular, pre-investigation of the Hyperloop vehicle dynamic

Energies 2021, 14, 3883. https://doi.org/10.3390/en14133883 https://www.mdpi.com/journal/energies Energies 2021, 14, 3883 2 of 13

characteristics is essential for vehicle design. Vehicle dynamic characteristics not only affect the driving stability and ride comfort, but also the major design parameters, such as vehicle size, weight, and suspension systems. It is evidently a challenging task to use a full-scale model to investigate the dynamic characteristics of the newly developed system. Instead, a reduced-scale vehicle model is more advantageous in many aspects. For example, various tests can be easily conducted under different conditions, as performed in previous studies on wheel-rail trains, and it is not necessary to consider the actual drive. In the previous studies, roller rigs simulating the rails against the wheels were generally used to examine the dynamic response of their systems by varying the driving conditions, such as the roller speed, contact angle, and force [13,14]. In related research, the similarity laws in wheel-rail vehicle dynamics was investigated [15], and based on this, reduced-scale vehicle models, were designed and validated [16,17]. The wheel/rail adhesion that is an important factor in vehicle dynamics was also analyzed by using the roller rig [18]. However, the roller rig cannot be applied to the Hyperloop model under development in this study because the model is based on , rather than wheel-rail contact. There are two reduced-scale systems to be noted as milestones. For the Japanese EDS system, a 1/12 scale vehicle was developed for the investigation of dynamic characteristics [19]. In this model, the Stewart platform operated by hydraulic actuators was used to realize the bogie motion, reflecting magnetic levitation forces and external disturbances. However, there are a few limitations. First, a reduced-scale vehicle does not have lateral degrees of freedom in the suspension units. Therefore, this system cannot represent the complete dynamic response of a full-scale vehicle. Another limitation is the use of hydraulic actuators incorporated in reduced-scale vehicles. If the actuators are replaced by electromagnetic actuators, the precision can be improved further. Finally, there is a lack of detailed explanations of the operating principles for the bogie motion realization, and there is no information on the validation. These are crucial for understanding bogie motion in the development process of novel systems. In addition to the abovementioned system, another reduced-scale vehicle was developed by Lee et al. [20]. However, the limitations indicated in the Japanese model are also true for this model. Therefore, for a more realistic dynamic response, a reduced-scale vehicle with lateral degrees of freedom in suspension units must be developed, and a thorough understanding and validation of the realized bogie motion are necessary. This study aims to develop a 1/10 scale model of the Hyperloop vehicle to resolve the aforementioned limitations of the previous models. The developed model is composed of two bogies operated by the Stewart platform driven by powerful linear electromagnetic ac- tuators, two secondary suspension units, and a car body. More importantly, biaxial motions resulting from the secondary suspension units can be obtained. Additionally, numerical simulations and analytical derivations are performed, and discussions are presented on the effects of system parameters and the discrepancy between the experimental and simulation results.

2. Materials and Methods 2.1. Design of the Reduced-Scale Vehicle Model The full-scale Hyperloop vehicle which has been researched by Korea Railroad Re- search Institute is conceptualized as illustrated in Figure1a. The vehicle (for 20 passengers) consists of two bogies and one passenger cabin, and its size and weight are 2.1 m × 2.3 m × 26 m (width × height × length) and 28 tons, respectively. The superconductor magnets on the bogie provide propulsion, levitation, and guidance force through the interaction with coils on the tube guideway, as shown in Figure1b. Especially, HTS (high-temperature superconducting) magnets with a detachable cryocooling system [21–23] is applied for lightweight vehicle. One magnet module contains 6 coils of HTS wires, and it weighs 2000 kg. Energies 2021, 14, x FOR PEER REVIEW 3 of 13

tion with coils on the tube guideway, as shown in Figure 1b. Especially, HTS (high-tem- perature superconducting) magnets with a detachable cryocooling system [21–23] is ap- plied for lightweight vehicle. One magnet module contains 6 coils of HTS wires, and it weighs 2000 kg. For propulsion, the vehicle uses a superconducting linear synchronous motor (SC- LSM) that is based on superconductor magnets as the rotor and air-core three-phase coils as the stator [24,25]. For levitation and guidance, the forces generated from the interaction between the superconductor magnets and null-flux coils are used, which allows the vehi- Energies 2021, 14, 3883 cle to maintain the normal driving position. This method is called the superconducting3 of 13 electrodynamic suspension (SC-EDS) [12].

(a)

(b)

FigureFigure 1. Conceptual 1. Conceptual diagram diagram of the of the Hyperloop Hyperloop system: system: (a) (vehicle,a) vehicle, (b) (tubeb) tube guideway. guideway.

A simplifiedFor propulsion, spring-mass the vehicle model uses is built a superconducting for a full-scale model linear with synchronous an assumption motor of (SC- a linearLSM) system. that is basedThe vertical on superconductor and lateral motions magnets in asthe the x-z rotor plane and and air-core x-y plane three-phase are consid- coils eredas theas shown stator [24in ,25Figure]. For 2a,b, levitation respectively. and guidance, As indicated the forces in generated[26], angular from motions the interaction also shouldbetween be considered the superconductor to analyze magnets the full and dyna null-fluxmics of coilsthe Hyperloop. are used, which However, allows since the vehicle the mainto maintainpurpose of the this normal study drivingis to validate position. developed This methodmodel by is using called minimal the superconducting (but essen- tial)electrodynamic dynamic characteristic suspension analyses, (SC-EDS) the [ 12model]. construction for angular motions was ig- nored. InA the simplified SC-EDS spring-mass system, there model exists is an built electromagnetic for a full-scale levitation model withstiffness an assumption (klev) and guidanceof a linear stiffness system. (kgud The) between vertical the and bogies lateral and motions guideway in thethat x-z establish plane anda primary x-y plane sus- are pensionconsidered system. as shownIn practice, in Figure the stiffness2a,b, respectively. varies depending As indicated on the in [driving26], angular conditions motions [27]; also however,should these be considered values can to analyzebe considered the full to dynamics be constant of thewhen Hyperloop. the driving However, speed is since fixed the [28,29].main In purpose this study, of this because studyis the to validatenormal driving developed speed model is set by to using 1000 minimal km/h, the (but constant essential) valuesdynamic of stiffness characteristic for this analyses,speed are the used. model Between construction the bogies for angularand the car motions body, was there ignored. are airIn springs the SC-EDS (kair(V), system,kair(L)) and there active exists actuators an electromagnetic for vibration levitation control in stiffness the vertical (klev) andand guidancelateral directionsstiffness that (kgud establish) between a secondary the bogies suspen and guidewaysion system. that The establish parameter a primary values associated suspension system. In practice, the stiffness varies depending on the driving conditions [27]; however, these values can be considered to be constant when the driving speed is fixed [28,29]. In this study, because the normal driving speed is set to 1000 km/h, the constant values of

