Comparison of Methods to Reduce Vibrations in Superconducting Maglev Vehicles b Primar Suspension Control* Erimitsu SUZUKI **, Jun SHIRASAKI ***, Ken WATANABE **, Hironori HOSHINO **, and Masao NAGAI *** **Electromagnetic Applications Laborator, Maglev Sstems Technolog Division, Railwa Technical Research Institute, -8-8 Hikari-cho, Kokubunji-shi, Toko, 185-854, Japan E-mail: esuuki@rtri.or.jp ***Department of Mechanical Sstems Engineering, Toko Universit of Agriculture and Technolog -4-16 Naka-cho, Koganei-shi, Toko, 184-8588, Japan Abstract The vehicles of the superconducting magneticall levitated transport (Maglev) sstem travel at high speeds of over 5 km/h. These vehicles are composed of lightweight car bodies and relativel heav bogies which are mounted with devices such as superconducting magnets (SCMs) and an onboard refrigerating sstem. The lightweight structure of the car bodies result in vibrations at relativel high frequencies, and are believed to be influencing the ride comfort. Furthermore, the passive electromagnetic damping is ver small in the primar suspension between the SCMs installed on the bogies and the ground coils installed on the guidewa. Therefore, it is effective to add active electromagnetic damping to this primar suspension. A linear generator device that is incorporated into an eisting bogie of the Maglev sstem generates onboard power and can also generate additional electromagnetic forces that can be used in the control of the primar suspension. This device has been demonstrated in full-scale vehicle eperiments to effectivel appl electromagnetic damping directl to the primar suspension, and reduce vibrations of relativel higher frequencies that are otherwise difficult to reduce b controlling onl the secondar suspension. Computations using a Maglev vehicle model eamine the effectiveness of reducing vibrations b appling this primar suspension control. Ke words: Railwa, Vibration Control, Electromagneticall Induced Vibration 1. Introduction *Received 1 Aug., 7 (No. 7-45) [DOI: 1.199/jmtl.1.] In the superconducting magneticall levitated transport (Maglev) sstem, passive damping resulting from electromagnetic interactions in the primar suspension between the bogie and guidewa is ver small. Vibration control of the primar suspension using forces output b a linear generator sstem integrated into the bogie (bogie-integrated linear generator) which is one method of generating onboard power has been proposed. Full-scale vehicle running tests have confirmed that this linear generator sstem can effectivel reduce vibrations of relativel high frequencies that are difficult to reduce b conventional methods of controlling onl the secondar suspension. (1) This paper presents a stud of the effectiveness of appling vibration control of the primar suspension in reducing vehicle vibrations. ()
Propulsion coil Levitation/guidance coil Car bod Superconducting magnet coil Linear generator coil Levitation/guidance coil Propulsion coil Bogie Guidewa Bogies (a) Guidewa (b) Fig. 1 Overview of the superconducting Maglev sstem. Overview of the superconducting Maglev sstem and vibration control using electromagnetic forces output b the bogie-integrated linear generator device As shown in the schematic diagrams of the superconducting Maglev sstem in Fig. 1, the vehicle is equipped with superconducting magnet (SCM) coils and linear generator coils on the left and right sides of each bogie. Levitation/guidance coils and propulsion coils are installed along the sidewalls of a concrete guidewa. The vehicle travels on this guidewa at high speeds of over 5 km/h. For purposes of eplanation, the coils of onl the right side of the vehicle and guidewa marked b the rectangular frame in the cross-sectional diagram of Fig. 1b are represented in Fig., though the same concepts appl smmetricall to the left side of the sstem. As shown in Fig. a, each SCM coil on the vehicle bogie forms a single oblong loop, while each levitation/guidance coil on the guidewa sidewall forms two loops in the shape of a figure eight. Each onboard SCM coil which carries large persistent electrical current passes b at a high speed, and induces electrical current in each levitation/guidance coil. Because of the figure-eight shape of the levitation/guidance coil, the induced current flows clockwise in the upper loop and counter-clockwise in the lower loop. The resulting electromagnetic interactions between the coils are shown in Fig. b, characteried b attractive force in the upper half and repulsive force in the lower half. Recalling that this