The authors propose a self-powered active control system that realizes active vibration control using energy regenerated by an energy regenerative damper and does not require external energy. In this study, self-powered active control is applied to an anti-rolling system for ships. The motor is required to act as an energy regenerative damper and an actuator, since the anti-rolling system is composed of one motor. The new control scheme that realizes self-powered active control with a single motor is proposed. Through numerical simulations and experiments using a basic model, the performance of the proposed system is examined. The results indicate that self-powered active control can be achieved in the anti-rolling system.

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In the first report on this subject, a new simulation method for obtaining the transient response of composite fluid line systems, such as gas transport networks, air brake systems, pressure instrument lines and pneumatic control systems, has been presented. This simulation is based on the wave diagram of the fluid line system and Brown’s approximate step response of a semi-infinite line. In this report, two kinds of wave reduction techniques are introduced for the effective computation of the transient response. One is the unification of equivalent and similar waves at any junction of lines from different traveling routes. The other is the elimination of small waves attenuated by the partial reflection and the long propagation distance. For computed response examples using these techniques, the step responses of composite fluid line systems (a loop line system and multiline branching systems) are also presented.

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The rotor vibration of two-pole induction motor with rotating magnetic field has been investigated. The vibration is measured at any relative location of the stator and the rotor with various power supply frequencies in the experiment and is analyzed in consideration of mechanical factors of the rotor. The following conclusion is obtained through the experiment and the analysis; (1) 2ω vibration of twice the power supply frequency ω is generated because of offset between the stator center and the gyrational center of the rotor. (2) Two vibrations of ω(1−s) and ω(1+s) where s is slip ratio are generated because of the rotor unbalance or the disagreement between the gyrational center and geometrical center of the rotor. (3) An unstable vibration is predicted in the analysis when the power supply frequency is equal to natural frequency of the rotor, however, the unstable vibration was not generated in the experiment because of the damping.

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Kinematic analysis and derivation of equations of motion for a mechanism with loops of different motion spaces are developed. First, it is shown that screw coordinates of a joint which expresses relative motion between two links must be expressed by the basis vectors of motion spaces of the loops to which it belongs. Then, it becomes possible to derive the same number of linear equations for joint velocities and accelerations of a loop as the dimension of its motion space, and joint velocities and accelerations can be determined by solving these linear equations. Next, it is described that the force analysis can be performed by expressing the joint wrench as a linear combination of basis vectors of a reciprocal space of a motion space and other linearly independent screw coordinates. Using the developed theorem, the computational scheme for kinematic and force analysis is derived. The method to derive the equations of motion for a mechanism is also clarified.

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This paper proposes a real-time human body posture estimation method using ANNs. The network is composed of three ANNs and a decision logic unit. The ANNs’ input is the result of a function analysis on a human silhouette’s contour extracted from camera images and the ANNs’ output indicates the feature points’ positions on the contour. The decision logic unit synthesizes each of the ANNs’ output vectors and then the 2D coordinates of the human body’s feature points are calculated. The proposed method is implemented on a personal computer and runs in real-time (17-20 frames/sec). Experimental results confirm both the feasibility and the effectiveness of the proposed method for estimating human body postures. By applying the proposed estimation method to a stereo vision system, real-time 3D human body posture estimation can also be achieved.

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In this paper, a neural network-based learning approach for robot impedance control is presented to accomplish a contact task. Firstly, a discrete-time impedance control algorithm is obtained to control the contact task of the robot. Secondly, on-line learning algorithms based on a new evaluation function are developed for the neural networks which adjust the inertia, damping and stiffness parameters of the robot in order to adapt it to the unknown contact environment. Thirdly, experiments are carried out and the effecttiveness of the present approach is verified by pressing a spring using a 6 degrees of freedom robot. The adaptiveness, stability and flexibility of the present approach are also confirmed by the experimental ersults.

