further research.
Rolling Mill Model and Control Problem
The  basic  physical representation of  the  process and  the
relevant variables involved in  the control problem are given in
Fig. 1, and summarized as:  fw is the rolling force, he  is the strip
thickness at entry of  stand; ha  is the strip thickness at output of
stand;  le and la  are the locations of the thickness sensors, so is  the
roll gap with zero rolling force; sr  is the dimensions  of roll stand
with zero rolling force; VI  is the stand input velocity; and vw  is
the stand output velocity.
The measured variables are he,  ha,  vi,  vw,  and  fwj.  As shown  in
Fig.  1,  the roll dynamics can  be  viewed  as  a damped spring
system with an effective displacement input of  so,  the roll gap
with rolling force zero Vw,  =  0).  The roll gap under operation will
be  larger  depending  on  the  entry strip thickness  he  and  the
elasticity  of the stand. The control objective is to keep ha  as close
as possible at a desired value ha,<,,. Basic Equations  -  Nonlinear Model
The bas  LC  equation which establishes  the relationship amon
the variables is given by the equilibrium point determined  by th
characterisi  ics  of the material  and the working curve of the stand
The characteristics of the stand can be represented by the linea
relation gil  en by where K  is the mean yield stress (in Newtons per square meter),
o  is  the mean  applied tension stress  (in Newtons per  square
meter), p  is the coefficient  of friction  between work roll and strip
in roll gap, R'  is the deformed  roll radius (in meters), andfe  is the
output elastic recovery (Newtons).
In order to simulate the system a simplified version of (2)  was
used, The equilibrium point is given by  the intersection of two curves
of forces, namely (I)  and (3).
As (3)  IS quadratic  it is possible to obtain a closed solution  for
the intersection point ha.  In fact, considering The  cutput thickness sensor  is  located  la meters from the
rolling mill. According to this distance,  the dead time associated
with the ineasurements  of ha  is Tu = Za/vw. On the other hand, for
he  there  i  i  associated a delay related to vi given by Te  = Ze/vl. The The basic control objective is to keep  the  thickness of  the
output material  ha  as close  as  possible  to  a reference value
Ha, rr The control variable  is so and the measurements available
are ha,  he,fw, vi,  and vw. The evaluation index is the integral of
the square error over the time elapsed, that is The input velocity  of the strip is given by a prespecified curve
with a certain period of acceleration  and deceleration  (a ramp up
from 1  to 5 ds,  constant, then ramp down). Any changes of the
strip input thickness he  are regarded as disturbances. Here, a
certain profile with steplike changes around the operating point
he = 5 mm is chosen. In  order to get an  idea of how  the nonlinearity of the steel
rolling mill will effect a conventional PI controller based on the
linearized plant, a short description  of the results obtained by the
linear approach is given. The basic  structure has  two parts, a
feedback controller and  a feedforward controller, as shown in
Fig. 2. This figure introduces the variables Ahe, and Aso, which 轧钢机英文文献和中文翻译(2):http://www.751com.cn/fanyi/lunwen_4452.html