Note: Descriptions are shown in the official language in which they were submitted.
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A METHOD FOR THE CONTROL OF A GROUNDWOOD PULPING PROCESS
The present invention relates to a method for the control
of a groundwood pulping process in order to achieve an
optimal value for both the drainability of the pulp and for
another characteristic of the pulp, preferably for the
S tearing resistance of the pulp.
In controlling the pulp grinding process one object is
usually to have a constant drainability value or freeness
(CF) of the pulp. The control is for instance made so that
the wood supply pressure is kept constant, whereby the wood
supply rate is allowed to vary. Alternatively the wood
supply rate can be kept constant and the supply pressure is
allowed to vary.
When only the CF value of the pulp is used as the measured
variable to control the process this of course has a
disadvantage in that the CF value will not provide all
information about the other quality properties of the pulp,
which can be characterised by many measured quantities,
such as tearing resistance and tensile strength, light-
scattering and opacity.
The Finnish patent FI 70438 proposes a method to control a
groundwood pulp process with the aid of a new quantity, the
plasticity of the wood, as the control parameter. A desired
pulp property is obtained at a given (constant) peripheral
speed of the grinding stone when the supply pressure and
the wood supply rate is selected so that during otherwise
constant operating conditions (constant wood quality,
constant peripheral speed and sharpness of the grindstone)
. a plasticity value is obtained.
From tests which are partly published and which are
summarised below, it is known that at a constant freeness
it is possible to improve the strength characteristics of
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the pulp, particularly the tearing resistance, by reducing
the peripheral speed of the grinding stone. According to an
article by Jan-Anders Fagerhed, "Development of wood
grinding", Paperi ja Puu - Paper and Timber 72 (1990):7,
the tearing resistance increases about 40 ~ at a grinding
overpressure of 0 to 1 bar when the peripheral speed of the
grinding stone is reduced from 30 m/s to 10 m/s.
Correspondingly, the tearing resistance increases about 20
at an overpressure of 2 bar, and about 8 ~ at an
overpressure of 3 to 4 bar. The same article also discloses
that the tensile strength (at a given freeness value) can
be affected to a certain amount by the peripheral speed of
the grinding stone, even if the effect is not as obvious as
concerning the tearing resistance. However, the tensile
strength increases about 35 ~ when the grinding is made at
atmospheric pressure and the peripheral speed is reduced
from 30 m/s to 10 m/s.
In the method presented according to FI 70438 there was not
proposed any variation of the peripheral speed in order to
obtain an improved tearing resistance in addition to the
desired freeness value.
The object of the present invention is to control the
pulping process so that an optimal pulp quality is
obtained, in other words so that optimal values are
obtained both for the CF value of the pulp and for another
quantity characterising the quality of the pulp, such as
the tearing resistance, which usually is stated as the tear
index (RI). As a criterion one uses the minimum sum of the
squares of the system deviation from the desired levels
concerning these quantities.
The features of the invention are presented in claim 1.
The method can be used in common stone pulping without
overpressure (so called stone groundwood or SGW pulp) as
well as in so called overpressure pulping (pressure
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groundwood or PGW).
In principle the pulping process can be controlled by two
control variables, i.a. the wood supply rate (or power) and
. the peripheral speed of the grinding stone. The supply rate
can keep the CF value of the pulp at a desired level, and
the peripheral speed of the stone can keep another variable
at a desired level. Thus it is possible to control the
process by a multivariable method with two input signals
and two output signals.
The control can be effected with the aid of a multivariable
control algorithm or with two SISO loops (single input,
single output).
The CF value and the tear index of the pulp are kept on a
desired level, and the sum of the deviations
( CFx-CFo ) z + ( RIX-RIo ) z
is minimised, where CFo = freeness set point; CFX = measured
freeness value; RIo = tear index set point; and RIX =
measured value of the tear index.
The multivariable control algorithm can also be made
adaptive in order to compensate for changes in the grinding
stone's sharpness with time.
The relation between the grinding stone's sharpness and the
properties of the mass has been earlier published (see for
instance Georg v. Alftan, "Valmistusolojen vaikutus
mekaanisen massan ominaisuuksiin", in the textbook
"Puukemia", Waldemar Jensen, Helsinki 1967.
Measurement data which has been published by Jan-Anders
Fagerhed (Development of wood grinding, Part 3 Effects of
casing pressure and pulpstone speed, Paperi-Puu - Paper and
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Timber 72 (1990):7, 680 - 686) and which is supplemented by
previously unpublished material are presented below.
