Note: Descriptions are shown in the official language in which they were submitted.
CA 02224878 1997-12-17
WO 97/39I8B PCT/FI97/00226
Method for overall regulation of the headbox and/or the former
of a paper machine or equivalent
The invention concerns a method for continuous overall regulation of the
single-layer
or mufti-layer headbox and/or the former of a paper, board or pulp-draining
machine.
In the following, when a paper machine and papermaking technology are spoken
of,
it should be emphasized that it is considered that these notions and, at the
same time,
the scope of the invention also include the manufacture of board and, where
appli-
cable, also pulp machines.
In a way known from the prior art, out of the slice opening of the headbox of
a
paper or board machine, a pulp suspension bet is fed onto the forming wire or
into
the gap between the wires. As is known from the prior art, the instrumentation
of
the headbox consists of machine controls and of quality and grade regulations,
which
include, in respect of the operation of the headbox, regulations of the
levels, flow
rates and pressures at the short-circulation pumps, sorters, de-aerators, and
equaliz-
ing tanks, controls of the valves of recirculation flows, dilution feeds and
edge flow
feeds, etc., as well as controls of the actuators of the headbox, which
controls
regulate, e.g., the geometry and the cross-direction profile of the slice
channel.
As is kmown from the prior art, as a rule, each individual actuator in the
headbox
has an analogical or digital regulator of its own, which receives its set
value from
the operator or from an optimal regulator operating in respect of some quality
or
- grade quantity. As an example of an optimal regulator can be mentioned the
prior-art
basis weight regulation system of a paper machine, which system is usually
based on
' profiling of the shape of the slice opening or of the supply of dilution
fluid. By
means of optimal regulators of the basis weight profile, attempts are made to
compensate especially for the shape of the basis weight profile which is
measured at
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2
the final end of the dryer section and which arises when water, fillers and
fibers are
removed out of the paper web in the former and in the press section possibly
unevenly in the cross direction, when the web is stretched in the machine
direction
while shrinking in the cross direction during drying of the paper, but also
faults in
the pulp jet arising in or before the headbox may be compensated for. '
From the prior art, a system for the control of the top slice bar at the
headbox of a
paper machine is known, which system comprises a bevel-gear stepping-motor
actuator, by whose means the slice-regulating top slice bar is controlled by
means of
regulation spindles attached to the bar at a spacing of about 7...15 cm, said
spindles
being displaced by means of said actuator provided at their opposite ends. As
a rule,
the profiling of the top slice bar of the slice opening takes place so that
each regula-
tion gear is controlled separately by means of a successive sequence of
treatment. In
order that the positioning could be carried out with the required precision of
about
10 ,um, an electronic system for measurement of the locations of the
regulation
spindles is also needed. In the way known from the prior art, the top slice
bar can
be controlled by means of an optimal system of regulation of the basis weight,
which
system is, according to the prior art, a response regulator based on the
measured
location and shape of unit response. Even though, by means of this system of
regulation based on the top slice bar, it is possible to affect the basis
weight profile
efficiently, a change in the geometry of the slice opening also has a great
effect on
the flow field in the jet, in particular on the velocity components in the
cross
direction and in the machine direction, which is commonly not taken into
account in
the prior-art regulators. The flow field determines the directions of the
fibers (fiber
orientation) in the structure of the paper, which again affects the
anisotropic behav-
lour of the strength and the deformation potential of paper.
As is known from the prior art, in papermaking technology, a pulp suspension
jet is '
fed out of the slice opening of the headbox onto the forming wire of the
former part
or into the gap between wires. Formers known from the prior art are
fourdrinier
formers and twin-wire formers. The twin-wire formers can be divided further
into
gap formers and hybrid formers. In gap formers the pulp suspension jet
discharged
CA 02224878 1997-12-17
WO 9'7139p82 PCTlFI97/a022d
3
from the headbox is fed directly into the farming gap between the forming
wires,
and in hybrid formers, before the twin-wire portion of the forming zone, a
single-
~ wire initial portion is used.
The scope of the method of the present invention includes various forming
parts or
formers of paper machines. lRecently, however, twin-wire formers have largely
replaced the single-wire fourdrinier formers, and the advantages and the
objectives
of the method of the present invention are accomplished to the greatest extent
expressly in twin-wire formers.
In the formers of paper machines, a number of different forming members are
employed. The principal objective of these members is to produce a compression
pressure and pressure pulsation in the fibrous layer that is being formed, by
means
of which pressure and pulsation the draining of water out of the web that is
being
formed is promoted and, at the same time, the formation of the web is
improved.
Said forming members include various forming shoes, which are usually provided
with a curved ribbed deck and over which the forming wires placed one above
the
other and the web placed between the wires are curved. In the area of these
forming
shoes, water is drained through the wire placed at the side of the outside
curve by
the effect of its tightening pressure, and this draining of water is aided
further by a
field of centrifugal force. braining of water also takes place through the
wire placed
at the side of the inside curve, which draining is, as a rule, enhanced by
means of
a vacuum present in a chamber in the forming shoe. The ribbed deck of the
forming
shoe produces said pressure pulsation, which both promotes the dewatering and
improves the formation of the web. Further, the prior-art forming members
include
what is called loading-element units, through which two wires placed one
opposite
to the other run as a straight or curved run. In the prior-art loading-element
units,
' inside the loop of one of the wires there is a pressure loading unit, and
inside the
loop of the opposite wire, a dewatering unit provided with a set of guide and
dewatering ribs has been fitted. As is known from the prior art, said loading-
element
unit is, as a rule, placed on the fourdrinier wire portion so that the loading-
element
unit is preceded by a single-ware portion of considerable length, in which
portion a
CA 02224878 2004-11-25
WO 97t3918Z PCTIFI97lOOZ26
4
substantial amount of draining of water takes place before the web runs as a
straight
run in the plane of the fourdrinier wire through the loading-element unit.
With respect to the patent literature related to the present invention,
reference is
made, by way of example, to the following papers: EP 0541457 AI, US-3, 666,
621,
US 4, 374, 703, US 4, 500, 968, US-4, 680, 089, US 4, 707, 779, US 4, 748,
400, and US
S, 071, 514.
Regarding the applicant's recent patents concerning systems of regulation of
the
headbox, reference is made to the FI Patents 81, 848 (equiv, to EP-0408894 A3)
and
85,731 (equiv. to EP-401188 and US 3,381,341).
In said FI Parent 85, 731, a system of regulation of a paper machine is
described in
which its various actuators are provided.with intelligent actuator
controllers, and the
data communication between a control device higher in the regulation hierarchy
and
the various actuator controllers has been arranged along a path common of the
different actuator controllers, and the different actuator controllers are
cormected to
the system of measurement and computing of the profiling of the web produced
by
means of the paper machine through a serial bus provided with a network
server.
The article: ICIAM/GAMM 95: applied sciences, especially mechanics,
minisymposia
contributions, Hamburg, 3-7 July 1995; edited by E. Kreuzer and O.
Mahrenholtz; Ber-
li_n_: A_k_a_ripmiP Vl_g~ 199f~,~ ~7Pitcr-hriffi flir angPyranritP
Mat?=Pm~til; pnd 1~/lPChan;lr ~l~ldd,-
226?; 76: Suppl. 4) pages 65-68 (Hamalainen J., Tiihonen T.; Modelling and
simulation
of fluid flows in a paper machine head box) seems to be the closest prior art
to our in-
venhon.
The article shows modelling and simulation of fluid flows in a paper machine
head box
in order to optimise the geometry of the head box. A flow model has been
developed
based on the geometry of the head box. Numerical solutions of the flow model
are cal-
culated in order to determine the optimal shape of a component in a head box.
Numeri-
CA 02224878 2004-11-25
4A
caI results of the flow model have been compared to measured velocity profiles
and
pressure profiles in a pilot machine. As the correlation was good it is stated
that the
model is accurate enough to be used in analysing global profiles in slice
channel flows.
