Dynamic Modeling of Systems With Translating Components

1991 ◽  
Vol 113 (3) ◽  
pp. 248-252 ◽  
Author(s):  
A. Garcia Reynoso ◽  
W. Seering
Keyword(s):  
Differential Equations ◽  
Dynamic Modeling ◽  
Translational Motion ◽  
Mechanical Systems ◽  
Angular Acceleration ◽  
Vibration Response ◽  
Optical Encoder ◽  
System A ◽  
Representative System

This paper summarizes a method for modeling the vibration response of mechanical systems whose configuration may vary during operation. A model of adjacent elements which experience relative translational motion is developed. System Differential equations are derived and then transformed to accept as input angular acceleration rather than torque information at the actuator shafts. A technique for determining this angular acceleration information from optical encoder signals is described. Finally, predicted and actual vibration response for a representative system, a cartesian robot, are presented and compared.

MULTIBODY DYNAMIC MODELING AND FLUTTER ANALYSIS OF A FLEXIBLE SLENDER VEHICLE

2012 ◽  
Vol 12 (06) ◽  
pp. 1250049 ◽  
Author(s):  
A. RASTI ◽  
S. A. FAZELZADEH
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
The Body ◽  
Elastic Deformations ◽  
Strip Theory ◽  
Multibody Dynamic ◽  
Flutter Analysis ◽  
Rigid Body Motions

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

Dynamic modeling and optimal robust approximate constraint-following control of constrained mechanical systems under uncertainty: A fuzzy approach

2015 ◽  
Vol 29 (2) ◽  
pp. 777-789 ◽  
Author(s):  
Shengchao Zhen ◽  
Kang Huang ◽  
Hao Sun ◽  
Han Zhao ◽  
Ye-Hwa Chen
Keyword(s):  
Dynamic Modeling ◽  
Mechanical Systems ◽  
Fuzzy Approach ◽  
Constrained Mechanical Systems

ON SUFFICIENT CONDITIONS OF EXPONENTIAL STABILITY FOR SYSTEMS OF LINEAR AUTONOMOUS DIFFERENTIAL EQUATIONS WITH AFTEREFFECT

2021 ◽  
Vol 28 (28) ◽  
pp. 73-83
Author(s):  
T. SABATULINA SABATULINA
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Fundamental Matrix ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Comparison System ◽  
System A ◽  
Differential Equa ◽  
Functional Differential ◽  
Autonomous Differential Equations

We consider systems of linear autonomous functional differential equa-tion with aftereffect and propose an approach to obtain effective sufficient conditions of exponential stability for these systems. In the approach we use the positiveness of the fundamental matrix of an auxiliary system (a comparison system) with concentrated and distributed delays.

Dynamic Modelling of a Three Degree-of-Freedom Planar Platform-Type Manipulator

1997 ◽  
Author(s):  
Hazem A. Attia ◽  
Maher G. Mohamed
Keyword(s):  
Differential Equations ◽  
Efficient Solution ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Dynamic Modelling ◽  
Degree Of Freedom ◽  
Constraint Forces ◽  
Dynamic Formulation ◽  
System Of Particles ◽  
Three Degree Of Freedom

Abstract In this paper, the dynamic modelling of a planar three degree-of-freedom platform-type manipulator is presented. A kinematic analysis is carried out initially to evaluate the initial coordinates and velocities. The dynamic model of the manipulator is formulated using a two-step transformation. Initially, the dynamic formulation is written in terms of the Cartesian coordinates of a dynamically equivalent system of particles. Since there is no rotational motion associated with a particle, then the differential equations of motion are derived by applying Newton’s second law to study the translational motion of the particles. The constraint forces between the particles are expressed in terms of Lagrange multipliers. Then, the differential equations of motion are written in terms of the relative joint variables. This leads to an efficient solution and integration of the equations of motion. A numerical example is presented and a computer program is developed.

AUTOMATIC PARALLELIZATION OF ELECTRO-MECHANICAL SYSTEMS GOVERNED BY ODEs

2002 ◽  
Vol 26 (3) ◽  
pp. 347-365
Author(s):  
C.A. Rabbath ◽  
A. Ait El Cadi ◽  
M. Abdonne ◽  
N. Lechevin ◽  
S. Lapierre ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Block Diagram ◽  
Time Integration ◽  
Mechanical Systems ◽  
Automatic Parallelization ◽  
Iteration Step ◽  
Control Laws ◽  
Loop Control ◽  
Novel Method

The paper proposes an effective approach for the automatic parallelization of models of electro-mechanical systems governed by ordinary differential equations. The novel method takes a nominal mathematical model, expressed in block diagram language, and portions in parallel the code to be executed on a set of standard microprocessors. The integrity of the simulations is preserved, the computing resources available are efficiently used, and the simulations are compliant with real-time constraints; that is, the time integration of the ordinary differential equations is performed within restricted time limits at each iteration step. The proposed method is applied to a two-degree-of-freedom revolute joint robotic system that includes an induction motor and two inner-outer loop control laws. Numerical simulations validate the proposed approach.

Differential equations of three-dimensional vibrations for one-dimensional mechanical systems with variable parameters

1984 ◽  
Vol 20 (1) ◽  
pp. 100-106
Author(s):  
E. P. Blokhin ◽  
A. V. Yurchenko ◽  
N. P. Yangulov
Keyword(s):  
Differential Equations ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Variable Parameters ◽  
One Dimensional

Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations

2009 ◽  
Author(s):  
Antranik A. Siranosian ◽  
Miroslav Krstic ◽  
Andrey Smyshlyaev ◽  
Matt Bement
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Design Method ◽  
Nonlinear Partial Differential Equations ◽  
Gain Scheduling ◽  
System Control ◽  
Nonlinear Feedback ◽  
Partial Differential ◽  
System A ◽  
Shear Beam

We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with a destabilizing in-domain nonlinearity is considered first. For this system a nonlinear feedback law based on gain scheduling is derived explicitly, and a statement of stability is presented for the closed-loop system. Control designs are then presented for a string and shear beam PDE, both with Kelvin-Voigt damping and potentially destabilizing free-end nonlinearities. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization-based design.

On the boundedness of motions of mechanical systems described by fuzzy ordinary differential equations

2005 ◽  
Vol 41 (12) ◽  
pp. 1407-1412 ◽  
Author(s):  
A. A. Martynyuk ◽  
V. I. Slyn’ko
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Mechanical Systems
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