BOUNDARY CONTROL AND STABILIZATION OF AN AXIALLY MOVING VISCOELASTIC STRING UNDER A BOUNDARY DISTURBANCE

In this paper, we consider a system modelling an axially moving viscoelastic string subject to an unknown boundary disturbance. It is controlled by a hydraulic touch-roll actuator at the right boundary which is capable of suppressing the transverse vibrations that occur during the movement of the string. The multiplier method is employed to design a robust boundary control law to ensure the reduction of the transvesre vibrations of the string.

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Exponential Stabilization of an Axially Moving Tensioned Strip by Passive Damping and Boundary Control

Journal of Vibration and Control ◽

10.1177/1077546304038103 ◽

2004 ◽

Vol 10 (5) ◽

pp. 661-682 ◽

Cited By ~ 42

Author(s):

Ji-Yun Choi ◽

Keum-Shik Hong ◽

Kyung-Jinn Yang

Keyword(s):

Boundary Control ◽

Steel Strip ◽

Active Vibration Control ◽

Passive Damping ◽

Control Laws ◽

Transverse Vibrations ◽

Control Objective ◽

Boundary Force ◽

Axially Moving ◽

The Right

In this paper, we investigate an active vibration control of a translating tensioned steel strip in the zinc galvanizing line. The dynamics of the moving strip is modeled as a Euler-Bernoulli beam with non-linear tension. The control objective is to suppress the transverse vibrations of the strip via boundary control. A right boundary control law based upon the Lyapunov second method is derived. It is revealed that a time-varying boundary force and a suitable passive damping at the right boundary can successfully suppress the transverse vibrations. The exponential stability of the closed-loop system is proved. The effectiveness of the control laws proposed is demonstrated via simulations.

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Tension and Speed Regulation of Axially Moving Materials

Volume 6: International Symposium on Motion and Vibration Control ◽

10.1115/detc99/movic-8463 ◽

1999 ◽

Author(s):

Siddharth P. Nagarkatti ◽

Fumin Zhang ◽

Christopher D. Rahn ◽

Darren M. Dawson

Keyword(s):

Dynamic Simulation ◽

Boundary Control ◽

Control Strategy ◽

Distributed Parameter ◽

Control Law ◽

Material System ◽

Speed Regulation ◽

Distributed Parameter Model ◽

Simulation Results ◽

Axially Moving

Abstract In this paper, the tension and speed of an axially moving material system are regulated using control torques applied to rollers at each end of a controlled span. Given a distributed parameter model, Lyapunov-type arguments produce a model-based boundary control law that exponentially stabilizes the material tension and speed at the desired setpoints. Dynamic simulation results compare the tension and speed setpoint regulation provided by the proposed control strategy with standard PID approaches.

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

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331216665685 ◽

2016 ◽

Vol 40 (2) ◽

pp. 685-697 ◽

Cited By ~ 3

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.

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Iterative Learning Velocity and Tension Control for Single Span Axially Moving Materials

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2957625 ◽

2008 ◽

Vol 130 (5) ◽

Cited By ~ 33

Author(s):

Haiyu Zhao ◽

Christopher D. Rahn

Keyword(s):

High Speed ◽

Feedforward Control ◽

Longitudinal Vibration ◽

Speed Control ◽

Iterative Learning ◽

Tension Control ◽

Control Law ◽

Left Boundary ◽

Axially Moving ◽

The Right

Precise tension and speed control of axially moving material systems enables high speed processing of paper, plastics, fibers, and films. A single span model is developed that includes distributed longitudinal vibration, a torque-controlled roller at the left boundary, and a speed-controlled roller at the right boundary. The speed trajectory of the right roller is assumed periodic but unknown. A proportional and derivative (PD) feedback and iterative learning control (ILC) feedforward control law is developed for the left roller torque based on the measured tension and speed at the left boundary. PD tension/speed control is proven to ensure boundedness of distributed displacement and tension. ILC is proven to provide the same theoretical result but greatly improved simulated response to an aggressive stop/start right roller speed trajectory.

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Infinite-dimensional disturbance-observer-based control for an axially moving non-uniform system with input constraint

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217731153 ◽

2017 ◽

Vol 40 (12) ◽

pp. 3525-3533 ◽

Cited By ~ 1

Author(s):

Zhijia Zhao ◽

Yu Liu ◽

Fei Luo

Keyword(s):

Boundary Control ◽

Disturbance Observer ◽

Direct Method ◽

Input Saturation ◽

Infinite Dimensional ◽

Uniform System ◽

Unknown Disturbances ◽

Saturation Constraint ◽

Axially Moving ◽

Boundary Disturbance

In this paper, the vibration control and input saturation constraint problem of an axially moving non-uniform system subject to unknown disturbances is investigated. The key control objectives are to control the vibration of the system and eliminate the effects of the input saturation constraint. To that end, a boundary control with an auxiliary system is designed by utilizing Lyapunov’s direct method. Additionally, a boundary disturbance observer is proposed to deal with the boundary disturbance, and an infinite-dimensional disturbance observer is introduced to mitigate the effects of the distributed disturbance. With the designed boundary control, uniformly bounded stability of the controlled system is achieved through rigorous Lyapunov analysis without any model reduction. Finally, simulation results are given to show the effectiveness of the designed control scheme.

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Finite-time Attitude Tracking for Spacecraft With Unknown Boundary Disturbance and Angular Velocity

2020 39th Chinese Control Conference (CCC) ◽

10.23919/ccc50068.2020.9188894 ◽

2020 ◽

Author(s):

Huang Qin ◽

Zhang Ying ◽

Zhang Rui

Keyword(s):

Angular Velocity ◽

Finite Time ◽

Unknown Boundary ◽

Attitude Tracking ◽

Boundary Disturbance

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Adaptive output feedback boundary control for a class of axially moving system

IET Control Theory and Applications ◽

10.1049/iet-cta.2018.6030 ◽

2019 ◽

Vol 13 (2) ◽

pp. 213-221 ◽

Cited By ~ 3

Author(s):

Fang Guo ◽

Fei Luo ◽

Yu Liu ◽

Yilin Wu

Keyword(s):

Boundary Control ◽

Output Feedback ◽

Axially Moving

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Boundary Control of an Axially Moving String Via Lyapunov Method

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2802425 ◽

1999 ◽

Vol 121 (1) ◽

pp. 105-110 ◽

Cited By ~ 66

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.

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