The optimal shape of the back wall of the header in the head box has been
calculated as
an example. The boundary condition has been that the velocity profile of the
flow com-
ing from the header is uniform in the cross direction of the machine. This
means that a
two-dimensional model can be used.
i0
The article discloses thus a method for modelling the flows within the head
box in order
to be able to design the geometry of the head box in an optimal way. The cost
function
in the article is only related to simulated and desired velocities of the
outflow boundary
of the header of the head box. This means that the geometry of a head box can
be opti-
15 mised during the construction of the head box by using this model, but the
model is not
aimed at actually controllin5 the head box.
The present invention is directed towards the further development of the prior
art so
that, by means of a paper machine, paper of better quality properties can be
pro-
20 duced more economically. As is well known, for example because of new
printing
methods, the quality requirements imposed on paper become constantly stricter
and
the requirements imposed on the economy of a paper machine become'ever higher.
As is well known, in a papermaking process the headbox and the former
component
which have an entirely decisive role and whose operation Largely determines
the
2S quality properties of the paper. Later compensation for "defects" produced
in the
paper in the headbox and the former are often not even possible, and this
compensa-
lion, for example regulation of various crass-direction profiles, is quite
complicated
and results in expenses, for example, in the form of various investments in
equip-
30 ment, their operation and maintenance.
CA 02224878 1997-12-17
WO 97139f8~ PCT/FI97/0022b
A starting point of the present investment has been the constant increase in
the
computing and data processing capacity of computers and the lowering of the
cost of
said capacity so that, for example in the regulation of a paper machine, it is
possible
to introduce novel applications which were fully impossible earlier because of
5 limitations of the capacity of computers and/or because of the cost of said
capacity.
Besides on the above increased computing and data processing capacity and
reduced
costs of computers, the present invention is partially also based on mapping
work
carried out by the applicant recently in the field of the flows and draining
of paper
I0 stock suspension.
It is a non-indispensable further object of the invention to provide a system
of
regulation of formers by whose means it is possible to make changes of paper
grades
taking place in a paper machine substantially quicker. As is known from the
prior
art, a change of paper grade takes a considerable period of time, typically
from ten
minutes to hours, which has a substantial effect on the operating time ratio
and on
the overall efficiency of the paper machine.
One starting point of the present invention has been the theoretical research
work
taking place both by the applicant and in different research institutes and
univer-
sities, with regard to which reference is made to the Doctoral Thesis
"Mathematical
Modelling and Simulation of Fluid Flows in the Headbox of Paper Machines"
by IVIr. Jari Hamaiainen, Ph. D. , one of the inventors of the present patent
applica-
tion, TJniversity of Jyvaskyla, Department of Mathematics, Report 57,
Jyvaskyla
1993. In the following, a quotation will be made from the beginning of said
Doctoral
Thesis as a background for the present invention.
"The pulp and paper industry is constantly challenged by complex and contra-
dictory problems of how to produce higher quality paper from lower quality
pulp at increased speeds and reduced production costs. Today, the situation is
further complicated by introduction of recycled fiber in the papermaking
furnish.
CA 02224878 2004-11-25
WO 97;39182 PCTlFI97/00226
6
Present day paper machine technology has been achieved mostly through
experimental. work in pilot plants. With increasing speeds and sophistication
of
mc~dern_ papermaking, this approac h has become too expensive and time
consuming, so that more effective ways must be found to carry out further
development of this technology. One such method is mathematical modelling
and numerical simulation. Well known fluid flow models and numerical
methods have been available for many years but only in the last few years has
the development of supercomputers rendered the use of computational fluid
dynamics in practical and industrial applications possible.
Fluid flow phenomena in a paper machine headbox establishes a number of
i.~yFoaant paper properties, chief of which are basis weight and iider orienta-
tion profiles in the three principal directions. The shape of the headbox
internal flow passages and the turbulence they generate are of utmost import-
ante, It is possible to study these phenomena through mathematical modelling
of the fluid flow.
Turbulence is a desirable flow phenomenon, as it contributes to fiber disper-
sion by breaking down fiber flocks and preventing new ones from forming.
The problem is how to model turbulence. Although a general fluid flow
model, the Navier-Stokes equations, exists, the execution of direct numerical
simulation of these equations for turbulent flows is practically impossible.
This
is because a mesh of finite element approximation should consist of an order
of 109 grid points which even today's supercomputers are not fast enough to
handle, nor do they have enough memory capacity. Because of practical
importance of turbulence, a number of models containing empirical laws have
been developed, The most widely used model and one which has also been
used in this work, is the k-a model."
CA 02224878 2004-11-25
WO 97/39182 PCT/FI97/~10022b
7
In accordance with one aspect of the present invention, there is provided a
method for
continuous overall regulation of a single-layer or mufti-layer head box and/or
a former
of a paper, board or pulp-draining machine, comprising the steps of
(a) forming a physical fluid flow model of a pulp suspension flow to be
regulated
in the head box andJor former;
(b) solving the flow model to obtain a simulated flow state based on data on a
geometry of the head box and/or former and initial and boundary conditions
related to the head box and/or former;
(c) obtaining a target flow state based on quality requirements of a paper
produced
from the pulp suspension flow and costs of operation and runnability of the
paper machine;
(d) determining a difference between the simulated flow state and the target
flow
state, the difference constituting a cost function, which is composed at least
of
target profiles of the finished paper; in particular of the basis weight and
fibre
orientation profiles or of values computed from these quantities;
(e) optimising the cost function and then determining optimal regulation
values
and set values for instrumentation devices and actuators of the head box
and/or
former, which affect the pulp suspension flow in the head box andlor the
drainage and flow state of the pulp suspension flow in the former, in view of
' the cost function; and
(f) providing the optimal regulation values and set values to the regulation
devices
of the head box and/or former such that the regulation devices of the head box
andJor former operate at the optimal regulation values to thereby realise the
optimisation of the cost function.
The system of regulation of the headbox of a paper machine that applies the
method
of the present invention is based on a physical model starting from equations
of fluid
dynamics. The physical flow equations of the system of regulation are solved
in the
geometry of the headbox that is being regulated on the basis of the boundary
conditions given by measurements of the headbox, said headbox geometry
consisting
of the shapes of the flow faces, such as walls that can be bent and the top
slice bar.
These boundary conditions may include measurements of the static pressure at
CA 02224878 2004-11-25
7A
different locations in the flow duct in the headbox, measurements of the flow
rates
and flow velocities in different ducts, such as the approach pipe, dilution
feeds and
edge flow feeds, measurements of the draining of water in the former, and
basis
weight profiles and fibre orientation profiles measured in the paper web.
These
CA 02224878 1997-12-17
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8
measurements are arranged so that the boundary conditions necessary for a
solution
of the flow equations can be determined unequivocally by means of the measure-
menu. The solving of the flow equations is carried out by means of a computer
of
high computing capacity by using numerical solution methods, such as known
finite
element methods (FEM) arid finite difference methods (FDM). By using the
solvable
physical flow model fixed by initial values and boundary conditions, the new,
optimal flow conditions in relation to the pre-determined cost function are
predicted.
This is carried out by means of known methods of optimizing. The control set
point
values determined by the optimal flow conditions are set to the actuator of
the
headbox, such as the slice bar or flow faces profilers, the flow valve
actuators and
the speed regulators of the pumps. This procedure is repeated within a time
period
which is short enough to ensure the quality of produced paper.
The continuous system of regulation of the headbox of a paper machine that
applies
the method of the present invention has sufficiently accurate knowledge of the
flow
state of the headbox based on the physical flow model, which is solved by
making
use of the data on the geometry of the headbox and of other initial and
boundary
conditions necessary for the solution of the flow model. The system of
regulation
that applies the invention seeks the best possible regulation and set values
for the
instrumentation devices and actuators of the headbox in relation to the given
cost
function. The cost function to be optimized is, as a solution of the flow
model, the
difference between the flow state obtained on the basis of measurements of
quality
of the paper, of the state and measurements of the instrumentation and of the
costs
of operation and the target flow state that meets the requirements of quality
and
costs. The target flow state is determined by means of the requirements of
quality of
the paper, which requirements depend on the flows in the headbox, and, if
necess-
ary, also by means of tile costs of operation of the headbox.
