Boundary Control of an Axially Moving String Via Lyapunov Method

1999 ◽  
Vol 121 (1) ◽  
pp. 105-110 ◽  
Author(s):  
Rong-Fong Fung ◽  
Chun-Chang Tseng
Keyword(s):  
Boundary Control ◽  
Lyapunov Method ◽  
Sliding Mode ◽  
Semigroup Theory ◽  
Active Vibration Control ◽  
Nonlinear Partial Differential Equation ◽  
Distributed Parameter ◽  
Axially Moving String ◽  
Active Vibration ◽  
Axially Moving

This paper presents the active vibration control of an axially moving string system through a mass-damper-spring (MDS) controller at its right-hand side (RHS) boundary. A nonlinear partial differential equation (PDE) describes a distributed parameter system (DPS) and directly selected as the object to be controlled. A new boundary control law is designed by sliding mode associated with Lyapunov method. It is shown that the boundary feedback states only include the displacement, velocity, and slope of the string at RHS boundary. Asymptotical stability of the control system is proved by the semigroup theory. Finally, finite difference scheme is used to validate the theoretical results.

Active Vibration Control of the Axially Moving String Using Space Feedforward and Feedback Controllers

1996 ◽  
Vol 118 (3) ◽  
pp. 306-312 ◽  
Author(s):  
S. Ying ◽  
C. A. Tan
Keyword(s):  
Vibration Control ◽  
Feedforward Control ◽  
Active Vibration Control ◽  
Upstream Region ◽  
Control Force ◽  
Feedback Controllers ◽  
Axially Moving String ◽  
Downstream Region ◽  
Active Vibration ◽  
Axially Moving

Active vibration control of an axially moving string using space feedforward and feedback controllers is presented. Closed-form results for the transverse response of both the uncontrolled and controlled string are given in the s domain. The space feedforward controller is established by employing the idea of wave cancellation. The proposed control law indicates that vibration in the region downstream of the control force can be cancelled. With the space feedforward control, the mode shapes of the axially moving string are changed such that the free response tends to zero in the downstream region. An interesting physical interpretation is that the control force acts effectively as a holder (active support) which limits the vibration of the string to the upstream region and eliminates any vibration in the downstream region. Simulation results show that the response of the string to both sinusoidal and random excitations is suppressed by applying the space feedforward control. The feedback controller is introduced to attenuate the response of the string due to undesired disturbances in the downstream.

Active Vibration Control of the Axially Moving String by Wave Cancellation

1993 ◽  
Author(s):  
C. H. Chung ◽  
C. A. Tan
Keyword(s):  
Vibration Control ◽  
Active Vibration Control ◽  
Closed Form Expression ◽  
Control Law ◽  
Closed Loop System ◽  
Controlled System ◽  
Axially Moving String ◽  
Active Vibration ◽  
Axially Moving ◽  
Actuation Devices

Abstract Active vibration control of an axially moving string by wave cancellation is presented. The control problem is formulated in the frequency domain. An exact, closed-form expression for the transfer function of the closed-loop system, consisting of the flexible structure, a feedback control law and the dynamics of the sensing and actuation devices, is derived. It is shown that all vibration modes can be stabilized and that the controlled system has no resonance. Moreover, the designed controller is applicable to the control of the string transverse vibration under various kinds of loading and constraint conditions. Results for the response of the controlled string under different excitations are presented and discussed along with the wave propagation and cancellation characteristics.

Active Vibration Control of the Axially Moving String in the S Domain

1991 ◽  
Vol 58 (1) ◽  
pp. 189-196 ◽  
Author(s):  
B. Yang ◽  
C. D. Mote
Keyword(s):  
Vibration Control ◽  
Controller Design ◽  
Active Vibration Control ◽  
Stabilizing Controller ◽  
Axially Moving String ◽  
The Laplace Transform ◽  
Modes Of Vibration ◽  
Active Vibration ◽  
Axially Moving ◽  
Actuation Devices

A new method is presented for active vibration control of the axially moving string, one of the most common models of axially moving continua. The control is formulated in the Laplace transform domain. The transfer function of a closed-loop system, consisting of the plant, a feedback control law and the dynamics of the sensing and actuation devices, is derived. Analysis of the root loci of the closedloop system gives two stability criteria. Stabilizing controller design is carried out of both collocation and noncollocation of the sensor and actuator. It is found that all the modes of vibration can be stabilized and that in principle the spillover instability can be avoided. Also, the steady-state response of the stabilized string to periodic, external excitation is presented in closed form.

Active Vibration Control of the Axially Moving String by Wave Cancellation

1995 ◽  
Vol 117 (1) ◽  
pp. 49-55 ◽  
Author(s):  
C. H. Chung ◽  
C. A. Tan
Keyword(s):  
Vibration Control ◽  
Active Vibration Control ◽  
Closed Form Expression ◽  
Control Law ◽  
Vibration Modes ◽  
Controlled System ◽  
Axially Moving String ◽  
Active Vibration ◽  
Axially Moving ◽  
Actuation Devices

Active vibration control of an axially moving string by wave cancellation is presented. The control problem is formulated in the frequency domain. An exact, closed-form expression for the transfer function of the controlled system, consisting of the flexible structure, a feedback control law and the dynamics of the sensing and actuation devices, is derived. It is shown that all vibration modes can be stabilized and that the controlled system has no resonance. Moreover, the designed controller is applicable to the control of the string transverse vibration under various kinds of loading and constraint conditions. Results for the response of the controlled string under different excitations are presented and discussed along with the wave propagation and cancellation characteristics.

Vibration Control of an Axially Moving String by Boundary Control

1996 ◽  
Vol 118 (1) ◽  
pp. 66-74 ◽  
Author(s):  
Seung-Yop Lee ◽  
C. D. Mote
Keyword(s):  
Boundary Control ◽  
Mechanical Energy ◽  
Semigroup Theory ◽  
External Boundary ◽  
Vibration Energy ◽  
Transverse Motion ◽  
Feedback Gain ◽  
Axially Moving String ◽  
Axially Moving ◽  
Time Required

The stabilization of the transverse vibration of an axially moving string is implemented using time-varying control of either the boundary transverse motion or the external boundary forces. The total mechanical energy of the translating string is a Lyapunaov functional and boundary control laws are designed to dissipate the total vibration energy of the string at the left and/or right boundary. An optimal feedback gain determined by minimizing the energy reflected from the boundaries, is the radio of tension to the propagation velocity of an incident wave to the boundary control. Also the maximum time required to stabilize all vibration energy of the system for any initial disturbance is the time required for a wave to propagate the span of the string before hitting boundary control. Asymptotic and exponential stability of the axially moving string under boundary control are verified analytically through the decay rate of the energy norm and the use of semigroup theory. Simulations are used to verify the theoretically predicted, optimal boundary control for the stabilization of the translating string.

scholarly journals Ultra-low frequency active vibration control for cold atom gravimeter based on sliding-mode robust algorithm

2018 ◽  
Vol 67 (2) ◽  
pp. 020702
Author(s):  
Luo Dong-Yun ◽  
Cheng Bing ◽  
Zhou Yin ◽  
Wu Bin ◽  
Wang Xiao-Long ◽  
...  
Keyword(s):  
Vibration Control ◽  
Sliding Mode ◽  
Active Vibration Control ◽  
Low Frequency ◽  
Cold Atom ◽  
Robust Algorithm ◽  
Active Vibration
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