stiffness for this speed are used. Between the bogies and the car body, there are air springs (kair(V), kair(L)) and active actuators for vibration control in the vertical and lateral directions that establish a secondary suspension system. The parameter values associated with the pure vertical and lateral dynamics of the full-scale vehicle model are summarized in the third column of Table1. These values are based on the design results, conducted by the Korea Railroad Research Institute. Energies 2021, 14, x FOR PEER REVIEW 4 of 13

with the pure vertical and lateral dynamics of the full-scale vehicle model are summarized Energies 2021, 14, 3883 in the third column of Table 1. These values are based on the design results, conducted4 of by 13 the Korea Railroad Research Institute.

(a)

(b)

Figure 2. Spring-mass model corresponding toto thethe vehicle:vehicle: (a)) verticalvertical modelmodel onon x-zx-z plane,plane, ((bb)) laterallateral modelmodel onon x-yx-y plane.plane.

To determinedetermine thethe scalescale factors factors and and design design the the reduced reduced model model setup, setup, a dynamica dynamic similar- simi- itylarity law law suggested suggested by Gretzschelby Gretzschel and and Jaschinski Jaschinski [16] [16] was was used used in this in this study. study. This This scaling scaling law waslaw was chosen chosen in consideration in consideration of the of actualthe actual fabrication fabrication of the of reduced-scalethe reduced-scale model. model. Let theLet actualthe actual length length and and reduced-scale reduced-scale length length be denoted be denoted by l 0byand l0 andl1, respectively. l1, respectively. Equation Equation (1) expresses(1) expresses the the scale scale factors factors for for the the lengths, length velocity,s, velocity, and and density density between between the the two two models. mod- els. l1 ϕl = l q0 𝑙 𝜑 = l1 ϕv = (1) l𝑙0 ϕD = 1 𝑙 (1) The other scale factors, with respect to𝜑 the = mass, time, force, stiffness, and acceleration 𝑙 can be obtained as follows: 3 ϕm = ϕD ϕ 𝜑√=1l ϕt = ϕl The other scale factors, with respect to= the mass,3 time, force, stiffness, and accelera- ϕ f ϕD ϕl (2) tion can be obtained as follows: ϕ f ϕc = ϕl ϕ f ϕ 𝜑= =𝜑=𝜑1 a ϕm

In this study, a 1/10 reduced-scale was𝜑 = chosen,𝜑 considering the actual size of the vehicle and the laboratory environment. Therefore, to maintain dynamic similarity between 𝜑 =𝜑𝜑 the actual (full-scale) and reduced-scale models, the selection of ϕl = 0.1 leads to the ratio(2) 𝜑 of weights, ϕ = 0.001, and that of suspension stiffness, ϕ = 0.01. In addition, the test time m √ 𝜑 = c period was reduced by 10. For example, the test𝜑 time period of 1 s in the reduced-scale test setup corresponds to 3.16 s in the actual model.𝜑 However, it should be noted that the 𝜑 = =1 acceleration measured from the reduced-scale𝜑 test setup is identical to that of the actual vehicle structure. In accordance with the aforementioned dynamic similarity, the design In this study, a 1/10 reduced-scale was chosen, considering the actual size of the ve- parameters for the reduced-scale model are summarized in the fourth column of Table1. hicle and the laboratory environment. Therefore, to maintain dynamic similarity between

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Table 1. Design parameters for the vehicle model.

Parameters Full-Scale Model Reduced-Scale Model

Car body mass (mc, kg) 10,000 10 Mass Bogie mass (mb1,b2, kg) 9000 9 Vertical stiffness of air spring (k N/m) 1,250,000 12,500 Secondary suspension air(V)1,2 Lateral stiffness of air spring (kair(L)1,2 N/m) 174,000 1740 Levitation stiffness (k N/m) 534,000 5340 Primary suspension lev1,2 Guidance stiffness (kgud1,2 N/m) 518,400 5184

2.2. Hardware Fabrication A reduced-scale vehicle system model was built with a 1:10 scale factor, as shown in Figure3a. As explained for the full-scale model in Section 2.1, the reduced-scale vehicle is also composed of two bogies operated by the Stewart platform, two secondary suspension units, and a car body made of aluminum plate. The details of the secondary suspension units are shown in Figure3b. Four columns, each of which comprises eight rubber springs in series, are connected with the car body and bogie, making it possible to cause motion in both the vertical and lateral directions. A few rubber springs are installed in the hardware system to render suspension stiffness, as presented in Table1. If design modifications are required in the future, the parameters can be easily tuned by changing the number of rubber springs. Additionally, thin shims are connected between rubber springs in the lateral direction, to adjust the ratio between the lateral and vertical stiffness. A higher number of shim connections increases the lateral stiffness without affecting the vertical Energies 2021, 14, x FOR PEER REVIEWstiffness. These shims can be simply assembled with rubber spring by passing6 the of 13 rubber

spring connecting screw through a hole in shims.

