scholarly journals Invariant-Based Inverse Engineering for Fast and Robust Load Transport in a Double Pendulum Bridge Crane

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 350
Author(s):  
Ion Lizuain ◽  
Ander Tobalina ◽  
Alvaro Rodriguez-Prieto ◽  
Juan Gonzalo Muga
Keyword(s):  
Natural Frequencies ◽  
Initial Conditions ◽  
Boundary Effects ◽  
Double Pendulum ◽  
Bridge Crane ◽  
Small Oscillations ◽  
Load Transport

We set a shortcut-to-adiabaticity strategy to design the trolley motion in a double-pendulum bridge crane. The trajectories found guarantee payload transport without residual excitation regardless of the initial conditions within the small oscillations regime. The results are compared with exact dynamics to set the working domain of the approach. The method is free from instabilities due to boundary effects or to resonances with the two natural frequencies.

Robust load transport by an overhead crane with respect to cable length uncertainties

2020 ◽  
Vol 26 (17-18) ◽  
pp. 1514-1522
Author(s):  
Daniel Martínez-Cercós ◽  
David Guéry-Odelin ◽  
Juan Gonzalo Muga
Keyword(s):  
Initial Conditions ◽  
Fourier Method ◽  
Initial Energy ◽  
Overhead Crane ◽  
Transport Protocols ◽  
Small Oscillations ◽  
Cable Length ◽  
Load Transport ◽  
The Stability

We exploit a Fourier method to inverse engineer fast load transport protocols for an overhead crane, which is robust with respect to the deviation of cable length, corresponding to an ideal value. In the small oscillations regime, the protocols guarantee final adiabatic energies, i.e. null excitation with respect to the initial energy, regardless of the initial conditions. We demonstrate with calculations for the exact dynamics the stability of this result.

Vehicle tip-over prevention using gain-scheduled State-dependent Riccati Equation–based anti-rollover controller

2020 ◽  
pp. 095440702094831
Author(s):  
Hari M Nair ◽  
C Sujatha
Keyword(s):  
Riccati Equation ◽  
Initial Conditions ◽  
Real Life ◽  
Lookup Table ◽  
Computational Time ◽  
Double Pendulum ◽  
Vehicle Model ◽  
State Dependent ◽  
Lift Off ◽  
Gain Scheduled

The most hazardous kind of vehicle crash among all road accidents is vehicle rollover. Present-day rollover prevention systems in commercial vehicles mitigate rollover by preventing any wheel lift-off from the ground. These systems make use of actuators such as differential brakes and demand all the wheels on the ground for satisfactory operation. Such systems are not effective in recovering a vehicle from intense rollover scenarios where the wheels on one side are lifted off the ground, and the vehicle is about to rollover to the other side after reaching the tip-over point. A few studies have investigated the possibility of reinstating a vehicle at the tip-over point with the wheels on a side lifted off. The high complexity and computation time of the optimal control strategies such as nonlinear model predictive controller make it unsuitable for real-time implementations. This study proposes a novel gain-scheduled State-dependent Riccati Equation–based optimal anti-rollover controller for reinstating a vehicle from the tip-over point. An inverted double pendulum on a cart vehicle model is used as the plant model. The anti-rollover controller is found to be presentable as a two-dimensional gain-scheduled lookup table with specific state dependencies in existence. It eliminates the necessity of solving the nonlinear performance index minimization problem online. State-dependent Riccati Equation method adequately accounts for the nonlinearities involved, yet possesses a small computational time per sample. The anti-rollover controller is evaluated with a 10 degrees of freedom full vehicle model with a nonlinear pure slip tyre model that incorporates the dynamical effects neglected in the controller formulation. Finally, the anti-rollover controller is evaluated in real-life initial conditions using a sophisticated pick-up truck model obtained from TruckSim® software through a co-simulation with the anti-rollover controller setup in MATLAB®/Simulink® environment. The State-dependent Riccati Equation controller was found to be effective in reinstating the higher-order models from the tip-over point in all the case studies conducted.

