• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.47.2-47
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• 2001

This paper is concerned with the limiting zeros, as the sampling period tends to zero, of a multivariable discrete-time system composed of an approximate fractional-order hold (AFROH), a continuous-time plant and a sampler in cascade. An approximate fractional-order hold is proposed to implement fractional-order hold (FROH) and is applied to instead of the zero-order hold (ZOH). The implementing problem of the fractional-order hold is overcome. The properties of the limiting zeros are studied and the location problem of them is solved. In addition, a stability condition of the zeros for sufficiently small sampling period is derived ...

• 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 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.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.593-596
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• 1997

This paper is concerned with the properties of zeros of discrete-time systems which are composed of a hold, a continuous-time plant and a sampler in cascade. Here the signal reconstruction is based on the fractional order hold. In order to overcome the implementing problem of the fractional order hold, the piecewise constant reconstruction method by use of the zero order hold is introduced. The properties of the zeros are explored in the limiting cases when the sampling period tends to zero. The stability conditions of the zeros for sufficiently small sampling periods are also presented.

• 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 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 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.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2765-2770
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• 2003

This paper introduces a novel control algorithm, energy bounding algorithm, for stable haptic interaction. The energy bounding algorithm restricts energy generated by zero-order hold within consumable energy by physical damping that is energy consumption element in the haptic interface. The passivity condition can always be guaranteed by the energy bounding algorithm. The virtual coupling algorithm restricts the actuator force with respect to the penetration depth and restricts generated energy. In contrast, energy bounding algorithm restricts the change of actuator force with respect to time and restricts generated energy by zero-order hold. Therefore, much stiffer contact simulation can be implemented by the energy bounding algorithm. Moreover, the energy bounding algorithm doesn’t is not computationally intensive and the implementation of it is very simple.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.44.4-44
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• 2002

This paper investigates some conditions such that zeros are added to the system with a monotone nondecreasing step response in order to hold the monotonicity as before. Two conditions are presented for the cases that a real zero and complex conjugate zeros are added to the system satisfying the monotonicity condition, respectively. To exemplify the proposed results, some simple examples via computer simulation are shown in this paper. Proposed conditions can be easily used in the control system design since they are only formulated in terms of pole-zero configurations.