Data processing: generic control systems or specific application – Specific application – apparatus or process – Product assembly or manufacturing
Reexamination Certificate
2001-07-16
2003-11-11
Paladini, Albert W. (Department: 2125)
Data processing: generic control systems or specific application
Specific application, apparatus or process
Product assembly or manufacturing
C700S028000, C700S129000, C162S198000, C162S262000
Reexamination Certificate
active
06647312
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to adaptive control methods and apparatus for automatically optimizing a control gain. More particularly, the invention relates to adaptive control methods and apparatus preferred in controlling cross-machine direction profiles in a paper machine.
The effect of feedback control varies greatly, depending on a combination of the period of a disturbance present in a process and a control gain. In other words, there are two types of disturbance, one of which has such a period as to enable the disturbance to be attenuated by feedback control and the other has such a period as to cause the disturbance to be amplified instead as the result of feedback control.
Conventionally, the tuning of control gains has been achieved by trial and error in the field, while observing controllability against cyclic disturbances present in a process. This conventional tuning method has been problematic, however. If a control gain is decreased in an attempt to prevent the amplitude of a short-period disturbance from increasing as the result of control, controllability against long-period disturbances or follow-up capability for setpoint changes will deteriorate. It is therefore desirable that the control gain be increased as much as possible within the given tolerance limits. On the other hand, it is difficult to search for the magnitude of control gain that gives the optimum balance.
Another problem is that the period and/or amplitude of disturbance present in a process varies with the state thereof. The interval of such variation is wide-ranging, from several hours to a few days, or even to a few months. This means that the control gain that is optimum at some point in time may be improper several hours or several days later. Consequently, controllability would deteriorate and in some cases the control gain must be re-tuned.
A general object of the present invention, therefore, is to provide adaptive control methods and apparatus whereby a control gain can be automatically optimized online.
2. Description of the Prior Art
FIG. 1
is a diagrammatic view showing the configuration of a paper machine. In the figure, produced paper
61
is smoothed in its entirety and tuned in its thickness profile by a calender
62
, and wound onto a reel
64
. A sensor
63
is placed immediately before the reel
64
to measure the moisture percentage and/or thickness of the produced paper
61
. A measurement signal detected by the sensor
63
is then input to a measurement computation unit
65
, where the profile of the signal is calculated. This profile is then input to the control unit
66
. The control unit
66
controls the paper machine according to the profile.
The sensor
63
scans the paper
61
in the cross-machine direction (from this side to the far side of the paper in the figure) to measure the moisture percentage and/or thickness. Since there are as many as 1200 measurement points in the cross-machine direction, the width of the paper is divided into multiple zones and the measured value of the midpoint of each zone is defined as the representative data point of that zone.
FIG. 2
is a schematic view showing the relationship between zones and measurement points. In
FIG. 2
, a numeral
71
indicates the way paper
61
is cut into rectangular slices and thus divided into N zones. A numeral
72
indicates the correspondence of these zones with measurement points. A plurality of measurement points are included in each zone (zone i), and the midpoint PC(i) among the plurality of measurement points is defined as the representative data point of that zone.
FIG. 3
is a block diagram showing the configuration of a system for controlling cross-machine direction profiles in a paper machine. In the figure, a setpoint variable R(s) and a control output variable C(s) (e.g., the measured value of paper thickness) of profile control are input to a calculation unit
81
, where a deviation variable E(s) which is a difference between the setpoint and control output variables is calculated. The deviation variable E(s) is input to a controller
82
of finite settling-time response control type for calculation and output of a manipulated variable W(s). The manipulated variable W(s) is input through a hold unit
83
to a process
84
that can be approximated using a dead time and a first-order delay. Consequently, the process
84
is placed under feedback control.
A symbol V(s) denotes cyclic disturbance present in the process
84
. Such cyclic disturbance includes interference due to a concentration or liquid level change in a system for blending various types of raw material or interference arising in the form of cyclic variations in the measurement signal of moisture percentage or paper thickness caused by an eccentricity in a rapidly rotating wire or roll. These cyclic disturbances have two types of period, one of which enables the disturbance to be attenuated by feedback control and the other causes the disturbance to be amplified instead as the result of feedback control.