A list of the symbols used below:
m - mass flow ( ) kg/h
P - grinding overpressure ( ) bar
Fn - supply pressure ( ) N
Vn - supply rate ( ) mm/s
VP - peripheral speed ( ) m/s
SER - specific energy requirement ) MWh/t
(
Tear - tear index ( ) mNm2/g
CFS - Canadian Standard Freeness ) ml
(
Results:
Table 1: Po T = C +/- 1 C
80
m P Fn Vn V CFS
SER
Tear
kg/h bar N mm/s P MWh/t mNm2/gml
m/s
0.97 0 180 0.56 30.0 1.90 2.90 68
1.97 0 200 0.71 30.0 1.52 3.00 120
1.60 0 265 0.85 30.0 1.37 2.80 146
1.85 0 240 1.05 30.0 1.26 2.90 157
0.84 0 185 0.56 20.0 1.58 3.85 75
1.17 0 320 0.64 20.0 1.38 3.80 110
1.47 0 290 0.80 20.0 1.23 3.40 110
1.57 0 355 0.92 20.0 1.07 3.15 180
0.66 0 280 0.36 10.1 1.44 3.75 90
0.92 0 380 0.50 10.0 1.29 4.20 100
1.12 0 500 0.58 9.9 1.14 4.35 150
1.23 0 465 0.69 10.0 1.01 4.20 170
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Table 2: P1 T = C +/_ 1 C
95
m P Fn Vn Vp SER CFS
Tear
5 kg/h bar N mm/s m/s MWh/t mNm2/gml
0.99 1.0 110 0.41 30.0 1.79 3.70 90
1.07 1.0 170 0.53 30.0 1.84 3.90 65
1.28 1.0 200 0.63 30.0 1.55 3.85 105
1.50 1.0 225 0.74 30.0 1.40 3.25 120
0.75 1.0 150 0.38 20.0 1.57 4.65 90
1.00 1.0 245 0.48 20.0 1.45 4.40 85
1.28 1.0 265 0.59 20.1 1.15 5.15 140
1.34 1.0 230 0.69 20.0 1.31 4.55 60
0.64 1.0 335 0.30 10.0 1.38 5.35 85
0.79 1.0 420 0.38 10.0 1.02 4.95 95
1.04 1.0 435 0.49 10.0 1.09 5.30 110
1.18 1.0 460 0.59 10.0 0.93 5.45 120
Table 3: Pz T 110 C +/- 1 C
=
m P Fn Vn Vp SER CFS
Tear
kg/h bar N mm/s m/s MWh/t mNmz/gml
0.94 2.0 110 0.51 30.0 1.61 4.55 120
1.28 2.0 210 0.62 30.0 1.39 5.05 130
1.66 2.0 200 0.76 30.0 1.06 4.80 220
1.88 2.0 195 0.94 30.0 1.18 4.50 175
0.81 2.0 80 0.41 20.0 1.34 5.40 100
0.88 2.0 210 0.51 20.0 1.20 5.10 145
1.35 2.0 310 0.61 20.0 1.45 5.25 135
1.44 2.0 220 0.69 20.0 1.67 4.70 95
0.57 2.0 285 0.28 10.0 1.44 5.85 75
0.73 2.0 355 0.38 10.0 1.24 5.55 160
1.01 2.0 425 0.49 9.9 1.09 5.10 195
1.21 1.9 475 0.59 10.0 0.95 6.05 255
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Table 4: P3 T = 120 +/- C
C 1
m P Fn Vn Vp SER CFS
Tear
kg/h bar N mm/s m/s MWh/t mNmz/gml
0.76 3.0 75 0.40 30.0 1.67 5.35 75
1.01 3.0 135 0.50 30.0 1.39 5.25 105
1.26 3.0 150 0.60 30.0 1.20 5.45 100
1.48 3.0 155 0.72 30.0 1.24 5.75 100
0.74 3.0 130 0.35 20.0 1.30 5.90 100
0.94 3.0 250 0.45 20.0 1.42 5.55 60
1.10 3.0 255 0.56 20.0 1.45 5.85 70
1.29 3.0 225 0.67 20.0 1.12 5.75 140
0.58 3.0 310 0.28 10.0 1.52 6.00 100
0.70 3.0 350 0.36 10.0 1.40 5.65 115
0.89 3.0 420 0.46 10.0 1.19 5.80 175
1.05 3.0 480 0.54 10.0 1.19 6.45 150
Table 5: P~ T = 130 +/- C
C 1
m P Fn Vn VP SER ear
T CSF
kg/h bar N mm/s m/s MWh/t mNm2/gml
0.77 4.0 95 0.40 30.0 1.71 5.35 70
0.95 4.0 120 0.50 30.1 1.60 4.95 65
1.05 4.0 145 0.58 30.0 1.25 5.30 120
1.26 4.0 165 0.67 30.1 1.09 5.00 155
0.64 4.0 120 0.33 20.0 1.06 5.75 130
0.8i 4.0 205 0.42 20.0 1.45 5.60 85
1.00 4.0 185 0.52 20.0 1.35 5.50 100
1.23 4.0 190 0.62 20.0 1.11 5.45 135
0.48 4.0 265 0.25 10.0 1.61 5.55 80
0.60 4.0 365 0.33 10.0 1.34 5.40 155
0.79 4.0 375 0.42 10.0 0.22 6.10 180
1.01 4.0 385 0.53 10.0 0.97 5.90 230
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Table 6: PS T = 140 C
m P Fn V" VP SER CSF
Tear
kg/h bar N mm/s m/s MWh/t mNm2/g ml