principle also applies smmetricall to the left side of the vehicle, the resulting forces maintain the levitation of the vehicle. The guidance function of null-flu cables (not shown in the figures) under the guidewa, connecting each pair of levitation/guidance coils on the left and right sidewalls, ensure lateral centering of the vehicle. In the Maglev bogie-integrated linear generator device, linear generator coils are attached to the outer vessel surface of the SCM, and generate power in the traveling vehicle using the harmonic magnetic fields in the levitation/guidance coils. This device can also be used to generate additional electromagnetic forces in the primar suspension to be used as control forces in reducing vehicle vibrations. The principles of additional electromagnetic forces output b the linear generator are shown in Figs. and 4. The equivalent configuration of the linear generator coil for the function of generating additional forces is epressed in Fig. a. Electrical current of amplitudes much smaller than that in the SCM Levitation/guidance coil Attractive force Superconducting magnet coil Repulsive force (a) Fig. Principles of levitation (b) 4
Equivalent linear generator coil Superconducting magnet coil attractive force induced current repulsive force Levitation/guidance coil (a) (b) (c) Fig. Principles of additional upward force acting on the bogie, generated b linear generator coils and used for vibration control Equivalent linear generator coil Superconducting magnet coil (a) Fig. 4 Principles of additional downward force acting on the bogie, generated b linear generator coils and used for vibration control coil is run through the linear generator coils. The resulting change in magnetic flu causes the alread eisting current in the levitation/guidance coil to increase slightl, indicated b the wide circular arrows in Figs. a and b. These additional currents generate additional forces indicated b the smaller additional arrows in Fig. c, resulting in an additional upward force acting on the bogie. Likewise, additional downward force acting on the bogie can be generated b reversing the direction of the current flowing in the linear generator coil, as shown in Fig. 4. B varing the amplitude and direction of the current in the linear generator coils according to the vertical motion of the vehicle bogie, this device can be used to control vertical vehicle vibrations. This method has the advantage of requiring no additional sstems solel for the purpose of generating electromagnetic forces. Furthermore, because the magnetic force is generated electricall, this method has minimal dela in response for high frequenc ranges of vibration, in comparison to conventional methods using hdraulic or pneumatic sstems. (1) Full-scale vehicle running tests on the Yamanashi Maglev Test Line confirmed the principles of magnetic forces output b the bogie-integrated linear generator device in the Japanese fiscal ear 1. (4) Vehicle running tests then confirmed the abilit of the linear generator device to control vibrations using the generated forces in the fiscal ear 4. (5). Computation model induced current Levitation/guidance coil (b) repulsive force attractive force This paper focuses on vibration control of an intermediate car bod in a train set. Considering the possibilit of vibrations of adjacent car bodies being transmitted through the articulated bogies, a structure consisting of three car bodies was used in the computation model. (6) The model of the articulated vehicle consisting of three car bodies and four bogies used in the computations is shown in Fig. 5. For simplicit, the car bodies and bogies were considered to be rigid. The car bodies were connected to the bogies using air springs and dampers to form the secondar suspension. In the primar suspension, the magnetic springs of the vertical and pitching directions were modeled using two linear vertical springs per bogie, one in the front and one in the rear of each bogie. The magnetic spring constants corresponding to the coupling of the (c) 5
