The invention relates to a method for the active compensation of periodic
disturbances of known frequency during hot or cold rolling, such as roll eccentricities,
by means of a control system, and to a corresponding device for carrying out such
a method according to the preambles of claim 1 and claim 9 respectively (see e.g.
EP-A 0 424 709).

In order to achieve a satisfactory quality of the rolled product,
such as strips, for example, in rolling mills on the basis of the existing eccentricities
of the rolls, the roll eccentricities must be compensated. The causes for the occurrence
of roll eccentricities are, for example, inexact roll grinding, non-circularities
in the roll bearings, non-uniform thermal expansion of the rolls or defects in the
barrel surface. This leads to periodic thickness fluctuations in the rolled strip
which can sometimes be very considerable (up to 40 µm in hot-rolling mills). The
thickness deviations of the strip caused by the eccentricities can be counted among
the limiting factors in complying with the tolerances by stipulating ever narrower
thickness tolerances (for example < 0.8%).

The active compensation of eccentricities is particularly in demand
whenever the aim, when revamping old rolling mills whose mechanical equipment is
not state of the art, is to achieve good strip qualities with new automation systems.

By contrast with passive methods, which merely prevent a gaining effect
of the eccentricity by the external thickness control loop, with the active compensation
methods an additional signal is generated in the force and/or position control loop
of the rolls, the result being that the influence of the eccentricity is effectively
suppressed.

For example, methods are known which determine the total axial displacement
of the roll from the available measured signals, see E. Teoh, G. Goodwin, W. Edward
and W.R. Davies, "An improved thickness controller for a rolling mill", Proc. 9th
IFAC Congress, Budapest, 1984. These methods have the disadvantage that they require
precise knowledge of the mill modulus and the plastic deformation coefficient, and
that an exact material tracking is required.

Other methods eliminate the influence of eccentricities directly in
the measurement signals, the eccentricity being identified in a first step, and
this identified eccentricity being further processed in a further step in a compensation
block (PI controller, filter, least squares methods), see EP-0 424 709-A2, for example.
These methods have the disadvantage that they react slowly to eccentricities which
occur, and can therefore be used only conditionally for short strips.

One object of the present invention consists in developing a method
which overcomes the disadvantages set forth and can be inserted in a simple way
into existing control loops for the thickness of the rolled material, the position
of the rolls and the roll force, the aim being that the method should not influence
the existing control loop to a greater extent.

The invention is characterized in that with the aid of a linear dynamic
controller which comprises a model that describes one part of the dynamic behaviour
of the controlled system, an output variable is determined from an input variable
on the basis of a reference variable, and in that a compensation signal is generated
on the basis of said output variable and a measured output variable of the controlled
system and is impressed on the input variable fed to the controlled system.

It is a novel feature of this invention that as a result, the tracking
control is decoupled from the disturbance control, and the controller according
to the invention can be inserted into existing control loops for the thickness of
the rolled material and/or for the position of the rolls and/or for the rolling
force and/or for the roll bending, because the set-point response is influenced
only slightly thereby. The compensation signal is generated without prior identification
of the eccentricity, which thus permits a more rapid correction of the disturbances.

One refinement of the invention consists in that in the frequency
domain of the disturbances the model describes the dynamic behaviour of the undisturbed
controlled system. If the model coincides with the actual undisturbed behaviour
of the roll stand in the frequency domain of interest, the required decoupling is
obtained.

A further refinement of the invention consists in that a compensation
signal u_{LMS} is generated on the basis of the difference between calculated
output variable and measured output variable and on the basis of at least one frequency
of a disturbance. This represents a simple possibility of compensating disturbances,
since only the frequency, but neither the amplitude nor the phase of the disturbance,
nor the disturbance dynamics (= the disturbance transfer function) need to be known.

