Parametric Oscillation Model of Crane with Lifting Motor Reducing Load Swing

2009 ◽  
Vol 16-19 ◽  
pp. 30-33
Author(s):  
Wei Li ◽  
Xiang Peng Hu
Keyword(s):  
Lagrange Equation ◽  
Standard Form ◽  
Vertical Motion ◽  
Hill Equation ◽  
Parametric Oscillation ◽  
Oscillation Model ◽  
Stable Map ◽  
Damped Oscillation ◽  
Load Swing ◽  
The Mathematical Model

Dynamic characteristic was analyzed for the hydraulic anti-sway system,and established the mathematical model of crane system by using Lagrange equation. For crane load swing problems, established the Parametric oscillation model of crane, through coordinate transformation, transformed the differential equation of crane into the standard form of Hill equation, and with research on Hill equation we can get the condition about damped oscillation. With the introduction of the parameter plane, the stable map of Hill equation can be drawed, i.e. the map of load damped oscillation. We used MATLAB-Simulink to simulate. The vertical motion of hoist has obvious influence on load sway. Through controlling cable length lifting motor has some good help to lowering sway angl of crane load.

scholarly journals Vertical Motions Damping Model Test of a Lifeboat Lowered Onto a Flat Sea Surface

2018 ◽  
Vol 25 (s1) ◽  
pp. 51-55
Author(s):  
Aleksander Kniat ◽  
Paweł Dymarski
Keyword(s):  
Mathematical Model ◽  
Model Test ◽  
Water Surface ◽  
Vertical Motion ◽  
Sea Surface ◽  
Damping Factor ◽  
Initial Speed ◽  
The Mathematical Model ◽  
Damping Model

Abstract The article presents the experiment’s results of the lifeboat model lowered with an initial speed and then released to fall onto a flat water surface. The purpose of the research is to determine the trajectory of the vertical boat motion and describe it with a mathematical model. This is closely related to determining the damping factor since the vertical motion is damped and the lifeboat gets balanced and stops moving after some time. The procedure of selecting parameters in the mathematical model to adjust to the results of the experiment was described in details. The summary describes the imperfections of the presented damping model and their probable causes.

A Damped Oscillation Model for Tracking Near Space Hypersonic Gliding Targets

2019 ◽  
Vol 55 (6) ◽  
pp. 2871-2890 ◽  
Author(s):  
Fan Li ◽  
Jiajun Xiong ◽  
Zhiguo Qu ◽  
Xuhui Lan
Keyword(s):  
Near Space ◽  
Oscillation Model ◽  
Damped Oscillation

Laryngeal Muscle Activity in Giggle: A Damped Oscillation Model

2008 ◽  
Vol 22 (6) ◽  
pp. 644-648 ◽  
Author(s):  
Ingo R. Titze ◽  
Eileen M. Finnegan ◽  
Anne-Maria Laukkanen ◽  
Megan Fuja ◽  
Henry Hoffman
Keyword(s):  
Muscle Activity ◽  
Laryngeal Muscle ◽  
Oscillation Model ◽  
Damped Oscillation

scholarly journals Simulation Analysis of One Degree of Freedom Motion of Electromagnetic Spherical Joint based on Maxwell

2021 ◽  
Vol 2085 (1) ◽  
pp. 012014
Author(s):  
Haoran Wang ◽  
Fucong Liu ◽  
Sai Lou
Keyword(s):  
Mathematical Model ◽  
Simulation Analysis ◽  
Lagrange Equation ◽  
Degree Of Freedom ◽  
Spherical Joint ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Structure And Motion ◽  
The Mathematical Model ◽  
The Relationship

Abstract In order to improve the stiffness of the spherical joint of the robot, reduce the difficulty of manufacturing and the complexity of the control system, this paper proposed a method of spherical joint and digital drive of the robot based on the electromagnetic principle. Firstly, introduces the structure and motion principle of the spherical joint of the robot, establishes the mathematical model of the spherical joint and establishes the dynamic model according to the second Lagrange equation. after that, the relationship between the number of ampire-turns of the electromagnet on the spherical joint, the attitude Angle of the rotor and the force of the rotor was obtained by simulating the single degree of freedom of the joint based on Ansys maxwell and Matlab, which provided a basis for the realization of the digital drive of the spherical joint.

Nonlinear Dynamics of a Smooth and Discontinuous Oscillator with Multiple Stability

2015 ◽  
Vol 25 (13) ◽  
pp. 1530038 ◽  
Author(s):  
Yanwei Han ◽  
Qingjie Cao ◽  
Jinchen Ji
Keyword(s):  
Nonlinear Oscillator ◽  
Large Scale ◽  
Lagrange Equation ◽  
Dynamic Stiffness ◽  
Ground Vibration ◽  
Large Scale Structures ◽  
Sd Oscillator ◽  
Closed Orbits ◽  
Geometry Configuration ◽  
The Mathematical Model

A novel nonlinear oscillator with multiple stabilities is proposed in this paper based on the original SD oscillator [Cao et al., 2006] and the generalized SD oscillator [Han et al., 2012; Cao et al., 2014]. The mathematical model of this system is formulated by using Lagrange equation. Even when all the springs are linear, the system admits strongly irrational nonlinearities due to the geometry configuration. The investigation shows that the nonlinear oscillator exhibits complex equilibrium bifurcations of single-, double-, triple- and quadruple-well properties, and the singular closed orbits of homoclinic, heteroclinic and homo-heteroclinic types as well for both smooth and discontinuous cases. The chaotic behaviors are also presented numerically for the perturbed system under the perturbation of both viscous-damping and external excitation. This oscillator can be extended to a high-order-quasi-zero-stiffness isolator and a nonlinear supporting system for ground vibration test for large-scale structures to achieve the high-static-low-dynamic-stiffness.

