Multi-Axis Electro-Dynamic(ED) shaking system has been controlled by using a feed-forward method which requires a pre-excitation of the system. However, the need to a new method which can avoid the pre-excitation is increasing recently. This means the system should be controlled by a modern feed-back method. In this paper, Two-Degree-of-Freedom Control with Adaptive Filter is applied to a Multi-Axis ED shaking system loaded with a resonant specimen. A successful result of adaptability of the controller to the change of the characteristics of the plant is shown.

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This paper deals with modeling and control of a crane mounted on a tower-like flexible structure. A fast transfer of the load causes swaying of the load rope and vibration of the flexible structure. Our object is to control both the sway and the vibration by the inherent capability of the tower crane. We have already succeeded in realizing a decentralized control consisting of two individual controllers. However, there is a possibility that the control worsened due to the decentralized control system because it did not take into account coupling between the up-and-down direction and the rotational direction. It is therefore necessary to examine the advantage of a decentralized control system precisely. This paper describes the design of a centralized control system considering coupling of both directions and compares it with a decentralized control system. From the results of the comparison of experiments and μ analysis, it is shown that the decentralized control system has almost the same performance and stability as the centralized one and that it is effective for the control of a tower crane.

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Unmanned helicopters are used lately to spray agricultural chemicals or take aerial photographs. In near future, it is expected that the aircraft will be used for a wide range of activities, such as observation and rescuing. An autonomous flight using several sensors is indispensable for such activities. In this paper, system identification experiments have been carried out for large-scale unmanned helicopter in order to obtain a numerical model of aircraft dynamics. First, system identification results are shown on the dynamics using the input and output data. Second, we show the constructed position control systems based on the H_∞ control theory. Finally, the effectiveness of these control systems is evaluated through position control experiments.

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This paper proposes a design method for vibration control of a multi-degree-of-freedom structure with an active dynamic vibration absorber involving actuator constraints. The linear parameter varying system is formulated taking account of both the maximum control input and the maximum stroke of the actuator by using a nonlinear function of hyperbolic tangent. The gain-scheduled control based on the linear matrix inequality is obtained so that the closed-loop system is stable and has good performance even if saturation phenomena of the actuator occur. The effectiveness of our proposed method is verified by experiments conparing the performance with that of an H_∞ fixed controller.

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This paper considers model reduction and robust control of an active vibration isolation system which is composed of a rigid platform and supporting air springs. The objective of control is to realize low compliance in the low frequency range for accurate position and attitude control, and maintain high compliance in the high frequency range for good vibration isolation properties. The system is modeled by identification theory, and the modeling error is described as multiplicative uncertainty. Model reduction is carried out by removing the state variables in the balanced realization, which neither contribute to the input-output relation of the model nor increase the modeling error. A controller is designed preserving robust stability, which minimizes the sensitivity in the low frequency range.

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A controller design method for a flexible arm with uncertain mass at its end is presented. The uncertainty is taken into consideration by using quadratic stability mode and a robust controller is obtained by using H∞ control law. An experimental system is built and parameters of the arm are identified. Computer simulations are carried out and the performance of the obtained controller is confirmed. The influence of the difference in nominal model to the control performance is also investigated.

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We have discussed a motion control of the legged robot Emu. In the research, we implicitly assumed that Emu stands upright on a level surface. However it is difficult to prepare the surface in practice because of an inclined plane. If we experiment in controlling Emu on the inclined plane under the assumption, Emu may fall down. Therefore we focus on an attitude control on a ramp of unknown slope. According to the stability analysis, we found that our proposed control system had a property of parametric stability. Thus we verify the parametric stability through some experiments.

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The superconducting Maglev system, which makes use of the non-contacting support, becomes attractive for further development. The running stability at low speed in straight line and curved line as well as riding comfort in levitated running are focused to be topics in the viewpoint of vehicle dynamics. Maglev vehicle is composed of lightweight car bodies and bogies which is mounted on the SCMs (superconducting magnets), the cooling device, etc. The vibration isolation performance degrades, since the ratio of sprung mass is nearly the unsprung mass. In the magnetically levitation system, the electromagnetic damping between the SCMs and ground coils is so small. Therefore, it is important to adjust the secondary suspension between car body and bogie. This paper focuses on the reduction of the lateral vibration of Maglev vehicle using the vibration control system designed by LQ control theory. Moreover, the case considering the effect of the electromagnetic damping is investigated.