The system of regulation that makes use of the method of the present invention
knows the effects of the regulation quantities on the flow state of the
headbox and,
thus, also on the flow state of the slice jet on the basis of the physical
flow model.
Thus, the system of regulation finds the best possible regulation and set
values by
CA 02224878 1997-12-17
WO 97139Y82 PCTIg'I971Om226
9
means of optimizing and flow computing, as a rule, without experimentally
estab-
lished responses or without having to slow down or to attenuate the system of
~ regulation of the headbox by means of long time constants and low
amplification
coefficients, which is necessary in the prior-art regulation systems. The
optimal
- 5 change computed by means of the flow model includes the overall changes
produced
by the operations of the actuators in the flow state in the headbox. In such a
case,
the change taking place as a result of optimizing is far more reliable than in
the
prior-art systems of regulation, and as a result of this, an optimal change
can be
carried out as a single operation. This makes the reaching of optimal quality
considerably quicker in paper grade and other changes and reduces the overall
costs.
The flow model of a headbox is based on the basic laws of fluid dynamics, i.e.
on
conservation laws (mass, momentum, energy, angular momentum) or on simplified
equations derived from same, whose numerical solution is possible by means of
a
computer of sufficiently high capacity. The initial and boundary conditions of
the
flow model are on-line or laboratory measurements and information provided by
the
operator, for example, concerning the runnability and costs.
As the basis of the flow model it is possible to use the headbox model
developed by
the applicant, which model consists of models of the header, the equalizing
chamber
and of the slice channel. By means of said models, it is possible to simulate
the flow
velocities, the static pressure, and the turbulence quantities. If it is
desirable to
simulate changes and profiles of consistency, equations for fiber consistency
are
needed. Such equations are known from the prior art, such as from the model
suggested by Morten Steen in his Doctoral Thesis for the accumulation and
destruc-
tion of fiber flocks, but it is a drawback of said model that the flow
velocity field is
not affected by the changes in consistency. A flow model that may possibly be
' applied in ,the present invention is a mufti-phase model which takes into
account the
reactions of the flow field to changes in consistency by means of interactions
of the
different phases (water, fibers, fillers, etc.).
CA 02224878 1997-12-17
WO 97/39182 PCT/FI97/00226
In addition to the headbox flow model, in the present invention a transfer
model is
needed, which determines the relationship between the jet discharged out of
the slice
opening of the headbox and the finished paper, among other things depending on
the
jet/wire ratio, because the measurements of basis weight and fiber orientation
are
5 made from the paper, whereas the headbox flow model calculates the flow up
to the
slice jet only. The transfer model must also include information between the
location
in the system of coordinates in the headbox and the location of the quality
quantity
measured from finished paper. Such a transfer model is known in itself, and it
is
used, for example, by the applicant in the prior-art headbox regulation
systems.
The fixing of the parameters in the flow model of a headbox to be applied in
the
present invention must be carried out specifically for each machine, and if
the flow
model includes an equation for consistency, the fixing must also be carried
out
specifically for the paper grade in respect of each paper grade to be
produced. In
such a case, both direct measurements from the headbox and measurements
carried
out from the paper are required.
The direct measurements are utilized for fixing the headbox model. All measure-
ments that are economically possible in practice are welcome, but it is
easiest to
measure static pressures from a number of different positions in the headbox.
Flow
velocities do not have to be measured, but the velocity profiles needed for
the flow
model must be known otherwise. In particular, it is necessary to know the
velocity
profile in the headbox approach pipe. It can be made known, for example, by
making the intake profile resistance invariable by means of a perforated
plate.
Further, data on the flow rates in the headbox are needed, such as the overall
flow
rate, the recirculation, and the edge feed flow rates.
The interdependence between the slice jet provided by the headbox flow model
and
the paper produced out of said jet is fixed by means of measurements carried
out
from dried paper. If the velocity of the slice jet is measured, for example,
in
connection with the starting of the paper machine, this measurement is
utilized for
verification both of the headbox flow model and of said transfer model.
CA 02224878 1997-12-17
WO 97139p82 PCT/FI97100226
11
For the purpose of fixing the flow model, it is necessary to know the geometry
of
the headbox in detail, also under pressure during operation, in order that the
flow
. model should simulate the flows in the correct geometry. Of course, it is
advisable
to carry out verification measurements from the jet or from paper, either
during the
' 5 starting of a flow-model based regulator or, for example, on-line
constantly during
operation of the machine. However, according to the present-day prior art, the
flow-
field models that have been developed, with their various parameters, are
already
sufficiently good to predict properties of paper so reliably that they can be
used in
optimal regulation in accordance with the present invention.
In the flow model itself, as adaptable and variable parameters needed by the
model
remain exclusively parameters dependent on the flowing material, such as
consist-
encies, viscosities, fiber and filler compositions and parameters that
represent
interactions of the different phases, etc. If these parameters vary within
narrow
limits only, they can also be fixed. For them, it is possible to make a model
of their
own, which is based on possible simple measurements of, for example,
temperature
and consistency etc. which can be integrated in the process, or said
information is
requested from the operator.
The fixing of the transfer model to be fitted between a flow model and the
quality
properties of paper depends on what measurements can be carried out by means
of
the measurement devices of the paper machine on-line or in the laboratory. On-
line
profile measurement of basis weight and formation have been included in the
prior
art for a long time. Currently, the fiber orientation profile is measured as a
routine
operation in the laboratory of the paper mill, from where the data can be
transferred
to the use of the regulation system, for example, by means of a local network.
From the basis weight profile, information is obtained for regulation of the
consist-
ency profile, the formation measurement reports on the turbulence level in the
flow
and on the fiber-flock interactions. From the fiber orientation, a direct
response is
obtained concerning the velocity field in the jet, and conventional regulators
based
on such a transfer model are in operation. In the flow model, the information
CA 02224878 1997-12-17
WO 97/39182 PCT/FI97/00226
12
obtained from the fiber orientation can be used for verification of the
geometry data
and of measurements in particular in respect of the shapes of the top slice
bar of the
headbox and of the header as well as, fox example, in respect of the flow
measure- '
ments of edge flow feeds. As a particularly important feature should be
mentioned
that, when a contradiction arises between the prediction given by the flow
model and
the quality measurements of paper, the headbox is most likely to be
contaminated so
that the contamination starts interfering with the operation of the headbox.
In this
way a clear indicator or diagnostic system can be produced as to when the
runna-
bility and the quality have deteriorated to such an extent that the paper
machine
should be run down for the purpose of washing.
An optimal regulator based on a flow model gives set values to sub-regulators,
such
as to those PI or PID regulators that take care of the control of individual
actuators,
such as valves of additional-feed pipes or spindles of the top slice bar, on
the basis
of flow measurement, position or location measurement, etc. An optimal
regulator
based on a flow model may simulate the flow state either on the basis of set
values
or directly based on measurement. The optimal regulator may take care of
failure
reporting if some actuator or regulator cannot reach the set value.
In order that the methods of optimization could be employed in the method of
regulation in accordance with the present invention, the whole of this method
step of
the invention must be formulated in the form of an assignment of mathematical
optimization. In such a case, what is required is a model as accurate as
possible for
the physical phenomenon concerned, regulation quantities by whose means the
optimum is sought, as well as the cost function that is minimized or
maximized. In
the invention, the regulation quantities may be, for example, dilution profile
of the
pulp suspension, slice-opening profile, recirculation and edge feed flows. The
regulation profiles must be given by means of a few parameters; for example,
the
regulation values of the top slice bar are given by means of the spacing of
its
spindles. The searching of optimal regulation values is carried out by means
of a
general optimizing method, such as in the commonly known OSD (Optimal Shape
Design) assignments, for example, by means of quasi-Newton's methods.
