THE BUBNOV–GALERKIN PROCEDURE IN PROBLEMS OF MOBILE (SCANNING) CONTROL FOR SYSTEMS WITH DISTRIBUTED PARAMETERS
Journal Title: Հայաստանի գիտությունների ազգային ակադեմիայի տեղեկագիր․ Մեխանիկա - Year 2015, Vol 68, Issue 3
Abstract
We suggest to apply the Bubnov–Galerkin procedure to solve scanning control problems for systems with distributed parameters. The algorithm is described in details for three-dimensional linear heat equation It allows to 54reduce the solution of control problem to finite-dimensional nonlinear moments problem. The procedure of derivation of moments problem is illustrated in details on the example of one-dimensional equation of thermal conductivity. The solution of obtained moments problem is found in a particular case. Based on obtained results a computer simulation is done using COMSOL Multiphysics platform in one-dimensional case for a rod. The main dependences of control function against input data of the problem are revealed. The state of the rod for several (constant) values of the source intensity is expressed in terms of graphs and illustrations. Corresponding illustrations are brought in case of control absence (null-power source) for comparison. An effective numerical scheme for solving the obtained system of nonlinear constraints is suggested in the case of extended class of admissible controls. Calculation of control parameters is reduced to the simplest problem of nonlinear programming.
Authors and Affiliations
Shant Arakelyan, Asatur Khurshudyan
Keywords
Related Articles
- EP ID EP600783
- DOI -
- Views 94
- Downloads 0
On flexure of the symmetrical densely perforated orthotropic plate.
c
Harmonic oscillation of longitudinal shear in an infinite cylinder of arbitrary cross-section with a system of inclusions
The problem of determining the stress state near the thin rigid inclusions in an infinite cylinder of arbitrary cross-section under oscillations of longitudinal shear. We propose an approach to satisfy the conditions sep...
Restoration of boundary conditions at the edges of a rectangular plate for given frequencies of spectrum with an inertial element at the edges
In this paper we consider the problem of finding the boundary conditions of a rectangular plate with an inertial element at two opposite edges, if several frequencies of proper transverse oscillations are known. It is as...
THE FREQUANCY DEPENDANCE OF THE FATIGUE FRACTURE CRITERION
Some recent fatigue tests [1, 2] indicate that the fatigue curves have two fatigue limits. Experiments [3] also indicate the strong frequency dependence of the fatigue fracture process. These two effects are the main top...
A non-linear diffraction problem for high frequency asymptotics.
c