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Control system design is discussed for a semi-active suspension system of vehicles. For the disturbance rejection problem, l₁ state feedback controllers are designed. An l₁ controller can specify the maximum magnitude of outputs against certain road disturbances in the time domain, regardless of the frequency of the road disturbances. That property enables a semi-active suspension to be formulated as an unconstrained linear system, while it is usually modeled as a bilinear system or a linear system with a constraint. In this paper, not only a controller for a nominal model, but also a controller considering robust performance is designed. Static nonlinear first order homogeneous state feedback controllers, which require a moderate amount of calculation, are constructed for the linear system by applying l₁ near-optimal control theory with an appropriate approximation method.

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As the automobile engine advances towards higher performance and higher power, the increase in displacement and the number of cylinders in the engine has led to larger engines. As a result, the need for rigidity countermeasures and reductions in size and weight have brought about the switch from in-line type engines to V-type engines. Currently, most of the V-type automobile engines produced have six or eight cylinders, and some large passenger cars produced in Europe and America have V-type engines with 10 or 12 cylinders. The bank angles of engines in these passenger are almost fixed based on the cylinder number. Therefore, the form of the V-type engine is limited according to the number of cylinders. The present study examines the bank angle of a V-12 engine by performing a detailed analysis of the relationship between the cylinder arrangement and the exciting moment. The goal of the present study is to find a bank angle that has as of yet not been applied to the V-type engine so that the layouts of the absorption and exhaust systems, as well as the attached apparatuses, can be reconfigured.

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In this paper, the two-orientation method is applied to the measurement of cross-sectional profiles along concentric circles on a spherical test surface using an interferometer. The influence of form errors along concentric circles on the reference surface of the interferometer can be removed by the combination of the measurement data before and after a rotation operation. Furthermore, the differential output is Fourier transformed and the cross-sectional profiles along concentric circles on the test surface are determined by a phase operation. The influence of random errors of sampling in the interferometer output data and that of the positioning error of angular displacement when rotating the test surface are investigated through simulation. Experimental results using a Fizeau type interferometer (ZyGo GPI-XP) that confirm the effectiveness of this method in improving measurement accuracy are also presented.

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Velocity and tension controls are important factors for the film in the coating machine. In this paper, an experimental coating machine is established to make control analyses. The mathematical model of the coating machine is firstly derived. Then, the sliding mode control (SMC) is used to control the tension and the velocity of the film. Finally, some experimental results are proposed to show the performance of the SMC scheme in the experimental coating machine.

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The paper is to present the detailed dynamic analysis of a vertically vibrating and rotating elliptic tube containing a particle. By subjecting to an external periodic excitation, it has shown that the system exhibits both regular and chaotic motions. By using the Lyapunov direct method and Chetaev’s theorem, the stability and instability of the relative equilibrium position of the particle in the tube can be determined. The center manifold theorem is applied to verify the conditions of stability when system is under the critical case. The effects of the changes of parameters in the system can be found in the bifurcation and parametric diagrams. By applying various numerical results such as phase plane, Poincaré map and power spectrum analysis, a variety of the periodic solutions and the phenomena of the chaotic motion can be presented. Further, chaotic behavior can be verified by using Lyapunov exponents and Lyapunov dimensions.

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Vehicle stability control system is a new idea which can enhance the vehicle stability and handling in the emergency situation. This system requires the information of the yaw rate, sideslip angle and road friction in order to control the traction and braking forces at the individual wheels. This paper proposes an observer for the vehicle stability control system. This observer consisted of the state observer for vehicle motion estimation and the road condition estimator for the identification of the coefficient of the road friction. The state observer uses 2 degrees-of-freedom bicycle model and estimates the system variables based on the Kalman filter. The road condition estimator uses the same vehicle model and identifies the coefficient of the tire-road friction based on the recursive least square method. Both estimators make use of each other information. We show the effectiveness and feasibility of the proposed scheme under various road conditions through computer simulations of a fifteen degree-of-freedom non-linear vehicle model.