Car bod No. 1 Car bod No. Car bod No. c1, c1 Air spring Damper Secondar supension lac c, c c, c b1, b1 1f 1r Bogie No. 1 Primar suspension Magnetic spring f b, b lab lmb r f Bogie No. Bogie No. b, b Fig. 5 Computation model r Electromagnetic damping b4, b4 4f 4r Bogie No. 4 vertical and pitching motions are ver small therefore omitted. In the primar suspension control model, the forces output b the bogie-integrated linear generator were used in Bogies No. and as damping forces in the vibration control. The aforementioned magnetic forces output b the linear generator were assumed to be ideal, and delas in responses were not considered. Furthermore, these magnetic forces of the linear generator are assumed to be equall distributed along the length of the bogie surface, such that the force at an longitudinal position on the bogie surface is of the same magnitude and same direction at an given time. For eample, if an upward control force acts on the front end of a bogie at a given instance in time, an upward force of equal magnitude simultaneousl acts on the rear end. Therefore, this force is assumed to have no influence on the bogie pitching motion. In the computation model, an equivalent vertical control force was concentrated on one point on each bogie at the center of mass of Bogies No. and. Although the force onl controls the vertical motion, the pitching vibrations are epected to be much smaller than the vertical vibrations in the passive case, making vertical control a priorit. Eternal disturbance is presented b irregularities in the alignment of coils on the sidewalls of the guidewa, considered onl for the vertical offsets in this paper (guidewa vertical irregularities). The irregularities were input at two points, one at the front and one at the rear, of each bogie. Aerodnamic influences were neglected. 4. Dnamic equations Dnamic equations were derived for the passive case of the model in Fig. 5. The major smbols used in the equations are defined in Table 1. Four air springs and four dampers are Table 1 Variable bi, (i = 1,,, 4): ci, (i = 1,, ): bi, (i = 1,,, 4): ci, (i = 1,, ): if, ir, (i = 1,,, 4): m b, m c : I b, I c : k : c : k m : k m : l ab, l ac : l mb : Variables used in the computation model Definition Bogie vertical displacements Car bod vertical displacements Bogie pitching angular displacements Car bod pitching angular displacements Guidewa vertical irregularities Masses of the bogie and car bod Pitching moments of inertia Vertical stiffness of a pair of air springs Vertical damping coefficient Vertical stiffness of magnetic springs per bogie Pitching stiffness of magnetic springs per bogie Half the distance between the front and rear air springs on the bogie and car bod Half the distance between the front and rear magnetic springs on the bogie 6
installed on each bogie. The subscripts b and c denote the bogie and car bod, respectivel, and the numbers immediatel following these subscripts denote the numbers of the bogies and car bodies. The guidewa vertical irregularities at the front of Bogie No. 1 are denoted b 1f and at the rear of Bogie No. 4 b 4r, as shown in Fig. 5. The magnetic spring constants are the values for a Maglev vehicle traveling at 5 km/h. The spring constants of the magnetic springs k mij have been derived from forces and moments acting in the i direction resulting from translational and angular displacements in the j direction. The attachment heights are based on measurements from mass centers of the car bod and bogie. The vehicle specifications from Watanabe et al. (6) was used in the computation model, and the values of the parameters used are shown in Table. Table Values of parameters used in the computation model Parameter Value Parameter Value m b : 6. 1 [kg] m c : 14. 1 [kg] I b : 1. 1 [kg m ] I c : 8. 1 4 [kg m ] k :. 1 5 [N/m] c : 5. 1 [Ns/m] k m : 4.7 1 6 [N/m] k m : 1. 1 7 [N/rad] l ab :. [m] l ac : 8.8 [m] l mb :. [m] Using the aforementioned smbols, dnamic equations of the passive model are epressed as follows: Bogie No. 1 vertical motion { ( ) ( ) ( ) ( ) m + k + l + l b b1 b1 c1 ab ac c1 { 1 1 1 km {( b 1 1f ) ( b 1 1 r) + c + l + l (1) b c ab ac c = + Bogie No. 1 pitching motion ( ) ( ) I + k l + c l b b1 ab b1 c1 ab b1 c1 k m 1 f 1r = b1+ + b1 lmb lmb Bogie No. vertical motion {( ) ( ) ( ) m + k + + l b b b c1 b c ac c c1 {( ) ( ) ( 1 1) km {( b f ) ( b r) + c + + l () b c b c ac c c = + Bogie No. pitching motion {( ) ( ) ( ) I + k l + l + l + l + l b b ab c1 c ab b ac c1 ab b ac c {( ) ( 1 1) ( ) + c l + l + l + l + l (4) ab c c ab b ac c ab b ac c k m f r = b + + b lmb lmb () 7