For this purpose, it can advantageously be provided that the angular
velocity of a roll is measured for the purpose of determining the frequency of a
disturbance. Use is thereby made of the fact that the frequencies of disturbances
on the basis of eccentricities correspond to the frequencies of the roll rotation.
It is also ensured thereby that the change in the frequencies of the disturbances
is also taken into account when there is a change in the strip speed.

It is possible for the feature that the frequencies of other disturbances
are determined with the aid of the geometrical data of the rolls from the measured
angular velocity of a roll, to be used to determine the frequencies of the disturbance
variables with adequate accuracy, even when the diameter of the rolls differ only
to a slight extent.

It is also advantageous that in the case of a plurality of frequencies
which occur, one compensation signal each is generated for each frequency, these
compensation signals being superimposed to form one compensation signal. This has
the advantage that a plurality of disturbances, such as, for example, a plurality
of eccentricities which differ in frequency from one another can be taken into account
and compensated.

A further feature of the method can consist in that the compensation
signal u_{LMS,k} is formed for a specific frequency ω in accordance
with the equation u_{LMS,k} = U_{1,k} sin(kωT_{a})
+ U_{2,k} cos(kωT_{a}) with the sampling time T_{a}
and the sampling step k, the factors U_{1,k} and U_{2,k} being determined
by a method which is suitable for solving a general quadratic optimization problem.
This represents a particularly simple solution adapted to periodic problems. Consideration
is given as methods of solution, for example, to online least squares methods, LMS
(Least Mean Squares) methods or the Biermann algorithm.

One embodiment of the invention provides that the input variable corrected
by the compensation signal is additionally subjected to non-linear control. Since
the method according to the invention is based on a linear input-output-behaviour
of the controlled system, the input-output-behaviour of the controlled system must,
if appropriate, be exactly linearized by a non-linear control. This is the case,
for example, when the servo current of the servo valve for the hydraulic cylinder
of the mill stand is used as input variable for the controlled system.

The method can be designed such that the force in the hydraulic cylinder,
or the roll force is used as output variable. These forces can be determined simply
and with an accuracy which suffices for the method. The force in the hydraulic cylinder
can be determined by measuring the pressure (in one chamber of the cylinder piston
in a single-acting cylinder) or the pressures (in both chambers of the cylinder
in a double-acting cylinder) in the hydraulic cylinder. The roll force can be determined
in the stationary state from the force in the hydraulic cylinder, taking account
of the weights of the rolls and any forces from the bending cylinders or by a dedicated
measuring device. The eccentricities can be rapidly reduced in this way. By contrast
with this, there is less advantage in using the strip exit thickness, since there
is a relatively large distance between the roll gap and thickness measuring instrument,
and the strip exit thickness is detected only with a time delay, the dead time not
being constant but depending on the strip exit speed.

A further variant of the method can be configured such that use is
made as output variable of a relevant signal of at least one bending or balancing
cylinder, such as the force in the cylinder or a input signal for the cylinder.
If the eccentricities to be suppressed are present in the measurement signals (force,
pressures, input signal), by comparison with the force in the hydraulic cylinder
or the rolling force this generally permits a reduction in the eccentricities which
is larger in absolute terms, but slower.

Finally, it has proved to be particularly advantageous that in sequential
time intervals use is respectively made as output variable of the force in the hydraulic
cylinder or the rolling force or a relevant signal of at least one bending or balancing
cylinder, such as the force in the cylinder or a drive signal for the cylinder.
It is thereby possible to make an optimum combination of the advantages of the two
embodiments of the invention.

The variant method that a phase shift between the input signal and
output signal of more than 90° is prevented serves the purpose of ensuring the mode
of operation of the control system and of avoiding a gaining effect of the disturbances
by the control system according to the invention.

It can be provided that for this purpose the compensation signal is
subjected to a transfer function C_{d} which obeys the condition |(C_{d}P_{u})(jω)-1|≈1
in the domain of the frequencies of the disturbance, P_{u} being the transfer
function of the controlled system without disturbance.