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Dynamics of a moving body restrained in a 3D trajectory is investigated.The equation of motion of the moving body is derived by using differential algebraic equations (DAE) method. The time history simulation analysis is performed concerning with the coupling motion and vibration between the trajectory and the moving body. And, the parameters study is done to clear the motion and vibration characteristics of the moving body up.

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Making carbody and trucks lightweight for high-speed railway vehicle has recently progressed in competition with the other transportation. However, it is known that the lightweight tends to reduce the bending stiffness of body and to cause the fundamental vertical bending vibration which brings about the deterioration of the riding comfort. This paper aims to analyze the elastic vibration of the lightweight high-speed railway vehicle, and to propose a method of designing the vibration control system to reduce its vibration mode. First, the finite element method (FEM) model of lightweight vehicle is designed, which is composed by carbody and trucks, and three-dimensional characteristics of vehicle are examined by performing natural frequency analysis. In this study, the mechanism of trucks is taken into consideration in the analysis and is utilized for the design of controller. Next, the control system is designed on the basis of the analytical result. An active vibration absorber installed under the body floor is used for the device of vibration reduction. The controller with high robustness is designed by applying the H∞/fEcontrol method considering parameter variations and model errors in uncontrolled modes simultaneously. As a result of numerical calculations the usefuness of the proposed method was verified.

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Authors proposed SSM(Sensor Steering Mechanism) which is an effective mechanism to improve the speed of lateral guided vehicle. Previous report shows that the lateral stability of the four-wheeled vehicle with SSM does not exist speed limit in the straight way. Moreover, the ability of the vehicle equipped with SSM by utilizing the simulated trajectory are compared to experimental results. Simulated and experimental results ware well correspond each other, and the validity was shown. This paper shows that SSM is able to use for the evaluation of the steering characteristics of the vehicles depending on the location of driving wheel. FF(Front engine Front drive) and RR(Rear engine Rear drive) vehicle are used for the simulation and experiment, and the results demonstrate the feature well.

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Recently the development of agriculture vehicles such as a tractor has brought new demands on cabin environment. Especially the improvement of ride comfort has become increasingly important. As the measures of vibration reduction, only rubber bushes are just installed in conventional tractors. Therefore the vibration from road is directly transmitted to the driver in the cabin, consequently the driver is continuously persecuted by this vibration. This paper presents the method of the vibration reduction of the using semi-active suspension system for cabin mount and horizontal direction to provide the comfortable working environment for the driver.

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In ropeway transport systems, the swing of carriers caused by a lateral wind is an important vibration problem because of transportation safety and ride comfort. This paper deals with a vibrational characteristics of ropeway carrier models which is suspended from two parallel hauling ropes. The bicable ropeway systems are described by a linear system with two degrees of freedom excited by lateral wind. These dynamical models which both with conventional rigid hangers and with new rotative hangers are analyzed theoretically. The semi-active control method is applied to the rotative hangers model, and carried out computer simulation. These results show that the carrier system using rotative hangers with the semi-active control damper are proved to be effective for reducing vibration.

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When a railway vehicle negotiates curved tracks at high-speeds, the car body contacts with lateral stopper due to the excessive centrifugal force, and the ride comfort gets worse. In this situation, there is possibility that vibration control in active suspension does not work effectively. This paper deals with the addition of centering control, that pulls back car body to the center position from the outer side. Considering the difference of frequency range to be controlled between the vibration control and the centering control, H_∞control law is employed. As a result, it is made clear that cooperative work of both controls can be realized although there is a trade-off relation between them.

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In order to reduce the lateral force between wheel and rail during curve negotiation of rail vehicle, various kind of steered truck have been developed and investigated. This paper deals with two types of actively steered truck, in which the control is based on wheelset behaviour. One type of the trucks has actuators connected with longitudinal stiffness in series, the other does in parallel. The running characteristics such as curving performance, stability and control energy are compared by numerical simulation between the two types. As for the running stability, which tends to get worse with the steering control, it is suggested that the use of low-pass filter for the measurement data can be effective for the improvement. And the running safety is also investigated considering the fail of actuators.