Bogie No. vertical motion m + k + + l {( ) ( ) ( ) b b b c b c ac c c {( ) ( ) ( ) km {( b f ) ( b r) b c b c ac c c = + + c + + l (5) Bogie No. pitching motion {( ) ( ) ( ) I + k l + l + l + l + l b b ab c c ab b ac c ab b ac c {( ) ( ) ( ) + c l + l + l + l + l (6) ab c c ab b ac c ab b ac c k m f r = b+ + b lmb lmb Bogie No. 4 vertical motion { ( ) ( ) ( ) ( ) m + k l + l b b4 b4 c ab ac c { 4 km {( b4 4 f ) ( b4 4r) + c l + l (7) b c ab ac c = + Bogie No. 4 pitching motion ( ) ( ) I + k l + c l b b4 ab b4 c ab b4 c k m 4 f 4r = b4 + + b4 lmb lmb (8) Car bod No. 1 vertical motion { ( ) ( ) ( ) m + k + + l l c c1 c1 b1 c1 b ab b c1 ac c1 { ( ) ( 1 1 1 ) ( 1) 1 + c + + l l = c b c b ab b c ac c Car bod No. 1 pitching motion { ( )( ) ( ) I + k l + l l + c c1 ab ac c1 b1 ac b1 b { ( ) ( ) ( ) + l + l l + + l l + l ac c1 b1 ab ac c1 b ab ac ac c1 ( )( ) ( ) + c l + l l + ab ac c1 b1 ac b1 b Car bod No. vertical motion ( 1 1) ( 1 ) ( ) + l + l l + ac c b ab ac c b {( ) ( ) ( ) m + k + + l + c c c1 b c1 b ab b b {( ) ( ) ( ) + c + + l + = c1 b c1 b ab b b Car bod No. pitching motion ab ac ac c1 + l l + l = {( ) ( ) ( ) I + k l + l + l + l + l c c ac b1 b ab b1 ac c ab b ac c {( ) ( ) ( ) + c l + l + l + l + l = ac b1 b ab b1 ac c ab b ac c (9) (1) (11) (1) 8
Car bod No. vertical motion m + k + + l + l { ( ) ( ) ( ) c c c b4 c b ab c b ac c { ( ) ( 4 ) ( ) + c + + l + l = c b c b ab c b ac c Car bod No. pitching motion { ( )( ) ( ) I + k l + l l + c c ab ac c b4 ac b4 b { ( ) ( ) ( ) + l + l l + + l l + l ac c b4 ab ac c b ab ac ac c ( )( ) ( ) + c l + l l + ab ac c b4 ac b4 b ( 4) ( ) ( l ) + l + l l + + l l ac c b ab ac c b ab 5. Design of the primar suspension control ac ac c + = Control of the primar suspension using vertical forces output b the bogie-integrated linear generator was considered, and control methods were eamined as described below. 5.1 Proportional force control In the proportional force control method, the control force is varied in proportion to the bogie vertical velocit, such that a constant damping coefficient value is maintained as epressed in Eq. 15. Fm = Cdamp b (15) (1) (14) Here, F m represents the control force and C damp the damping coefficient. The computations assume that the bogie vertical velocit b which is the control feedback variable is derived b using accelerometers to measure the acceleration of the vertical vibration of the bogie, then integrating this acceleration to derive the absolute velocit. Equation 15 was added to the dnamic equations of the vertical motions of Bogies No. and (Eqs. and 5). The computations assumed that the control force of each bogie could be applied independentl of each other. 5. Maimum force control In the maimum force control method, in order to full utilie the generated force, the maimum possible force output b the linear generator device is used at all times, with the polarit of the force switched according to the polarit of the bogie vertical velocit as epressed in Eq. 16. (7) ( ) F = sign f (16) m b m Here, F m represents the control force and f m the maimum possible vertical force output b the linear generator device. Equation 16 was added to the dnamic equations of the vertical motions of Bogies No. and (Eqs. and 5). As in the case of the proportional force control method, the computations again assumed that the control force of each bogie could be applied independentl of each other. 6. Computation results and comparison of the effectiveness of the control methods Because the maimum force control approach is non-linear, the effectiveness of the control depends on the amplitude of the eternal disturbance, and it is difficult to evaluate 9
1 1 1 1 1-1 1 - m]1 Guidewa irregularit PSD, S(k) [(mm ) S(k) =. k -1.8 1-1 - 1-1 1 Wave number, k [1/m] Fig. 6 Power spectral densit of vertical irregularities in the alignment of coils on the sidewalls of a Maglev guidewa used in the time-domain simulations this control method directl b frequenc response. Therefore, time-domain simulations were performed using time-domain input of eternal disturbance, and the aforementioned two methods were compared in terms of their effectiveness in controlling vibrations. (8) The eternal disturbance modeling the influence of the guidewa vertical irregularities of the ground coil alignment was derived from a variation of Watanabe et al., (9) based on the power spectral densit (PSD) of the straight line shown in Fig. 6, and generated using a random number function to result in the PSD characteristics of the plot beneath this line. Results of a time-domain simulation of the maimum force control are shown in Fig. 7. In this computation, the vertical force f m of Eq. 16 was set to 4 kn, and applied to Bogies No. and. The car bod vertical acceleration for the case without control is characteried b a fundamental wave with a frequenc of about 1 H, on to which another wave with a higher frequenc of about 5 H is superimposed. The graph shows that the vibration control greatl reduced the amplitude of the higher frequenc vibrations, such that