Note: Descriptions are shown in the official language in which they were submitted.
~ 3
ROLLING MILL STRIP THICKNESS CONTROLLER
TECE~NICAL FIELD
This invention relates to a method of, and
apparatus for, control of a rolling mill and more
particularly to control of thickness on hot and cold
metal rolling mills.
BACKGROUND ART
A common configuration of rolling mill has four or
more rolls mounted in a vertical plane with two smaller
diameter work rolls supported between larger diameter
back-up rolls. Such mills may oper~te in isolation or
in tandem with other simi~ar mill stands.
~ particular problem of importance in mill control
arises from out-of roundness in one or more of the rolls
which produces cyclic variations in the gap between the
rolls. These variations in gap cause corresponding
changes in roll separ~ting force, metal velocities and,
most import~ntly, in the thickness of the product
issuing from between the rolls.
Control of output product thickness is usually
effected by changlng the relative gap between the
''`~'1
-2~
work rolls by means of a motor driven screw or hydraulic
cylinder acting on the back-up roll bearings. Usually
the bearing position is measured with respect to the
support frame (the so-called "rollgap p~sitionn). The
separation of the work rolls cannot be directly measured
by the roll gap position because of significant elastic
deformations in the mill stand components.
It is conventional practice to provide a rolling
mill stand with a transducer for measuring the total
deformation force applied to the workpiece and another
for measuring the roll gap position.
Furthermore, it is often desirable to install a
thickness measuring gauge after the stand to monitor the
operation of the process and the effectiveness of any
thickness control system which may be installed.
It is well known to those skilled in this art that
the dynamic response of a feedback control system is
deleteriously affected if a time delay occurs between
the creation of a change and measurement of the change
and for this reason techniques have been developed for
estimating the rolled strip thickness from a knowledge
of the nominal gap between the rolls and the change in
this gap due to elastic deformations which are
calculated as a function of measured force and nominal
material width. This 'iinstantaneous" estimate of
product thickness can be used for feedback control to
the stand on which measurements were obtaîned or for
feedforward control to downstream stands. Major
benefits are gained by use of this technique if the
rollgap adjusting mechanism has a response time which is
significantly less than the time delay to the measured
thickness obtained downstream.
A major drawback of the feedback and feedforward
control techniques described above is that if the mill
work rolls and backup rolls are not perfectly round, the
measured rollgap position is not equal to the true roll
gap position, and eccentricity induced signal components
appear in the force and thickness measurements. These
lead to an incorrect l'estinated thicknessll whicn results in
the control systems correcting non-existent errors,
thereby creating worse product thickness deviations than
are likely to arise with no control.
Numerous techniques have been proposed for
overcoming this problem including tuned filters,
adjustable deadbands, the addition of force control
systems and direct measurement of the eccentricity
effects as the rolls rotate with subsequent subtraction
to cancel their effect. The latter technique has been
shown to have some beneficial results but suffers from
the need to install eccentricity measuring equipment on
the rolls producing the eccentricity com~onent in the
transducer signals.
Normally the back-up rolls are the major source of
the eccentricity signal components although the work
rolls or other, intermediate rolls, m~y al50 contribute~
5~
It is an object of the present invention to provide
a simple and effective method for eliminating the effect
of multiple, superimposed cyclic variations caused by
the individual roll eccentricity signals~ The method
proposed is capable of operation without direct
measurement of the angular position of all the rolls.
However, if such information is available, it may be
used in the proposed method to obtain further benefits.
Accurate, angular speed or position information is
readily available for the driven rolls, usually the work
rolls in a four-high configuration. The angular
position measurement is preferred to an integrated speed
measurement because of its inherently greater accuracy.
These signals and a knowledge of all the roll diameters
is sufficient to implement the proposed method of roll
eccentricity control.