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In designing railway vehicles, designers decide new parameters for the planned vehicle with referring parameters of existing vehicle. But it is difficult to find more suitable parameters that are far from those of the existing vehicle even if they are feasible. In this research, we use a multiobjective optimization method with various evaluate items to solve this problem. The target is the lateral vehicle dynamics (sham half body on a test bench). We report that more suitable parameter search is possible than by the usual method when the multiobjective optimization method is applied.

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In Japan, the railway has many curved sections. In future, since the railway will become more complicated and require more speed, the railway vehicle needs to improve its curving ability. The indices of curving performance are wheel-load, lateral wheel-rail force, coefficient of derailment, and extra centrifugal acceleration. The wheel-load and lateral wheel-rail force are closely related to derailment. Therefore, it is effective to control them in order to balance each wheel-load and to reduce lateral wheel-rail force. In this study, the control method of sudden change of each wheel-load in the curved section particularly in the transition curve is presented. The railway vehicle is modeled as a multibody by using mechanical analysis software, such as ADAMS and DADS. And the curving dynamics of wheels, truck and cars is analyzed by the numerical calculation. Furthermore, motion control using air suspension is attempted.

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In order to improve the ride comfort for passengers, reducing a lateral acceleration is necessary. This paper treats the railway vehicle which run in curve sections. As a determination method of tilting control quantity operated at present, there are 2 kinds of methods that is divided roughly. One is a system for using in Japan, and it has curve data of the travel interval in the on-board, and it is a method for the tilting order according to the position signal detected from the ground. Another is a system mainly used in Europe, and curve information shouldn't not be used, and over centrifugal acceleration which affects the car body is obtained from lateral acceleration in not tilting car truck division, and the inclination quantity has been deduced. The basis of the tilting control method for realizing the inclination goal is also the feedforward tilitng control on both systems. In this paper, it is examined the inclination quantity designed by the feedback control that can be more closely control performance is realizable according to set inclination goal, and the car body vibration can be also additively reduced is anticipated. Especially, the curvature is operated from detection value of the car body condition as orbit information under curving behavior, and the new tilting control method using this is proposed. By computer simulation according to dynamic model and experiment by the model equipment, the control effect is verified.

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In this paper, the tracking control problem and the anti-sway control problem for the rubber tired transfer crane are considered. Since the tired transfer crane swerves form the demanded course, it needs the tracking control to keep the demanded course. At the same time, the anti-sway control is needed to control the vibration of the building. Generally, since the model of the transfer crane can be expressed as one of nonholonomic system, it is difficult to design a controller. This paper propose a design method of a controller to keep the demanded course and control the vibration.

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This paper presents a sliding mode controller for electronically controlled automotive transmissions. During the shift, each multiple-disc clutch or band brake in the transmission must be controlled properly with a hydraulic actuator to avoid torque fluctuations in a transaxle output shaft. However the dynamics of the actuator varies largely with the oil temperature. It is shown through numerical simulations and experiment that the proposed controller enables highly robust performance against the model uncertainties of the hydraulic actuator

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In this paper, we offer a new design method for the flight control of a nonlinear non-minimum phase VTOL aircraft. The non-minimum phase property is caused by the small coupling between rolling moments and lateral acceleration, and a few researchers have derived control laws by neglecting the coupling. We show that the true model can be transformed equivalently into a model with zero coupling by changing the plant output from the center of mass to the Huygens center of oscillation. Then, we design a controller by applying a linear high gain approximation of backstepping to the model where we call this method briefly as two-step linearization. Computer simulation shows that the control law robustly stabilizes the true model with good tracking for both small and large couplings. Experiments for a twin rotor helicopter model also show such a good performance.

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This paper deals with motion control method of a snakelike robot. Serpentine which is one of characteristic motion of snake, is realized under restriction that all links can not sideslip. And twineing as another characteristic motion, is realized under restriction that all links can slideslip. However no research is reported to perform both of these motion using the same robot, until now. We consider a snakelike robot which consists of 10 links and 9 motors. Each link has passive wheels, so links are difficult to sidesliding. When Realizing serpentine motion, the snakelike robot is controlled under wheel restriction. And twineing is realized by adding the force that exceed friction force to each of link. This paper proposes a motion control metohd of snakelike robot that realize serpentine and twineing motion by controling sideslip force.