mainl onl the fundamental wave remains in the case with control. The amplitudes of the higher frequenc vibrations of the bogie vertical acceleration and velocit were also greatl reduced. In the case of the maimum force control, high frequenc waves with etremel small amplitudes that are visible in the bogie vertical velocit result in high frequenc square waves in the control force. Therefore, techniques such as robust filter processing are necessar when appling the control to full-scale vehicles. [m/s] [m/s ] [m/s ] [kn].5 -.5 1-1.5 -.5 5 Car Bod No., vertical acceleration Bogie No., vertical acceleration Bogie No., vertical velocit [mm] -5 5 Bogie No., vertical control force -5 1 sec. Guidewa coil alignment irregularities Without control With control Fig. 7 Time-domain simulation results of maimum force control (4 kn) of the primar suspension of Bogies No. and 1
Car bod vertical acceleration PSD [(m/s ) /H] 1 1-1 1-1 - 1-4 Proportional force control Without control With control 1-1 1 1 1 1 Frequenc [H] Fig. 8 Power spectral densit of Car bod No. vertical acceleration with proportional force control ( kn s/m, 4 kn ma.) of the primar suspension of Bogies No. and Car bod vertical acceleration PSD [(m/s ) /H] 1 1-1 1-1 - Without control With control 1-1 1 1 1 1 Frequenc [H] 1-4 Maimum force control Fig. 9 Power spectral densit of Car bod No. vertical acceleration with maimum force control (4 kn) of the primar suspension of Bogies No. and 6.1 Proportional force control Results of computations of the vertical acceleration PSD for Car bod No. are shown in Fig. 8, for the case of proportional force control applied to the primar suspension of both Bogies No. and. Based on Watanabe et al. (), the control force was designated with C damp = [kn s/m] in Eq. 15. With this value of C damp, the maimum value of the resulting control force F m is about 4 kn. Two large peaks of acceleration are visible in this figure. The peak at about 1 H originates from the car bod vertical and pitching motions, and the peak at about 5 H from the bogie vertical rigid bod motions. Appling the proportional force control to the primar suspension reduces the acceleration peak at about 5 H to about one-fourth of the case without control, confirming the effectiveness of the vibration control method. Because the secondar suspension is not controlled, there is no reduction of the peak at about 1 H. 6. Maimum force control Guidewa vertical irregularities were input similarl to the method described in the previous section, and the effective of maimum force control was eamined b time-domain response. The vertical generated force f m in Eq. 16 was set to 4 kn, and applied to both Bogies No. and. Results are shown in Fig. 9. The application of this control method, the peak at about 5 H originating from the bogie motions was reduced to about one-ninth of the case without control. 6. Comparison of the effectiveness of the control methods The maimum force control method was found to be more than twice as effective as the proportional force control method in terms of reducing the peak at about 5 H originating from the bogie motions. Neither method had much effect on reducing the peak at about 1 H originating from the car bod motions, but the maimum force control method was slightl more effective than the proportional force control method. A maimum generated force of about 4 kn was eamined up until the previous section, but much larger generated forces are assumed to be possible in this section for the purpose of comparing the 11
Normalied RMS car bod_ vertical acceleration [db] - -4-6 -8 Proportional force control Maimum force control 4 1 Control force [kn] Fig. 1 Normalied RMS values of the Car bod No. vertical acceleration PSD in the control of the primar suspension of Bogies No. and effectiveness of the two methods in controlling vibrations. The root-mean-squared (RMS) values of the Car bod No. vertical acceleration PSD were computed using the aforementioned guidewa vertical irregularities. The RMS values of the acceleration PSD normalied with respect to the case without control are shown in Fig. 1 for the two control methods. The RMS values of the car bod vertical acceleration PSD of the maimum force control are smaller than that of the proportional force control when the maimum generated force is smaller than kn, demonstrating the effectiveness of the vibration control. Furthermore, the difference between the RMS values of the proportional and maimum force control methods is the largest when the maimum generated force is about 4 kn, with a