0.80 5.0 175 0.39 30.1 1.64 5.30 80
0.98 5.0 165 0.50 30.0 1.28 5.70 95
1.21 5.0 125 0.60 30.0 1.02 5.40 215
1.29 5.0 160 0.69 30.1 1.19 5.75 125
0.70 5.0 180 0.33 20.0 1.56 5.65 65
0.85 5.0 140 0.42 20.0 1.13 5.35 120
0.93 5.0 155 0.51 20.0 1.19 5.70 120
1.19 5.0 225 0.60 20.0 1.03 5.35 145
0.45 5.0 215 0.25 10.0 1.51 5.65 65
0.62 5.0 320 0.32 10.0 1.41 6.45 150
0.41 5.0 210 0.21 10.0 1.49 4.85 75
0.77 5.0 270 0.42 10.0 1.11 6.10 210
The relation between quantities characterising the pulp
properties (freeness, tear index) and the operating
conditions of the process can be determined by regression
analysis based on the measurement data presented above.
The results show that the mass flow can be kept rather
constant despite the lower peripheral speeds because the
supply pressure is increased.
The method according to the invention also reduces the
specific energy consumption (SER).
Control methodics:
An adaptive (self-adjusting) control algorithm is presented
below. The controller is a generalisation of the
multivariable control algorithm of ~strom and Wittenmark
(1973).
The process can be described by the equation below:
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Y(t) + AiY(t-1) + ... + Any(t-n) -
- Bou ( t-k-1 ) + . . . + Bn-iu ( t-k-n ) + a ( t ) +
+ Cleft-1) + ... C"e(t-n) , (1)
where a is the input vector and y is the output vector, and
~e(t)} is a sequence of independent evenly distributed
random vectors with a mean value of zero and the covariance
E[e(t)eT(t) ] - R
The dimension of all vectors u, y and a is p, and the
dimension of all matrices Al, Bi and Ci is pxp. The matrix Bo
is non-singular.
Now we introduce the shift operator q-1 defined as
q 1(t) - Y(t-1)
and the polynomial matrices
A( z ) - I + AiZ + . . . + A~,zn
i5 B( z ) - Bo + Blz + . . . + Bn-1Zn'1
C(Z) - I + C1Z + ... + Cnzn
It is assumed that all zeros of B{z) are outside the unit
circle. Bo is non-singular. The system (1) can be written as
A{q 1)Y(t) - B{q 1)u(t-k-1) + C(q l)e(t) {2)
In each sampling interval the adaptive algorithm performs
an identification based on the least squares method
according to the model presented below.
The obtained parameters are used for calculation of the
control strategy.
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Estimation
The algorithm estimates the parameters for the model
Y(t) + A(ql)Y(t) - B~q')Y(t-k-1) + E(t)
so that the error E(t) is minimised according to the least
squares.
In the model (3) k is selected as the dead time for the
process (2), and A(z) and B(z) are pxp polynomial matrices
according to
A( z ) - Ao + A lz + . . . + A~,~znn
B( Z ) - Bp + BlZ + . . . + BnHZnB
First we assume that
Bo = I
and
Bo = I
where Bo is a matrix in the constant term of B(z) for the
process (2).
Now we introduce the column vectors
0 o na nA
8 i = ~ 06i 1 . . . OGip . . . OGi 1 . . . ~P
~ili . . . ~ipl . . . ~ilaB~ . , ~jiPn87T' i = ~ ~ . . . i p
where air'' is the ( i, j ) 'h element in the matrix A,~; iii jk is the
(i,j)'h element in the matrix Bk, and so on. Then the column
vector 61 can be considered to contain the coefficients of
the i''' row in the model ( 3 ) .
