scholarly journals Asymptotic Analysis of a Deterministic Control System via Euler's Equation Approach

2018 ◽  
Vol 10 (1) ◽  
pp. 115
Author(s):  
Gladys Denisse Salgado Suárez ◽  
Hugo Cruz-Suárez ◽  
José Dionicio Zacar´ias Flores
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Equilibrium Point ◽  
Necessary Conditions ◽  
Equation Approach ◽  
Unique Equilibrium ◽  
Control Sequence ◽  
Euler’S Equation ◽  
Euler's Equation ◽  
Deterministic Control

This paper provides necessary conditions in order to guarantee the existence of an unique equilibrium point in a deterministic control system. Furthermore, under additional conditions, it is proved the convergence of the optimal control sequence to this equilibrium point. The methodology to obtain these statements is based on the Euler's equation approach. A consumption-investment problem is presented with the objective to illustrate the results exposed.

scholarly journals The Optimization of Solutions of the Dynamic Systems with Random Structure

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Miroslava Růžičková ◽  
Irada Dzhalladova
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Random Process ◽  
Control Systems ◽  
Dynamic Systems ◽  
Lyapunov Functions ◽  
Necessary Conditions ◽  
Random Structure ◽  
Random Transformation ◽  
Linear Differential

The paper deals with the class of jump control systems with semi-Markov coefficients. The control system is described as the system of linear differential equations. Every jump of the random process implies the random transformation of solutions of the considered system. Relations determining the optimal control to minimize the functional are derived using Lyapunov functions. Necessary conditions of optimization which enables the synthesis of the optimal control are established as well.

Temperature Control System for Transformer Three-Phase 50 Hz 2500 kVA

2017 ◽  
Vol 3 (2) ◽  
pp. 88
Author(s):  
Suci Rahmatia ◽  
Marsah Zaysi Makhudzia
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Heat Loss ◽  
Temperature Control ◽  
Electrical Energy ◽  
Temperature Control System ◽  
Iron Core ◽  
Electrical Device ◽  
Optimal Control System ◽  
Three Phase

<p><em>Abstrak <strong>- </strong></em><strong>Transformator adalah peralatan listrik yang sangat vital dalam proses pembangkitan maupun transmisi energi listrik karena transformator dapat menaikkan atau menurunkan tegangan. Pada proses menaikkan dan menurunkan tegangan biasanya sering timbul panas akibat rugi – rugi tembaga pada inti besi dan kumparannya sehingga pada kondisi overload akan menimbulkan pemanasan yang berlebih dan dapat mempengaruhi kinerja transformator. Oleh karena itu dibuat sistem kontrol temperatur pada transformer yang dapat mengontrol temperatur di dalam transformator saat bekerja pada kondisi overload, sehigga transformatornya tidak terbakar. Dial thermometer digunakan sebagai alat yang mengontrol temperatur transformator pada sistem kontrol temperatur. Agar mendapatkan sistem kontrol yang optimal, maka setting temperatur pada dial thermometer di sesuaikan dengan temperatur maksimal tranformator dapat bekerja. Sehingga pada saat temperatur tertentu dial thermometer dapat memberikan sinyal untuk membunyikan alarm dan mengaktifkan kontrol kipas sehingga kipas dapat bekerja menurunkan temperatur transformator.<em></em></strong></p><p><strong><em> </em></strong></p><p><strong><em>Kata kunci - </em></strong><em>transformator, rugi – rugi tembaga, temperatur, sistem kontrol, dial thermometer<strong>.</strong></em></p><p><strong><em> </em></strong></p><p><em>Abstract <strong>- </strong></em><strong>A transformer is an electrical device that is vital in the generation and transmission of electrical energy because the transformer can raise (stepping up) or lower (stepping down) the voltage. In the process of raising and lowering the voltage is usually often caused heat loss of copper in iron core and coil so that the overload condition will cause excessive warming and can affect the performance of the transformer. Therefore, a temperature control system on the transformer can control the temperature inside the transformer while working under overload conditions, so the transformer is not burned. Dial thermometer is used as a device that controls the temperature of the transformer in the temperature control system. In order to obtain an optimal control system, the temperature setting on the dial thermometer adjusted to the maximum transformer temperature can work. So that when a certain temperature dial thermometer can provide a signal to sound the alarm and activate the fan control so that the fan can work down the transformer temperature.</strong></p><p><strong> </strong></p><p><strong><em>Keywords -  </em></strong><em>transformator, loss of copper, themperature, control system, dial thermometer<strong></strong></em></p>

scholarly journals Research of Trajectory Optimization Approaches in Synthesized Optimal Control

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 336
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Trajectory Optimization ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Control Object ◽  
Symbolic Regression ◽  
Optimal Location ◽  
Stable Equilibrium Point ◽  
Stabilization System

This article presents a study devoted to the emerging method of synthesized optimal control. This is a new type of control based on changing the position of a stable equilibrium point. The object stabilization system forces the object to move towards the equilibrium point, and by changing its position over time, it is possible to bring the object to the desired terminal state with the optimal value of the quality criterion. The implementation of such control requires the construction of two control contours. The first contour ensures the stability of the control object relative to some point in the state space. Methods of symbolic regression are applied for numerical synthesis of a stabilization system. The second contour provides optimal control of the stable equilibrium point position. The present paper provides a study of various approaches to find the optimal location of equilibrium points. A new problem statement with the search of function for optimal location of the equilibrium points in the second stage of the synthesized optimal control approach is formulated. Symbolic regression methods of solving the stated problem are discussed. In the presented numerical example, a piece-wise linear function is applied to approximate the location of equilibrium points.

Study on the Geometrical Properties and Existence of Orbit Homoclinic to a Saddle Point in n-Dimensional Autonomous Vector Field with Polynomials

2018 ◽  
Vol 28 (14) ◽  
pp. 1850169
Author(s):  
Lingli Xie
Keyword(s):  
Vector Field ◽  
Saddle Point ◽  
Equilibrium Point ◽  
Necessary Conditions ◽  
Continuous System ◽  
Homoclinic Bifurcation ◽  
Stable And Unstable Manifolds ◽  
Geometrical Properties ◽  
Unstable Manifolds

According to the theory of stable and unstable manifolds of an equilibrium point, we firstly find out some geometrical properties of orbits on the stable and unstable manifolds of a saddle point under some brief conditions of nonlinear terms composed of polynomials for [Formula: see text]-dimensional time continuous system. These properties show that the orbits on stable and unstable manifolds of the saddle point will stay on the corresponding stable and unstable subspaces in the [Formula: see text]-neighborhood of the saddle point. Furthermore, the necessary conditions of existence for orbit homoclinic to a saddle point are exposed. Some examples including homoclinic bifurcation are given to indicate the application of the results. Finally, the conclusions are presented.

Optimal Control of the Industrial Furnace System

2011 ◽  
Vol 383-390 ◽  
pp. 3077-3080
Author(s):  
Xin Tong Tang ◽  
Chang Qing Cai
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Energy Consumption ◽  
Industrial Furnace ◽  
Gas Temperature ◽  
Furnace Temperature ◽  
Control Temperature ◽  
Target Control ◽  
Fuel Rate ◽  
General Goal

Control system of industrial furnace is optimized based on the aspect of the combustion. General goal of the control system is to achieve the lowest fuel with the constraints of ensuring the target control temperature of the equipment. And in different output and different fuel quantity conditions, the air-fuel rate is automatically optimized to achieve the goal of energy consumption combined with gas temperature of furnace temperature, oxygen and many parameters.

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