DISCLOSURE OF THE INVENTION
According to one aspect, the invention consists of
a method for automatically controllin~ the thic~ness of
product emerging from a rolling stand comprising the
$teps of producing a first input signal indicative of
total roll force, producing a second input signal
indicative of rollgap position, producing a third input
signal indicative of the angular position of a first
mill roll, producing a fourth input signal indicative of
product thickness at a predetermined downstream location
relative to the rollgap and deriving from 6aid fir~t,
6econd, third and fourtl- input 6ignals a first output
signal indicative of the total roll eccentricity
affecting the true instantaneous rollgap position as a
function of the first mill roll angular position. This
signal varies with time as the rolls rotate and the
relative phase and amplitude of the various roll
eccentricity co~onents alters.
In preferred embodiments of the invention, the
first output signal is filtered by means employing an
algorithm which requires an accurate knowledge of the
period of each significant component which contributes
to the roll eccentricity signal and produces a second
output signal representing the predicted composite roll
eccentricity at the rollgap.
A further recommended step is to estimate the
instantaneous product thickness from the first signal
(F) and the second signal (S) and to modify this
thlckness estimate by the second output signal, thereby
compensating for the effect of roll eccentricity and
producing an eccentricity compensated, instantaneous
thickness estimate. This latter signal is then used as
the input signal to a feedback thickness controller
which adjusts the gap between the work rolls.
If the individual roll periods cannot be estimated
directly ~rom angular position measurements or
indirectly from roll diameter or speed ratios and other
roll angular position measurements, then adaptive
techniques ~hould be invoked to estimate the fundamental
sigrlal period for each roll which is considered to be
-6~ x~
capable of producing eccentricity related thickness
errors.
Further improvement in performance may be achieved
by adding a suitably synchronised proportion of the
second output signal to the output of the feedback
thickness controller. This technique is not
particularly demanding to implement and enables the true
actuator response to be fully utilised for thickness
control. For preference the control design incorporates
other features which explicitly compensate for the
influence of product dimensions, material properties,
bearing characteristics, dependence of the time delays
in the process upon rolling speed and variations in
stand defor~,nation behaviour.
According to a second aspect the invention consists
in:
apparatus for controlling the thickness of material
produced by a rolling mill stand comprising;
means for producing a first input signal indicative
of the roll force (F);
means for producing a second input signal
indicative of rollgap position ~S);
means for producing a third input signal indicative
of roll angular position (v);
means for producing a fourth input 6ignal
indicative of product thickness at a predetermined
downstream position relative to the rollgap (h);
means for derivlng from the first, 6econd, third
_7_ ~ 5~
and fourth input signals a first output signal
indicative of total roll eccentricities;
means for filtering the first output signal to
minimise the influence of noise and produce a second
output signal representing the predicted, composite roll
eccentricity at the roll gap for all rolls whose periods
are specified by angular position or speed measurements
or roll diameter information;
means for deriving from the first input and second
input signal a third output signal indicative of
instantaneous product thickness at the rollgap, and
means for utilising the second output and third
output signals to adjust the rollgap position whereby to
control product thickness independently of roll
eccentricity disturbances.
If desired, a deadzone may be introduced to reduce
the effect of any unfiltered error components in the
instantaneous thickness estimate.
An advantage of a pre~erred embodiment is its
ability to compensate for any hysteresis which may arise
due to sliding ~riction between moving parts of the
stand components or hydraulic cylinders and pistons.
The method of the invention is made possible by the
development of a new eccentricity estimation and
filtering algorithm which may be implemented in a
digital computer and applied to one or more stands in a
rolling mill train.
-8-
BP~IEF DESCRIPTION OF THE DRAWINGS
By way of example an embodiment of the invention is
described hereinafter with reference to the accompanying
drawings wherein:
Fig. 1 shows schematically a conventional rolling
mill stand and control system.
Fig. 2 shows schematically an embodiment of a
rolling mill control system according to the invention.
Fig. 3 shows schematical:Ly a particular form of
Control System structure tested by computer simulation.
Fig. 4 shows an Example of an eccentricity period
estimation algorithm for a case where the true period
was l.Os.
Fig. S shows a filtering arrangement for multiple
eccentric rolls with four different periods.
Fig. 6 shows computer simulation results for
nominal rolling conditions for the case of one periodic
eccentricity.
Fig. 7 shows results corresponding to the previous
figure when errors exist in the mill modulus and
plasticity parameters.