(a) (b) (c)

Figure 3. Reduced-scaleReduced-scale vehicle vehicle model: model: (a) ( afull) full view, view, (b) ( bsecondary) secondary suspension suspension unit, unit, (c) voice (c) voice coil motor. coil motor.

StewartFor future platforms vibration are developed control investigation, to generate a vehicle three voice bogie coilmotion, motors as shown (two forin Fig- vertical uremotion 4. Each and Stewart one for platform lateral motion)adopts coreless are placed-shaft inlinear each electromagnetic secondary suspension motors with unit. In negligibleaddition, thrust biaxial ripples load cells of cogging whose resolutionas driving andactuators bandwidth to achieve is 1 gfan andimproved 10 kHz, accuracy respectively, andare speed. installed The under relative the linear secondary motions suspension between the units. shafts These and load stators, cells which measure are NdFeb the vertical permanentand lateral magnets forces exerted and layered on the coils, secondary are achieved suspension along units,the linear and themotion measured (LM) guide. values are Theprovided actuators to theare Stewartplaced between platform the controller upper moving in real plate time. and Additional lower stationary details plate on the of load thecells Stewart are provided platform, in and Section their 2.3ends. are connected to the two plates using universal joints and spherical joints. The details of the Stewart platform and linear electromagnet actuator Stewart platforms are developed to generate a vehicle bogie motion, as shown in are summarized in Table 2. Figure4. Each Stewart platform adopts coreless-shaft linear electromagnetic motors with negligible thrust ripples of cogging as driving actuators to achieve an improved accuracy and speed. The relative linear motions between the shafts and stators, which are NdFeb permanent magnets and layered coils, are achieved along the linear motion (LM) guide. The actuators are placed between the upper moving plate and lower stationary plate of the

(a) (b) Figure 4. Stewart platform: (a) configurations, (b) linear electromagnetic actuator.

Table 2. Details of the Stewart platform.

Items Value Comment Maximum displacement ±5 mm In x, y, z directions Stewart platform Bandwidth 20 Hz When the displacement is ±0.2 mm Continuous thrust force 350 N Maximum stroke ±10 mm Linear electromagnetic Bandwidth 50 Hz When the displacement is ±0.015 mm actuator Continuous thrust force 70 N Maximum thrust force 210 N

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(a) (b) (c) Figure 3. Reduced-scale vehicle model: (a) full view, (b) secondary suspension unit, (c) voice coil motor.

Stewart platforms are developed to generate a vehicle bogie motion, as shown in Fig- ure 4. Each Stewart platform adopts coreless-shaft linear electromagnetic motors with negligible thrust ripples of cogging as driving actuators to achieve an improved accuracy Energies 2021, 14, 3883 and speed. The relative linear motions between the shafts and stators, which are6 ofNdFeb 13 permanent magnets and layered coils, are achieved along the linear motion (LM) guide. The actuators are placed between the upper moving plate and lower stationary plate of theStewart Stewart platform, platform, and and their their ends ends are connected are connect toed the to two the plates two plates using universalusing universal joints and joints andspherical spherical joints. joints. The The details details of the of Stewart the Stewart platform platform and linear and linear electromagnet electromagnet actuator actuator are aresummarized summarized in Tablein Table2. 2.

(a) (b)

FigureFigure 4. 4. StewartStewart platform: platform: ( (aa)) configurations, configurations, ((bb)) linear linear electromagnetic electromagnetic actuator. actuator.

TableTable 2. Details ofof thethe StewartStewart platform. platform.

Items ItemsValue Value CommentComment Maximum displacement ±5 mm In x, y, z directions ± Maximum displacement 5 mm In x, y, z directions ± StewartStewart platform platform BandwidthBandwidth 20 Hz 20 Hz When When the the displacement displacement is ± 0.2is mm0.2 mm ContinuousContinuous thrust force thrust force 350 350N N MaximumMaximum stroke stroke ±10± mm10 mm Linear electromagnetic BandwidthBandwidth 50 Hz 50 Hz When When the the displacement displacement is ± 0.015is ±0.015 mm mm actuator Linear electromagnetic ContinuousContinuous thrust force thrust force 70 N 70 N actuator Maximum thrust force 210 N Continuous current 2.6 A Encoder resolution 1 µm

2.3. Controller for Bogie Motion Realization Because the bogie motion is governed by external disturbance (guideway irregularity), stiffness of levitation and guidance, and the interaction between the bogie and car body, all of these factors should be considered to develop a control algorithm for the operation of the Stewart platform. To understand the bogie motions driven by the Stewart platform, the spring-mass model discussed in Section 2.1 must be considered here. For vertical motions (Figure2a), the equation of motion for Bogie 1 is given by ..  mb1zb1 = kair(V)1(zc − zb1) − klev1 zb1 − zg1 (3)

Equation (3) is a second-order differential equation representing the bogie motion (zb1), the displacement of the upper moving plate in the Stewart platform. In Equation (3), the first term on the right-hand side, (kair(V)1(zc − zb1)), represents the vertical force (FV) produced by the relative displacement between the bogie and car body (i.e., the vertical force exerted by the secondary suspension unit), and this force is directly measured by a load cell installed under the secondary suspension unit. Because mb1 (bogie mass), klev1 (levitation stiffness), and zg1 (guideway irregularity in the vertical direction) are given Energies 2021, 14, 3883 7 of 13

and FV is measured in real time, Equation (3) can be solved numerically to obtain zb1 as a function of time. For example, the following recursive equation can be used.

. zb1[k+1] = zb1[k] + ∆tzb1[k] . . .. zb1[k+1] = zb1[k] + ∆tzb1[k] (4) ..   z = 1 F − k z + k z b1[k] mb1 V[k] lev1 b1[k] lev1 g1[k]

Here, ∆t is the time interval, and subscript k represents the calculation step. In this study, the Stewart platform controller uses the Runge–Kutta numerical method to solve this differential equation because this method can be conveniently implemented and guarantees a satisfactory accuracy. Once zb1 is obtained, the displacement of each actuator in the Stewart platform is determined based on the inverse kinematics algorithm [30], and the bogie motion is finally realized by combining the displacement of each actuator. Similarly, the lateral bogie motion can be achieved in the same manner as that in the analysis for the vertical direction above.

