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.

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.

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 Vibration Control of an Axially Moving String

1999 ◽  
Vol 121 (1) ◽  
pp. 41-49 ◽  
Author(s):  
M. S. de Queiroz ◽  
D. M. Dawson ◽  
C. D. Rahn ◽  
F. Zhang
Keyword(s):  
Control Strategies ◽  
Adaptive Controller ◽  
String Tension ◽  
Control Force ◽  
Control Laws ◽  
Axially Moving String ◽  
Model Based ◽  
Parameter Field ◽  
Axially Moving ◽  
Mechanical Guide

In this paper, the displacement of an axially moving string is regulated using a control force and a control torque applied to the string via a mechanical guide. Given the hybrid model of the string system (i.e., distributed parameter field equation coupled to discrete actuator equations), Lyapunov-type arguments are utilized to design model-based and adaptive control laws that exponentially and asymptotically stabilize the string displacement, respectively. The proposed control laws are based on measurements of the string displacement, velocity, slope, and slope rate at the mechanical guide. While the model-based controller requires exact knowledge of the actuator/string parameters (e.g., actuator mass and string tension), the adaptive controller estimates the parameters online. Dynamic simulation results demonstrate the vibration damping provided by the control strategies.

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