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Further we introduce the row vector
~(t-k-1) - [-yT(t-k-1) ... -yT(t-k-1-nA)
uT( t-k-2 ) . . . uT( t-k-1-ng) ( 5 )
The ith row in model (3) can be written as
5 E(t) - yi(t) - ui(t-k-1) - ~(t-k-1)Ai
According to the least squares criterion the vector 8i at
each moment N is calculated so that
N
VN(6i) - 1/N E Ei2(t), i = 1, ... , P (6)
is minimised. This results in a least squares estimation of
10 each row in (2) based on data which is available at the
moment N. When N is large, the initial values are of
insignificant importance in (6). The criterion (6) can be
written as
N
~N(e~) - 1/N E y~(t) - u~(t-k-1) - ~(t-k-1)ei)z
=f
i = 1, ..., p (7)
n
The value 9i which minimises (7) is given by the normal
equations, see Astrom and Eykhoff (1971).
N
[ E ~ (t-k-1)~(t-k-1) ]9i(N) -
~=f
- E ~T(t-k-1)[Yi(t)-ui(t-k-1))
~=1
i = 1, ... p (8)
Control
At each moment t the control strategy is calculated from
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B(q 1)u(t) - A(q i)Y(t) (9)
where the polynomial matrices A(z) and B(z) are obtained
from the current value of the estimated parameters.
The control strategy can be written as
ui(t) - -~(t)6i(t) i = 1, ..., P (10)
The parameters for the controller are the same as the
estimated parameters. When we use
a = [e,,e2, ... ep] (11)
the strategy (10) can be written as
uT(t) - -~(t)8(t) (12)
The estimated parameter vector 6i in (8) can be recursively
calculated from
ei(t)=ei(t-1) + K(t-1)[Yi(t)-u~(t-k-1)-~(t-k-1)Ai(t-1)]
K(t-1)=P(t-1)~T(t-k-1)[1+~(t-k-1)P(t-1)~T(t-k-1)]-1 (13)
P(t)=P(t-1)-K(t-1)[1+c~(t-k-1)P(t-1)~T(t-k-1)]KT(t-1)
P(t) is a normalised covariance matrix of the estimated
n
parameters 9i.
The initial values of P(t) are assumed to be the same for
all parameter vectors 6i. The corresponding amplification
vectors K(t-1) will also be the same for all estimators.
Sometimes it may be useful to introduce an exponential
weighting for the parameter estimation. This can be done by
modifying the criterion (6) to
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N
E ~lN+1 tEiz ( t ) i = 1 , . . . P ; ~, -< 1 ( 14 )
~=1
The last equation in (13) changes to
P(t)= 1/7l{P(t-1)-K(t-1)[1+~(t-k-1)P(t-1)~T(t-k-1)]
x KT(t-1) ] (15)
Another possibility is to use Kalman filters. The
covariance matrix P(t) is supplemented by adding to it a
matrix R1 instead of the division by A.
Then the equation (15) will be
P(t) - P(t-1)-K(t-1)[1+~(t-k-1)P(t-1)~T(t-k-1)]
x KT ( t-1 ) + R1
It should be noted that the algorithm can be construed as a
union of a plurality (here 2) of simple self-adjusting
controllers. For instance the controller 2 controls the
output signal y2(t) by using the control variable u2(t).
yl(t-i) and ul(t-1-i) (i >_ 0) can be used as feedforward
signals. This means that the two simple self-adjusting
controllers can operate in a cascade mode.
The possibilities for this feature strongly depend on the
process properties regarding the model (2) and character of
the minimum variance strategy. The multivariable self-
adjusting control algorithm can in some circumstances
result in the minimum variance, in other words when C(z) -
I (the process interference is white noise).
Another possibility is an exclusively multivariable minimum
variance control algorithm, which is not adaptive.
At a pulping overpressure of 0 to 2 bar the control of the
tear index at lower peripheral speeds results in great
advantages (40 ~ to 20 ~). As the multivariable control
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algorithm also is adaptive, changed sharpness is taken into
account by increasing the peripheral speed. During this the
freeness can be freely selected.
At higher pulping overpressures the advantage is an
improvement of about 10 % concerning the tear index, and
the changes in sharpness can be controlled in the periods
between sharpening actions. During these periods the
freeness can be freely selected.
If the sharpening is not made with pressurised water or
similar at regular intervals, then the sharpening is made
at Pm"~ at the maximum power consumption.