3. Results and Discussion 3.1. Guideway Irregularity Following Performance The guideway irregularity following performance of the Stewart platform hardware was validated, which is closely related to the capability of motion realization by the hardware system. In other words, the system performance depends on how closely the Stewart platform follows the given guideway irregularity. For the test, guideway irregularity was created based on the railway irregularity generation method with reference to the EDS guideway irregularity characterized by the power spectral density [31,32]. In this validation test setup, a constant driving velocity of 1000 km/h was assumed. In addition, as indicated by Equations (1) and (2), to maintain the dynamic similarity between the actual and reduced-scale models,√ the amplitude and time period of the guideway irregularity was reduced to 1/10 and 1/ 10, respectively. The laser displacement-measuring sensor, whose Energies 2021, 14, x FOR PEER REVIEW 8 of 13 resolution was 13 µm installed outside, was used to measure the actual displacement of the Stewart platform, as shown in Figure5.

(a) (b)

Figure 5. Stewart platformFigure displacement 5. Stewart platform measurement displacement obtained measurement using laser obtained displacement-measuring using laser displacement-measuring sensor: (a) vertical displacement, (b) lateralsensor: displacement. (a) vertical displacement, (b) lateral displacement.

The experimentalThe experimental results (Figureresults 6(Figure) show that6) show the overall that the Stewart overall platform Stewart displace- platform displace- ment isment in good is in agreement good agreement with the with given the guideway given gu irregularity.ideway irregularity. As shown As in shown Table3 ,in Table 3, becausebecause the maximum the maximum following following errors are errors almost are negligible almost negligible compared compared with the realized with the realized bogie displacementbogie displacement (this will (this be discussedwill be discussed in the following in the following section), itsection), can be concludedit can be concluded that the hardware performance of the Stewart platform is appropriate for realizing the bogie motion.

0.05 0.15 Guideway irregularity(given) Guideway irregularity(given) 0.04 Stewart platform displacement Stewart platform displacement

0.1 0.03

0.02 0.05 0.01

0 0 -0.01

-0.02 -0.05

-0.03

-0.04 -0.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(s) Time(s) (a) (b) Figure 6. Stewart platform displacement with respect to the given guideway irregularity: (a) vertical direction, (b) lateral direction.

Table 3. Guideway irregularity following error of Stewart platform.

Maximum Following Error in Displacement of Realized Bogie Motion Error Ratio to Bogie Motion Stewart Platform (mm) (mm, Maximum Peak-to-Peak) Vertical direction 0.009 0.251 3.6% Lateral direction 0.035 0.939 3.7%

3.2. Dynamic Characteristics of the Developed Model Dynamic test runs were performed to investigate the dynamic characteristics of the reduced-scale vehicle. Based on the motion algorithm, the bogies were in motion with the simultaneous application of the guideway irregularity on both the front and rear bogies in the test run. The measured items in the test runs were the bogie displacement, car body

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(a) (b) Figure 5. Stewart platform displacement measurement obtained using laser displacement-measuring sensor: (a) vertical displacement, (b) lateral displacement.

The experimental results (Figure 6) show that the overall Stewart platform displace-

Energies 2021, 14, 3883 ment is in good agreement with the given guideway irregularity. As shown in8 Table of 13 3, because the maximum following errors are almost negligible compared with the realized bogie displacement (this will be discussed in the following section), it can be concluded that the hardware performance of the Stewart platform is appropriate for realizing the bogiethat the motion. hardware performance of the Stewart platform is appropriate for realizing the bogie motion.

0.05 0.15 Guideway irregularity(given) Guideway irregularity(given) 0.04 Stewart platform displacement Stewart platform displacement

0.1 0.03

0.02 0.05 0.01

0 0 -0.01

-0.02 -0.05

-0.03

-0.04 -0.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time(s) Time(s) (a) (b)

FigureFigure 6. Stewart 6. Stewart platform platform displacement displacement with withrespect respect to the to given the given guideway guideway irregularity: irregularity: (a)( avertical) vertical direction, direction, (b ()b lateral) lateral direction. direction. Table 3. Guideway irregularity following error of Stewart platform. Table 3. Guideway irregularity following error of Stewart platform. Maximum Following Error in Displacement of Realized Bogie Motion Displacement of Realized Bogie Error Ratio to Bogie Motion MaximumStewart Platform Following (mm) Error (mm, Maximum Peak-to-Peak) Motion (mm, Maximum Error Ratio to Bogie Motion Vertical direction in Stewart 0.009 Platform (mm) 0.251 3.6% Peak-to-Peak) Lateral direction 0.035 0.939 3.7% Vertical direction 0.009 0.251 3.6% Lateral direction 0.035 0.939 3.7% 3.2. Dynamic Characteristics of the Developed Model

3.2. DynamicDynamic Characteristics test runs were of the performed Developed to Model investigate the dynamic characteristics of the reduced-scale vehicle. Based on the motion algorithm, the bogies were in motion with the Dynamic test runs were performed to investigate the dynamic characteristics of the simultaneous application of the guideway irregularity on both the front and rear bogies reduced-scale vehicle. Based on the motion algorithm, the bogies were in motion with the insimultaneous the test run. application The measured of the items guideway in the irregularity test runs were on both the thebogie front displacement, and rear bogies car in body the test run. The measured items in the test runs were the bogie displacement, car body acceleration, and the forces exerted on the secondary suspension. Dynamic motions were obtained via individual tests in the vertical or horizontal direction, to avoid interference. Figure7a shows the experimental results obtained from a vertical test: time history of displacement in the front bogie, force between the car body and the bogie, and car body acceleration in the vertical direction. For car body acceleration, the accelerometer mounted on the car body was read. For comparison, the simulation results for the vertical direction are shown in Figure7b. For the simulation, the following equations of motion for the vertical direction are solved numerically.