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In multi-axis force sensors, compliance matrices representing structural behavior of internal sensor bodies play an important role in decoupled sensing and accuracy. Recently, error propagation through compliance matrices has been studied via approximation approach. However the upper bound of measured force error has not been known. In this paper, error propagation in force sensing is analyzed in a unified way when both strain measurement error and compliance matrix error exist, and the upper bound of the measured force error is derived (not approximately). The validity of the analysis is investigated through a numerical example.

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This paper proposes an output sliding-mode control under three assumptions given to the system matrices and the matching uncertainty. Based on these assumptions, first one important transformation matrix is introduced and then a state-estimator is constructed. The output sliding-mode control is designed when the system state is well estimated. Finally, a numeric example is included to demonstrate the developed controller.

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In this paper we propose a new nonlinear controller design method, called nonlinear quadratic Gaussian/H-infinity/loop transfer recovery (NQG/H_∞/LTR), for nonlinear servo systems with hard nonlinearities such as Coulomb friction, dead-zone. We consider a H_∞ performance constraint for the optimization of statistically linearized systems, by replacing a covariance Lyapunov equation into a modified Riccati equation of which solution leads to an upper bound of the nonlinear quadratic Gaussian (NQG) performance. As a result, the nonlinear correction term is included in coupled Riccati equation, which is generally very difficult to have a numerical solution. To solve this problem, we use the modified loop shaping technique and show some analytic proofs on LTR condition. Finally, the NQG/H_∞/LTR controller is synthesized by inverse random input describing function techniques (IRIDF). It is shown that the proposed design method has a better performance robustness to the hard nonlinearity than the LQG/H_∞/LTR method via simulations and experiments for the timing-belt driving servo system that contains the Coulomb friction and dead-zone.

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In this paper, a robust integrated control for engine and automatic transmission systems is investigated. The modeling of powertrain system is split into five subparts including an engine, a torque converter, an automatic transmission, clutch torque generation, and a drivetrain. For improving the ride quality, a two-stage control strategy, torque phase and inertia phase, is proposed. During the torque phase, the slip in first gear is maintained to near zero, while the reaction carrier speed and turbine speed during the inertia phase are controlled to track their desired speeds. The reaction carrier speed is adjusted by the second clutch torque, and the turbine speed is controlled by engine throttle angle and spark advance. Due to the uncertainty and unmodelled dynamics of the system, the uniform ultimate boundedness of the error signals is assured by applying the Lyapunov stability analysis. Simulation results are provided.

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In this paper, a robust model reference adaptive control of a radiative heat equation with unknown time-varying coefficients and spatiotemporally varying disturbance is investigated. In the adaptive control of time-varying plants, the derivative of a Lyapunov function candidate, which allows the derivation of adaptation laws, is not negative semi-definite in general. Under the assumption that the disturbance is uniformly bounded, the proposed robust adaptive scheme guarantees the boundedness of all signals in the closed loop system and the convergence of the state error near to zero. With an additional persistence of excitation condition, the parameter estimation errors are shown to converge near to zero as well. Simulation results are provided.

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The chip regeneration mechanism during chatter is influenced by vibrations in three directions when milling cutters with ball end, bull nose, or inclined cutting edges are used. A three dimensional chatter stability is modeled analytically in this article. The dynamic milling system is formulated as a function of cutter geometry, the frequency response of the machine tool structure at the cutting zone in three Cartesian directions, cutter engagement conditions and material property. The dynamic milling system with nonlinearities and periodic delayed differential equations is reduced to a three dimensional linear stability problem by approximations based on the physics of milling. The chatter stability lobes are predicted in the frequency domain using the proposed analytical solution, and verified experimentally in milling a Titanium alloy with a face milling cutter having circular inserts.