Moreover, with regard to the linear dynamic controller, the method
can provide that the model is a mathematical model. This permits individual adaptation
to the real behaviour of the mill stand by mathematically taking account of the
corresponding effects which occur.

Another possibility consists in setting up the model on the basis
of an identification method. In this case, the behaviour of the mill stand in the
frequency band of interest can be determined from measured data such as input and
output variables for the roll stand. This does not constitute a disadvantage, since
this operation is performed only once to determine the model and need not be repeated
continuously during the rolling process, as in the case of the identification of
eccentricities.

The method can also be configured such that the control system according
to the invention is integrated into the control loop for a bending or balancing
cylinder.

The device for the active compensation of periodic disturbances of
known frequency during hot or cold rolling, such as roll eccentricities, using a
control unit, is characterized in that the control unit has a linear dynamic controller
which comprises a model that describes one part of the dynamic behaviour of the
controlled system and which determines an output variable from an input variable
on the basis of a reference variable, and in that the controller is connected to
a disturbance controller which generates a compensation signal from the difference
between a measured output variable of the controlled system and the determined output
variable, and in that the disturbance controller is connected to the input of the
controlled system for the purpose of feeding the compensation signal to the input
variable. The decoupling of the tracking control from the disturbance control is
thereby achieved.

The possible design that a non-linear controller is additionally arranged
at the input of the controlled system serves the purpose of exactly linearizing
the input-output-behaviour of the controlled system in the entire operating range.

The possible design that a device for determining the angular velocity
of at least one roll is connected to the disturbance controller permits the generation
of a compensation signal taking account of the frequency of the disturbance, which
corresponds to the frequency of rotation of the roll.

The invention is explained in more detail with the aid of an exemplary
refinement and of Figures 1 to 8.

Figure 1 shows a diagrammatic representation of the general configuration on
which the control system according to the invention is based, with a linear dynamic
controller.

Figure 2 shows a diagrammatic representation of the mill stand.

Figure 3 shows the position and force control loop.

Figure 4 shows a control system according to the invention with a disturbance
controller.

Figure 5 shows the force characteristic and strip exit thickness characteristic,
with and without control according to the invention and with the use of one compensation
variable.

Figure 6 shows the force characteristic and strip exit thickness characteristic,
with and without control according to the invention and with the use of two compensation
variables.

Figure 7 shows the force characteristic and strip exit thickness characteristic,
with and without control according to the invention and in the case of a step in
the reference variable.

Figure 8 shows the corresponding characteristics of the position of the hydraulic
cylinder and the servo valve in relation to Figure 7.

Illustrated in Figure 1 are the input variable u, which represents
the manipulated variable or input variable acting on the system 1, and the disturbance
variable d, which represents a harmonic disturbance of known frequency but unknown
phase and amplitude. The input variable u is subjected to a transfer function P_{u},
and the disturbance variable d is subjected to a transfer function P_{d},
the result being the measured variable or the variable to be controlled or the output
variable y. The transfer function P_{u} can be assumed as known in the frequency
domain of interest from a mathematical model or from an identification method. Since
it is generally not possible to determine exactly at which point in the system 1
the disturbance acts, it must be assumed in the case of the disturbance transfer
function P_{d} that the latter is unknown, or can even change during the
process. This is the case whenever the disturbance acts at a different point in
the system. This is the case, for example, with a four-high roll stand when prior
to a roll change only the work roll has a significant eccentricity, and after the
roll change only the backup roll has a significant eccentricity.

The general solution consists in using a linear dynamic controller
2 having two degrees of freedom C = [C_{r}, C_{y}] in its most general
form. It holds for a controller having one degree of freedom (P, PI, PD, PID controllers)
that C_{r} = C_{y}. With the secondary condition that the disturbance
transfer function P_{d} is not exactly known and the frequency of the disturbance
changes, it is not possible to determine C with the aid of standard methods such
that the effect of the disturbance variable d in the measurement signal y is effectively
suppressed and immediately follows the desired reference signal r as effectively
as possible.