.. mczc = −kair(V)1(zc − zb1) − kair(V)2(zc − zb2) ..  mb1zb1 = kair(V)1(zc − zb1) − klev1 zb1 − zg1 (5) ..  mb2zb2 = kair(V)2(zc − zb2) − klev2 zb1 − zg2

The experimental and simulation results for the lateral direction are shown in Figure8 . Energies 2021, 14, x FOR PEER REVIEW 9 of 13

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acceleration, and the forces exerted on the secondary suspension. Dynamic motions were obtainedacceleration, via individualand the forces tests exerted in the verticalon the secondary or horizontal suspension. direction, Dynamic to avoid motionsinterference. were obtainedFigure via 7a individual shows the tests experimental in the vertical results or horizontal obtained fromdirection, a vertical to avoid test: interference. time history of displacementFigure 7a shows in the thefront experimental bogie, force resultsbetween ob thetained car bodyfrom anda vertical the bogie, test: and time car history body ofacceleration displacement in the in verticalthe front direction. bogie, force For betwcar bodyeen theacceleration, car body andthe accelerometerthe bogie, and mounted car body accelerationon the car body in the was vertical read. Fordirection. comparison, For car the body simulation acceleration, results the for accelerometer the vertical mounteddirection areon the shown car body in Figure was 7b.read. For For the comparison, simulation, thethe simulationfollowing equationsresults for of the motion vertical for direction the ver- ticalare shown direction in Figure are solved 7b. For numerically. the simulation, the following equations of motion for the ver- tical direction are solved numerically. 𝑚𝑧 =−𝑘()(𝑧 −𝑧) −𝑘()(𝑧 −𝑧) 𝑚𝑧 =−𝑘()(𝑧 −𝑧) −𝑘()(𝑧 −𝑧) 𝑚𝑧 =𝑘()(𝑧 −𝑧) −𝑘(𝑧 −𝑧) (5) 𝑚𝑧 =𝑘()(𝑧 −𝑧) −𝑘(𝑧 −𝑧) (5) 𝑚𝑧 =𝑘()(𝑧 −𝑧) −𝑘(𝑧 −𝑧) 𝑚𝑧 =𝑘()(𝑧 −𝑧) −𝑘(𝑧 −𝑧) The experimental and simulation results for the lateral direction are shown in Figure

Energies 2021, 14, 3883 8. The experimental and simulation results for the lateral direction are shown9 ofin 13Figure 8.

Bogie displacement Bogie displacement 0.5 0.5 Bogie displacement Bogie displacement 0.5 0.5 0 0

0 0 -0.5 -0.5 0246810 0246810 -0.5 Load between bogie and carbody -0.5 Load between bogie and carbody 1 0246810 1 0246810 Load between bogie and carbody Load between bogie and carbody 1 1 0 0

0 0 -1 -1 0246810 0246810 -1 Carbody acceleration -1 Carbody acceleration 0.50246810 0.50246810 Carbody acceleration Carbody acceleration 0.5 0.5 0 0

0 0 -0.5 -0.5 0246810 0246810 -0.5 Time(s) -0.5 Time(s) 0246810 0246810 Time(s)(a) (Time(s)b) (a) (b) Figure 7. Dynamic characteristics in vertical direction: (a) experiment, (b) simulation. FigureFigure 7. 7. DynamicDynamic characteristics characteristics ininvertical vertical direction: direction: (a )(a experiment,) experiment, (b) simulation.(b) simulation.

Bogie displacement Bogie displacement 1 1 Bogie displacement Bogie displacement 1 1 0 0

0 0 -1 -1 0246810 0246810 -1 Load between bogie and carbody -1 Load between bogie and carbody 2 0246810 2 0246810 Load between bogie and carbody Load between bogie and carbody 2 2 0 0

0 0 -2 -2 0246810 0246810 -2 Carbody acceleration -2 Carbody acceleration 0.50246810 0.50246810 Carbody acceleration Carbody acceleration 0.5 0.5 0 0

0 0 -0.5 -0.5 0246810 0246810 -0.5 Time(s) -0.5 Time(s) 0246810 0246810 Time(s)(a) (Time(s)b) (a) (b) FigureFigure 8. 8. DynamicDynamic characteristics characteristics ininlateral lateral direction: direction: (a )(a experiment,) experiment, (b) simulation.(b) simulation. Figure 8. Dynamic characteristics in lateral direction: (a) experiment, (b) simulation. ForFor clarity, clarity, allall the the time time history history signals signals obtained obtained from thefrom experiments the experiments and simulations and simula- tionsareFor transformedare clarity,transformed all into the theinto time frequency the history frequency domain signals doma and, obtainedin thereafter, and, fromthereafter, superimposedthe experiments superimposed together and together simula- in Figure9. All the frequency plots, either for the vertical or lateral direction, reveal that the intions Figure are transformed9. All the frequency into the plots,frequency either doma for thein and,vertical thereafter, or lateral superimposed direction, reveal together that amplitude transformed from the experimental data is smaller than that from the simulation in Figure 9. All the frequency plots, either for the vertical or lateral direction, reveal that data. In addition, the experimental peak frequencies are higher than the simulation peak frequencies in the vertical direction frequency plots, and vice versa for the lateral direction frequency plots. Table4 summarizes the quantitative differences between the experimental and simulation results.

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the amplitude transformed from the experimental data is smaller than that from the sim- ulation data. In addition, the experimental peak frequencies are higher than the simula- tion peak frequencies in the vertical direction frequency plots, and vice versa for the lateral Energies 2021, 14, 3883 direction frequency plots. Table 4 summarizes the quantitative differences between10 of 13 the experimental and simulation results.

(a) (b)

FigureFigure 9. 9. DynamicDynamic characteristics in in the the frequency frequency domain: domain: (a )(a vertical) vertical direction, direction, (b) ( lateralb) lateral direction. direction.

