VIBRATION SUPPRESSION OF A NON-LINEAR AXIALLY MOVING STRING BY BOUNDARY CONTROL

1997 ◽  
Vol 201 (1) ◽  
pp. 145-152 ◽  
Author(s):  
S.M. Shahruz ◽  
D.A. Kurmaji
Keyword(s):  
Boundary Control ◽  
Vibration Suppression ◽  
Axially Moving String ◽  
Non Linear ◽  
Axially Moving

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.

Suppression of Vibration in a Nonlinear Axially Moving String by the Boundary Control

1997 ◽  
Author(s):  
Shahram M. Shahruz
Keyword(s):  
Boundary Control ◽  
Negative Feedback ◽  
Linear Boundary ◽  
Axially Moving String ◽  
Axially Moving ◽  
Nonlinear String

Abstract In this note, a nonlinear axially moving string is considered. It is proved that the nonlinear string can be stabilized by the linear boundary control, which is the negative feedback of the transversal velocity of the string at one end.

Adaptive Boundary Control of an Axially Moving String System

2002 ◽  
Vol 124 (3) ◽  
pp. 435-440 ◽  
Author(s):  
Rong-Fong Fung ◽  
Jinn-Wen Wu ◽  
Pai-Yat Lu
Keyword(s):  
Boundary Control ◽  
Tracking Error ◽  
Torque Control ◽  
Control Force ◽  
Unknown Parameters ◽  
System Equation ◽  
Axially Moving String ◽  
Coupling System ◽  
Axially Moving ◽  
Adaptive Boundary Control

This paper proposes an adaptive boundary control to an axially moving string system, which couples with a mass-damper-spring (MDS) controller at its right-hand-side (RHS) boundary. Unknown parameters appearing in the system equation are assumed constant and estimated on-line by using adaptation laws. The adaptive computed-torque control algorithm applied to robot manipulators of lumped systems is extended to design the adaptive boundary controller for the coupling system. It is found that the control force and update laws depend only on the displacement, velocity and slope of the string at the RHS boundary. Lyapunov stability guarantees the convergence of the tracking error to zero. Finally, the performance of the proposed controller is demonstrated by numerical simulations.

Vibration control of an axially moving accelerated/decelerated belt system with input saturation

2016 ◽  
Vol 40 (2) ◽  
pp. 685-697 ◽  
Author(s):  
Yu Liu ◽  
Zhijia Zhao ◽  
Fang Guo ◽  
Yun Fu
Keyword(s):  
Boundary Control ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Direct Method ◽  
Input Saturation ◽  
Unknown Boundary ◽  
Disturbance Adaptation ◽  
Axially Moving ◽  
Adaptation Law ◽  
Belt System

This article describes an investigation of a boundary control for vibration suppression of an axially moving accelerated or decelerated belt system with input saturation. Firstly, after considering the effects of the high acceleration or deceleration and unknown distributed disturbance, an infinite-dimensional model of the belt system is described by a nonhomogeneous partial differential equation and a set of ordinary differential equations. Secondly, by synthesizing boundary control techniques and Lyapunov’s direct method, a boundary control is developed to suppress the belt’s vibration and to stabilize the belt system at its equilibrium position globally; an auxiliary system is proposed to compensate for the nonlinear input saturation characteristic; a disturbance adaptation law is employed to mitigate the effects of unknown boundary disturbance; and the S-curve acceleration/deceleration method is adopted to plan the belt’s axial speed. Thirdly, with the proposed boundary control, the wellposedness of the closed-loop belt system is mathematically demonstrated and uniformly bounded stability of the closed-loop system is achieved without any discretization of the system dynamic model. Finally, simulation results are presented to verify the validity and effectiveness of the proposed control scheme.

Sign in / Sign up

Export Citation Format

Share Document