CA 02224878 1997-12-17
WO 9'7139182 PCTlF197100226
13
Said cost function comprises at least the target profiles of finished paper
(basis
weight and orientation), but additionally it may also include components
related to
. runnability and/or to consumption of energy. For example, if a certain
quality level
is set for the paper, it is possible to seek the lowest possible recirculation
so that the
required quality level (and cost level) are achieved. Different weights axe
used for
different costs; for example, tine quality of the paper is adopted as the most
import-
ant factor, andlor, if the runnability can be improved and/or energy be saved
without
deteriorating the quality, this is carried out by means of the method of
regulation of
the present invention. If quality quantities are added to the cost function to
be
optimized, they must be indicated by means of the velocity profiles and the
turbu-
lence of the jet, i.e., in practice, the jet discharged out of the slice
opening is
optimized.
In accordance with the invention it is possible to accomplish a system of
optimization of the regulation parameters of the former part of a paper
machine.
This system is based on a mapping of the draining process that produces the
structure of the paper that is being dewatered, in particular of the flow
field of said
process, by means of a physical model. Above this model in the system of
regulation
in accordance with the present invention, an optimizing system of regulation
operates, by whose means all of the regulation parameters of the former part
are
regulated by means of overall regulation, such as the vacuum levels of the
forming
rolls, loading-element boxes, forming shoes, and/or vacuum flatboxes, the
positions
of the forming rolls and/or forming ribs, and or loading forces and/or
positions of
the water-draining elements, tensions of the forming wires, and/or retention
and its
profiling, as well as other parameters that affect the web formation and the
draining
of water taking place out of the web in the former.
The method of regulation in accordance with the invention does not necessarily
require any direct measurements in the wire part.
It is a substantial advantage of the invention that, based on the model that
is applied,
in real time, the system of regulation of the invention based on the physical
model
CA 02224878 1997-12-17
WO 97/39182 PCT/FI97100226
14
"knows" what is taking place in the wire part and what is the state of
operation of
the wire part. Further, the model that is applied in the invention "predicts"
what will
take place within the wire and what kind of a fiber mesh is being formed.
Thus, by
means of the model-based regulation in accordance with the invention, it is
possible
to enhance the control of paper quality and the operation of the former and to
reduce
the costs of operation continuously arid as an overall control and regulation.
In particular in situations of change of grade in a paper machine, the present
invention provides the advantage that by means of the model it is possible to
predict
new optimal regulation values for the future situation, i.e, for the paper
grade to be
run next. In this way the time taken by the change of grade can be reduced
decisive-
ly, and the operating time ratio and the overall efficiency of the paper
machine can
be increased substantially.
I5 If necessary, in connection with the present invention, it is possible to
apply direct
measurement of retention, or alternatively the retention is obtained from the
model
that is applied in the present invention.
As a rule, the present invention is applied most advantageously so that the
cross-
direction profiles of the paper web, such as the basis weight profiles and the
fiber
orientation profiles, are controlled by means of the headbox by making use of
conventional systems of regulation of the headbox and/or of regulation by
means of
dilution and/or, particularly favourably, by making use of the overall system
of
regulation of the headbox based on mapping and described. However, the scope
of
the invention does not exclude embodiments in which cross-direction profiling
of the
web, such as profiling of water draining pressure and/or of retention, is also
carried
out by means of the former while, if necessary, also making use of the system
of
regulation in accordance with the present invention and of the optimization
carried
out by said system.
'
The system of regulation of the former of a paper machine that applies the
method
of the present invention is based on a physical model starting in particular
from
CA 02224878 1997-12-17
Wd 9'7139~~2 PCTlFI97/00226
equations of fluid dynamics. The physical flow equations of the model and
possible
other, corresponding equations are solved in the geometry of the former that
is being
regulated on the basis of the boundary conditions given by the measurements.
Further, the data on the state of the flow coming from the headbox to the
former
5 (velocity, consistency, turbulence) are required. For fixing of the
parameters of the
model, if necessary, measurements of the draining of water in the former and
basis
weight profiles and fiber orientation profiles measured in the paper web are
utilized.
These data are arranged so that the boundary conditions necessary for a
solution of
the model formed by the flow equations and equivalent can be determined
unequivo-
10 cally. The solving of the flow equations and equivalent is carried out by
means of a
computer of high computing capacity by using numerical solution methods, such
as
known finite element methods (FEM) and finite difference methods (FDM). By
means of the solvable physical flow model fixed by initial values and boundary
conditions, the new regulation values optimal in relation to the pre-
determined cost
i5 function are predicted. This is carried out by means of known methods of
optimizing. The control set point values determined by the computed optimal
flow
conditions are set to the necessary actuators of the former, such as the
actuators that
regulate the vacuums in the suction rolls and/or suction boxes and the wire
tensions.
This procedure is repeated with a time period which is short enough to ensure
the
quality of produced paper in consideration of the circumstances.
The continuous system of regulation of the former of a paper machine that
applies
the method of the present invention has sufficiently accurate knowledge of the
state
of the former, in particular of the flow state, based on the physical model,
which is
solved by making use of the data on the geometry of the former and of other
initial
and boundary conditions necessary for the solution of the model. The system of
regulation that applies the invention seeks the best possible regulation and
set values
- for the actuators of the former in relation to the given cost function.
Also the flow model of a former is based on the basic laws of fluid dynamics,
i.e.
on conservation laws (mass, momentum, energy, angular momentum) or on sim-
plified equations derived from same, whose numerical solution is possible by
means
CA 02224878 1997-12-17
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i6
of a computer of sufficiently high capacity. The initial arid boundary
conditions of
the flow model are on-line or laboratory measurements and information provided
by
the operator, for example, concerning the runnability and costs. -
As the basis of the flow model it is possible to use a mufti-phase model, in
which
there is a law of conservation of momentum and mass for each phase (water,
fibers,
fillers, air} as well as interaction terms for the transfer of the momentum
between
the different phases.
In addition to the former flow model, in the present invention a transfer
model is
needed, which determines the relationship between the formed web after the
former
and the finished paper, depending on the operation of the press section and
the dryer
section and of possible finishing devices, if any. Such a transfer model is
known in
itself, and it is used, for example, by the applicant in the prior-art headbox
regula
tion systems.
The fixing of the parameters in the flow model of a former to be applied in
the
present invention must be carried out specifically for each machine and
specifically
for each paper grade to be produced. In such a case, both direct measurements
from
the former, such as measurements of draining of water, and measurements
carried
out from the paper are required. . The direct measurements are utilized for
fixing the
former model. All measurements that are economically possible in practice are,
as
a rule, useful, but it is easiest to measure draining of water from a number
of
different positions in the former. Further, it is necessary to know the state
of the
flow fed from the headbox to the former.
The interdependence between the web provided by the former flow model and the
finished paper is fixed by means of measurements carried out from dried paper.
For the purpose of fixing the flow model, it is necessary to know the geometry
of
the former part (rolls, shoes) and the flow coming from the headbox, in order
that
the flow model should simulate the flows in the correct geometry. As a rule,
it is
CA 02224878 1997-12-17
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17
advisable to carry out verification measurements from the slice jet or from
the paper,
either during the starting of a flow-model based regulator or on-line
constantly
during operation of the machine.
From the basis weight profile, information is obtained for regulation of the
consist-
ency profile, and the formation measurement reports on the turbulence level in
the
flow and on the fiber-flock interactions.
An optimal regulator based on a flow model gives set values to sub-regulators,
such
as to those PI or PID regulators that take care of the control of individual
actuators,
such as the control of vacuum levels and wire tension, if necessary, based on
measurements of pressure and wire tension.