TableTable 4. Comparison ofof experimentexperiment and and simulation simulation based based on on the the fast fast Fourier Fourier transform transform results. results.

VibrationVibration Amplitude Amplitude Vertical DirectionVertical Direction Lateral Lateral Direction Direction ExperimentExperiment (at 3.8 Hz) (at 3.8 Simulation Hz) Simulation (at 3 Hz) (at Experiment3 Hz) Experiment (at 5.4 Hz) (at 5.4 Simulation Hz) Simulation (at 6 Hz) (at 6 Hz) BogieBogie displacement displacement (mm) (mm) 0.055 0.055 0.115 0.115 0.145 0.145 0.290 0.290 LoadLoad between between bogie bogie and and car body (N) 0.161 0.242 0.382 0.661 0.161 0.242 0.382 0.661 Carcar body body acceleration (N) (m/s2) 0.044 0.048 0.108 0.132 Car body acceleration 0.044 0.048 0.108 0.132 (m/s2) The amplitude discrepancy can be attributed to the absence of a damping element. In the simulation, no damping element was included in the secondary suspension in EquationThe amplitude (5) at an early discrepancy stage, although can be attributed it was recognized to the absence that of damping a damping is element.present in In var- iousthe simulation, parts of the no manufactured damping element reduced-scale was included model. in the secondaryFor example, suspension the friction in Equation in the con- (5)nectors at an and early linear stage, guides although of itthe was actuators recognized can that generate damping damping is present forces in various in the parts secondary of the manufactured reduced-scale model. For example, the friction in the connectors and suspension units. Considering this damping element, Equation (5) should be modified as linear guides of the actuators can generate damping forces in the secondary suspension follows: units. Considering this damping element, Equation (5) should be modified as follows: 𝑚.. 𝑧 =−𝑘()(𝑧 −𝑧) −𝑘()(𝑧 −𝑧)−𝑐() . (𝑧 . −𝑧 )−𝑐() . (𝑧 .−𝑧 ) mczc = −kair(V)1(zc − zb1) − kair(V)2(zc − zb2) − cair(V)1 zc − zb1 − cair(V)2 zc − zb2 .. . . = − − −  + −  mb𝑚1zb1𝑧 k=𝑘air(V())1(zc (𝑧zb−𝑧1) k)lev−𝑘1 zb1 (𝑧zg1−𝑧cair)+𝑐(V())1 zc (𝑧z b1−𝑧 ) (6) (6) ..  . .  mb2zb2 = kair(V)2(zc − zb2) − klev2 zb1 − zg2 + cair(V)2 zc − zb2 𝑚𝑧 =𝑘()(𝑧 −𝑧) −𝑘(𝑧 −𝑧)+𝑐()(𝑧 −𝑧 ) Here, the damping coefficients in the secondary suspension units of Bogie 1 and Bo- Here, the damping coefficients in the secondary suspension units of Bogie 1 and Bo- gie 2 are denoted as cair(V)1 and cair(V)2, respectively. To understand the effect of damping, giethe 2 exact are denoted amount ofas which𝑐() is notand known 𝑐() yet,, respectively. simulations To are understand performed againthe effect based of ondamp- ing,Equation the exact (6).The amount results of arewhich shown is not in Figureknow n10 yet,, which simulations shows the are effect performed of the damping again based onelement Equation on the (6). vibration The results amplitude. are shown Because in Figu there 10, exact which value shows of the the damping effect of coefficient the damping elementis unknown, on the the vibration percentage amplitude. of the stiffness Because value th ise exact arbitrarily value assigned. of the damping For example, coefficient 1% is unknown,in the vertical the motion percentage simulation of the impliesstiffness the value usage is ofarbitrarily a damping assigned. coefficient For of example, 125 Ns/m, 1% in whichthe vertical is 1% ofmotion the stiffness simulation value implies (12,500 N/m).the usage The of simulation a damping results coefficient indicate of that 125 the Ns/m, whichdamping is element1% of the decreases stiffness the value vibration (12,500 amplitude. N/m). The Therefore, simulation it can results be inferred indicate that that the the damping elementelement present decreases in the the secondary vibration suspension amplitude. unit Therefore, of the reduced-scale it can be inferred model that has the dampingreduced the element vibration present amplitude in the in secondary the experiments. suspension unit of the reduced-scale model has reduced the vibration amplitude in the experiments.

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Energies 2021, 14, x FOR PEER REVIEW 11 of 13 Energies 2021, 14, 3883 11 of 13

(a) (b) Figure 10. Effect of damping element on the vibration amplitude: (a) vertical direction, (b) lateral direction.

We now consider another source that causes the difference between the simulations