Fig. 8 shows controller simulation results for the
case of four different roll diameters in a four-high
mill, each containing a similar eccentricity amplitude.
Figure 9 shows results of application of an
embodiment of the invention to a tandem mill.
_EST MODE OF PERFORMANCE
With reference to Fig. 1 there is shown
- - - 9 -
schematically a conventional mill stand having a frame
1, upper back up roll 2, upper work roll 3, lower work
roll 4 and lower backup roll 5. The mill is driven by
motors 6.
Rollgap position controls hydraulic cylinders 7
which act on bearings 8 of backup roll 5.
The mill is provided with a ~orce transducer 9
producing a signal indicative of total roll force F' and
a roll gap transducer producing a roll gap position
signal S.
One or more roll angular position signals v are
available from transducers associated with the drive
system. Roll angular position signals (v2-v4) may
optionally be available for other rolls as well. Gauge
11 measures the thickness of strip 12 downstream of the
work rolls and produces a thickness signal h'. Signals
v, h', F' and S are fed to a thickness controller,
together with a reference thickness signal h*. A roll
gap actuator control signal is output by the thickness
controller and adjusts hydraulic cylinders 7 which act
on backup roll bearings 8 to control the gap between the
work rolls.
An embodiment according to the invention is shown
schematically in Fig. 2. The same numerals and letters
are used in Fig. 2 to identify parts and signals as were
used in Fig. 1 to identify corresponding parts and
signal6.
In ~ig, 2,Cl to C~ represent conventional
~2~
control algorithms. It will be understood that in
general signals may be processed via an algorithm by
means of digital or analogue computing apparatus per se
known in the art.
The mill stand of Fig. 2 provides signals F'
(measured force), S (rollgap positior~, v (roll speed
tachometer or position detector) and h' (downstream
thickness) from suitable transducers or measuring
instruments.
The measurements are processed via a thickness
estimator algorithm 13 and an eccentricity predictor
incorporating a smoothing filter 16. Sets of position
synchronised measurements are analysed and the periodic
component obtained by a specified mathematical
substitution.
The eccentricity predictor 16 produces a roll
eccentricity estimate signal 17 which is used by the
thickness estimator 13 to produce a compensated
thickness estimate signal h. This signal h and the
measured thickness signal h' are used in a conventional
manner for feedback control. A further element is added
via a feedforward controller C4 which uses the roll
eccentricity estimate signal to make rollgap position
adjustments before an error is detectable.
A deadzone 18 may optionally be inserted to operate
on the thickness signal h to filter out noise or other
undesirable components which have not been eliminated by
the thickness estimator.
5~8
A variety of controll configurations of varying
complexity may be generated. Most simply this can be
done by redefining the four different control algorithms
~1 to C4 of Fig. 2.
Another feasible configuration could be generated
~y deleting the rollgap position feedback signal to the
rollgap position controller and changing the settings of
controllers Cl to C4 and the process gain
compensation function.
By way of further explanation, the strip exit
thickness h, is given by:
h = S(F,I1) + (S-S0) ~ e (1
where S(F,W) is the elastic deformation of the stand
components, W is the strip width, S is the rollgap (or
screw~ position with respect to an arbitrary datum, S0
is a constant and e is the effective total eccentricity
signal for the complete set of rolls in the mill. S
is normally a constant however, on mills with oil film
bearings, it includes the effective rollgap position
change induced by the backup-roll bearing (a function of
load and angular speed).
During rolling, the variations in roll force are
typically less than 15 percent of the average value and
a linear model F/M~ (for the non-linear function S(F,W)
may be assumed and equation ~1), in linearised form
becomes:
QF - M(Qh - e - QS) (2)
where the ~ill modulus M i6 defined as ~ { a - F- (FrW~}
-12- ~2~
The roll force E' must also satisfy the nonlinear
plastic deformation eyuation if inertial effects are
negligible, that is:
F = W P
where the specific roll force P is a function of h,
rolling parameters and strip disturbances. The linear
form of this eguation is:
AF = ah ~h ~ Fd ~3)
where Fd is a force change due to external
disturbances other than roll eccentricity.
