Tandem mill feed forward gage control with speed ratio error compensation

A method for controlling metal strip thickness in a multi-stand rolling mill is provided which employs feed forward control to adjust the main drive armature current at the upstream mill stand when strip thickness data arrives at the downstream mill stand, establishes a control signal representing the desired speed of the first stand as a function of the second stand's measured speed, the strip thickness measurements, and the scheduled speeds of the first and second stands, develops an armature current reference modifier which is added to the current reference developed by the conventional speed regulator and thereby improves gage control by reducing the response time for upstream stand speed changes and by correcting upstream stand speed for unplanned changes in downstream stand speed.

BACKGROUND OF THE INVENTION 
This invention relates generally to multi-stand metal rolling mills and, 
more particularly, to a method of improved control of strip thickness in 
such mills. 
Modern multi-stand cold rolling mills commonly employ a form of 
feed-forward gage control which acts between adjacent stands of such 
mills. A thickness gage situated between these stands measures strip 
thickness and sends a strip thickness data signal, with some inherent time 
delay, from the thickness gage to the downstream rolling stand. Upon 
arrival at the downstream stand a control action is initiated, most 
commonly an adjustment to the upstream speed reference in proportion to 
the thickness change from an initial measurement, or from some nominal 
thickness. For example, if a strip's thickness increases by one percent 
from its initial thickness, then upon arrival of the thicker strip region 
at the downstream stand a one percent reduction of the initial upstream 
stand speed reference would be made. The resulting decrease in upstream 
stand speed would cause an increase in interstand tension which would 
reduce the downstream stand rolling force and, accordingly, the gage 
exiting the downstream stand. In another common control arrangement, 
tension between adjacent stands is controlled by adjustment of the roll 
gap of the downstream stand. There the roll gap is closed to restore 
tension to some reference level, so as to reduce the downstream stand exit 
gage by an amount more nearly proportional to the upstream stand speed 
change. 
An objective of feed-forward control is to improve the uniformity of strip 
thickness out of the downstream stand. Control of the absolute strip 
thickness is the objective of later control action, such as feedback 
control based on final thickness measurements, and is not the subject of 
this invention. 
These control strategies and operating practices are well known and have 
been thoroughly described in the rolling literature, for example 
"Thickness Control in Cold Rolling" by D. J. Fapiano and D. E. Steeper, 
Iron and Steel Engineer, November 1983, and "New Approaches to Cold Mill 
Gage Control" by W. D. King and R. M. Sills, AISE Yearly Proceedings, 
1973, p. 187. 
There are two principal weaknesses in prior art embodiments of the feed 
forward gage control strategy. First, upstream stand speed changes are 
delayed by the response time of the stand speed regulator. Considerable 
design effort by others has been directed to improvement of this response 
time by various forcing functions. Second, assumptions are made that the 
strip thickness exiting the downstream stand will be uniform if the 
upstream stand speed is adjusted in proportion to the changes in strip 
thickness entering the downstream stand. This assumption is not sufficient 
if the downstream stand speed changes, as a result of a change in 
interstand tension produced by the change in upstream stand speed. In 
older mills employing screw type gap controls, the tension control by gap 
adjustment is relatively slow and results in tension changes which produce 
transient load disturbances on both adjacent stands. These, in turn, 
produce speed changes that oppose the desired change in relationship 
between the speeds of the adjacent stands. The temporary tension increase 
produced by lowering the upstream stand speed would cause downstream stand 
speed to fall so that the resulting gage correction would be less than 
desired. While this problem might be addressed by some form of approximate 
compensation, the required compensation would depend on schedule dependent 
factors which are difficult to model, and in fact, have not been included 
in known feed-forward control systems. 
To overcome the deficiencies of the prior methods, it is desirable to 
determine and apply the feed-forward corrections in a manner which 
accounts for the speeds of both adjacent stands, and also to improve the 
responsiveness of the main drive control to the feed-forward corrections. 
It is, therefore, an objective of the present invention to provide an 
improved method of rolling metal strip. 
It is a further objective to provide a method of strip thickness control 
which reduces strip thickness variations caused by inadequate response of 
main drive speed regulators and by unplanned variations in rolling mill 
speeds. 
SUMMARY OF THE INVENTION 
In accordance with the present invention a method for controlling metal 
thickness is provided in a rolling mill having at least two mill stands 
and means for adjusting the stand rolling speed. The method of the present 
invention controls strip thickness leaving a downstream stand by measuring 
strip thickness with a thickness measuring means situated between stands. 