Since the disturbance variable d is periodic, and its frequency is
present as measured variable, the control can be effected by the control concept
according to the invention as described below.

The design of a four-high stand is shown diagrammatically in Figure
2. The hydraulic piston 3 of the hydraulic cylinder 4 acts in accordance with the
arrow on the axis of the upper backup roll 5. The backup rolls 5 engage with the
work rolls 6. The variables named below are fed to the automation system 8, p_{h1},
p_{h2} and s_{h} denoting the pressures and the position of the
hydraulic cylinder 4, x_{spool} denoting the position of the servo valve
7, ω_{roll} denoting the angular velocity of one of the rolls, in
this case the upper work roll 6, and h_{ex} denoting the strip exit thickness
of the strip 17. The servo current i_{servo} is prescribed for the servo
valve 7 by the automation system 8.

The force acting on the hydraulic cylinder 4 is represented as F_{h}
and is calculated from the measured pressures p_{h1}, p_{h2} of
the two chambers of the hydraulic cylinder 4. The force F_{h} corresponds
in the stationary state to the rolling force corrected for weights and possible
forces of bending cylinders. The force thus measured is available with sufficient
accuracy despite the occurrence of the effects of hysteresis and friction, and of
quantization errors.

Represented in Figure 3 is the position or force control loop, which
comprises an inner control loop for the servo valve with the servo controller 10,
and an outer control loop with a non-linear controller 9 for compensating the non-linearity
of the hydraulic cylinder, and a linear dynamic controller 2. The servo controller
10 prescribes the servo current i_{servo}, which acts on the system 15.
The eccentricity force F_{ecc} reproduces the influence of the eccentricity
on the system 15. The system 15 takes account of the operations 11 in conjunction
with the servo valve, the operations 12 in conjunction with the hydraulic cylinder,
the stand dynamics 13 and deformation processes 14. With the aid of p_{h1},
p_{h2} and s_{h}, the system 15 delivers as measurement results
the pressures and the position of the hydraulic cylinder, which are fed to the non-linear
controller 9. One of the two variables is fed to the linear dynamic controller 2
as output variable y. A possible further output variable y (not represented) would
be the pressure in a bending or balancing cylinder. The variable x_{spool}
denotes the position of the servo valve, and ω_{roll} denotes the
angular velocity of one of the rolls.

By comparison with classical control concepts, which take account
only of the static non-linearity in the case of the non-linear controller 9, an
exact linear input-output-behaviour can be generated using the methods of differential
geometry (see, for example, A. Isidori, "Nonlinear Control Systems", Springer Verlag,
1989) or flatness-based control systems,. With this assumption, that the system
in Figure 3 from the input u to the output y (p_{h1} and p_{h2},
s_{h}, pressure in a bending or balancing cylinder) behaves linearly in
the operating region (the one where eccentricities are to be expected), it is possible
to describe the elements of non-linear controller 9 servo controller 10 and system
15 with the aid of the system 1 represented in Figure 1, the linear dynamic controller
2 again being considered in its most general form as a controller having two degrees
of freedom C = [C_{r}, C_{y}].

The linear dynamic controller 2 of Figure 3 can be represented as
in Figure 4 for BIBO-stable transfer functions P_{u} (BIBO = bound input
bound output) by factorizing all internally stabilizing controllers on a control
loop (see, for example, M. Vidyasagar, "Control System Synthesis: A Factorization
Approach", MIT-Press, 1987). In this case, P_{u} is a model of the
transfer function P_{u}, it being possible to decouple the tracking control
and disturbance control in the frequency domain of interest given agreement between
P_{u} and P_{u}. This has the advantage that a possibly existing
control loop, as represented in Figure 3, can be retained for the output variable
y, all that need be done is to change the implementation. K and Q are controllers
whose properties are calculated from the controllers used.