Since the elastic and plastic deformation forces
are always in equilibrium, solving equations (2) and (3)
and eliminating ~F gives:
~ S = (1 + a)~h - Fd/M - e (4)
where
a = - ~ M.
~ his equation defines the control change required
to achieve a specified thickness correction or to
compensate for a known force disturbance.
Because of friction between the roll-neck bearings
and the mill frame, and also in the cylinders of a
hydraulic actuation mill, the measured roll force F' may
not be equal to the roll force ~ exerted on the strip by
the work-rolls. Although the friction force may be less
than 2 percent of the average roll force, it can lead to
6ignificant errors in the estimated thickness
deviations. As5uming that the friction force i6
~ 13~ 5~
proportional to the applied force and has its direction
determined by the direction of the rollgap actuator,
(i.e. Sign (S) ), we may write an equation for the
total friction force Ff as:
Ff = ~EF Si~n(S) (5)
where ~f is a constant friction factor and S is assumed
to be positive when the rollgap is opening. That is,
the rolling force F is related to the measured force F'
by the equation:
F = F'- Ff = [1 - ~f Siqn(S)]F (6)
where the measured force is derived from a load cell
placed between the hydraulic cylinder and the frame.
Similar equations may be derived for other
configurations of measurement and hysteresis models.
The estimate for the combined eccentricity and
steady state offset eO is obtained by substituting the
above expression for roll force F in equation (1), that
i S:
(e + eO) = h - (S-SO) - S(F,W). (7)
Finally, to complete the process model formulation, a
dynamic model for the open-loop actuator response S, as
a function of the input velocity reference signal S* is
required. This may be written as:
S = S /s(l ~ s~a), Ig I s Smax (8)
where s denotes the Laplace transform variable. This
means that the closed loop, actuator position response
will have the characteristics of a 6econd order system.
-14- ~2~5~
It may be assumed that mill modulus M, strip width
W, the hysteresis force coefficient ~f , and the time
delay to the thickness gauge Td are known.
A known key concept in the control strategy is to
use equation (7) to estimate the eccentricity and offset
signal (ê + êO) directly from process measurements,
with the instantaneous thickness replaced by the
downstream thickness h' which corresponds to the exit
thickness rolled at a time Td earlier where Td is the
transport delay between the rollgap and the thickness
gauge. The time delay may be determined from a
knowledge of the work roll speed or angular position and
the nominal forward slip ratio which is defined as the
product exit speed divided by the work roll surface
speed. The forward slip ratio may be calculated from
well-known equations as a function of product dimensions
and properties and nominal processing conditions. Thus,
past values of S and F' must be stored so that
(2 + eO) at time (t -Td) can be estimated as
O)t-Td ht + S(Ft_Td~W) - (St ~ - So) (9)
If the eccentricity signal has period T, then we
can estimate the current value of (e + eO) t as:
(ê + eO) (ê + O t-T (10)
Finally, we can again use equation (7) to give an
instantaneous estimate of the strip exit thickness as;
ht = S(Ft,W) + (St - SO) + (ê-~êO) (ll)
where (e + eO) is obtained from (9) and ~lO).
Equations (9) to (ll) will ~e referred to as the
-15- ~ 5~3~
"eccentricity compensated" thickness estimator and
desirably include additional compensation ~erms for
hysteresis and eccentricity. If the response time of
the thickness gauge is appreciable, then appropriate
filters can be introduced to compensate measured force
and rollgap position.
Numerous combinations of loop design could be
considered to exploit the availability of the thickness
estimate h. Even the simplest system, consisting of a
single loop controller with an input of h and an output
to the actuator speed reference S* gave excellent
results. Further improvement was achieved with three
separate feedback loops for actuator position control,
fast thickness estimate h control, and slower acting
integral control of the measured thickness h'. (See
Fig. 3.)
