Investigation of the optimal control of metal solidification for a complex-geometry object in a new formulation

2014 ◽  
Vol 54 (12) ◽  
pp. 1804-1816 ◽  
Author(s):  
A. F. Albu ◽  
V. I. Zubov
Keyword(s):  
Optimal Control ◽  
Complex Geometry ◽  
Metal Solidification ◽  
New Formulation

scholarly journals Optimal control problem of variable-order delay system of advertising procedure: Numerical treatment

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nasser H. Sweilam ◽  
Taghreed A. Assiri ◽  
Muner M. Abou Hasan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Analytic Solutions ◽  
Delay System ◽  
Variable Order ◽  
Delay Model ◽  
Standard Difference ◽  
New Formulation ◽  
Number Of Customers

<p style='text-indent:20px;'>This paper presents an optimal control problem of the general variable-order fractional delay model of advertising procedure. The problem describes the flow of the clients from the unaware people group to the conscious or bought band. The new formulation generalizes the model that proposed by Muller. Two control variables are considered to increase the number of customers who purchased the products. An efficient nonstandard difference approach is used to study numerically the behavior of the solution of the mentioned problem. Properties of the proposed system were introduced analytically and numerically. The proposed difference schema maintains the properties of the analytic solutions as boundedness and the positivity. Numerical examples, for testing the applicability of the utilized method and to show the simplicity, accuracy and efficiency of this approximation approach, are presented with some comprising with standard difference methods.</p>

Optimal control of thermal processes with phase transitions

2021 ◽  
Author(s):  
Yury Evtushenko ◽  
Vladimir Zubov ◽  
Anna Albu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Crystallization Process ◽  
Automatic Differentiation ◽  
Phase Interface ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Phase ◽  
Metal Solidification

The optimal control of the metal solidification process in casting is considered. Quality of the obtained detail greatly depends on how the crystallization process proceeds. It is known that to obtain a model of a good quality it is desirable that the phase interface would be as close as possible to a plane and that the speed of its motion would be close to prescribed. The proposed mathematical model of the crystallization process is based on a three dimensional two phase initial-boundary value problem of the Stefan type. The velocity of the mold in the furnace is used as the control. The control satisfying the technological requirements is determined by solving the posed optimal control problem. The optimal control problem was solved numerically using gradient optimization methods. The effective method is proposed for calculation of the cost functional gradient. It is based on the fast automatic differentiation technique and produces the exact gradient for the chosen approximation of the optimal control problem.

The Zone Method: A New Explicit Matrix Relation to Calculate the Total Exchange Areas in Anisotropically Scattering Medium Bounded by Anisotropically Reflecting Walls

2002 ◽  
Vol 124 (4) ◽  
pp. 696-703 ◽  
Author(s):  
J. M. Goyhe´ne`che ◽  
J. F. Sacadura
Keyword(s):  
Complex Geometry ◽  
Anisotropic Scattering ◽  
Radiative Properties ◽  
Scattering Medium ◽  
Zone Method ◽  
Indirect Exchange ◽  
Matrix Relation ◽  
Definition Of ◽  
New Formulation ◽  
Total Exchange

A new explicit matrix relation for the calculation of the total exchange areas (TEA) in emitting, absorbing and anisotropically scattering semi-transparent medium bounded by emitting, absorbing and anisotropically reflecting walls has been established. It has been used to directly determine the TEA as a function of radiative properties and geometry of the medium and its boundaries. Computation calls for direct exchange areas (DEA) and indirect exchange areas (IEA). A new definition of these exchange areas reduces their integration order and provides practical energy balance relations for their computation in the case of complex geometry elements. The new formulation is applied in the case of an emitting, absorbing and linearly anisotropic scattering semi-transparent slab bounded by black surfaces. This method is also applicable to nongray medium using the weighted sum of gray gases model.

Optimal control of interconnected, electric energy systems—A new formulation

1972 ◽  
Vol 60 (10) ◽  
pp. 1239-1241 ◽  
Author(s):  
E.C. Tacker ◽  
C.C. Lee ◽  
T.W. Reddoch ◽  
T.O. Tan ◽  
P.M. Julich
Keyword(s):  
Optimal Control ◽  
Electric Energy ◽  
Energy Systems ◽  
New Formulation

Hybrid SN-PN Solution of the Radiative Transfer Equation in Multi-Dimensional Media

2011 ◽  
Author(s):  
Maathangi Sankar ◽  
Sandip Mazumder
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Complex Geometry ◽  
Radiative Transfer Equation ◽  
Discrete Ordinates ◽  
Differential Approximation ◽  
Discrete Ordinates Method ◽  
Surface Exchange ◽  
New Formulation ◽  
Ray Effects

The Modified Differential Approximation (MDA) was originally proposed for solution of the radiative transfer equation (RTE) in order to remove the shortcomings of the P1 approximation in scenarios where the radiation intensity is strongly directionally dependent. In the original MDA approach, the wall-emitted component of the intensity is determined using a surface-to-surface exchange formulation that makes use of geometric viewfactors. Such an approach is computationally very expensive for complex geometry and/or inhomogeneous media. This article presents a new formulation in which the wall-emitted component is solved using the Discrete Ordinates Method (SN approximation), while the medium-emitted component is solved using the P1 approximation, resulting in a hybrid SN-PN RTE solver. Results show that the hybrid Discrete Ordinates-P1 method (DOM-P1) is computationally very efficient, but its accuracy is poor in optically thin situations where ray effects, inherent in the Discrete Ordinates Method, are pronounced. To circumvent this problem, the control-angle Discrete Ordinates Method (CADOM) is finally employed, and the accuracy of the hybrid CADOM-P1 method is found to be far superior to the hybrid DOM-P1 method.

scholarly journals Fundamentals of Synthesized Optimal Control

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 21
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko ◽  
Vladimir Serebrenny ◽  
Peter Zentay
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Method ◽  
Direct Method ◽  
Equilibrium Points ◽  
Control Object ◽  
Optimal Control Method ◽  
Optimal Value ◽  
New Formulation ◽  
The Mathematical Model

This paper presents a new formulation of the optimal control problem with uncertainty, in which an additive bounded function is considered as uncertainty. The purpose of the control is to ensure the achievement of terminal conditions with the optimal value of the quality functional, while the uncertainty has a limited impact on the change in the value of the functional. The article introduces the concept of feasibility of the mathematical model of the object, which is associated with the contraction property of mappings if we consider the model of the object as a one-parameter mapping. It is shown that this property is sufficient for the development of stable practical systems. To find a solution to the stated problem, which would ensure the feasibility of the system, the synthesized optimal control method is proposed. This article formulates the theoretical foundations of the synthesized optimal control. The method consists in making the control object stable relative to some point in the state space and to control the object by changing the position of the equilibrium points. The article provides evidence that this approach is insensitive to the uncertainties of the mathematical model of the object. An example of the application of the method for optimal control of a group of robots is given. A comparison of the synthesized optimal control method with the direct method on the model without disturbances and with them is presented.

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