Energy decay estimates for an axially travelling string damped at one end

We study the small vibrations of an axially travelling string with a dashpoint damping at one end. The string is modelled by a wave equation in a time-dependent interval with two endpoints moving at a constant speed $v$. For the undamped case, we obtain a conserved functional equivalent to the energy of the solution. We derive precise upper and lower estimates for the exponential decay of the energy with explicit constants. These estimates do not seem to be reported in the literature even for the non-travelling case $v=0$.Comment: 14 Pages, 2 Figure

Enhancing vibration control in cable-tip-mass systems using asymmetric peak detector boundary control

In this study, a boundary controller based on a peak detector system has been designed to reduce vibrations in the cable–tip–mass system. The control procedure is built upon a recent modification of the controller, incorporating a non-symmetric peak detector mechanism to enhance the robustness of the control design. The crucial element lies in the identification of peaks within the boundary input signal, which are then utilized to formulate the control law. Its mathematical representation relies on just two tunable parameters. Numerical experiments have been conducted to assess the performance of this novel approach, demonstrating superior efficacy compared to the boundary damper control, which has been included for comparative purposes"This work has been funded by the Generalitat de Catalunya through the research projects 2021-SGR-01044."Peer ReviewedPostprint (published version

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

Vibration attenuation control of ocean marine risers with axial-transverse couplings

The target of this paper is designing a boundary controller for vibration suppression of marine risers with coupling mechanisms under environmental loads. Based on energy approach and the equations of axial and transverse motions of the risers are derived. The Lyapunov direct method is employed to formulated the control placed at the riser top-end. Proof of existence and uniqueness of the solutions of the closed-loop system is provided. Stability analysis of the closed-loop system is also included

Vibration suppression and angle tracking of a fire-rescue ladder

This paper mainly considers vibration suppression and angle tracking of a fire-rescue ladder system. The dynamical model is regarded as a segmented Euler–Bernoulli beam with gravity and tip mass, described by a set of motion equations and boundary conditions. Based on the nonlinear Euler–Bernoulli beam model, two active boundary controllers are proposed to achieve the control objectives. The elastic deflection and the angular error in the closed-loop system are proven to converge exponentially to a small neighborhood of zero. Numerical simulations based on finite difference method verify the effectiveness and the ascendancy of active boundary controllers

Boundary stabilization of a vibrating string with variable length

We study small vibrations of a string with time-dependent length $\ell(t)$ and boundary damping. The vibrations are described by a 1-d wave equation in an interval with one moving endpoint at a speed $\ell'(t)$ slower than the speed of propagation of the wave c=1. With no damping, the energy of the solution decays if the interval is expanding and increases if the interval is shrinking. The energy decays faster when the interval is expanding and a constant damping is applied at the moving end. However, to ensure the energy decay in a shrinking interval, the damping factor $\eta$ must be close enough to the optimal value $\eta=1$, corresponding to the transparent condition. In all cases, we establish lower and upper estimates for the energy with explicit constants.Comment: 14 pages, 3 figure

Adaptive boundary control of an axially moving system with large acceleration/deceleration under the input saturation

We present the dynamical equation model of the axially moving system, which is expressed through one partial differential equation (PDE) and two ordinary differential equations (ODEs) obtained using the extended Hamilton's principle. In the case of large acceleration/deceleration axially moving system with system parameters uncertainty and input saturation limitation, the combination of Lyapunov theory, S-curve acceleration and deceleration (Sc A/D) and adaptive control techniques adopts auxiliary systems to overcome the saturation limitations of the actuator, thus achieving the purpose of vibration suppression and improving the quality of vibration control. Sc A/D has better flexibility than that of constant speed to ensure the operator performance and diminish the force of impact by tempering the initial acceleration. The designed adaptive control law can avoid the control spillover effect and compensate the system parameters uncertainty. In practice, time-varying boundary interference and distributed disturbance exist in the system. The interference observer is used to track and eliminate the unknown disturbance of the system. The control strategy guarantees the stability of the closed-loop system and the uniform boundedness of all closed-loop states. The numerical simulation results test the effectiveness of the proposed control strategy

Boundary control of flexible mechanical systems

Ph.DDOCTOR OF PHILOSOPH

Modeling and Control of Marine Flexible Systems

Ph.DDOCTOR OF PHILOSOPH