and experiments. The force measured by the load cell in the reduced-scale model did not (a) (b) reflect the exact amount of force between the bogie and the car body. Owing to the loss Figure 10. Effect of dampingcaused by element the friction on the vibration in the secondary amplitude: suspension (a) vertical direction, unit, a force ((b)) laterallateral smaller direction.direction. than the actual force between the bogie and the car body is transferred to the load cell, which results in an unexpectedWe now consider dynamic another response. source Figure that 11 causescaus showses the the difference experimental betweenbetween results the focusing simulationssimulations on theand effect experiments. of the load The cell force value measured on the peak by the frequency load cell response. in the reduced-scale Here, 0% implies model equiva- did not lencereflectreflect to the the exact value amount measured of force(red) betweenby the load the cell, bogie whereas and the 30% car and body. 60% Owing indicate to the val- lossloss uescaused deliberately by the friction increased in the by secondary30% and 60% suspension from the unit,original a force value, smaller respectively. than the The actualactual re- sultsforce for betweenbetween vertical thethe motions bogiebogie and andshow the the that car car the body body larger is is transferred trtheansferred load cell to to theforce, the load load the cell, lower cell, which which is the results vibrationresults in anin frequencyanunexpected unexpected (i.e., dynamic fromdynamic 3.8 response. Hzresponse. to 3.67 Figure FigureHz); 11 this shows11 renders shows the the experimentalthe experimentalexperimental results resultsand focusing simulation focusing on there-on sultstheeffect effect comparable. of the of loadthe load cell For cell value lateral value on motion, the on peakthe apeak frequencylarger frequency load response. cell response. value Here, leads Here, 0% to implies 0%a higher implies equivalence vibration equiva- frequencylenceto the to value the (i.e., value measured from measured 5.4 (red)Hz to (red) by 5.53 the by Hz). load the load cell, cell, whereas whereas 30% 30% and and 60% 60% indicate indicate the the values val- uesdeliberately deliberatelyUnlike simulations, increased increased by friction 30%by 30% and as and 60%a damping 60% from from the element originalthe original cannot value, value, be respectively. ignored, respectively. and The it reduces The results re- thesultsfor force vertical for verticalexerted motions motionson the show secondary show that that the suspension the larger larger the theunit load load in cell the cell force,developed force, the the lower reduced-scalelower is is thethe vibrationvibration model. Consequently,frequency (i.e., (i.e., anfrom from outcome 3.8 3.8 Hz Hz toquite to 3.67 3.67 different Hz); Hz); this this fromrenders renders the the initial the experimental experimental expected andresponse and simulation simulation was ob- re- tained.sultsresults comparable. comparable. For For lateral lateral motion, motion, a alarger larger load load cell cell value value leads leads to to a higher vibration frequency (i.e., from 5.4 Hz to 5.535.53 Hz).Hz). Unlike simulations, friction as a damping element cannot be ignored, and it reduces the force exerted on the secondary suspension unit in the developed reduced-scale model. Consequently, an outcome quite different from the initial expected response was ob- tained.

(a) (b)

FigureFigure 11. EffectEffect of of load load cell cell value value on vibration frequency: ( aa)) vertical vertical direction, direction, ( b) lateral direction.

4. ConclusionsUnlike simulations, friction as a damping element cannot be ignored, and it reduces the force exerted on the secondary suspension unit in the developed reduced-scale model. (aIn) this study, a 1/10 reduced-scale model, based on(b )the dynamic similarity law, was developedConsequently, for the an outcomedynamic quitecharacteristic different invest from theigation initial of expectedthe Hyperloop response vehicle. was obtained.Both the Figure 11. Effect of load cell value on vibration frequency: (a) vertical direction, (b) lateral direction. 4. Conclusions 4. ConclusionsIn this study, a 1/10 reduced-scale model, based on the dynamic similarity law, was developed for the dynamic characteristic investigation of the Hyperloop vehicle. Both In this study, a 1/10 reduced-scale model, based on the dynamic similarity law, was developedthe vertical for and the lateral dynamic motions characteristic were successfully investigation realized of the Hyperloop by virtue of vehicle. the secondary Both the suspensions of the model allowing biaxial motion. The Stewart platform, driven by

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powerful linear electromagnetic actuators, was used to accurately realize the bogie motion, reflecting the external disturbance, SC-EDS characteristics, and the interaction between the bogie and the car body. Through the experiment and simulation, it was confirmed that the actual bogie motion was realized, and the complete dynamic characteristics were successfully represented by the developed model. It was also found that the friction existing in various parts of the model plays a significant role, leading to differences in the dynamic responses between the simulation and experiment. In future studies, the dynamic characteristics under various driving conditions will be investigated using this model. Furthermore, an experiment on the active actuator control will be conducted to improve the ride comfort of the car body to reduce the harmfulness to the human body.

Author Contributions: Conceptualization, J.L. (Jinho Lee) and W.Y.; methodology, J.L. (Jinho Lee) and W.Y.; software, J.L. (Jinho Lee) and J.L. (Jungyoul Lim); validation, J.L. (Jinho Leeand) and J.-Y.L.; formal analysis, J.L. (Jinho Lee) and J.L. (Jungyoul Lim); writing—original draft preparation, J.L. (Jinho Lee), J.-Y.L.; writing—review and editing, J.L. (Jinho Lee) and J.-Y.L.; visualization, J.L. (Jinho Lee); supervision, J.L. (Jinho Lee) and W.Y.; project administration, K.-S.L.; funding acquisition, K.-S.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by a grant from the R&D Program of the Korea Railroad Research Institute, Korea. Conflicts of Interest: The authors declare no conflict of interest.

