Improve algorithms in optimal control for a distributed parameter system with time delay

Journal of Science & Technology 113 (2016) 041-046

Improve Algorithms in Optimal Control for a Distributed Parameter

System with Time Delay

Nguyen Huu Cong

Thai Nguyen University. Tan Thinh ward, Thai Nguyen city Viet Nam

Received: January !9, 2016; accepted: April 24, 2016

Abstract

^0'" a distributed parameter system with time delay. One of the

th^ tlm f ® controlling the embiyos heating process in the oven so that after a given time

% n t c o r f t e % T ” ® sma/tesi error compared with the d e s ir Z tem peraturl TƯ/e are 7wo

w/.ap/ace transform method to solve partial differential equations along with

ầĩnnr?thm fp ^ d e n c e by using numerical methods, the author has pointed out the

The contents of research are proven by simulation and opens the possibility to practical applications.

Keywords: Optimal control, distributed parameter system, non-linear programming, linear programming.

I. Introduction

In many technological processes, heating the

materials is an inevitable important step. The heated

materials can be sewn to produce the final product

for example baking ceramic tiles, ceramics, annealing

mechanical parts, optical fiber, optical glass

tempering, fabrication ferromagnets materials etc...

but can also seiwe as the next outsourcing, means that

baked semi-finished products such as metal to cater to

the hot rolling mill, hammer or forging machines.

Thus prosed a problem is how to control the

temperature distribution in the firing object to satisfy

a certain technical criteria required by the technology.

In terms of controls, materials heating process is

the process control for object with distributed

parameters, with time delay. It means that the

controlled object is not only described by ordinary

differential equation, but also is described by partial

differential equations, with time delay.

This article solves the optimal control problem

for a distributed parameters systems, with time delay

in which controlled object is described by the heat

transfer equations. The problem arises as to

minimize descrepancies between the distribution of

actual temperature in firing materials with

temperature distribution requirement in a given time

T.

To solve this problem, [4] used the numerical

method; however, the optimal solution required a

complex non-linear programing solution. This

research can improve the previous solution.

2. Problem statement

2.1. Object model

The process of one-sided burning in the kiln is

depicted by equation [I] as follows

^~q(x,t) ỡq(x,t)

Ỡ X - ~ ổt (1)

In which, q(x,t) is the distribution of

temperature in object, that depends on the spatial

coordinate X with (0 < X < 5) and the time t with (0 < t

< T ) .

a is the temperature-conducting factor

Ỗ is the thickness of object,

T is the allowed burning time.

The initial conditions and boundary conditions

are given in [1], [4],

q(x,0) = 0 *

* Coưesponding author: Tel.: (+84) 913.589.758

Email: [email protected]

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