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In the design of sliding mode controllers for semi-active suspensions it is difficult to guarantee the existence of the sliding mode completely, which provides robust properties to the systems, because of the passivity constraints. This paper presents a new strategy for the design methods to hold the sliding mode as long as possible, using the Integral Sliding Mode theory, which was proposed by V.Utkin and J.Shi. The straregy is roughly described as follows: when the value of the switiching funct ion is almost equal to zero, the nonlinear control input used to reject undesired disturbances is better when it is as small as possible. This straregy leads to a dead zone algorithm. Numerical simulations and experimental results show the validity of the effectiveness of the controller.

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Control of the Acrobat type hopping robot is considered in this paper. The Acrobot consists of two links connected by an actuated revolute joint, and is a good example of many underactuated mechanical systems. This property makes it impossible to apply the control methodology used in Raibert's well-known hopper. During a hopping gate, the dynamics of the system is divided into three phases called stance, flight, and collision, respectively. We consider the forces acting to the foot from the ground, i.e. the constraint force in stance phase and constraint impulse in collision phase. This idea has its origin in the necessity to avoid slipping during a hopping gate. We formulate the control system by taking the direction of constraint force as the output, and demonstrate the possibility of hopping without slip by giving this system a proper reference input. Next, a soft landing problem at touchdown is presented based on the analysis on constraint impulse in collision phase.

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The Functional Model method proposed formerly is optimum method for nonlinear modeling. In this research, the nonlinear observer described by Functional Model method is proposed. And numerical simulation to control nonlinear mechanism is executed by status feedback.

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This paper considers the problem to design force controller for a one-link robot manipulator with contact motion to environments. Generally, the environmental characteristics that the manipulator is in contact with are not often known, and some of them have nonlinearity. Therefore we assume the environmental characteristic which is identified in real time as the spring element, and make it scheduling variable. We propose a new type of sliding mode controller with gain scheduling type variable hyperplane. By using this controller, hyperplane can be changed for various environments and adapted to nonlinearity of the environmental characteristic.

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This study deals with a nonlinear T_∞ state feedback control problem. The solvable condition of this problem is given by the Hamilton-Jacobi equality(HJE) or the Hamilton-Jacobi inequality (HJI). Recently, the study of the control design using the viscosity solution of HJE has been proposed. But, the viscosity solution is not partial differentiable, so the solution must be approximated to design control laws. It is unknown what kind of nonlinear systems have the viscosity solution of HJE or HJI. In this paper, the control object is limited to bilinear system. And it is shown that HJE or HJI of the nonlinear H_∞ state feedback control problem have the viscosity solution by the dynamic programming approach. And also, we propose the method to approximate the viscosity solution for control designs.

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As one of the control technique for nonholonomic systems, the method to design controllers using Time-State Control Form was proposed. But this method needs input switching, so there is a demerit that the switching conditions may spoil the stability of the whole system. From the above backgrounds, this research considers the property of the control method based on Time-State Control Form from the viewpoint of hybrid systems. Then, we derive the switching conditions which stabilize the systems by using Lyapunov functions for each mode. Furthermore, the control objects are limited to chained systems, and the conditions to stabilize the systems are shown by introducing the Lyapunov functions which are invariant to input switching. Then, we propose a method to design controllers based on the conditions.

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In this paper, a simple and stable generator with high-Tc superconducting levitation is presented in terms of vibration. This system has new methods in levitation, generator, damper and emergency brake. In order to have stable levitation, a superconductor and a permanent magnet are used, and 3 permanent magnets support the top of the shaft. In the part of generator, 8-pole permanent magnet and 8 coils are used to avoid resonance frequencies accordance of self-excited vibration and Lorenz forces. 4-pole permanent magnet and 4 coils are used as magnetic damper. This damper has braking force by the change of the magnetic flux density at the coils.

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A hysteresis amplifier using an H-bridge drive circuit was developed for self-sensing magnetic suspension. The H-bridge switches are composed of a pair of transistors and a pair of diodes. The switching characteristics of the hysteresis amplifier were studied experimentally. Self-sensing suspension was achieved with the developed hysteresis amplifiers; the displacement of the suspended object was estimated based on the period time measurement of the switching signal during control.

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The axial gap combined motor-bearing has both rotation and axial position control capabilities. This paper reports the self-sensing technique of the axial gap displacement from the stator current waveforms. When stator winding is driven by a pulse width modulated switching amplifier, the current waveform includes a high frequency switching ripple including an axial gap information. The axial gap are estimated by demodulating this ripple using filters. Fundamental self-sensing property is examined by the theoretical analysis and simulation.

