• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.152-154
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• 2007

Anew discretization method for the input-driven nonlinear continuous-time system with time delay is proposed. It is based on the combination of Taylor series expansion and first-order hold assumption. The mathematical structure of the new discretization scheme is explored. The performance of the proposed discretization procedure is evaluated by case studies. The results demonstrate that the proposed discretization scheme can assure the system requirements even though under a large sampling period. A comparison between first order hold and zero-order hold is simulated also.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.4
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• pp.389-394
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• 2014

This paper presents the effect of a reflective force computed from a first-order-hold method on the stability of a haptic system. A haptic system is composed of a haptic device with a mass and a damper, a virtual spring, a sampler and a sample-and-hold. The boundary condition of the maximum virtual stiffness is analytically derived by using the Routh-Hurwitz criterion and the condition shows that the maximum virtual stiffness is proportional to the square root of the mass and the damper of a haptic device and also is inversely proportional to the sampling time to the power of three over two. The effectiveness of the derived condition is evaluated by the simulation. When the reflective forces are computed by using the first-order-hold method, the maximum available stiffness to guarantee the stability is increased several hundred times as large as when the zero-order-hold method is applied.

• Journal of Institute of Convergence Technology
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• v.10 no.1
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• pp.41-45
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• 2020

This paper presents the effects of a virtual mass on the stability boundary of a virtual spring in the haptic system with first-order-hold. The virtual rigid body is modeled as a virtual spring and a virtual mass. When first-order-hold is applied, we analyze the stability boundary of the virtual spring through the simulation according to the virtual mass and the sampling time. As the virtual mass increases, the stability boundary of the virtual spring gradually increases and then decreases after reaching the maximum value. The results are compared with the stability boundary in the haptic system with zero-order-hold. When a virtual mass is small, the stability boundary of a virtual spring in the system with first-order-hold is larger than that in the system with zero-order-hold.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.1
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• pp.12-17
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• 2018

In order to enhance the realism of a virtual environment, a method of maximizing the stiffness of the virtual environment model is needed, which maintains the stability of the haptic system. In our previous research, we proposed a haptic system with a first order hold, instead of a zero order hold, and showed that the maximum available stiffness of a virtual spring with the first-order hold is larger than that with the zero-order hold. However, in terms of real system implementation, the zero order hold is a more common and easy method. In this paper, we propose an extrapolation method and a high frequency zero-order-hold output method in order to obtain the stability region using a zero order hold, which is equivalent to the method using the first-order-hold. The simulation results shows that the stability range of the virtual spring becomes almost the same as that of the method using the first order hold when the sampling period of the high frequency zero-order-hold method is decreased. Moreover, the stability range of the proposed method is several times to several tens of times greater than that of the method using the zero order hold only. Therefore, it is expected that the proposed method can enhance the realism of rigid bodies in a virtual environment.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.1
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• pp.572-578
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• 2017

Haptic systems help users feel a realistic sensation when they manipulate virtual objects in the remote virtual environment. However, there are communication time delays that may make the haptic system unstable. This paper shows the relationship between communication time delay, properties of a haptic device, and the stability of the haptic system with the first-order hold method in a simulation. The maximum available stiffness of a virtual spring with the first-order hold method is larger than in the zero-order hold method when there is no time delay. However, when the communication time delay is much larger than the sampling time, the maximum available stiffness to guarantee the stability becomes the same, irrespective of the sample-hold methods. Besides, the maximum available stiffness increases in inverse proportion to the communication time delay and in proportional to the damping coefficient of the haptic device.

• Journal of Institute of Convergence Technology
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• v.4 no.2
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• pp.17-21
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• 2014

This paper presents the effects of the time delay on the stability of the haptic system that includes a virtual wall and a first-order-hold method. The model of a haptic system includes a haptic device model with a mass and a damper, a virtual wall model, a first-order-hold model and a time delay model. In this paper, the time delay is considered as the computational time delay that is assumed to be as much as the sampling time. As the time delay increases, the maximal available stiffness of a virtual wall model is reduced reversely. The relation among the time delay and the maximum available stiffness, the mass and the damper of the haptic device are analyzed using the MATLAB simulation.

• Journal of Institute of Convergence Technology
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• v.3 no.2
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• pp.23-29
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• 2013

When a human operator interacts with a virtual wall that is modeled as a virtual spring model, the lager the stiffness of the virtual spring is, the more realistic the operator feels that the virtual wall is. In the previous studies, it is shown that the maximum available stiffness of a virtual spring to guarantee the stability can be increased when the first-order-hold method is applied, however the effects of a human impedance on the stability are not considered. This paper presents the effects of a human impedance on stability of haptic system with a virtual spring and a first-order-hold (FOH) method. The human impedance model is modeled as a linear second-order system model. The relations between the maximum available stiffness of a virtual spring and the human impedance such as a mass, a damping and a stiffness are analyzed through the MATLAB simulation. It is shown that the maximum available stiffness is proportional to the square root of the human mass or damping respectively.

• Journal of Institute of Convergence Technology
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• v.5 no.2
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• pp.37-42
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• 2015

This paper presents the effects of the computational time-varying delay on the stability of the haptic system that includes a virtual wall and a first-order-hold method. The model of a haptic system includes a haptic device model with a mass and a damper, a virtual wall model, a first-order-hold model and a computational time-varying delay model. In this paper, the maximum of the computational time-varying delay is assumed to be as much as the sampling time. Using the simulation, it is analyzed how the sample-hold methods and the computational time-varying delay affect the maximum available stiffness. As the maximum of computational time-varying delay increases, the maximal available stiffness of a virtual wall model is reduced.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.20 no.6
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• pp.396-401
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• 2019

A virtual rigid is modeled as the parallel structure of a virtual spring and a virtual damper. The reflective force from the virtual model is designed to be as large as possible to improve the realism of the virtual environment while maintaining the stable interaction. So, it is important to analyze the stability boundary of the virtual spring and damper. In the previous researches, the stability boundary is analyzed based on the zero-order-hold (ZOH) method, but it is analyzed based on the first-order-hold (FOH) method and the virtual damper in the paper. The boundary value of the stable virtual damper is inverse proportional to the sampling time and the maximum value of stable virtual stiffness is inverse proportional to the square of the sampling time. And the maximum value in the FOH method is increased to 110% of the value in the ZOH method. If the virtual damper is smaller than about 50% of the boundary value of the virtual damper in the FOH method, the stable virtual stiffness in the FOH method is several times larger than that in the ZOH method.

• Journal of Institute of Convergence Technology
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• v.2 no.2
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• pp.35-39
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• 2012

This paper presents the effect of data-hold methods on stability of haptic system with a virtual wall. When a human operator interacts with virtual wall, the lager the stiffness of the virtual wall is, the more realistic the operator feels that the virtual wall is. However, if the stiffness of the virtual wall becomes extremely large, the system may be unstable. When a virtual wall is designed, it is necessary to analyze the maximum available stiffness to guarantee a stable haptic interaction. The simulation model in this paper is developed based on the haptic device model, sampler, a virtual wall model, and data hold methods to compute the maximum stiffness for stability. The effectiveness of the simulation is evaluated through comparing the results of previous studies with the results of this simulation. In addition, the effects of two data hold methods, that is, zero-order hold (ZOH) and first-order hold (FOH) on the stability are analyzed and the values of the maximum available stiffness are compared through the simulation.