References 1. Hyperloop Alpha. Available online: https://www.tesla.com/sites/default/files/blog_images/hyperloop-alpha.pdf (accessed on 30 April 2021). 2. Van Goeverden, K.; Milakis, D.; Janic, M.; Konings, R. Performances of the HL (Hyperloop) transport system. In Proceedings of the 2017 BIVEC-GIBET Transport Research Days, Liège, Belgium, 18–19 May 2017; pp. 29–43. 3. Deng, Z.G.; Zhang, Y.; Wang, B. Present situation and prospect of evacuated tube transportation system. J. Southwest Jiaotong Univ. 2019, 54, 1063–1072. 4. Stryhunivska, O.; Gdowska, K.; Rumin, R. A Concept of Integration of a Vactrain Underground Station with the Solidarity Transport Hub Poland. Energies 2020, 13, 5737. [CrossRef] 5. Stryhunivska, O.; Gdowska, K.; Rumin, R. Key Points of the Management System for the Safety of Passengers Travelling with Low-Pressure Trains. New Trends Prod. Eng. 2020, 3, 462–471. [CrossRef] 6. Gkoumas, K.; Christou, M. A Triple-Helix Approach for the Assessment of Hyperloop Potential in Europe. Sustainability 2020, 12, 7868. [CrossRef] 7. One Website. Available online: https://virginhyperloop.com (accessed on 30 April 2021). 8. Hyperloop Transportation Technologies Website. Available online: https://www.hyperlooptt.com (accessed on 30 April 2021). 9. Zhang, Y. Numerical simulation and analysis of aerodynamic drag on a subsonic in evacuated tube transportation. J. Mod. Transp. 2012, 20, 44–48. [CrossRef] 10. Oh, J.-S.; Kang, T.; Ham, S.; Lee, K.-S.; Jang, Y.-J.; Ryou, H.-S.; Ryu, J. Numerical analysis of aerodynamic characteristics of Hyperloop system. Energies 2019, 12, 518. [CrossRef] 11. Guo, Z.; Zhou, D.; Chen, Q.; Yu, P.; Li, J. Design and analysis of a plate type electrodynamic suspension structure for ground high speed systems. Symmetry 2019, 11, 1117. [CrossRef] 12. Lim, J.; Lee, C.-Y.; Lee, J.-H.; You, W.; Lee, K.-S.; Choi, S. Design Model of Null-Flux Coil Electrodynamic Suspension for the Hyperloop. Energies 2020, 13, 5075. [CrossRef] 13. Myamlin, S.; Kalivoda, J.; Neduzha, L. Testing of railway vehicles using roller rigs. Procedia Eng. 2017, 187, 688–695. [CrossRef] 14. Jaschinski, A.; Chollet, H.; Iwnicki, S.; Wickens, A.; Würzen, J. The application of roller rigs to railway vehicle dynamics. Veh. Syst. Dyn. 1999, 31, 345–392. [CrossRef] 15. Jaschinski, A. On the Application of Similarity Laws to a Scaled Railway Bogie Model. Ph.D. Thesis, Delft University of Technology, Delft, Netherlands, 1990. 16. Gretzschel, M.; Jaschinski, A. Design of an active wheelset on a scaled roller rig. Veh. Syst. Dyn. 2004, 41, 365–381. [CrossRef] 17. Aceituno, J.F.; Chamorro, R.; García-Vallejo, D.; Escalona, J.L. On the design of a scaled railroad vehicle for the validation of computational models. Mech. Mach. Theory 2017, 115, 60–76. [CrossRef] 18. Zhang, W.; Chen, J.; Wu, X.; Jin, X. Wheel/rail adhesion and analysis by using full scale roller rig. Wear 2002, 253, 82–88. [CrossRef] 19. Suzuki, E.; Watanabe, K.; Hoshino, H.; Yonezu, T.; Nagai, M. A study of maglev vehicle dynamics using a reduced-scale vehicle model experiment apparatus. J. Mech. Syst. Transp. Logist. 2010, 3, 196–205. [CrossRef] Energies 2021, 14, 3883 13 of 13

20. Lee, J.-H.; You, W.-H.; Lee, K. Development of the Small Scale Testbed for Running Dynamic Characteristics Analysis of the Capsule Train. J. Korea Acad. Ind. Coop. Soc. 2020, 21, 643–651. 21. Lee, C.-Y.; Lee, J.-H.; Lim, J.; Choi, S.; Jo, J.-M.; Lee, K.-S.; Chung, Y.D.; Kim, S.; Lee, H. Design and evaluation of prototype high-tc superconducting linear synchronous motor for high-speed transportation. IEEE Trans. Appl. Supercond. 2020, 30, 3602205. [CrossRef] 22. Mun, J.; Lee, C.; Kim, K.; Sim, K.; Kim, S. Operating thermal characteristics of REBCO magnet for maglev train using detachable cooling system. IEEE Trans. Appl. Supercond. 2019, 29, 3603305. [CrossRef] 23. Lim, J.; Lee, C.-Y.; Choi, S.; Lee, J.-H.; Lee, K.-S. Design optimization of a 2G HTS magnet for subsonic transportation. IEEE Trans. Appl. Supercond. 2020, 30, 5203305. [CrossRef] 24. Choi, S.Y.; Lee, C.Y.; Jo, J.M.; Choe, J.H.; Oh, Y.J.; Lee, K.S.; Lim, J.Y. Sub-sonic linear synchronous motors using superconducting magnets for the Hyperloop. Energies 2019, 12, 4611. [CrossRef] 25. Lee, J.-H.; Lee, C.-Y.; Jo, J.-M.; Lim, J.; Choe, J.; Sun, Y.; Lee, K.-S. Analysis of the influence of magnetic stiffness on running stability in a high-speed train propelled by a superconducting linear synchronous motor. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit 2019, 233, 170–186. [CrossRef] 26. Kisilowski, J.; Kowalik, R. Displacements of the Levitation Systems in the Vehicle Hyperloop. Energies 2020, 13, 6595. [CrossRef] 27. Ohashi, S.; Ohsaki, H.; Masada, E. Equivalent model of the side wall electrodynamic suspension system. Electr. Eng. Jpn. 1998, 124, 63–73. [CrossRef] 28. Watanabe, K.; Yoshioka, H.; Suzuki, E.; Tohtake, T.; Nagai, M. A Study of Vibration Control Systems for Superconducting Maglev Vehicles (Vibration Control of Lateral and Rolling Motions). J. Syst. Des. Dyn. 2007, 1, 593–604. 29. Hoshino, H.; Suzuki, E.; Watanabe, K. Reduction of vibrations in Maglev vehicles using active primary and secondary suspension control. Q. Rep. Railw. Tech. Res. Inst. (RTRI) 2009, 49, 113–118. [CrossRef] 30. Huang, C.I.; Chang, C.F.; Yu, M.Y.; Fu, L.C. Sliding-mode tracking control of the Stewart platform. In Proceedings of the 2004 5th Asian Control Conference (IEEE Cat. No. 04EX904), Melbourne, VIC, Australia, 20–23 July 2004; Volume 1, pp. 562–569. 31. Claus, H.; Schiehlen, W. Modeling and simulation of railway bogie structural vibrations. Veh. Syst. Dyn. 1998, 29, 538–552. [CrossRef] 32. Furukawa, A.; Hashimoto, S. Power Spectrum Density of MAGLEV Guideway Irregularity and Riding Quality Level. RTRI Rep. 1993, 7, 11–18.