Optimal and Hierarchical Control for Hot Rolling Processes

Copyright © IFAC Large Scale Systems, London, UK, 1995

OPTIMAL AND HIERARCmCAL CONTROL FOR HOT ROLLING PROCESSES

Yu-Qing Liu and Cang-Pu Wu

Department of Automatic Control, Beijing Institute of Technology Beijing , 100081, P. R. CHIN Tel. (861) - 8416688 ext. 2468

Abstract In this paper a study is presented of applying optimal and hierarchical control techniques to realize the overall optimization and control for the hot rolling line. The optimization of schedule for the whole hot rolling production line may be formulated as a two-level planning programming problem. Optimization and coordination methods are also presented. A computational method that transforms the two-level planning programming problem into a single-level nonlinear programming problem is developed. The numerical results confirm the convergence property and feasibility of the algorithm. Keywords: Hierarchical control; hierarchical decision making; optimization problems; steel industry; algorithms.

1. INTRODUCTION

The system is a distributed computer control system with three-level network . The microcomputers of DDC level control the production equipments, rolling mills, rolling up machines etc.. The SCC level computers realizes the adapting control and optimal control. At the same time, the sampled process parameters are analyzed, processed, stored and printed in the computers. The process control level computer harmonizes the whole production line. It finishes the coordination of two mills and calculates the load distributions, and realizes the complicated algorithms etc ..

In recent year the application of computers in steel rolling industry has already reached an advanced level. With the ever-increasing demands for steel plate and strip products (good flatness and gauge, good variety and reasonable price ), it demands to increase the productivity and utilization radio of equipments and reduce the cost of energy as possible in order to cut down the total cost under the rolling products' quality is guaranteed. Therefore the automatic control in steel rolling has been developed from the traditional type based on AGC(automatic control of gauge), APC(automatic control of position ), ATC(automatic control of temperature ) to the production processes, realizing supervision and coordination for the whole production line. The control range of computers has been spreaded the whole hot rolling line.

In the past the optimization of rolling schedules for .

universal and rough mills only implement the local optimal control, so it can't realize the overall optimal control for the large and complicated hot rolling production line. The overall optimal objective is to minimize the drop of temperature in rolling processes under each mill's load values(rolling pressure , rolling power , moment of force , tensile stress etc.) are not exceed the range limit. The main purpose is to cut down the output temperature of steels in furnace under the finish temperature is specified for reducing the cost energy.

In this paper a study is presented of applying optimal and hierarchical control techniques to realize the overall optimization and control for the hot rolling line . The construction of our hierarchical control scheme is depicted in Fig. I. 315

N,

1 1 = minL[Ktt; +KN(N p; -Np(i_I ))2]

systems each of which processes its own decision vectors, objective function and constrained conditions. The process control system in the upper. level has the function of coordinating the regional systems through planning the load allocation for subsystems.

(1)

;= 1

is

heret;

the

pass, ( N p;

time

taken

by

i-th

rolling

N P( ;_I ) ) is the fluctuation of electrical

-

In the above two-level planning problem, A set of optimization problems of the subsystems are regarded as the constraints imposed upon the process control system's decision with respect to x. We give an algorithms for solving this bilevel programs.

machinery power for each rolling pass. Kt and K N are

weight

K _ N -

coefficients

where

Kt

=1- 50,

1

max N

max N is maximum allowing

power. NI is the number of the total rolling passes of

A model for a two-level planning problem is presented in the form of a static stackelberg game , in which the upper-level can influence the actions of the lower-level through a set of coordination variables while the lower-level responses may partly determine the upper-level payoff.

rough mill. The universal mill's rolling schedule is built on the objectives of having equalized pressure in every rolling pass and good accuracy of gauge. On ahead several passes, adopt the equalized pressure as the objective in order to fully developing the ability of rolling mills, reducing the rolling time, reasonable using rolling mills; On the last two passes, adopt equalized convex coefficients as the objective to guarantee the equality of production.

12

= min

N 2-3

N2

;=1

;=N 2 -3

L (P; - P;_1)2 + L (;; - ;;_1)2

In the standard formulation of a stackelberg game the dominator player is designed the 'the leader' and has control over the decision vector X

EX

e Rn, while the 'follows' individually control

=

the decision vectors Yp E ~ eRn" ,p 1"", P . It will be assumed that the leader is given the first choice and selects an X E n( X) e X to minimize his objective function F. In light of this decision, the

(2)

followers select ayE p n p(X) e- Yp to minimize

here Pi is the rolling force of. i-th pass,;; is convex coefficient of the steel on i-th pass N2 is the number of the total rolling passes of universal mill.

their individual objective functions Jp , where

F:XxY ~R I ,

The overall optimal objective is to minimize the drop of temperature on the whole rolling processes under a certain terminate temperature through decisioning the load allocation on 2 mills. This major is to reduce the cost of energy.

Y=Y.I xy.2 x···xYP eR n2 ,

(4)

Jp :XxYp ~ RI, and the sets

n( X)

and

n p (X)

place additional

restrictions on the feasible regions of the leader and followers, For the static case, this leads to the bilevel programming problem given below.

(3)

min F(x,y(x)) subject to: X EX = {x :H(x)

x I ,x2 is the amount of load allocated to the mill i ; YI ' Y2 is the value of the output temperature for the

~

O}

min Jp (x ,yp)

mill i , i=I,2.

subject to :

gp(x,yp)~O

y p E Yp 4. OPTIMAL AND COORDINATE MEmODS

= {y p:Gp (y p) ~ O}

p= 1,···,P

The optimization of schedule for the whole hot rolling production line may be formulated as a twolevel planning problem, i.e., an bilevel programming problems. The lower-level consists of two regional 317

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