Combining the outputs of the two outer loops yields
a signal Ah*, which represents the desired change in
strip thickness:
* * ~ r *
~h = kl(h -h) + k2 J (h - h )dt (12)
~here kl, and k2 are tuning constants and h* is the
reference thickness. This is converted to a rollgap
position change by multiplying by the factor (l~a)
derived in equation (4). This calculation is
implemented by box ~0. To this a further predictive
term [(ê~êO) - (e-êO)) may be added to give a
rollgap position reference S~ which takes account of
future eccentricity 6ignals and their effect on the gap
- -16~ 5~8
between the work-rolls. Therefore the control equation
for S* becomes:
S = (l+a)[kl(h -h) ~ k2J(h -h )dt~ + L(ê+êO) - (ê+êO)~ ~SO (13)
where S*O is the initial rollgap positi~n when control
is initiated at the beyinning of a coil. That is,
referring to Fig. 3, k
Cl ~' C2 = S (ST +l) ' C3 = k3 and C4 = 1 (14)
Compensation for actuator non-linearity may be
necessary to prevent overshoot in response to large
amplitude disturbances. This is due to integrator
operation when the actuator speed is constrained to its
maximum value. Alternatively, different controller
algorithms Ci may be introduced.
The controller gain k2 is mill speed dependent
and should be varied as a non-linear function of the
ratio (Ta/~d) . This function is best determined by
simulation, however, if the actuator response is
sufficiently fast, such that ~a/Td is always less
than 0.3, then k2 may be represented by a linear
function of speed.
The previous sections have described the prediction
of the eccentricity signal in a purely deterministic
environment and when there is only one fundamental roll
period in the eccentricity signal. In practice, all
measurements will be corrupted by noise and therefore we
are concerned with the prediction of a periodic signal
from noisy measurements. It has been shown that a
suitable prediction for the filtered estimate Et may
-17~
have the form. A
Et ~ ~Et ~ )(e + eO) , O s ~ s 1 (15)
Inspection of equation ~15) shows tha~ past data i~
given an exponential weighting in forming the predicted
estimate. The parameter ~ affects the memory of the
filter such that if ~ is near 1 then the filter will
have a long memory, good noise discrimination and a slow
response to dynamic changes in the eccentricity
waveform. Conversely, if ~ is near O the filter will
have a short memory with poor noise discrimination but
rapid adaptability. Thus the choice of ~ is a
cornpromise between speed of response and noise
immunity. A fixed value of a was found to be adequate
for the the majority of rolling mill applications. If
necessary, it could be varied in response to a suitable
signal characteristic.
When there are multiple eccentric rolls with
different periods a separate eccentricity estimator E,
similar to that described previously, must be introduced
for each of the m sets of rolls having distinct periods.
The algorithms for each of the filters may be
processed in any order. The input signal to each filter
should preferably be calculated from the eccentricity
si~nal, as determined by equation 7, minus the
cumulative sum of the previously processed filters.
That is, for filter number i, the input is:
m-l
i êOi) - (ê + êO) _ ~ (Ej), i = 1 m (16)
When forming the estimate E~, of the correct
-18~ S ~
value of the composite eccentricity signal for all
rolls, the individual outputs of each filter must be
combined with appropriate synchronisation.
That is,
m
t j-l j' j (17)
This is shown diagrammatically in Fig. 5 for the
case of four different period rolls.
The availability of an accurate, measured thickness
reading for the estimation of the eccentricity siynal
ensures that errors in the elastic deformation and
hysteresis models are corrected by internal feedback
within the estimation algorithms. That is, in the
"steady state", the estimated thickness h is equal to
the measured thickness h' at all sample points on the
eccentricity function. This leads to a remarkable
robustness property which reduces the dependence of the
eccentricity compensation performance upon assumed
nominal model parameters. Of course, the accuracy of
the elastic deformation model does influences the
disturbance attenuation properties of the fi control
loop. The steady state error attenuation factor ~ of
this loop in isolat-on may be shown to be a function of
the controller gain kl and the mill modulus estim~te,
M:
1 + kl(l+aE)
~ 1 + klE(l + a) (1~)
where ~ MJM)
Simulation results, presented hereinafter,
-19-
confirmed that, if the various control loops which
contain product dependent gains are compensated
using equation (13~, then it is feasible to maintain a
fast, consistent response over a wide range of rolled
products.