The thickness measurements are stored and then retrieved after a delay 
equal to the strip travel time between the thickness measuring means and 
the downstream stand. The instantaneous desired speed of the upstream 
stand is calculated as a function of the actual speed of the downstream 
stand, the planned speeds of both stands, the strip thickness of the strip 
increment arriving at the downstream stand, and its thickness change from 
the initial strip thickness. The reference to the upstream stand current 
regulator is adjusted as a function of the difference between the 
instantaneous desired speed and the actual measured speed of the upstream 
stand.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 shows in schematic form a typical pair of any two adjacent mill 
stands, such as might be employed in the implementation of the method of 
the present invention. It is to be understood that the depiction of FIG. 1 
is simplified to show only the essential elements which are pertinent to 
the present invention. Further, it is understood that the depiction of 
FIG. 1 may be any two adjacent stands of a multistand rolling mill. 
In FIG. 1, a workpiece 18 is passed through opposed workrolls 3 and 4 of a 
first upstream mill stand 1 and opposed workrolls 5 and 6 of a second 
downstream rolling mill stand 2 and passes through thickness sensing means 
7 and over tension sensing means 8, both situated between the stands. 
Workrolls 3 and 4 are driven by motor 9 and workrolls 5 and 6 by motor 10. 
Speed sensors 11 and 12 are connected to motors 9 and 10, respectively, 
and provide speed feedbacks 25 and 26 to main drive controls 13 and 14, 
respectively. Drive controls 13 and 14 maintain stand 1 and stand 2 
rolling speeds at reference levels 23 and 24, respectively, determined by 
computer 17. As the workpiece 18 passes through thickness sensing means 7, 
thickness measurements 20 are made and transmitted to and stored 
sequentially in computer 17. 
FIG. 2 illustrates essential elements of the main drive control 13 in 
simplified block diagram form. Speed reference 23 is compared with speed 
feedback 25 to produce speed error, Ve, which is operated on by the speed 
error or velocity error amplifier 27, to produce the current regulator 
reference Irs. The main drive power supply and motor armature circuit are 
shown combined in armature current regulator 28. The current regulator 
controls the main drive power supply so as to produce the desired armature 
current, I, which results in motor torque, Tm, in accordance with well 
known principles of motor control. The current reference modifier, dIr, 
produced by the method of the present invention, is added to the current 
reference Irs to produce the modified current reference, Ir. Resulting 
armature current, I, produces motor torque Tm which combines with load 
torque, Tl, to produce a corresponding acceleration (.tau.cc) and speed 
change dV. 
Certain elements of the present invention are shown in FIG. 2 to illustrate 
its relation to the conventional main drive speed control. The stand 1 
speed reference V1r is compared with measured stand speed V1 to produce 
the speed error Ve'. This is operated on by the controller 34 to provide 
the current reference modifier dIr which is added to the speed regulator 
current reference Irs to produce the modified current reference Ir. 
Several elements which are not part of the present invention have been 
included in FIG. 1 to assist in complete understanding. It is useful to 
understand that the gap between opposed workrolls 5 and 6 of stand 2 is 
and must be adjustable. In older mills the roll gap is adjusted by screw 
21 under the control of gap control 16. Alternatively, the gap may be 
adjusted by hydraulic cylinders as in many newer rolling mills. Tension 
control 15 receives a strip tension signal 22 from tension sensing means 
8, compares it to the tension reference signal 33, then directs gap 
control 16 to adjust screw 21 so as to reduce the difference between 
signals 22 and 33. The action of these tension and gap control elements 
completes the gage changes initiated by the method of the present 
invention. 
Reference values to the many control equipments required to operate a 
multi-stand rolling mill are typically generated by a set-up computer 17, 
such as the Digital Equipment Corporation VAX-11-780 computer. The desired 
stand velocities 23 and 24 and the desired strip thickness 19, which are 
relevant to the present invention, are among information produced by 
computer 17. Other inputs not pertinent to the present invention are shown 
as carried over bus 30 and would include, as well known in the art, such 
elements as rolling schedule data, operator inputs, etc. Other outputs are 
shown as carried over bus 31. 