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A control system that utilizes the concept of reflex control in animals is proposed for a biped walking machine with consideration of compensation of external disturbances. A walking machine was modeled as a sequential machine, and a series of single-reflex motions was synthesized for it. A hierarchical three-level control system was constructed. As disturbances, two types of external forces were considered: “impulsive” force with a large magnitude and short action-time and “continuous” force with a small magnitude and long action time. Appropriate state variables for rapid and reliable sensing of each disturbance were investigated and the thresholds of their values used as the triggers for changing the gait from a periodic gait to a disturbance compensation one were determined. Motions of disturbance compensation gaits were determined by combining some single-reflex motions. A control system for an experimental biped walking machine whose mass is 18kg, total height is 0.66m, step length is 0.25m and walking cycle is 133 steps/min was constructed and tested. The proposed control system enabled the walking machine to successfully avoid tumbling when it was subjected to the two external forces and return to a periodic gait.

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A 6 degrees of freedom parallel mechanism actuated by vertically fixed linear actuators was developed for heavy material handling and machining. The mechanism allows easy trajectory generation, since the vertical arrangement of the linear actuators simplifies the caluculation of its inverse kinematics. This paper presents inverse kinematics and Jacobian matirix solutions. Way to avoid component interference, which is divided into three types, is proposed. The combination of design parameters is decided by comparing the characteristics of area of movement, resolution and velocity. The working space is then shown. The singularity is analyzed by evaluating determinants of the Jacobian matrix. Lengthening the connecting rods and limiting the range of the end effector rotational angles are effective in avoiding the singular configurations as well as interference. Finally, the developed prototype mechanism is introduced, and its application to tool positioning and machining is described.

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This paper proposes a motion tracking system to be used for a visual sensing for an autonomous space docking system. The proposed system combines a stereo vision for three-dimensional measuerment and object recognition together with a monocular system for real-time motion tracking. The architecture is carried out using multi-thread parallel processing. The monocular vision thread detects only the feature points of the object using high speed image processing. Then, the three-dimensional features are reconstructed through corresponding each feature point with a point in the previous frame whose three-dimensional coordinate value has already been obtained using stereo measurement. Real-time motion tracking in the three-dimensional space is achieved by repeating this process. A hardware experiment is used to demonstrate the efficiency of the proposed vision system.

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An analytical model of head-positioning error due to rotational vibration of a hard disk drive is proposed. The model takes into account the rotational vibration of the base plate caused by the reaction force of the head-positioning actuator, the relationship between the rotational vibration and head-track offset, and the sensitivity function of track-following feedback control. Error calculated by the model agrees well with measured error. It is thus concluded that this model can predict the data transfer performance of a disk drive in read mode.

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Some dielectric fluids such as dibutyl decanedioate generate jet flow between a pair of electrodes. One of authors discovered electroconjugate fluid (ECF hereafter), which is considered to be a kind of functional fluid. In this study, a micro motor that utilizes ECF is proposed. In the proposed motor, are pairs of electrodes located inside a cylindrical tube (stator) filled with ECF. In the stator, rotational flow is induced by ECF jets. By extracting the rotational flow power with a rotor, micro motors are easily realized. In this paper, the fabrication of micro ECF motors having an I.D. of φ3mm, φ4mm or φ8mm is described. Basic characteristics such as rotational velocity, load characteristics, output power and efficiency are experimentally examined. Also, mathematical models of the ECF motors are proposed and verified with experimental data. Finally, miniaturization characteristics are examined using the fabricated ECF motors.