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The general structures of controllers achieving current regulation for unbalance force are derived for voltage-controlled magnetic bearings. In the derivation, the controllers achieving virtually zero power control were refered to because they also regulate current for stepwise force. When control input is constructed only from the displacement, the controllers have the same structure as the controllers for current-controlled magnetic bearings.

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Much effort on modeling, identification and tuning of control parameters are required to stabilize magnetic levitation systems because of their negative stiffness and non-linearity. The purpose of this study is to propose a new control which achieves the stability of the levitation system within the moving range without trial and error. In this paper, a controller consisting of a balanced current compensator and PD elements is introduced. Then the balanced current compensator and control parameters of the PD elements are designed using simple experimental data. Finally the stable levitation of the object is realized in an experimental one-degree-of-freedom system.

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A Lorentz force type magnetic bearing is introduced in this paper. It is intended for the magnetic bearing to reduce the rotating loss drastically. The rotor is composed of a ring type permanent magnet and back yoke which produce a constant magnetic flux in the gap. The stator is composed of four concentrated coils which are installed in the airgap. The bearing force is produced by the stator coil current in the constant gap flux. A simple experimental setup is made to confirm the operation principle of the proposed magnetic bearing.

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Hybrid active magnetic bearing (AMB) type self-bearing motor has been proposed. It is intended for a motor to have both functions of rotation and radial position control. Miniaturization is necessary to install in small rotary machines. In this paper, HB slice motor is proposed. Outer rotor type motor is designed. The rotor is actively controlled only in radial directions while the axial and tilt directions are passively stable due to the disc structure of the rotor. First, the concept of proposed HB slice motor is introduced. Then the minimum pole number is theoretically derived which guarantees the control independency of rotation and levitation. Finally, the experimental setup is made to confirm the capability of the proposed motor. The results show high stability and high rotating torque of the proposed motor.

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This paper proposes an active vibration control method for multiple high-rise buildings connected with control device. This method has a merit of obtaining sufficient control force under low frequency and it is possible to control vibration of the super tall buildings against strong winds and earthquake motion. In this paper, two model buildings are connected by an actuator consisted of a DC servo motor, ballscrew and plate springs. The objective of this experiment is to control the first and second bending mode of each building. Control effects have been validated through simulation studies and experimental result.

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Recently, base isolation control of buildings has been devised to raise safety and comfort for the great earthquake. The Sliding Mode Control (SMC) theory which is one of nonliear control theory is applied to a semi-active base isolation control in this study. The advantage of the SMC method is the simplicity of design methodology and the robustness of control low. However it is important to use the disturbance information to obtain high performance. The purpose of this study is to propose the Disturbance-Accommodating Sliding Mode Control (DA-SMC). In this method the switched hyperplane is designed by augmenting the state space to that including the disturbance dyanamics. This study deals with the control problem of a ten-degree-of-freedom structural model with semi-active base isolation. In order to investigate the performance of the proposed method, computer simulation was caried out, and as a result, the effectiveness of the method was shown.

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This paper proposes a new method to control vibration using interactive force of a pair of identical flexible structures arranged in parallel such as solar panels of a space station. The main advantage of this new method is that the connecting arms with actuators can be located at a different position between the two flexible structures. It is demonstrated through simulation and experiment that the first four bending and torsional modes of the identical flexible structures are well controlled using our proposed modeling method and robust control.

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A smart structure is composed of the piezoelectric film sensors and actuators in order to reduce the structural vibration. H_2 controller is designed with the reduced order model of the smart structure which is obtained by finite element and modal analyses. The control forces are applied by the piezoelectric film actuators and the feedback signals are detected by the piezoelectric film sensors or the accelerometers in the system. The modal control and the displacement control with the appropriate actuator placement are conducted by selecting the modal coordinates and the spatial displacement as the controlled response, resulting in the effective vibration reduction. Efficient optimization algorithm based on a two step procedure is employed in the simultaneous optimization of structural/piezoelectric shape and H_2 control system. It is verified by some applications that the enhanced performance for the vibration suppression can be achieved by the simultaneous optimization.

