• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2000년도 춘계학술대회논문집A
• /
• pp.579-584
• /
• 2000

In this study. the time varying boundary control using the right boundary transverse motion on the basis of the energy flux between the moving string and the boundaries is suggested to stabilize the transverse vibration of an axially moving string. The effectiveness of the active boundary control is showed through experimental results. Sliding mode control is adopted in order to achieve velocity tracking control of the time varying right boundary to dissipate vibration energy of the string effectively. For the unmoving and moving string at various velocity under various tension the performance of the transverse vibration control using the time varying right boundary control with the suggested control scheme is experimentally demonstrated.

• 대한기계학회논문집A
• /
• 제25권1호
• /
• pp.135-144
• /
• 2001

In this study, the time varying boundary control using the right boundary transverse motion is suggested to stabilize the transverse vibration of an axially moving string on the basis of the energy flux between the moving string and the boundaries. The effectiveness of the active velocity boundary control is showed through the FDM simulation results. Sliding mode control is adopted in order to achieve velocity tracking control of the time varying right boundary to dissipate vibration energy of the string effectively. Optical sensor system for measuring the transverse vibration of an axially moving string is developed, and the angle of the incident wave to the right boundary, which is the input of the velocity boundary controller, is obtained. Experimental research is carried out to examine the validity and the performance of the transverse vibration control using the suggested velocity right boundary control scheme.

• 대한기계학회논문집A
• /
• 제28권1호
• /
• pp.11-21
• /
• 2004

In this paper, an active vibration control of a tensioned elastic axially moving string is investigated. The dynamics of the translating string ale described by a non-linear partial differential equation coupled with an ordinary differential equation. The time varying control in the form of the right boundary transverse motions is suggested to stabilize the transverse vibration of the translating continuum. A control law based on Lyapunov's second method is derived. Exponential stability of the translating string under boundary control is verified. The effectiveness of the proposed controller is shown through the simulations.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2005년도 ICCAS
• /
• pp.2260-2265
• /
• 2005

In this paper, an active vibration control of a tensioned elastic axially moving string is investigated. The dynamics of the translating string are described by a non-linear partial differential equation coupled with an ordinary differential equation. A time varying control in the form of right boundary transverse motions is proposed in stabilizing the transverse vibrations of the translating continuum. A control law based on Lyapunov's second method is derived. Exponential stability of the closed-loop system is verified. The effectiveness of the proposed controller is shown through simulations.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2001년도 춘계학술대회논문집
• /
• pp.385-392
• /
• 2001

Time-dependent frequency and energy of free vibration of the Spagetti problem, that is the axially moving continuum with time-varying length, are investigated. Exact expressions for the natural frequency and time-varying vibration energy are derived by dealing with traveling waves. When the string length is increased, the vibration period increases, but the free vibration energy varies as a function of both translating velocity and boundary velocity of the continuum. However, when the string undergoes retraction, the vibration energy increases with time, String tension together with non-zero instantaneous velocity at the moving boundary results in energy variation.

• International Journal of Control, Automation, and Systems
• /
• 제3권4호
• /
• pp.601-611
• /
• 2005

In this paper, an active vibration control of a tensioned, elastic, axially moving string is investigated. The dynamics of the translating string are described with a non-linear partial differential equation coupled with an ordinary differential equation. A right boundary control to suppress the transverse vibrations of the translating continuum is proposed. The control law is derived via the Lyapunov second method. The exponential stability of the closed-loop system is verified. The effectiveness of the proposed control law is simulated.

• 소음진동
• /
• 제10권5호
• /
• pp.838-842
• /
• 2000

The vibration of an axially moving string is studied when the string has geometric non-linearity and translating acceleration. Based upon the von karman strain theory, the equations of motion are derived considering the longitudinal and transverse deflection. The equation for the longitudinal vibration is linear and uncoupled, while the equation for the transverse vibration is non-linear and coupled between the longitudinal and transverse deflections. These equations are discretized by using the Galerkin approximation after they are transformed into the variational equations, i.e. the weak forms so that the admissible and comparison functions can be used for the bases of the longitudinal and transverse deflections respectively. With the discretized nonlinear equations, the time responses are investigated by using the generalized-$\alpha$ method.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2005년도 ICCAS
• /
• pp.2474-2479
• /
• 2005

The control objectives in this paper are to move the gantry of a container crane to its target position and to suppress the transverse vibration of the payload. The crane system is modeled as an axially moving nonlinear string equation, in which control inputs are applied at both ends, through the gantry and the payload. The dynamics of the moving string are derived using Hamilton's principle. The Lyapunov function method is used in deriving a boundary control law, in which the Lyapunov function candidate is introduced from the total mechanical energy of the system. The performance of the proposed control law is compared with other two control algorithms available in the literature. Experimental results are given.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2004년도 추계학술대회논문집
• /
• pp.387-392
• /
• 2004

The control objectives in this paper are to move the gantry of a container crane to its target position and to suppress the transverse vibration of the payload. The crane system is modeled as an axially moving string equation, in which control inputs are applied at both ends, through the gantry and the payload. The dynamics of the moving string are derived using Hamilton's principle for systems with changing mass. The Lyapunov function method is used in deriving a boundary control law, in which the Lyapunov function candidate is introduced from the total mechanical energy of the system. The performance of the proposed control law is compared with other two control algorithms available in the literature. Experimental results are given.

• East Asian mathematical journal
• /
• 제37권1호
• /
• pp.141-147
• /
• 2021

In [1], we studied the PDE system with time-varing delay. Time delay occurs due to loosening in a high-speed moving axially directed membrane (string, belt, or plate) at production. Our purpose in this work derives a mathematical model with internal time delay. First, we consider the physical phenomenon of axially moving membrane with respect to kinetic energy, potential energy and work done. By the energy conservation law in physics, we get the second order nonlinear PDE system with internal time delay.