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A slipping clutch capable of delivering a constant resistant torque is described in this paper. Its principle is based on the resistance to slipping offered by the askew disposed cylindrical rollers rolling and slipping between the two specially shaped races. There are three types of this slipping clutch, namely the Right, Left and Cross Skewing respectively, which are distinguished by the directions of the roller askew arrangement and the rotation of the driving race. As a newly developed engineering surface, the surface of the races is in the spatial line contact with the skewed cylindrical rollers. After the equations of the race surface is established, the contact geometry of the tangency between the roller and races is investigated. This is essential for understanding the clutch properties and furthering the contact stress and EHL analyses. In addition, the analyzing procedure used here is also helpful for the study of other sophisticated line contact problems. Based on the assumptions of the maximum static friction force and the uniform distribution of the applied axial force along the contact line, the limiting torque characteristics are discussed in detail. The analysis of the maximum resistant torque clarifies the existence of self-locking problems under certain design parameters. On the other hand, the analysis of the minimum resistant torque shows how the resistant torque approaches the minimum values with changes of the geometrical parameters. These analyses provide the design principals for this slipping clutch in order to optimize the torque characteristics. The preliminary experiments are conducted with two types out of the three and the results prove those concluded from the theoretical analyses very well.

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This paper deals with a finite element analysis of gas-lubricated herringbone groove journal bearings operating at high speeds. An efficient finite element procedure is specially devised to predict static and dynamic performance characteristics of high-speed gas herringbone groove journal bearings operating at large journal eccentricities. The novel procedure is founded on the Galerkin weighted residual method employing a new class of high-order shape functions, which are derived from an approximate solution to the non-linear Reynolds equation within an element. Numerical predictions of bearing load capacity, attitude angle and dynamic force coefficients show the behavior of gas grooved journal bearings at high operating speeds.

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We discuss the design synthesis problem of mechanical systems with an example of configuration design of chain-type mechanisms. Mechanisms are used as system elements in various products, and each mechanism system is composed of mechanism pairs. In the design process, the functional structure of mechanisms and their spatial configuration are determined. The former means the sequential chains of pairs, and the latter means the arrangement and geometry of mechanism elements. We propose a framework for simultaneously considering both issues for designing a certain level of complicated mechanism systems. The concepts of marker sequences and cell-based planar representation are introduced to manipulate a design. Each marker corresponds to an abstracted representation of a particular mechanism element. Each cell corresponds to a region for such a marker. The computational design process is organized by generating marker sequences, assigning markers to cells, refining both of them, and embodying the configuration and arrangement of mechanisms. Finally, a prototype CAD system implemented under the proposed concepts is applied to several design examples. In the conclusion, we show the necessity of fictitious media for representing and computerizing the conceptual and configurational phases of a design process.

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With the increase of painting works and the decrease of skilled workers, the demand for robot painting of the large-scale steel product is rapidly increasing. But there are many technical problems in the development of the painting robot for this use. The collision between a robot and a work-piece is one of the most important problems, because the robot operates in a small space of a work-piece. Above all, the collision of the painting material supply hose with painted film on a work-piece is very serious. To avoid the hose collision, we propose an in-line type of paint supply mechanism using swivel joints. The key point in this system is the sealing performance and its durability, and we propose the piping system with compliance to strengthen the sealing performance. In this paper, the design method of this system is discussed on the basis of the analysis of the fluctuatinal elastic deformation of a O-ring in the swivel joint. We produced a prototype of the painting robot with the in-line system designed by this method. Application of this robot to the painting of ship-hull block is also discussed. Results from this application show the effectiveness of the in-line system.

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A built-up hob for a screw-compressor rotor is proposed. The hob is composed of cutter blades and a hob head. The blade is cut out from a tempered planar plate of high speed tool steel by wire-cut electrodischarge machining (EDM). During the wire cutting process, the wire electrode has a fixed angle to ensure both the side and the end relief angle of the cutting edge, so that the rake face regrinding sharpens the cutting edge without changing the profile of the rake face. In other words, theoretically, the hob has no accuracy deterioration due to rake face regrinding. The formulae of rack tooth profile are derived from the female rotor tooth profile experssed by numerical formulae. Next, the fundamental helicoid of the hob the profile of the cutting edge of the blade are calculated. The hob was fabricated and the rotor hobbing was carried out.