An investigation of hoist-induced dynamic loads on bridge crane structures

1996 ◽  
Vol 23 (4) ◽  
pp. 926-939 ◽  
Author(s):  
D. A. Barrett ◽  
T. M. Hrudey
Keyword(s):  
Initial Conditions ◽  
Bending Moment ◽  
Bridge Crane ◽  
Test Results ◽  
Design Standards ◽  
Dynamic Factors ◽  
Time Histories ◽  
Payload Mass ◽  
Two Degree Of Freedom ◽  
Dynamic Ratio

A series of tests were performed on a bridge crane to investigate how the peak dynamic response during hoisting is affected by the stiffness of the crane structure, the inertial properties of the crane structure, the stiffness of the cable-sling system, the payload mass, and the initial conditions for the hoisting operation. These factors were varied in the test program and time histories were obtained for displacements, accelerations, cable tension, bridge bending moment, and end truck wheel reactions. Values for the dynamic ratio, defined as peak dynamic value over corresponding static value, are presented for displacements, bridge bending moment, and end truck wheel reactions. A two degree of freedom analytical model is presented, and theoretical values for the dynamic ratio are calculated as a function of three dimensionless parameters that characterize the crane and payload system. The predicted dynamic ratios are found to be conservative when compared with the test results. A general format is suggested for dynamic factors in design standards that apply to bridge cranes with constant speed motors. Key words: bridge crane, hoist, dynamic load.

Combination Resonances of a Circular Plate With Three-Mode Interaction

1995 ◽  
Vol 62 (4) ◽  
pp. 1015-1022 ◽  
Author(s):  
Won Kyoung Lee ◽  
Cheol Hong Kim
Keyword(s):  
Circular Plate ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Initial Conditions ◽  
Resonance Condition ◽  
Equilibrium Points ◽  
Nonautonomous System ◽  
Mode Interaction ◽  
Resonance Frequencies

A nonlinear analysis is presented for combination resonances in the symmetric responses of a clamped circular plate with the internal resonance, ω3≈ω1+2ω2. The combination resonances occur when the frequency of the excitation are near a combination of the natural frequencies, that is, when Ω≈2ω1+ω2. By means of the internal resonance condition, the frequency of the excitation is also near another combination of the natural frequencies, that is, Ω≈ω1−ω2+ω3. The effect of two near combination resonance frequencies on the response of the plate is examined. The method of multiple scales is used to solve the nonlinear nonautonomous system of equations governing the generalized coordinates in Galerkin’s procedure. For steady-state responses, we determine the equilibrium points of the autonomous system transformed from the nonautonomous system and examine their stability. It has been found that in some cases resonance responses with nonzero-amplitude modes don’t exist, and the amplitudes of the responses decrease with the excitation amplitude. We integrate numerically the nonautonomous system to find the long-term behaviors of the plate and to check the validity of the analytical solution. It is found that there exist multiple stable responses resulting in jumps. In this case the long-term response of the plate depends on the initial condition. In order to visualize total responses depending on the initial conditions, we draw the deflection curves of the plate.

scholarly journals White Noise Tests on the LSTM Model Trained with Double Pendulum

2021 ◽  
Vol 2137 (1) ◽  
pp. 012032
Author(s):  
Xisen Wang
Keyword(s):  
Time Series ◽  
White Noise ◽  
Time Series Data ◽  
Initial Conditions ◽  
Correlation Coefficients ◽  
Series Data ◽  
Double Pendulum ◽  
Auto Correlation ◽  
State Dependent ◽  
Auto Regressive

Abstract This paper describes the intrinsic qualities of a simple double pendulum (DP), with a visual representation, a rigorous deduction of the Lagrangian equation, and a concrete factor analysis. LSTM model was utilized to simulate the double pendulum’s periodic and chaotic behaviors and evaluates the effectiveness of the model. The auto-correlation coefficients was calculated. Meanwhile, Box-Pierce test and Ljung-Box tests for various state-dependent time series were conducted to give various initial conditions to explore the DP system’s random characteristics. The research results are as follows: 1) Chaos did not lead to direct randomness; 2) seasonality could coexist with chaos; 3) the highly auto-regressive nature of DP’s time series data are found. Therefore, it can be concluded that the chaos in a double pendulum has particular patterns (such as the positive relationship with the likelihood of being a random white noise series) that could be further explored.