scholarly journals Mathematical model of a flexible asymmetrical rotor for active magnetic bearing reaction wheel

2018 ◽  
Vol 158 ◽  
pp. 01025
Author(s):  
Miroslav Polyakov ◽  
Anatoliy Lipovtsev ◽  
Vladimir Lyanzburg
Keyword(s):  
Mathematical Model ◽  
Lagrange Equation ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Active Magnetic Bearings ◽  
Ansys Software ◽  
Mass System ◽  
Linear Elastic ◽  
Orbit Control ◽  
The Mathematical Model

The paper introduces the mathematical model of rotor for active magnetic bearing reaction/momentum wheels, used as actuator in spacecraft attitude and orbit control system. Developed model is used for estimation of critical speeds and forced oscillation magnitudes with a glance of the rotor modes. Rotor is considered as a two-mass system, consisting of a shaft and a rim, active magnetic bearings are assumed to be a linear elastic springs. The equations of the rotor motion are derived using the Lagrange equation. Developed model is verified by comparing the calculated Campbell diagrams with the results of the finite-element modal analysis, performed in the ANSYS software.

Design and Implementation of Self-Balancing Electric Vehicle Control System

2015 ◽  
Vol 738-739 ◽  
pp. 950-954
Author(s):  
Ben Sheng Qi ◽  
Kang Wang ◽  
Xuan Xuan Xiao ◽  
Hong Xia Miao
Keyword(s):  
Control System ◽  
Electric Vehicle ◽  
Lagrange Equation ◽  
Linear Quadratic Regulator ◽  
Optimization Method ◽  
Vehicle Control ◽  
Linear Quadratic ◽  
Design And Implementation ◽  
Vehicle System ◽  
The Mathematical Model

In order to further optimize the control system of self-balancing electric vehicle, the method of linear quadratic regulator (LQR) based on genetic algorithm (GA) was presented in this paper. Firstly, the mathematical model of self-balancing electric vehicle was established by Lagrange equation, and then matrix Q and R in LQR which is used to control self-balancing electric vehicle system were optimized by GA. Thus the optimal control of self-balancing electric vehicle control system was realized. The optimization method was proved to be effective by comparing the simulation results of the optimized controller with the original.

Modeling and Controller Comparison for Quarter Car Suspension System by Using PID and Type-1 Fuzzy Logic

2014 ◽  
Vol 598 ◽  
pp. 524-528 ◽  
Author(s):  
Abdullah Çakan ◽  
Fatih Mehmet Botsalı ◽  
Mustafa Tinkir
Keyword(s):  
Fuzzy Logic ◽  
Degrees Of Freedom ◽  
Lagrange Equation ◽  
Active Vibration Control ◽  
Suspension System ◽  
Car Suspension ◽  
Road Profile ◽  
Active Vibration ◽  
Quarter Car ◽  
The Mathematical Model

Ensuring vehicle drive comfort and securing drive safety are the leading topics among the most interested issues for researchers in vehicle dynamics area. In this paper, a method utilizing a linear actuator is proposed for active control of the vehicle vibrations which are caused by road profile, intending to improve drive comfort and safety of road vehicles. The mathematical model belonging to the system that is evaluated as two degrees of freedom quarter car suspension system is derived by using Lagrange Equation of Motion and MATLAB/Simulink software. In addition to modeling technique, dynamic model of proposed system is created in MSC-ADAMS software and it is simulated in both Matlab and Adams programs together. Moreover two different controllers are designed, which are PID and Artificial Neural Network Based Fuzzy Logic (ANNFL) control in order to use in active vibration control simulations. Performances of the designed controllers are examined and the suitability of the designed controllers is studied by comparing their performances in case of using two different road profile functions.

scholarly journals A Predictive Control Strategy for Aerial Payload Transportation with an Unmanned Aerial Vehicle

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1822
Author(s):  
Norberto Urbina-Brito ◽  
María-Eusebia Guerrero-Sánchez ◽  
Guillermo Valencia-Palomo ◽  
Omar Hernández-González ◽  
Francisco-Ronay López-Estrada ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Predictive Control ◽  
Control Strategy ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Lagrange Formulation ◽  
Aerial Vehicle ◽  
Load Swing ◽  
The Mathematical Model ◽  
Three Dimensional Space

This paper presents the results of a model-based predictive control (MPC) design for a quadrotor aerial vehicle with a suspended load. Unlike previous works, the controller takes into account the hanging payload dynamics, the dynamics in three-dimensional space, and the vehicle rotation, achieving a good balance between fast stabilization times and small swing angles. The mathematical model is based on the Euler–Lagrange formulation and considers the dynamics of the vehicle, the cable, and the load. Then, the mathematical model is represented as an input-affine system to obtain the linear model for the control design. A constrained MPC strategy was designed and compared with an unconstrained MPC and an algorithm from the literature for the case of study. The constraints to be considered include the limits on the swing angles and the quadrotor position. The constrained control algorithm was constructed to stabilize the aerial vehicle. It aims to track a trajectory reference while attenuating the load swing, considering a maximum swing range of ±10∘. Numerical simulations were carried out to validate the control strategy.

Sign in / Sign up

Export Citation Format

Share Document