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Ultraprecision positioning is examined for a fine feed system utilizing the elastic deformation of lead screws accompanying the change in the preload in a double nut. The nonlinear deformation due to Hertzian contact of the ball screw can be ignored within a feed of 1μm under an dequate initial preload. No effect of table load on nanometer-order displacement is observed in the range from 10 to 50 kg. The table displacement obtained under an increase in the preload coincides well with the result under a decrease in the preload. Feed control with preload change based on a one-to-one correspondence of preload change and displacement is effective for avoiding the hysterisis phenomenon of the piezoelectric acturator adopted as a deformable spacing part in a double nut. In addition, the preload can be used as a measure to detect the table displacement in place of a position sensor which sometimes shows unreliability owing to unstable performance in the nanometer region. The minimum step feed deduced from preload change is 1nm for a sliding screw and 5nm for a ball screw.

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It has been recognized from many investigations on water jet cutting mechanism that visualization of a cutting front is very effective to deepen understanding of the mechanism. However, an in-process visualization method, especially those applicable to opaque materials such as metals has not been established even now. This paper newly proposes a method of visualization of cutting front using ultrasonic waves. Several experiments have shown that in-process visualisation of a shape of the cutting front, inclination and profile waviness of cutting surface can be realized using the proposed method. Furthermore, this paper also proposes a water jet cutting process model based on detail analyses of visualization results.

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The purpose of this study is to introduce a new approach for predicting chatter in high-speed end milling by using a fuzzy neural network. First, a milling experimental setup is built and a set of valuable experimental data is acquired under different tool wear states and carefully selected cutting parameters. Second, the experimental system is simplified into a fuzzy neural network model that is trained in the experimental data. Third, some simulation results are obtained on the basis of the trained model. Finally, the calculated results are compared with the experimental ones in order to check the effectiveness of the method described.

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In order to pave the way for development of a new field of cup-forming (i.e. ‘precision cup-forming’), shape quality of formed cups is investigated in detail, for no such data have been reported thus far. Cups are formed by the processes of deep-drawing and stretch-drawing with or without ironing action. The shape quality is evaluated by the radius distribution of the cup wall, which is displayed as three-dimensional colored maps, representing clearly the distortion pattern of the cup. The materials tested are four kinds of metal, including pue titanium. Spring-back occurs very irregularly in three dimensions, whose magnitude differs from material to material depending on the process type. Initial planar anisotropy cannot explain the distortion pattern, which suggests that its strain-history dependency plays a significant role. The cup wall radius becomes larger than the die cavity radius over some region around the cup lip and smaller over other regions. Generally, the cup shape is better for greater ratio of ironing, but notable exceptions may exist for some materials.

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Using robots in precision machining fields, such as grinding and polishing, is becoming more prominent in recent years. This paper presents original research results of aluminum alloy surface polishing using a rubber polishing disk in a robotic polishing system. A rotary hand-polishing system is held by the actuator of a six-axis articulated robot to perform the polishing task. The workpiece is an aluminum alloy block fixed on a piezo-electric type dynamometer. For finding the optimal tool angle to obtain the best polished surface, some polishing experiments were carried out using various tool angles. The effects of the number of polishing strokes on the surface roughness and depth of machining have been also estimated. Finally, calculated results and experimentally obtained results of a multi-stage polishing were compared. The obtained experimental results are useful for finding the optimum machining conditions for making an autonomous robotic polishing system.

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Manufacturers must be able to develop new products within a specified time period. This paper discusses a method for developing high performance products from a limited number of experiments, utilizing the concept of “function error”. Unlike conventional methods where the sequence of design, prototyping and experiment must be repeated several times, the proposed method can determine optimal design values directly from experimental data obtained from the first prototype. The theoretical basis of the method is presented, then its effectiveness proven by applying it to design an extrusion machine and a CNC lathe.