Now the method of controlling a paper machine is described with reference to FIG.
3
. The transfer functions of the hold unit
83
and process
84
that can be approximated using a dead time and a first-order delay are represented by equations (1) and (2) below:
Transfer function of hold unit
83
H
(
s
)
=
1
-
ⅇ
-
Ts
s
(
1
)
Transfer function of process
84
P
(
s
)
=
Ke
-
Ls
1
+
T
0
s
(
2
)
where
K=Process gain
T=Sampling interval
T
0
=Time constant
L=Dead time (L=mT, where m is 0 or a natural number).
Assuming HP(s)=H(s)P(s), then
HP
(
s
)
G
(
s
)(−
C
(
s
))+
V
(
s
)=
C
(
s
)
holds true from FIG.
3
. Changing this equation gives
V
(
s
)=(1+
HP
(
s
)
G
(
s
))·
C
(
s
)
From this equation, the control output C(s) is determined as
C
(
s
)
=
1
1
+
HP
(
s
)
G
(
s
)
V
(
s
)
(
3
)
Z-transforming equation (3) results in equation (4) below.
C
(
z
)
=
1
1
+
HP
(
z
)
G
(
z
)
V
(
z
)
(
4
)
From equations (1) and (2) noted above, z-transforming HP(s) gives equation (5) below.
HP
(
z
)
=
[
1
-
ⅇ
-
Ts
s
·
Ke
-
Ls
1
+
T
0
s
]
=
K
(
1
-
z
-
1
)
z
-
m
·
Z
[
1
s
(
1
+
T
0
s
)
]
=
K
(
1
-
z
-
1
)
z
-
m
·
Z
[
1
s
-
1
s
+
T
0
-
1
]
=
K
(
1
-
z
-
1
)
z
-
m
(
1
1
-
z
-
1
-
1
1
-
ⅇ
-
T
/
T
0
z
-
1
)
=
K
(
1
-
α
)
z
-
(
m
+
1
)
1
-
α
z
-
1
where
α
=
ⅇ
-
T
/
T
0
.
(
5
)
The transfer function G(z) of a controller of finite settling-time response control type is given by equation (6) below:
G
(
z
)
=
1
K
*
(
1
-
α
k
)
(
1
-
α
k
z
-
k
)
(
1
-
α
z
-
1
)
(
1
-
α
z
-
1
)
-
(
1
-
α
)
(
1
-
α
k
)
z
-
(
m
+
1
)
(
1
-
α
k
z
-
k
)
(
6
)
where K* denotes a control gain.
Now let us define a symbol g as g=K/K* (g>0) and refer to g as a control gain ratio. From equations (5) and (6), we obtain equation (7) below:
1
+
HP
(
z
)
G
(
z
)
=
1
+
K
(
1
-
α
)
z
-
(
m
+
1
)
1
-
α
z
-
1
1
K
*
(
1
-
α
k
)
(
1
-
α
z
-
1
)
(
1
-
α
k
z
-
k
)
(
1
-
α
z
-
1
)
-
(
1
-
α
)
(
1
-
α
k
)
z
-
(
m
+
1
)
(
1
-
α
k
z
-
k
)
=
1
+
g
(
1
-
α
)
z
-
(
m
+
1
)
(
1
-
α
k
z
-
k
)
(
1
-
α
k
)
{
(
1
-
α
z
-
1
)
-
(
1
-
α
)
(
1
-
α
k
)
z
-
(
m
+
1
)
(
1
-
α
k
z
-
k
)
}
=
(
1
-
α
z
-
1
)
-
(
1
-
α
)
(
1
-
α
k
)
z
-
(
m
+
1
)
(
1
-
α
k
z
-
k
)
+
g
(
1
-
α
)
(
1
-
α
k
)
z
-
(
m
+
1
)
(
1
-
α
k
z
-
k
)
Kojima Moonray
Paladini Albert W.
Rodriguez Paul
Yokogawa Electric Corporation
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