In order that the methods of optimization could be employed in the method of
regulation in accordance with the present invention, the whole of this method
step of
the invention must be formulated in the form of an assignment of mathematical
optimization. In such a case, what is required is a model as accurate as
possible for
the physical phenomenon concerned, regulation quantities by whose means the
optimum is sought, as well as the cost function that is minimized or
maximized. In
the invention, the regulation quantities may be, for example, vacuum levels,
loadings
of the water-draining members etc, such as positions of forming members. The
searching of optimal regulation values is carried out by means of a general
optimizing method, such as in the cornrnonly known assignments of optimization
of
shape and regulation (Optimal Shape Design), for example, by means of quasi-
Newton's methods.
Said cost function comprises at least the target properties of finished paper
(forma-
tion and orientation level), but additionally it may also include components
related
to runnability and/or to consumption of energy. For example, if a certain
quality
' 30 level is set for the paper, it is possible to seek the lowest possible
wire tension so
that the required quality level (and cost level) are achieved and the wear of
the wire
is reduced. Different weights are used for different costs; for example, the
quality
CA 02224878 1997-12-17
WO 97/39182 PCT/FI97/00226
18
of the paper is adopted as the most important factor, and/or, if the
runnability can
be improved and/or energy be saved without deteriorating the quality, this is
carried
out by means of the method of regulation of the present invention.
The efficiency of numerical flow computing and optimization have a direct
effect on
how quickly the regulation system can react to changes in the running
situation.
Therefore, in the present invention, both advanced numerical algorithms and
high
capacity of computers are required in order that the regulation of the headbox
and/or
the former by means of the flow model should be sufficiently rapid in
practice. if
necessary, the numerical computing can be accelerated by means of a number of
techniques. The optimization is based on changes in the cost function (partial
derivatives) in relation to the regulation quantities. Sensitivities in
respect of each
regulation quantity can be assumed to be independent from one another, in
which
case they can be computed in parallel by means of computers of several
processors.
The computing that is being carried out by each processor can be enhanced, for
example, by means of the perturbation theory. A sensitivity analysis can be
carried
out in an environment of a Iinearized solution so that the flow model is
solved by
means of the perturbation theory (a sort of Iinearization). Even if the
perturbation
theory is not absolutely accurate for a non-linear flow model, it, however,
predicts
a change in the cost function in the correct direction, which is sufficient in
the
computing of the gradient of the cost function.
The sensitivity of a cost function in relation to the regulation quantities
can also be
solved by numerically solving a so-called adjoint state equation. Besides the
solver
of the flow model, this technique also requires a solver of the adjoint state
equation.
When the gradient (sensitivity) has been computed, elsewhere a real non-linear
model is used for optimizing, in which case the optimizing proper is based on
the
real flow model, and inaccuracies produced by the perturbation theory or by
the
solution of the adjoint state equation are riot seen in the final result of
the
optimization.
CA 02224878 1997-12-17
WO 97139182 PCTlFI97100226
19
Said parallel computing can be used both in the optimization in the way
described
above and in numerical solution of the flow model. For example, in the finite-
element method the numerical integration is carried out over every element,
and at
this stage information is not needed concerning the surrounding elements.
' S
Further, if the flow model of the headbox and/or the former consists of a
number of
sub-models, the sub-models can be solved at the same time, and in between data
are
updated between the different processors {sub-models) depending on the
solutions of
the sub-models. The computing can also be enhanced by dividing the
optimization
into parts. Certain regulation quantities are likely to have a greater effect
on the
quality of paper than others, in which case the most important parameters are
optirraized more frequently while reacting to the changes quickly, while other
parameters are optimized less frequently.
An optimal regulation of the sort described above can be carried out while
making
use of a flow model also with some instructible model, such as a neuro-
network, or
with some other statistical model. In such a case, the physical flow model is
solved
in said geometry with several different initial and boundary conditions in
advance,
and with these results, for example, a statistical model can be adapted or
instructed
for the flow state of the headbox/former and/or for the dependence of the cost
function in respect of each individual headbox/former, its flow geometry or
flow
properties.
In the following, an exemplifying embodiment of the invention and an
environment
of application of same will be described in detail with reference to the
illustrations
in the figures in the accompanying drawing, the invention being in no way
strictly
confined to the details of said illustrations.
Figure 1 is a schematic illustration of a single-layer headbox with its most
important
measurement and regulation devices and flow quantities.
CA 02224878 1997-12-17
WO 97/39182 PCT/FI97/00226
Figure 2 shows the same as Fig. 1, to which illustration the measurement and
regulation quantities and the necessary indications of coordinates applicable
to a
single-layer headbox of the present invention have been added. ,
5 Figure 3 is a schematic vertical sectional view of a two-layer headbox given
as an '
environment of application of the invention.
Figure 4 is an illustration similar to Fig. 3 of a three-layer headbox given
as an
environment of application of the invention, and said headbox may also be a
headbox
10 in accordance with the applicant's Patent Application FI-933030 (equivalent
to EP
Appl. 94850116 and equivalent to US Pat. Appl. 08/269348).
Figure 5 illustrates a system of regulation that makes use of the method of
the
present invention as a block diagram.
Figure 6 is a schematic illustration, as an environment of application of the
inven-
tion, of a former with its most important regulation devices and quantities.
Figure 7 illustrates a system of regulation that makes use of the method of
the
present invention as a block diagram of principle.
Figure 8 illustrates a mode of carrying out of a stage of optimizing included
in the
method of the invention as a flow diagram.
Figs. 1 and 2 illustrate a single-layer headbox I00 of a paper machine, which
comprises an approach pipe 10 for the paper stock suspension flow Q~, which
pipe
is connected with the header I2 of the headbox. As is well known, the header
i2
becomes narrower in the flow direction y of the stock suspension. The end of
the '
header 12 opposite to the approach pipe IO communicates with a recircuiation
pipe
13, whose flow rate Qrec is measured. The recirculation flow Qrec is regulated
by
means of the regulation valve 14. The front wall of the header 12 is connected
with
the turbulence generator 15, which comprises one or two successive tube
batteries.
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WO 97/39182 PCTlFI97/00226
21
When two tube batteries are used, there may be an equalizing chamber (not
shown)
in itself known between said batteries. The downstream side of the turbulence
- generator IS is connected to the slice channel 16, which becomes narrower in
the
flow direction x and out of whose slice opening 17 the pulp suspension jet J
is
' S discharged onto the forming wire or into the forming gap between two
wires.
In the illustrations in the present application, the steps and devices of the
paper-
making process following after the headbox 100 are not illustrated in more
detail,
because they are known in themselves to a person skilled in the art. To these
process
steps, reference is made just by the block 200 in the block diagram in Fig. 5.
As is shown in Figs. 1 and 2, in connection with the front wall of the header
12
and/or in connection with the turbulence generator 15, the feed ducts 18 for
dilution
water, preferably white water, are opened, which ducts are provided with
regulation
IS valves IBa, by whose means the distribution of the flow of dilution water
is regu-
lated, and in this way the distribution of the consistency of the headbox flow
rate in
the cross direction y is regulated (Fig. 2). Further, the headbox 100 may be
pro-
vided with regulation spindles 20 for regulation of the cross-sectional flow
area of
the header 12. At both sides of the headbox, edge flow feeds 21 of stock have
been
arranged, which are provided with regulation valves 21a. The slice channel 16
is
provided with regulation spindles 19, by whose means the narrowing of the
slice
channel and/or the profile of the height of the slice opening I7 is/are
regulated in the
cross direction y. At the upstream side of the slice channel 16, in the flow
direction,
a series of detectors 22 for measurement of static pressure are fitted. Also,
if
necessary, the tubes in the turbulence generator 15 can be provided with
actuators,
such as throttle valves, which regulate the pressure loss profile in the cross
direction
y. These devices are not shown in the illustrations.
In accordance with the denotations used in Fig. 2, the quantities of
measurement and
regulation of a single-layer headbox will be given in the following: y = cross
direction of the web, x = machine direction of the web, and z = direction of
thickness of the web. When a quantity has been denoted as a function of y,
i.e. f(y),
CA 02224878 1997-12-17
WO 97/39182 PCT/FI97/00226
22
a cross-direction profile is concerned, which is regulated or computed in
accordance
with the present invention.