The previous section discussed the steady state
sensitivity vf the control law ~o model errors.
Clearly, the transient performance depends upon all
pararneters in the model, especially M, a, T, andTd,
The parameter M is a property of the mill and strip
width and can reasonably be assumed to be known within
10~. The time delay Td can be accurately calculated
from the instantaneous work-roll velocity measurements
and the distance from the stand to the thickness
measuring gauge. A good initial estimate for T can be
obtained in a similar way by using the nominal diameter
of the backup-rolls and forward slip ratio. However,
this can be refined, if desired, by substituting T
or T where T is defined as;
t A ^ )2
j O (17)
The appropriate value for To and the frequency of
updating T will depend on the particular application in
a similar mannner to ~ . Updating Of T should be
avoided if the eccentricity signal is small or the mill
speed is varying.
~ inally, the parameter a can vary fr~m coil to coil
depending on rolling conditions and the material grade.
The simulation tests indicated a high degree of
-20- ~2~5~
insensitivity to this parameter, however, if desired, it
can be determined from an adaptive model during the
rolling of each coil.
Fig. 4 illustrates the estimation of ~he period
under noisy conditions. Results such as these suggested
that the estimated period should be estimated with an
accuracy of better than 2%, provided that a sufficient
number of samples is obtained during each roll
revolution.
An extensive simulation evaluation of the new
design performance has been completed whose aim was to
observe the controller performance under ideal and
non-ideal conditions. In the ideal case, when all
relevant parameters are assumed known, the effect of
roll-eccentricity on the strip exit thickness can be
eliminated, provided that the eccentricity disturbances
is within the capability of the rollgap positioning
system~ In the non-ideal case r when parameters are not
e~ual to their true values, it has been found that the
design exhibited a hiyh degree of robustness.
A range of simulated responses are provided in
Figs. 6 and 7 to illustrate typical behaviour and the
robustness of the control system to parameter variations
for a fast rollgap actuator capable of responding to a
0.1 mm rollgap change in 0.06 s. Signals are identified
in Fig. 3. Key simulation parameters were:
* mill modulus: 3.5 MN/mm
~ strip width: 1000 mm
5~18
-21-
* plasticity constant: 2.0
~ time delay: 0.4 s
* control gains: kl=4 , k2=1.0 s 1, Tf = 0.25S
Fig. 6, presents typical simu]ation results for a
composite input thickness disturbance consisting of a
step followed by a negative ramp change and then a
harmonic signal with a period 1.5 timesthe stand 1
backup-roll period. The periodic backup-roll
eccentricity signal is comprised of a first and third
harmonic each of 0.04mm peak to peak amplitude. For the
nominal conditions shown aboVe the attenuation factor
is equal to S.0 and this may be discerned from the step
response components of the simulated thickness
behaviour. The effectiveness of the eccentricity
compensator is evident from a comparison of the response
with and without the eccentricity compensator.
Fig. 7 shows results corresponding to Fig. 6 for
the case where parameter values are not equal to their
nominal values. Specific results are provided for the
case of a mill modulus error of 15~ and a plasticity
parameter of 3.0 (nominal value was 2.0).
Fig. 8 shows controller simulation results for the
case of four different roll diameters in a four-high
mill, each roll containing a similar eccentricity
amplitude.
Results h~ve been obtained from the implementation
of the recommended control system on a tandem cold mill
having an electro-hydraulic position control system
S~8
-22-
which is comparatively 610w by modern standards. Istep
response time for a 0.1 mm change in rollgap position is
0.5 5.) The slow positioning system precludes effective
dynamic cancellation of the eccentricity disturbance
when the mill is rolling at full speed. However, at a
reduced speed, improved performance resulted from the
combined operation of the eccentricity compensator and
gaugemeter controller as is evident in Fig. 9.
As will be evident to those skilled in the art, the
invention herein described may be adapted to different
configurations of mill and to employ control algorithms
other than herein exemplified and such modified
embodiments are deemed to be within the scope hereof.
