Payload motion control for a varying length flexible gantry crane

Cranes play a very important role in transporting heavy loads in various industries. However, because of its natural swinging characteristics, the control of crane needs to be considered carefully. This paper presents a control approach to a flexible cable crane system in consideration of both rope length varying and system constraints. At first, from Hamilton\u27s extended principle the equations of motion that characterized coupled transverse-transverse motions with varying rope length of the gantry are obtained. The equations of motion consist of a system of partial differential equations. Then, a barrier Lyapunov function is used to derive the control located at the trolley end that can precisely position the gantry payload and minimize vibrations. The designed control is verified through extensive experimental studies

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

A Direct Lyapunov-Backstepping Approach for Stabilizing Gantry Systems with Flexible Cable

Trolley positioning and payload swinging control problem of a flexible cable gantry crane system are addressed in this paper. The system’s equations of motion that couple the crane’s cable and actuators dynamics are derived via extended Hamilton’s principle. The control signal is designed based on the Lyapunov direct method to derive control force and backstepping technique is employed to determine input signal for the actuator. The stability of the closed loop system is proven analytically. Numerical simulations are included to demonstrate the effectiveness and robustness of the closed-loop system

Nonlinear Control of Flexible Two-Dimensional Overhead Cranes

Considering gantry cable as an elastic string having a distributed mass, we constitute a dynamic model for coupled flexural overhead cranes by using the extended Hamilton principle. Two kinds of nonlinear controllers are proposed based on the Lyapunov stability and its improved version entitled barrier Lyapunov candidate to maintain payload motion in a certain defined range. With such a continuously distributed model, the finite difference method is utilized to numerically simulate the control system. The results show that the controllers work well and the crane system is stabilized

Systems control theory applied to natural and synthetic musical sounds

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute

Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions

We establish the exponential decay of the solutions of the damped wave equations in one-dimensional space where the damping coefficient is a nowhere-vanishing function of space. The considered PDE is associated with several dynamic boundary conditions, also referred to as Wentzell/Ventzel boundary conditions in the literature. The analysis is based on the determination of appropriate Lyapunov functions and some further analysis. This result is associated with a regulation problem inspired by a real experiment with a proportional-integral control. Some numerical simulations and additional results on closed wave equations are also provided

An acoustic model for automatic control of a slide flute

International audienceIn this paper, we consider the problem of modeling and control of a slide flute : a kind of recorder without finger holes but which is ended by a piston mechanism to modify the length of the resonator. A previous study has been done (see [3]), but with a very simple boundary condition for the mouth, corresponding to an ideal situation assuming that the acoustic pressure is zero at the entrance of the resonator. In this work, we have taken into account a more realistic model, describing the coupling effects between the jet and the pipe. The jet is obtained by blowing through a flue channel and formed by flow separation at the flue exit, and finally directed towards a sharp edge, called the labium. The resulting structure can then be seen as a nonlinear oscillator coupled with the pipe which is a linear acoustic resonator. The pressure obtained through this model has been compared to the pressure measured on an actual instrument, a recorder closed at its end. A modal analysis is then performed using the linearized boundary conditions which can also be used to compute the suitable blowing pressure and the suitable pipe length to obtain a desired fundamental frequency or equivalently a desired pitch. This will constitute the basis of our control algorithm. A possible musical application of such a device is to build a flue instrument with a pitch independent of the dynamical level