Pina Cin~ Qin static pressure, consistency and flow rate of the
stock flow into the header I2;
Uin(x~Z) velocity profile of the flow into the header 12;
p'in(Y) profile of cross-sectional area of header 12;
C(Y)~ QD(Y) profiles of consistency and flow rate of the
dilution feed 18;
I0 Opt(y), CD(y) pressure-loss profile of turbulence generator 15,
consistency profile produced by dilution at the
outlet end of turbulence generator;
Qrec~ Qel ~ Qe2 recirculation flow rate and additional-feed flow
rates at forward edge and rear edge;
IS b(x,y) _ (measured/regulated) shape of slice channel 16 in
machine (x) and cross direction (y);
u(y), v(y), w(y) velocity components of slice jet J:
a = velocity component in machine direction, v
20 = in cross direction, and w = in z-direction;
cjet(y)~ tjet~Y)~ Ejet(Y) consistency, thickness, and turbulence-energy
profiles of the slice jet J;
Qjet,tot overall flow rate of slice jet J.
25 Fig. 3 is a schematic vertical sectional view in the machine direction of a
mufti-layer
headbox construction, while the same reference numerals are used as in Fig. 1.
Fig.
3 shows a headbox 100, in which the stock flow passage 10. ..15,16 has been
divided
into two layers placed one above the other. In the area of the slice channel
16, there
is an intermediate plate 23. In the three-layer headbox as shown in Fig. 4,
the stock
30 suspension flow duct 10. . . 15,16 has been divided into three layers
placed one above
the other, and in the area of the narrowing slice channel 16 there are two
intermedi-
ate plates 23. Out of the slice channels 16, component jets J1,J2 and J3 are
dis-
CA 02224878 2004-11-25
WO 97!39182 PCTIFI97/00226
23
charged, which are combined into the slice jet J. When the invention is
applied in a
multi-layer headbox as shown in Figs. 3 and 4, it is necessary to tape into
account
the static and dynamic pressures between the different layers and the forces
applied
from said pressures to the plate 23 separating the layers. If the plates) 23
islare
fixed, said forces are limited by the strength of the construction. If the
plates) 23
islare provided with hinges and/or is/are flexible, in the program that is
applied in
the present invention the factual location of the plate or plates 23 must be
computed.
This computing can be made as a part of the regulation process based on
measure-
ments provided by the instrumentation of the headbox.
Before the environment (the former) of application of the invention
illustrated in Fig.
6 is described in more detail, it should be stated that the former shown in
Fig. 6 is
just one environment of application of the invention, and attempts have been
made
to choose such a former for said environment of application in which there is
a
number as high as possible of actuators to be controlled by means of the
regulation
method in accordance with the present invention. It should be emphasized that,
of
course, the invention can be applied in highly different environments, most
advan-
tageously in twin-wire formers, but also in fourdrinier wire pans and in
former
sections of board and pulp machines.
The former 100 of a paper machine shown in Fig. 6 comprises a lower-wire 10
loop, which is guided by the guide rolls 11',11'a,ll'b,ll'c and by the first
f~orming-
suction roll 12'. The former 100 comprises an upper-wire 20' loop, which is
guided
by the guide rolls 21',21'c, by the breast roll 21'a, and by the second
forming roll 2~1'.
Through the slice channel 16 of the headbox 100 of the paper machine, a pulp
suspension
jet J is fed into the forming gag G defined by the forming wires 10' and 20',
after
which gap G the twin-wire zone starts directly. The first forming-suction roll
12' is
placed inside the Iower-wire loop 10', and the forming gap G is defined from
above
by the upper wire 20' running over the breast roll 21'a. The position of the
breast roll
21'a is adjustable (arrow A), by means of which adjustability it is possible
to act
upon the magnitude of the sector sl of the twin-wire zone placed on the
suction zone
12'a of the forming roll 12' and, thereby, upon the web formation.
CA 02224878 2004-11-25
WO 97139182 PCT/F'I97/OOZ26
24
The twin-wire zone is in contact with the first forming roll 12' on the sector
sl,
which is followed by the run of the wires 10',20' on which, inside the lower-
wire
loop 10', there is the stationary forming shoe 13'. The forming shoe 13' has a
ribbed
deck 13'a with a large curve radius, whose curve centre is at the side of the
lower
wire 10'. Facing the forming shoe 13', inside the upper-wire loop 20', there
is a
suction-deflector box 23', at whose rear edge there is a deflector rib 23'a
operating
against the inner face of the upper wire 20'..The water that is drained from
the web
W through the upper wire 20' above and ahead of the forming shoe 13' is.
passed
through the space 26' below the box 23' and dough the suction-deflector duct
27', in
the direction of the arrow F1, into the box 23', from which the water is
removed
through the duct 25' communicating with the barometric leg 36. A suitable
vacuum
level p i is maintained in the box 23' by means of a first blower 29 operated
by a first motor
29M. The blower 29 communicates with the box 23' through the duct 28, and air
is
removed from the box in the direction of the arrow Al.
As is shown in Fig. 6, after the second forming-suction roll 24', in the twin-
wire
zone, there follows the MB-unit 50. In said MB-unit 50, there is a water drain
box
30, which communicates with the barometric leg 36 through the duct 34, the
water
level in said leg 36 being denoted with WA. Below the water drain box 30,
there is
a stationary set of support ribs 35. The MB-unit SO includes two successive
water
drain chambers 30a and 30b. The first chamber 30a is a suction-deflector
chamber,
whose suction duct 33a is opened above the first stationary support rib 35.
The first
chamber 30a communicates with a second blower 29a operated by a second motor
29aM through
the duct 32a. The water is drained from the chamber 30a through the duct 34a
into
the barometric leg 36. Below the first suction chamber 30a there is a loading
unit
15', which comprises loading ribs 16', which are loaded by means of pressures
passed
into the hoses 17' and which are placed facing the gaps between the stationary
support ribs 35. Through the gaps between the support ribs 35 the water is
drained
through the upper wire 20' through the space 39 into the duct 33b and from the
duct
further in the direction of the arrow F2 into the second suction chamber 30b.
The
second suction chamber communicates through the duct 32b and through the
regulation valve 53 with a source 55 of vacuum. From the chamber 30b the water
CA 02224878 2004-11-25
WO 97/3918'r PCT/Ft97/002:6
is drained through the duct 34b communicating with the barometric leg 36. The
vacuum level p? and p3 in each chamber 30a and 30b can be regulated
independently
from one another by means of valves 53. Through u'~e suction-deflector duct
33a of
the first chamber 30a, primarily the water is drained that is separated from
the web
5 W directly after the second suction roll 24'.
After the set of ribs 35!16 of the MB-unit 50, inside the lower-wire loop 10',
there
follow three successive suction flatboxes 18, the web W being separated from
the
upper wire 20 in the area of the middle one of said boxes and being guided to
follow
10 the lower wire 10, from which the web is separated at the pick-up point P
and
passed on the pick-up fabric to the press section (not shown).
