Biography

Abstract

Library

Lincs

Return оf search

Individual task

DonNTU Portal of master's

Masters DonNTU Mirgoyazova Antonina Vladimirovna

Mirgoyazova Antonina Vladimirovna

Faculty: Computers technologies of informations and automation

Speciality: Control and automation systems(CSA-06м)

Theme of master's work:

"Research of universal rail and structural rolling mill drives optimum control system dinamics with use of qvadratic quality craterion "

Leader of work: c.t.s., docent Raficov Giyaz Shagiyevich

E-mail: antoninka_kiss@ukr.net

Introduction

Mathematical model

Got results

List of the used literature

About abstract...

On this page such reductions are accepted:

URSM – universal rail and structural rolling mill;
ACS TP - the automatic technological process control system;
ACS - the automatic control system;
LQ-regulator - a linearly-quadratic regulator;
LQG-regulator - a linearly-quadratic Gaussion regulator;
AP - an application package.

A b s t r a c t

Introduction

         A large value has a production of metal for development of national economy and growth of welfare of people. On successful development of metallurgy to a great extent providing of engineer, building, transport, agriculture and other areas of national economy depends a metal.
         A technological process of receipt of the prepared rental is the finishing stage of metallurgical production. Almost all steel, smelted in steel-smelting workshops, passes through rolling shops, therefore along with multiplying the production of rental there is a problem of increase of efficiency of rental production and quality of the prepared product.
         The feature of development of rental production is passing to the continuous processes of rolling.
         Actuality of the control system consists of that applied presently in industry regulators do not provide the optimum modes of operations of flattings mills in most cases.
         The purpose of this work is automation of synthesis of algorithms of optimum management by the quadratic criterion of quality the process of rolling, being many connected and multidimensional object of management. The necessity of consideration of many connected object is explained to influence of processes of rolling in horizontal and vertical directions.
         The optimum functioning of ACS is provided following: by a choice the optimum structure of ACS; by preparation of optimum programmatic influences or optimum structure of questioner device; by optimization of parameters of local regulators. Procedure of optimum synthesis of ACS in general case is directed for development of structure and algorithms, by the best appearance responding to request to exactness, shake and fast-acting of transitional processes; to the management economy. These requirements abstract as a task of minimization of integral quadratic functional of quality. Such task can be decided by principle of a maximum of Pontryagina, methods of classic variation calculation, dynamic programming and other. As it applies to the examined object of management most expedient is the use of principle of a maximum of Pontryagina.

Mathematical model of technological process of rolling of purveyance on co-ordinate axes

A flatting mill is intended for forming of types of rectangular section from the heated metallic purveyances – blanks. The desired type is provided by the rollers of rentals, as shown on a fig. 1:

Figure 1 - Forming of type of rectangular section

The desired form is squeezed out from the purveyance of cylindrical rollers (on one on each of geometrical axes) which move by hydraulic drives two pair.
A management purpose is providing of constancy of thickness of rental on the axes х and у within the limits of the set admittances. Rejection in the thickness of type can be caused two reasons:

by variation of thickness and hardness of purveyance;
by the presence of eccentricity of rollers of rentals.

In order to decrease influencing of these indignations, it is necessary to regulate the size of gap due to introduction of contour of feed-back. As a gap between fellings measuring is difficult, in place of measuring of thickness of type force of pressure of rollers is measured.
Deviation of thickness of purveyance from nominal is designed indignation as "white" noise of wi, skipped through the filter of low frequencies with a transmission function:

function (1)

where KFi - is an amplification factor; TFi - permanent time.
Indignation, related to eccentricity of rollers, - it a function, near to periodic, with frequency, to equal frequency of rotation of rollers. Acceptable model – indignant at "white" noise we signal on the output of filter of the second order with a transmission function:

function (2)

         where psi - is a fading coefficient.
         Force of pressure of rollers is combination of force, developed a hydraulic drive and indignations, rollers caused eccentricity and by deviation of thickness of purveyance from nominal.
         On the basis of these assumptions it is possible to build the following flow diagram for the model of process of rolling on every axis:

Figure 2 - is the Flow diagram of process of rolling on every co-ordinate axis х and у

Here u – management, a delta - deviation of size of gap from nominal (мм), f –deflection forces of pressure of rollers nominal, g – coefficient of transmission, we , wi – "white" noises, imitating indignations, H(s) – transmission function of water driving gear:

function (3)

Mathematical model of the broken a secret system on each of axes it is possible to present in a kind [5]:

function (4)

where х(t)- vector of state of dimension (n x 1), n=5; u(t)- vector of external influences of dimension (m x 1), m=3:

function (5)

y(t) - vector of weekend of variables of dimension (r x 1), r=2:

function (6)

To decide criterion of optimumness of synthesis of automatic regulator of the control the flatting mill of such kind system:

function (7)

         where the first element of criterion is characterized by exactness of work of the system, and the second element is expenses of energy on a management.
         Obviously, choosing the matrices of Q and R properly, it is possible to get a compromise decision between exactness and fast-acting of the examined dynamic system.
         The task of optimization consists of to find the aggregate of vectors of managing influences, providing a minimum of criterion of kind (7):

function (8)

where х(t) - an estimation of vector of state of the system variables; K - matrix of coefficients of optimum management of dimension (mxn).

Got results

On the basis of the algorithms of optimum management got in an analytical form software is developed for automation of the analytical constructing of linearly-quadratic regulators, applied at management the drives of URSM.
Job of the program performances:

Figure 3 - Rejection of thickness of type at the broken (blue) a secret and reserved (black) one-measuring system for the axis of x, and then y

At the closed system, at a LQG-regulator the rejection of thickness of type diminishes approximately in four times, as for the axis of x and for y.

Figure 4 - Reaction on indignations of the broken (blue) a secret and reserved (black) contours of the system with a LQG-regulator, expected for the multidimensional system without taking into account cross connections for the axis of x, and then y

It ensues from the presented graphs, that adjusting descriptions were worsened, as a maximal rejection of thickness of rental is approximate in four times more than at the design of the one-measuring systems. Consequently, synthesis of LQG-regulator without taking into account cross connections it is impossible to acknowledge satisfactory at the real level of to influence of channels.
With the purpose of improvement of management quality will make the synthesis of multidimensional LQG-regulator for the complete system taking into account influencing of cross connections:

Figure 5 - Transitional processes in the broken (blue) a secret and reserved (black) contours of management at the use in the feed-back of multidimensional LQG-regulator for the axis of x, and then y

At the use of multidimensional LQG-regulator will confront the level of rejections of thicknesses of rental with rejections, got for one-measuring system. Results, got at an experimental design, illustrated considerable advantages of direct synthesis of multidimensional regulators.