difference of about db. For the same limit of maimum generated force, the maimum force control is naturall more effective for reasonabl small values of maimum generated force below the crossing point at kn, since the method utilies the maimum possible force output b the linear generator device at all times, while the proportional force control utilies onl a fraction of the maimum possible force in proportion to the magnitude of the bogie vertical velocit for a majorit of the time. When the maimum generated force is about kn in the proportional force control method, the damping coefficient C damp in Eq. 15 would be about.5 [MN s/m]. However, such a large coefficient is not realisticall possible, considering that the corresponding damping coefficient for the 1-series Shinkansen has a value on the order of.1 [MN s/m]. Nevertheless, these large values were used in the computations for the purpose of investigation. 7. Conclusions A Maglev vehicle model of the vertical and pitching motions was used to eamine the effectiveness of controlling vibrations originating from the primar suspension. When the maimum generated force is particularl limited, the maimum force control method is more effective in reducing vibrations than the proportional force control method. Considering that the maimum generated force possible in the currentl eisting sstem is about 4 kn, selecting the maimum force control method was confirmed to have a larger 1
influence in controlling vibrations. Current plans for future work include studies of primar suspension control methods with improved precision of computations more closel modeling actual situations, considering details such as delas in response and car bod bending vibration. Acknowledgment The authors would like to epress their sincere gratitude to Mr. Takauki Kashiwagi and Mr. Yasuaki Sakamoto, for their indispensable suggestions regarding the tet and figures eplaining the principles of vibration control using the linear generator device. References (1) Erimitsu Suuki and Ken Watanabe, Results of vibration control of a Maglev vehicle utiliing a linear generator, Proceedings of the American Societ of Mechanical Engineers (ASME) 5 International Design Engineering Technical Conferences (IDETC 5), DETC5-8498, 5. () Ken Watanabe, Hironori Hoshino, Erimitsu Suuki, and Hiroshi Yoshioka, Eperimental results of vibration control of Maglev vehicles utiliing forces generated b a distributed-tpe linear generator, 17 th Smposium on Electromagnetics and Dnamics (SEAD 17), 5, pp. 159-16 (in Japanese). () Ken Watanabe, Erimitsu Suuki, Hiroshi Yoshioka, Toshiaki Murai, Takauki Kashiwagi, and Minoru Tanaka, Vibration control of Maglev vehicles utiliing a linear generator, Proceedings of the 18 th International Conference on Magneticall Levitated Sstems and Linear Drives (Maglev 4), Volume 1, 4, pp. 59-549. (4) Hitoshi Hasegawa, Toshiaki Murai, and Takamitsu Yamamoto, Running tests of a combined SC tpe linear generator, Institute of Electrical Engineers of Japan (IEEJ) Transactions on Industr Applications, Volume 1-D(),, pp. 156-16 (in Japanese). (5) Yasuaki Sakamoto, Toshiaki Murai, Takauki Kashiwagi, Minoru Tanaka, Erimitsu Suuki, and Katsua Yamamoto, The development of linear generator sstem combined with magnetic damping function, Institute of Electrical Engineers of Japan (IEEJ) Transactions on Industr Applications, Volume 16-D(), 6, pp. 19-198 (in Japanese). (6) Ken Watanabe, Hiroshi Yoshioka, Erimitsu Suuki, Takauki Tohtake, and Masao Nagai, A stud of vibration control sstems for superconducting Maglev vehicles (vibration control of vertical and pitching motions), Transactions of the Japan Societ of Mechanical Engineers, Volume 71-C(71), 5, pp. 1-18 (in Japanese). (7) Ken Watanabe, Hiroshi Yoshioka, Erimitsu Suuki, Eiji Watanabe, Masao Nagai, and Takauki Tohtake, A stud of combined control of primar and secondar suspension of a Maglev vehicle, 15 th Smposium on Electromagnetics and Dnamics (SEAD 15),, pp. 491-494 (in Japanese). (8) Ken Watanabe, Hiroshi Yoshioka, Erimitsu Suuki, Eiji Watanabe, Masao Nagai, and Takauki Tohtake, A stud of combined control of primar and secondar suspension of a Maglev vehicle, Proceedings of the International Smposium on Speed-up and Service Technolog for Railwa and Maglev Sstem (STECH ),, pp. 467-471. (9) Ken Watanabe, Hiroshi Yoshioka, Eiji Watanabe, Takauki Tohtake, and Masao Nagai, A stud of the vibration control sstem for a superconducting Maglev vehicle, Proceedings of the 6 th International Conference on Motion and Vibration Control (MOVIC ),, pp. 97-91. 1