In Fig. 6, the system of regulation and optimization of the former 100' in
accordance
with the present invention is illustrated schematically as the block 1?0,
which system
15 will be described in mare detail later. From this system 1?0, the
regulation signals
al,a2,a3,a4,a5,a~,b,cl,c2,c3 and c~ which control the operation of the former
100 are
obtained. By means of the regulation signals al...a6 the vacuum levels pl...p6
of the
forming members 23,30a,30b,12,24,18 are controlled. The regulation signal al
controls the speed of rotation of the first motor 29M of the first blower 29,
and thus, by its
20 means, it is possible to regulate the vacuum pl in the box 23'. gy means of
the
regulation signal a2, the speed of rotation of the second motor 29aM of the
second blower 29a
is controlled, and thus, by its means, it is possible to regulate the vacuum
p2 in the
box 30a. By means of the regulation signal a3, the regulation valve 53 is
controlled,
by whose means it is possible to regulate the vacuum p3 in the box 30b
communicat-
25 ing with the suction pump 55. By means of the regulation signal a4, the
regulation
valve 53 is controlled, by whose means it is possible to act upon the vacuum
level
in the suction zone 12'a of the forming roll 12'. Similarly, by means of the
regulation
signal a$, the vacuum level p~ in the suction zone 24'a of the forming roll
24' is
affected. By means of the regulation signal a6, the vacuum level p6 in the
suction
hatboxes 18' is affected by means of the regulation valve 53. By means of the
regulation signal b, the pressures of pressure media are regulated with which
the
loading ribs 16' in the unit 15' of the MB-unit 50, placed inside the forming
wire 10',
CA 02224878 2004-11-25
WO 9739182, PCT/FI97/00226
26
are loaded against the stationary ribs 35 placed aboire. By means of the
regulation
signals cl and c~, it is possible to act upon the wire 10',20' tensions T1 and
T2. By
means of the regulation signal cl, the pressures passed to the actuators, such
as
first hydraulic cylinders 51, of the tensioning roll l lc are regulated, and
in this way the
tension TI of the lower wire 10' is affected. By means of the regulation
signal c2, the
actuators, such as the pressure of second hydraulic cylinders 52, of the
tensioning roll
21'c of the upper wire 20' are affected, and in this way the tension T2 of the
upper
wire 20 is regulated. By means of the regulation signal c3, the position of
the breast
roll 21 and, thus, the length of the curve sector sl at the initial end of the
twin-wire
zone, is affected (arrow A). By means of the regulation signal c~, it is
possible to
act upon the speed v of the wires 10',20'. This regulation of speed is
represented by
the connection of the reg',~laticr. signal c4 with the drive 11'k of the roll
11'b of the
lower wire 10'.
Fig. 5 is a schematic illustration of the construction of the system of
regulation that
carries out the method of the present invention as a block diagram. Fig. 5
'shows the
headbox 100, which was described above and which forms the fiber structure of
the
paper web W. The properties of the fiber structure are obtained by solving the
flow
CA 02224878 2004-11-25
WO 97139182 PCTlFI97/00226
27
model. The entire papertnaking process after the headbox 100 , which process
is in
itself known, is represented by the block 200. The block 200 represents the
press
section and the dryer section of the paper machine and also possible finishing
devices. The transfer function of this process pan 200, i.e. the transfer
model
mentioned above, is known, and it is utilized in the invention in the way that
was
describe: above and that will be described later. The proper ties of the
finished paper
W, such as quality properties and profiles, are measured before the reel-up by
means
of on-line or off line measurements in themselves known, which is illustrated
by the
block I20. Said block 120 communicates with the block 145, which illustrates
the
above transfer model of the headbox 100 . The properties of the slice jet J
are
measured by means of on-line or off line measurements or computed by means of
the flow model of the headbox.
According to Fig. S and 7, the core of the system of regulation is the optimal
controller I30, to which the target values or set values SW are given in
respect of
the properties of the paper W and in respect of the production costs through
the
operator control interface 135. The headbox 100 and the former 100' are
connected
with its instrumentation, which is illustrated schematically by the block 105,
from
which the necessary measurement results M are obtained, which are passed to
the
optimal controller 130. From the optimal controller 130, the set values and
the
regulation quantities C are received for the instrumentation 105 of the
headbox 100
and the former 100' .
The optimal controller 130 includes a computer 140 of high computing capacity,
in
which the software has been stored that controls the various steps of the
method and
carries out the necessary computing. The same computer 140 may also operate as
a
computer that controls the entire papermaking process. The system of
regulation
includes devices 150 that effect the alarms concerning contamination of the
headbox
100 and the condition of the wires and failure operations of the regulation
system,
said devices being connected with the rest of the system of regulation through
the
operator control interface 135.
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The optimal conuoller 130 has knowledge of the geometry of the headbox 100 and
the former 100', receives information on the state of the headbox 100 and the
former
100' by means of measurements and mechanical controls, and
on their basis computes the overall flow state of the headbox 100 and the
former
S 100' at each particular time. Starting from the basic equations of the flow,
from the
quality properties and profiles of the paper W, which can be measured either
in an
on-line process or from off line paper, from the flow properties of the stock
(consist-
ency, composition, fiber length, etc.), the optimal controller 130 computes
the set
values for the insuumentation 105 and for the auxiliary devices of the headbox
100,
such as pumps, in relation to the quality and production-cost target values
set by the
operator through the operator control interface I35 so as to accomplish a
coordinated
optimal flow state. Of the production, c;.sts concerning the headbox 100, it
is
possible to analyze, for example, the extent of the recirculation flow rate
Q~e~ and
the necessary overall flow, which determine the necessary quantity of water
and the
pumping costs. Of the quality and grade quantities should be mentioned, for
example, the basis weight and fiber-orientation and formation profiles, all of
which
are directly and simultaneously dependent on the velocity field and the
consistency
and turbulence state of the slice jet J, which are obtained as a result of
computing.
Of the production costs concerning the former I00' , it is possible to
mention, for
example, the operating output. Of the quality quantities should be mentioned,
for
example, the formation, retention, and orientation level, all of which depend
on the
flow state of the former, which is obtained as a result of computing.
According to Fig. 5 and ?, as to its main principles; the system of regulation
that
makes use of the method of the present invention is a closed, feedback-
connected
system of regulation, whose "actual values" are the various quality properties
and y-
direction cross profiles of the paper web VV coming from the papermaking
process
200, and whose set values SW are formed in the unit 155, in which the
information
necessary for the operator is formed and displayed and reports are given on
the
paper W quality and on the production costs as well as the predictions based
on
simulation. On their basis, the instrumentation 105 of the headbox 100 and the
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29
former are controlled by means of the optimal controller 130. The outer and
wider
regulation loop in the system of regulation in accordance with the present
invention
is a loop formed by the instrumentation 105 of the headbox 100 and the former
100',
by the measurements M, by the optimal controller 130, by the transfer model
145>
and by the set values SW, and the inner, narrower cycle of revelation is C -'
105 -
M --3 130.
On the other hand, in Fig. 7, the connection CAM between the blocks 100' and
105
represents the regulation signals al...a6, b, cl...c4 illustrated in Fig. 6
and possible
measurement signals, which are not needed necessarily and which are not
illustrated
in Fig. 6.
Also, in Fig. 7, as the block 60CSI, a system of regulation and
instrumentation of
the headbox is illustrated, which system controls the headbox 100. The system
60CSI
can be an overall system of regulation and optimization similar to that
described
above and afterwards.
The operation of the system of regulation sketched in Fig. 5 and 7 is based on
the
idea that the flows in the headbox 100 and the former 100' are illustrated as
precise-
ly as possible by means of a physical flow model, which is solved numerically
by
means of the computer 140.
As an example of a physical flow model should be mentioned the Navier-Stokes
equations (1) and (2):
- ~ ~ fN~(Du+~uT)l + p(~W)~ + Gp = p f (1)
at
D ~ a = 0 (2)
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wherein a is the flow velocity, p is the static pressure, f is the volumetric
force
(e.g. gravitation), ~, is the effective viscosity of flowing material, and p
is the
density of said material.
5 For the fiber suspension flow in the headbox 100 and in the former 100',
besides for
the fluid flow, equations are also needed for the dry solids and for the
turbulence,
It is a substantial feature of the physical flow model that it is derived
starting from
basic equations of physics and not, for example, by fitting values that have
been
measured from the processes statistically into simple interdependences or
response
10 models.
in the final part of the papermaking process 200, the properties of the paper
W are
measured on-line (block 120 in Fig. 5 and 7). Further, it is possible to make
use of
off line laboratory measurements. The most important properties of paper W
are, for
IS example, the basis weight and fiber orientation profiles in the direction
of width of
the machine, i.e. in the cross direction y.