In the present invention as well as in prior art, control action associated 
with the thickness in a particular increment of strip is delayed until 
that element arrives at stand 2. In the method of the present invention, 
the speed of stand 2 is combined with the thickness change to generate a 
stand 1 speed reference signal V1r in accordance with the following 
relations: 
EQU V1r=V2 * (V1ro-(dH2 / H2) * V1ro) / V2ro 
where: 
V1r=stand 1 speed reference 
H2=stand 2 entry strip thickness 
H2o=initial value of H2 
dH2=H2-H2o=change in strip thickness entering stand 2 
V2=stand 2 speed 
V1ro=stand 1 scheduled speed reference 
V2ro=stand 2 scheduled speed reference 
The method of the present invention differs from prior art not only in the 
manner in which the speed reference V1r is developed, but also in its use 
to develop the current reference modifier, dIr. In the present invention, 
V1r is compared with the measured stand 1 speed V1 to produce a speed 
error Ve'. Ve' is operated on by a controller to develop the current 
reference modifier, dIr. In a preferred embodiment, that controller 
utilizes proportional and derivative functions of Ve' to produce the 
current reference modifier, dIr. The relationship is: 
EQU dIr=(V1r-V1) * K * (1+Td*s) / (1+Tl*s) 
where: 
K=proportional gain constant 
Td=derivative or lead time constant 
Tl=lag time constant 
s=the operator d/dt 
The current reference modifier, dIr, is added to the current reference, 
Irs, generated by the speed error amplifier 27, to produce the total 
current reference Ir. Simulation and field experience with typical drives 
suggests that good results may be obtained with the following settings: 
##EQU1## 
The method of the present invention can be applied in parallel with the 
prior art method. This would be useful in eliminating cumulative errors in 
the speed regulator. When so used, the present invention would act to 
produce those components of armature current which are required to correct 
for the speed regulator's slow response, as well as to correct stand 1 
speed so as to maintain its proper relation to stand 2 speed. 
While the control methods and associated signals have been described as 
continuous, feed-forward strategies of this type are most typically based 
on sampled deviations from an initial thickness. The translation from 
continuous signal form to sampled data form is well known in control 
design and will not be reviewed here, although one factor of interest in 
the sampled data embodiment is of interest. Particularly, in the sampled 
data form, the computations and transmission of new control references 
associated with each successive thickness change occur at a chosen 
sampling frequency. It is known in the design of closed loop regulating 
systems that sampling frequency within a control loop must be high enough 
with respect to the control loop response to avoid excessive phase shift 
and possible instability. In the method of the present invention, however, 
the main drive current control loop stability is not affected by the 
sampling frequency of the feed-forward control. For this reason, sampling 
frequency need be high enough only to satisfy the gage performance 
requirements. For example, tests indicated that good results in the 
sampled data form are obtained with thickness samples and current 
reference modifier calculations at 0.25 second intervals, although 
intervals of about 0.1 second were required to fully match continuous 
system results. 
FIG. 3 illustrates a computer simulation of feed-forward gage control 
employing a prior art method to correct incoming strip thickness 
variations. A typical sequence of incoming thickness variations to stand 1 
was chosen arbitrarily to illustrate the performance differences. Speed 
reference changes proportional to the gage changes entering stand 2 are 
applied to the stand 1 speed controller. Thickness measurements, i.e., 
gages, are sampled four times per second in this example. Trace I 
indicates thickness leaving stand 2. Trace 2 indicates V1r, the correct 
speed for stand I considering the incoming thickness changes and the speed 
of stand 2. Trace 3 indicates the actual speed of stand 1, which is seen 
to diverge significantly from the desired course indicated by trace 2. 
Thickness leaving stand 2 varied about 0.001 inch over the sample length. 
FIG. 4 illustrates a computer simulation of an improved prior art method of 
feed-forward gage control employing compensation of the main drive dynamic 
response, as was suggested in the previously cited Fapiano et al article 
"Thickness Control in Cold Rolling". The responsiveness of stand 1 speed 
(trace 3) is clearly improved, but there is no significant reduction in 
thickness variation (trace 1) because the change in stand 2 speed has not 
been considered in generating the reference to the speed regulator. 
FIG. 5 illustrates the results of a computer simulation which repeats the 
conditions of FIG. 3 and FIG. 4 but employs the method of the present 
invention. Stand 1 speed follows the desired course (trace 2) more 
accurately and thickness variations leaving stand 2 are reduced about 50% 
compared with the prior art methods. The improvement results from the 
consideration of stand 2 speed changes, which are due largely to the 
tension-induced load changes, and, to a lesser extent, from the additional 
response improvement achieved by supplementing the speed regulator current 
reference, Irs, with the current reference modifier dIr, to achieve the 
desired speed at stand 1. 
The present invention is thus seen to eliminate the principal problem with 
previous methods of feed forward gage control, and in a manner which can 
be readily applied to both new and existing rolling mill gage control 
systems. 
While there has been shown and described what is at present considered to 
be the preferred embodiment of the present invention, modifications will 
readily occur to those skilled in the art. For example, the proportional 
and derivative functions of the controller could be supplemented with an 
integral component to further compensate for poor response in the speed 
regulator. Although such compensation is not essential, it may also 
require means for preventing long term drift in the integrator. 
Furthermore, while thickness deviations have been described as differences 
from an initial measured thickness, likewise, deviations could also be 
defined with respect to a planned or nominal downstream stand entry 
thickness. It is not desired, therefore, that the invention be limited to 
the specific arrangement shown and described and it is intended to cover, 
in the appended claims, all such modifications as fall within the true 
spirit and scope of the invention.