The suppression of the periodic disturbances d is performed with the
aid of a control concept which is based on the projection theorem in Hilbert space
(see, for example, D.G. Luenberger, "Optimization by Vector Space Methods", John
Wiley & Sons, 1968). The application of the projection theorem leads to the
disturbance controller 16 in Figure 4 with the input variables y_{LMS} and
ω_{roll} and the output variable u_{LMS}.

The transfer function C_{d} is fixed in this case so as to
fulfil the condition |(C_{d}P_{u})(jω)-1|≈1 with the imaginary
unit j in the frequency domain where eccentricities can occur. The disturbance controller
16 comprises a reference generator which, at the instant kT_{a}, generates
the signals e_{1,k} = sin(kωT_{a}) and e_{2,k} = cos
(kωT_{a}) with the sampling time T_{a}, the sampling step
k and the known eccentricity frequency o, which is proportional via geometry factors,
to the measured angular velocity ω_{roll} of the rolls. The output
variable u_{LMS} at the instant kT_{a}, u_{LMS,k} follows
via the relationship u_{LMS,k} = U_{1,k}e_{1,k} + U_{2,k}e_{2,k}.
According to the projection theorem, the variables U_{1,k} and U_{2,k}
are the online solutions of a general quadratic optimization problem which can be
solved using methods known per se, such as, for example, using the recursive least
squares method (L. Ljung, "System Identification: Theory for the User", Prentice
Hall, 1987) or using an adaptive LMS = (Least Mean Squares) algorithm (M. Gevers
and G. Li, "Parametrizations in Control, Estimation and Filtering Problems", Springer
Verlag, 1993).

In the case of the adaptive LMS algorithm, the recursion rule for
U_{1} and U_{2} is

with a suitably selected µ > 0, but small enough in order to guarantee convergence.

According to Figure 4, the output variable y is compared to the corresponding
values calculated by the model P_{u}, the difference being fed to
the controller K as P_{d}d&supand; and the disturbance
controller 16 as y_{LMS}.

In the lower illustration, Figure 5 shows the strip exit thickness
deviation (in metres) with eccentricity compensation according to the invention
(thick line) and without it (thin line), as a function of time t, the force F_{h}
of the hydraulic cylinder serving here as compensation variable. In the upper illustration,
the deviation ΔF_{h} (in newtons) of the force F_{h} from
the set point is represented as a function of time t, respectively with eccentricity
compensation according to the invention (thick line) and without it (thin line).

In the case of the use of the force F_{h} of the hydraulic
cylinder as relevant compensation variable, the eccentricity in the force F_{h}
certainly does vanish almost completely, and the residual eccentricity remaining
in the strip exit thickness is now a function, on the one hand, of the friction
forces and, on the other hand, of the ratio of plastic deformation coefficient to
mill modulus and the roll weights. In the case indicated, there was a pronounced
work roll eccentricity in conjunction with a strip having a low material stiffness
coefficient.

If it is desired to achieve a further suppression of the residual
eccentricity, depending on the stand design recourse must be made to other signals
such as pressures in the bending cylinders. In Figure 6, the lower illustration
shows the strip exit thickness deviation (in metres) with eccentricity compensation
according to the invention (thick line) and without it (thin line), as a function
of time t, use having been made as compensation variable of the force F_{h}
of the hydraulic cylinder for the period from t=0 to t_{1}, and of the pressure
or the force in the bending cylinder for positive bending in the case of the full
Mae West mill stand design for the period from t_{1} onwards. The upper
illustration once again shows the deviation ΔF_{h} (in Newtons) of
the force F_{h} from the set-point, as a function of time t, respectively
with eccentricity compensation according to the invention (thick line) and without
it (thin line).