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In the present study, depressions of the GMA weld pool due to the impact of droplets are numerically investigated. The numerical simulations is performed on the basis of the Navier-Stokes equation and the volume of fluid (VOF) functions. The kinetic energy of the transferring droplets produces a depression on the weld pool surface. The surface active element affects the depression of the weld pool. In GMAW, the droplet transferred to the surface of the weld pool is one of the factors to produce the finger shape penetration at high current.

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The problem of adaptive observer synthesis for a class of Lipschitz nonlinear systems is investigated. A new algorithm to the design of adaptive observer scheme is proposed and the respective observer gains are obtained through the solution of a Riccati equation with linear constraints. Solvability conditions for such a Constrained Riccati Problem (CRP) are derived and a systematic algorithm for obtaining adaptive observers which guarantee the error convergence of the state estimates is provided.

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Contact ratio (CR) and transmission error (TE) are two significant indices for gear tooth strength and dynamics. This work investigated the CR, contact teeth (CT) and TE of a helical gear pair, composed of an involute pinion and a modified circular-arc gear. Point contact and built-in parabolic TE are obtained due to the modification of the gear’s tooth profile. Tooth contact analysis(TCA) is applied to determine the TE as well as the CR of the proposed helical gear set under various assembly condition. The effect of gear design parameters on the CRs and TEs are also investigated in numerical examples.

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In this paper, we experimentally evaluate a new Variable Remote Center Compliance (VRCC). Its structure is able to adjust the position of the compliance center easily by rotating the elastomer shear pads (ESP) about each vertical axis of the VRCC. For the experiments, the VRCC was manufactured and the position of the compliance centers were measured for various ESP rotation angles. The measured values agreed with the theoretic values very well.

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In this paper, the objective is to reduce the interior noise in a specific frequency band by using the predicted acoustical characteristics of a porous material. To identify the interior sound field of an enclosure, the Green’s function is used and the analytical results are verified by comparing with experimental results. Foamed aluminum is used an absorption material to used as absorption materials to reduce the interior sound pressure of the enclosure. Foamed aluminum is generally known as a metallic porous sound absorption material that has desirable attributes such as lightweight and high absorbing performance. Predicted acoustical parameters of foamed aluminum are used in the analysis to predict sound pressure levels in an enclosure and these results are compared with those of the experiments. To verify the predicted characteristics of the porous material, the analytical results obtained for the acoustical transmission matrix are compared with the experimentally obtained results from a two-microphone arrangement. Based on these results, an appropriate thickness of foamed aluminum is provided for pressure reduction in a specific frequency band.

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The tunnel booming noise generated during the train-tunnel interaction has been one of the most serious constraints in the development of the high-speed trains. It is well known that the nose shape of the train has the significant influence on the intensity of the booming noise. In this study, the nose shape has been optimized by using the response surface methodology and the axi-symmetric compressible Euler equations. The parametric studies are also performed with respect to the slenderness ratio, the blockage ratio and the train speed to investigate their sensitivities to the optimization results. The results show that it is possible to befine more general design space by introducing the Hicks-Henne shape functions, resulting in the more effective nose shape than that of Maeda. The mechanism and the aspects of the train-tunnel interaction were also investigated discussed from the results of the parametric study.

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In this paper, the works on the stability problem for singularly perturbed systems are extended to include the factors of uncertainties and time delays, which often cause the instability of the systems. The properties of H_∞-norm are used throughout this paper to derive the robust stability criterion. A frequency-domain sufficient condition for the asymptotic stability of the slow subsystem (reduced-order model) and the fast subsystems of the nominal system is first presented. Under the condition that the slow and fast subsystems of the nominal system are both asymptotically stable, we then propose the allowable bounds for the system uncertainties such that the slow and the fast subsystems of the original uncertain system is asymptotically stable. Finally, an upper bound ε^* of the singular perturbation parameter ε is given such that the original uncertain system is asymptotically stable for any ε∈ (0,ε^*). A numerical example is provided to illustrated our main results.

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