Modeling and Control of a Variable Length Flexible Cable Overhead Crane Using the Modified Galerkin Method

2007 ◽  
Author(s):  
Kamal A. F. Moustafa ◽  
Mohamed B. Trabia ◽  
Mohamed I. S. Ismail
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Operating Conditions ◽  
Overhead Crane ◽  
Modeling And Control ◽  
Flexible Cable ◽  
Space Transformation ◽  
Non Linear ◽  
Non Linear System ◽  
State Space Transformation

A mathematical model that accurately represents an overhead crane with flexible cable and load hoisting/lowering is developed. The analysis includes the transverse vibrations of the flexible cable and the trolley motion as well as the load hoisting/lowering motions. A set of highly non-linear partial differential equations and ordinary differential equations that govern the motion of the crane system within time-varying spatial domain is derived via calculus of variation and Hamilton’s principle. Variable-time modified Galerkin method has been used to discretize the non-linear system. State space transformation is then used to get a set of first order ordinary differential equation. A proportional derivative control scheme is applied to derive the underlying crane so that the cable and payload swing are damped out. Numerical simulations for the control performance of the considered system are presented for various operating conditions.

Position Control of Hydraulic Actuators Using Fuzzy Pulse Width Modulation (PWM)

2015 ◽  
Vol 735 ◽  
pp. 294-298 ◽  
Author(s):  
Wei Ying Lai ◽  
Nurfarahin Onn ◽  
Collin Howe Hing Tang ◽  
Mohamed Hussein
Keyword(s):  
Fuzzy Logic ◽  
Pulse Width ◽  
Pulse Width Modulation ◽  
Solenoid Valve ◽  
Operating Conditions ◽  
Hydraulic Actuators ◽  
Non Linear ◽  
Fuzzy Logic Approach ◽  
Logic Approach ◽  
Non Linear System

Hydraulic actuators are widely employed for industrial automation for its high power over weight ratio, functionality in tough operating conditions and low cost. However, the dynamics of hydraulic systems are non-linear and the system subjected to non-smooth and discontinuous non-linearities due to directional change of valve opening, friction, valve overlap and changes of hydraulic pressure acted on valve spool. Taking into account the effect of nonlinear parameter variations such as bulk modulus, compressibility of oil or viscosity of oil, fuzzy logic approach is chosen. Fuzzy control can adapt the inconstant working condition and non-linear system alongside of its robustness. For PWM controlled hydraulic component such as solenoid valve, effective approximation of the flow properties in a solenoid valve is essential. In this paper, the effect of fuzzy logic approach incorporated on pulse width modulation (PWM) controlled hydraulic system is to be investigated and experimentally verified.

scholarly journals A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations

BIOMATH ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 1608111
Author(s):  
Ishwariya Raj ◽  
Princy Mercy Johnson ◽  
John J.H Miller ◽  
Valarmathi Sigamani
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Numerical Method ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Initial Value ◽  
First Order ◽  
Non Linear ◽  
Perturbation Parameters ◽  
Non Linear System

In this paper an initial value problem for a non-linear system of two singularly perturbed first order differential equations is considered on the interval (0,1].The components of the solution of this system exhibit initial layers at 0. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be almost first order convergent in the maximum norm uniformly in the perturbation parameters.

scholarly journals Application of the Poor Man’s Navier–Stokes Equations to Real-Time Control of Fluid Flow

2011 ◽  
Author(s):  
James B. Polly ◽  
J. M. McDonough
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Real Time ◽  
Stokes Equations ◽  
Discrete Dynamical System ◽  
Navier Stokes ◽  
Control Force ◽  
The Poor ◽  
Non Linear ◽  
Non Linear System

Control of fluid flow is an important, and quite underutilized process possessing significant potential benefits ranging from avoidance of separation and stall on aircraft wings and reduction of friction factors in oil and gas pipelines to mitigation of noise from wind turbines. But the Navier–Stokes (N.–S.) equations governing fluid flow consist of a system of time-dependent, multi-dimensional, non-linear partial differential equations (PDEs) which cannot be solved in real time using current, or near-term foreseeable, computing hardware. The poor man’s Navier–Stokes (PMNS) equations comprise a discrete dynamical system that is algebraic—hence, easily (and rapidly) solved—and yet which retains many (possibly all) of the temporal behaviors of the full (PDE) N.–S. system at specific spatial locations. In this paper we outline derivation of these equations and present a short discussion of their basic properties. We then consider application of these equations to the problem of control by adding a control force. We examine the range of PMNS equation behaviors that can be achieved by changing values of this control force, and, in particular, consider controllability of this (non-linear) system via numerical experiments. Moreover, we observe that the derivation leading to the PMNS equations is very general, and, at least in principle, it can be applied to a wide variety of problems governed by PDEs and (possibly) time-delay ordinary differential equations such as, for example, models of machining processes.

scholarly journals Bilateral approximations and periodic solutions of systems of differential equations with impulses

1985 ◽  
Vol 31 (2) ◽  
pp. 293-307
Author(s):  
S.G. Hristova ◽  
D.D. Bainov
Keyword(s):  
Periodic Solution ◽  
Linear System ◽  
Differential Equations ◽  
Periodic Solutions ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Non Linear ◽  
Impulsive Perturbations ◽  
Non Linear System

The paper justifies a method of bilateral approximations for finding the periodic solution of a non-linear system of differential equations with impulsive perturbations at fixed moments of time.

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