Feasibility of Two-Dimensional Control for Ship-Mounted Cranes

2001 ◽  
Author(s):  
Eihab M. Abdel-Rahman ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
Major Axis ◽  
Double Pendulum ◽  
Spherical Pendulum ◽  
Safe Operation ◽  
Control Effort ◽  
Pendulum System ◽  
Out Of Plane ◽  
The One

Abstract We test the feasibility of employing an exclusively planar control effort to suppress unsafe ship-mounted crane pendulations induced by sea motions. The new crane configuration, designed to apply the control effort, is modeled and the proposed control effort, employing Coulomb friction and viscous damping, is applied. The three-dimensional nonlinear dynamics of the crane is then investigated. The new crane configuration, dubbed Maryland Rigging, transforms a crane from a single spherical pendulum to a double pendulum system. The upper pendulum, a pulley riding on a cable suspended from the boom, is constrained to move over an ellipsoid. The major axis of the ellipsoid is the boom and the foci are the two points at which the riding cable attaches to it. The lower pendulum, the payload suspended by a cable from the pulley, continues to act as a spherical pendulum. Due to the geometry of the ellipsoid, the natural frequencies of the crane in the plane of the boom (in-plane) are almost equal to the out-of-plane natural frequencies. The model is used to examine the response of a Maryland rigged crane to direct, in-plane, harmonic forcing. The frequency of the excitation is set almost equal to the crane’s lowest natural frequency. It is found that under this excitation and due to the one-to-one internal resonance between the lowest in-plane and out-of-plane natural frequencies, significant out-of-plane motions are induced by applying a purely in-plane forcing. Thus an in-plane control mechanism is not adequate for safe operation of the crane. To guarantee safe operation of a ship-mounted crane, one must apply both in-plane and out-of-plane control efforts.

scholarly journals Spherical Pendulum Small Oscillations for Slewing Crane Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Alexander V. Perig ◽  
Alexander N. Stadnik ◽  
Alexander I. Deriglazov
Keyword(s):  
Reference Frame ◽  
Natural Frequencies ◽  
Computational Results ◽  
Numerical Estimation ◽  
Spherical Pendulum ◽  
Lagrange Equations ◽  
Uniform Rotation ◽  
Small Oscillations ◽  
Mechanical Interpretation ◽  
Lagrange Mechanics

The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies’ problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown.

The Performance Analysis of Double Beam Bridge Crane Based on Computer Simulation Technology

2013 ◽  
Vol 584 ◽  
pp. 107-111
Author(s):  
Qing Yu ◽  
Xu Dong Mao
Keyword(s):  
Strain Field ◽  
Theoretical Basis ◽  
Natural Frequencies ◽  
Maximum Load ◽  
Mode Shapes ◽  
Stress And Strain ◽  
Bridge Crane ◽  
Double Beam ◽  
Beam Bridge ◽  
Load Conditions

Due to lifting large loads and lifting smooth, it is widely used for double beam bridge crane in machinery industry. The numerical analysis of stress and strain field for 200t×28m double beam bridge crane is done under maximum load conditions by using ABAQUS finite element platform in this paper, the distribution and largest area under load of bridge is obtained. At the same time three natural frequencies and mode shapes of double beam bridge crane is analyzed, which the results provide a theoretical basis and reference for double beam bridge crane designer.

A single and double closed-loop compound anti-sway control method for double-pendulum bridge cranes locating at random position

2021 ◽  
pp. 014233122110464
Author(s):  
Minghui Xia ◽  
Xiaokai Wang ◽  
Qingxiang Wu ◽  
Lin Hua
Keyword(s):  
Closed Loop ◽  
Control Method ◽  
Smooth Transition ◽  
Double Pendulum ◽  
Bridge Crane ◽  
Special Equipment ◽  
Pendulum Model ◽  
Bumpless Transfer ◽  
Random Position ◽  
Pendulum Dynamics

In the assembly workshops of some heavy special equipment, the bridge cranes for payload lifting often needs to be located frequently. However, the locating position is often determined by the operator, which is random and results in significant payload oscillation and difficulties in trolley positioning. Furthermore, in practice, the bridge crane always exhibits more complicated double-pendulum dynamics compared with single-pendulum crane. To solve these problems, this paper establishes the double-pendulum model of bridge crane. Derived from the proportional-derivative (PD) control, the single closed-loop is designed based on the hook oscillation during acceleration and transporting; when locating, the double closed-loop is presented by utilizing the position and the hook oscillation. Combining the two control methods, a single and double closed-loop compound anti-sway control (SDCAC) method for the bridge crane is proposed. On this basis, to improve the performance of the SDCAC system, the sequential quadratic optimization (SQP) method is adopted to optimize PD parameters. Besides, a novel bumpless transfer control method is proposed to realize the smooth transition between the two control modes. Finally, the simulations and experiments are conducted. The results demonstrate the effectiveness of the proposed method.

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