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This paper presents both simulation and experimental investigations into the simultaneous design of a steering wheel and its control system for vibration suppression. The research can be divided into two stages. In the first stage, the simultaneous design is formulated as a nonlinear programming problem in which the H_∞ norm of the closed-loop system is minimized with respect to both the structural and control parameters. For convenience of using existing control design tools, a nested approach in which only the structural parameters are treated as explicit design variables is used to solve the original problem. The design obtained by simultaneous optimization is compared with the original structure and the effectiveness of the simultaneous optimization is shown by simulation. In the second stage, experiments are performed to evaluate the design of simultaneous optimization. To consider the effects of modeling error and system uncertainty, μ synthesis instead of H_∞ control is adopted in the experimental evaluation. The experimental result shows that the optimized structure is still superior to the original one after the controllers are redesigned in the framework of μ synthesis.

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This paper proposes a design method for response control of a structure involving stroke constraint of an auxiliary mass on a hybrid mass damper. In the vibration control of the structure by using the tuned mass damper, stroke of the auxiliary mass is so limited that it is difficult to control vibration of the structure in case of large disturbance input. In this paper, in order to suppress the relative displacement of the auxiliary mass, force for stopping the auxiliary mass is generated by actuator for active control. The force is assumed as damping force, then, the damping coefficient is considered as variable parameter. The variety of the damping coefficient is expressed by using of a function which can be increased expornential according to increasing relative displacement and velocity of the auxiliary mass. The control system is designed over linear parameter variable system, and the gain-scheduled control based on the LMI can be applied. By simulations, effect of vibration control with proposed control system is verified.

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This paper presents a new method for motion and vibration controls of a three dimensional flexible shaking table. The shaking table is need of lightweight for reproducing the earthquake wave and the variety of input signal exactly. However, then the elastic modes appear on shaking table in operating frequency region. So it is important to control motion and vibration of shaking table simultaneously. The research purpose is to control the vibration and motion of the shaking table by using the reduced order modeling technique and LQ and LQI control theory. The modeling procedure and the control design are described. Control simulations on the discrete model are carried out to demonstrate the effectiveness of the method. Experimental work is shown to demonstrate a final verification.

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Recently, the case that a stairs elevator is installed on from the 1st floor to the 2nd floor has been increasing along with the fulfillment of the welfare machine. This paper describes the preliminary investigation of the vibration control to secure the comfortability of a stairs elevator. A stairs elevator is considered as a movement body restrained on the three-dimentional orbit. The response vibration at the seat in the top-bottom, front-back, and left-right direction is analyzed taking the stiffness, the damping etc as parameters, and these effects are investigated.

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A machine with the lift mechanism for high lift work often generates a vibration at the lift operation. This paper describes the simulation analysis of the dynamic behavior of telescopic mechanism which is one of the lift mechanism of a machine for high lift work. We make the dynamic analytical model of the two-step lift mechanism composing of elastic bodies. An equation of motion is derived using a differential alegebraic equation (DAE). the preliminaray in vestigation on vibration control is performed for a operation so as to operate it easily and safty. As a result, it become clear that the velocity of the telescopic mechanism have much affect on the generation of vibration.

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We made a prototype actuator that utilizes an air -jet reaction forces pulsated by electromagnetic valves. Dynamic characteristics of the air pulse actuator were tested to use it as a control actuator for vibration control of a framed structure. Experiments of the vibration control based on the sliding mode control theory were carried out and their results verified the validity of the actuator performance.

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For the precision machinery the mechanical property is one of the very important factors to determine the precision and function of itself; but it is difficult to measure the response property as to micro-vibration. To improve the accuracy of micro-vibration generation and the testing frequency band-width, the authers developed a new hybrid testing device with piezoelectric and pneumatic actuators. The device can generate any required vibration waves precisely while deliminate the micro-vibration from the ground with actuators capable of acting from low to high frequencies. The properly designed digital controller is used to form both feedback and feedforward control at high speed and high resolution.

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Recently, the superfine devices in semiconductor manufacturing fields have been rapidly developing. As the IC patterns processed by them is getting finer, the effect of microvibration is more. Nowadays, in addition to making vibration environment as low aw possible, the superfine devices are needed to clarify the characteristics to microvibration. The purpose of this study is to develop the microvibration simulator which has stability robustness and good attenuation performance with H_∞ controller, furthermore applying feedforward control, to improve the follow-up performance to desired values.

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