When the properties Rp of paper W (p = paper) are known by means of measure-
ments (block 120), and when the properties of the jet R~ (j = jet) are known
by
20 means of the flow model, based on these properties it is possible to form a
transfer
mapping T, i.e. the above transfer model for the effect of the papennaking
process
200 on said property when moving from the jet J of Fig. 2 to finished paper W:
T : R~ --~ Rp (3)
The property R mentioned above is, for example, basis weight profile, i.e. R~
is the
numerically simulated basis weight profile in the jet J, and Rp is the
measured basis
weight profile in the finished paper W ,
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The inverse mapping of this mapping is:
T' 1 : Rp -~ R~ (,4)
When the properties Rp of paper W (p = paper) are known by means of measure-
ments (block 120), and when the properties of the web after the former Rf (f =
former) are known by means of the flow model, based on these properties it is
possible to form a transfer mapping T , i.e. the above transfer model for the
effect
of the papermaking process 200 on said property when moving from the former of
Fig. 2 to finished paper W:
T : Rf --~ Rp ~ (3 a)
The property R mentioned above is, for example, moisture profile, i.e. Rf is
the
numerically simulated volumetric proportion of water after the former, and Rp
is the
measured moisture profile in the finished paper W.
The inverse mapping of this mapping is:
T' 1 : Rp ~ Rf (4a)
For the optimal controller 130 it must be defined what is aimed at in the
optimizing.
Some of the most important aims of the stage of optimizing in the method of
the
present invention are the quality requirements of the paper W . When the
inverse
mapping of the transfer function T is known, by its means it is possible to
set the
targets for the slice jet of the headbox 100 and for the former 100' . For
example, if
an orientation profile Bp(y) is desired for the paper, it is reported to the
system of
regulation that in the jet J the orientation profile must be T'1(Bp(y)) =
Bily) and that
after the former the orientation profile must be T'1(Bp(y)) = 8f(y): In a
correspon-
ding way, a target basis weight profile of paper W is transferred to be the
target
basis weight profile in the slice jet J and of the former 100'. Moreover, it
can be set
as a target to reach these quality requirements with minimal costs of
operation of the paprr
machine.
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The target of the stage of optimizing of the headbox I00 is written as a cost
func-
tion. The cost function determines in a mathematical form how near or far the
desired target is. Generally, the cost function is of the form:
n m
F = E wk ~~ R~k - R~k* ~~ + E el (~ Et - El* ~~ (5)
k=I 1=1
wherein RJk means the property k=I,...,n simulated by means of the flow model
in
the jet, and R~k* means the target property obtained by means of an inverse
mapping
from the properties of the paper in the slice jet J, i.e. R~k* = T-1(Rp).
The target of the stage of optimizing of the former 100' is written as a cost
function.
IS The cost function determines in a mathematical form how near or far the
desired
target is. Generally, the cost function is of the form:
n m
F = E wk ~~ R k - R g* ~~ + E e~ ~) E1 - EI* ~~ (Sa)
k=1 1=1
wherein R ~ means the property k=1,...,n simulated by means of the flow model
after the former, and R k* means the target property obtained by means of an
inverse
mapping from the properties of the paper in the former, i.e. R k* = T-t(Rp).
The weight function wk determines the relative weights of the different
properties in
the cost function. In the second part of the cost function it has been
produced as a
pattern how close the other economical, energy-consumption or runnability
targets
E~ are to the preset targets El* as weighted with the target-specific weight
coefficient
e~ (I = 1,...,m). Here the norm (~ X-X* ~~ means the distance of the actual
value X
from the target X*, which can be defined over a certain geometry, for example
as
the L2-norm, i.e integral of the second power of the difference:
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33
L
~y_x n = 3 ~ «r_ v )z y
0
The value or" the cost function F depends on the solutions Sk of the flow
model of
the headbox 100 and the former 100' , which again depends on the set values of
the
regulation quantities a = [a 1. . . an] of the headbox 100 and of the former
100' .
Thus, the cost function for the headbox 100 is obtained in the form:
n m
F(s~> = E wk II R'k(Sr» - T-lk(Rp) II + ~ e, II E~ - E~* II
k=1 t=1
The cost function for the former 100' is in the form:
n m
F(s(«)) _ ~ Wk II R k(S~) - T lk(Rp) II + E e, II EI - En II
k=1 ~=1
The first part of the cost function to be optimized for the headbox 100 can
also be
formed directly for the quality requirements of paper W by using the pattern
T,
because
II R~(S(~) - T-1(Rp) II = II T(R~(S~)) - Rp II (8)
The first part of the cost function to be optimized for the former 100' can
also be
formed directly for the quality requirements of paper W by using the pattern
T,
because
~I Rf~Sc«~) - T 1(RP) II = ~I T(Rf~s(~)) - Rp 11 (8a)
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and when the properties Rp of the paper W can be represented sufficiently
unequivocally by means of the properties R~ of the jet J or the properties Rf
of the
web. In such a case, the weight coefficients of the cost function must be
considered
in relation to the properties Rp of the paper W and not in relation to the
properties
R~ of the jet or not in the relation to the properties Rf of the web after the
former
100', i.e. either
(1) one moves from the properties of the paper W to the properties of the
slice
jet J or of the former 100' by means of the inverse mapping T-1 or
(2) from the properties of the slice jet J or of the former 100' to the
properties
of the paper W by means of the mapping T.
The purpose of the optimizing stage applied in the present invention is to
minimize
the cost function (F(S(«~)) so that the solution S(a) carries into effect the
flow model
of the headbox 10/former 100' and that the values of the regulation variables
C = a = [«I...«n] are included in the admissible regulation values.
On the other hand, it is desirable to maximize some quantity, for example Eg,
the
norm ~~ g(Eg) ~~ in respect of said property can always be written so that the
value
of the cost function reaches the minimum while the quantity g(Eg) is maximized
or
while the quantity -g(Eg) is minimized.
For the practical conditions, the operator may look for the best combinations
of the
weight coefficients wk and el of the cost function (formula (5) and (Sa)) by
using the
flow model of the optimal regulator of the headbox and the transfer model 145
to
simulate the effects of the combinations of different regulations and weight
coeffi-
cients on the paper W that is being manufactured.
The stage of optimal regulation applied in the invention operates, for
example, in
accordance with the following algorithm (a corresponding flow diagram is given
in
the accompanying Fig. 8):
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0. The necessary flow-rate, stock-grade and geometry data of the headbox
100/former 100' are read. The optimizing is started from the default values
«(1),i=0, and the value F(1) of the cost function is computed by solving the
flow model of the headbox 100/former 100' .
S
I. The gradient ~F(') of the cost function with the regulation values «~')
concerned is computed. The computing of the gradient (= sensitivity of the
cost function in relation to the regulation) requires solution of the flow
model
of the headbox 100/former 100' .
2. The direction ~(') is determined which states in what direction the
regulation quantities must be changed in order to lower the value of the cost
function. At the simplest, the direction can be the direction ~(i) _ -OF(')
obtained by means of the gradient. This is what is called the gradient
method, i.e. the steepest descent direction method. Other gradient-based
methods are, for example, the conjugate gradient method and the quasi-
Newton's methods.
3. The new values of the regulation values «('+~) (Fig. 8) are obtained by
varying them in said direction optimally
a(i + 1 ) = a(i) + ~(i) ~(i) ~ (9)
i.e. the step length A(1) is determined so that the cost function receives a
lower value than with the preceding iteration, F(1+1) < F('), and the regula-
tion quantities «(i+I) are permitted. Tn the search for a good step length,
computing of the values of the cost function and, thus, solution of the flow
model are required.
' 30 4. If the value of the cost function is not yet sufficiently low, an
index for
iteration step is increased, i = i+l, and optimizing is continued from point
I . In the contrary case, optimizing is discontinued, and the values of
optimal
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36
regulation quantities C = «('+1) are transmitted to the regulation devices 105
of the headbox I00/former 100' .
In the following, the patent claims will be given, and the various details of
the
invention may show variation within the scope of the inventive idea defined in
said
claims and differ even considerably from the exemplifying embodiments
described
above for the sake of example only.