It is to be seen that, by comparison with Figure 5, it was possible
for the strip exit thickness deviation to be further reduced. In the case of the
use of the force F_{h} as compensation variable, the eccentricity defect
in the strip exit thickness decreases rapidly, and a further, but slower reduction
in the eccentricity defect can be achieved by the subsequent use of the pressure
or the force in the bending cylinder as compensation variable.

In the lower illustration, Figure 7 shows the strip exit thickness
deviation (in metres), with eccentricity compensation according to the invention
(thick line) and without it (thin line), as a function of time t, and, here again,
the force F_{h} of the hydraulic cylinder serving as compensation variable.
In the upper illustration, the deviation ΔF_{h} (in newtons) of the
force F_{h} from the set-point is represented as a function of time t, respectively
with eccentricity compensation according to the invention (thick line) and without
it (thin line).

In the upper illustration, Figure 8 shows the associated time characteristic
of the position s_{h} of the hydraulic cylinder, and in the lower illustration
the time characteristic of the position x_{spool} of the servo valve, respectively
with eccentricity compensation according to the invention (thick line) and without
it (thin line).

In the case both of a work roll and of a backup roll, there is a corresponding
eccentricity here, the rolled strip having a relatively low material stiffness.
After 1 second, there is a step in the reference variable by 100 micrometres in
the position control loop for s_{h}, in order to cause the reduction in
the strip exit thickness. It is to be seen that the reference step after 1 second
is not impaired by the compensation according to the invention, and that the suppression
of the eccentricity in the strip exit thickness is very good.

The invention is not limited to the application in four-high stands,
but can be used for any type of roll stands in the case of cold-rolling or hot-rolling
mills, plus also for two-high roll stands.

Anspruch[de]

Verfahren zur aktiven Kompensation periodischer Störungen mit bekannter Frequenz
beim Warm- oder Kaltwalzen, wie Walzenexzentrizitäten, mittels einer Regelung,dadurch
gekennzeichnet, dass mit Hilfe eines linearen dynamischen Reglers (2), der ein
Modell (P_{u}) für einen Teil der Vorgänge auf einer Regelstrecke
(1) umfasst, aufgrund einer Führungsgröße (r) aus einer Eingangsgröße
(u) eine Ausgangsgröße (y) ermittelt wird und dass aufgrund dieser
und einer gemessenen Ausgangsgröße (y) der Regelstrecke (1) ein Kompensationssignal
(u_{LMS}) erzeugt und der der Regelstrecke (1) zugeführten Eingangsgröße
(u) aufgeschaltet wird.

Verfahren nach Anspruch 1, dadurch gekennzeichnet, dass das Modell (P_{u})
im Frequenzbereich der Störungen (d) die Vorgänge auf der ungestörten Regelstrecke
(P_{u}) beschreibt.

Verfahren nach Anspruch 1 oder 2, dadurch gekennzeichnet, dass aufgrund
der Differenz (y_{LMS}) zwischen berechneter Ausgangsgröße (y) und
gemessener Ausgangsgröße (y) und aufgrund von zumindest einer Frequenz einer
Störung (d) ein Kompensationssignal (u_{LMS}) erzeugt wird.

Verfahren nach einem der Ansprüche 1 bis 3, dadurch gekennzeichnet, dass
zur Bestimmung der Frequenz einer Störung (d) die Drehwinkelgeschwindigkeit (ω_{roll})
einer Walze (5, 6) gemessen wird.

Verfahren nach Anspruch 4, dadurch gekennzeichnet, dass die Frequenzen
anderer Störungen (d) mit Hilfe der geometrischen Daten der Walzen (5, 6) aus der
gemessenen Drehwinkelgeschwindigkeit (ω_{roll}) einer Walze (6) bestimmt
werden.

Verfahren nach einem der Ansprüche 1 bis 5, dadurch gekennzeichnet, dass
bei mehreren auftretenden Frequenzen für jede Frequenz je ein Kompensationssignal
erzeugt wird, wobei diese Kompensationssignale zu einem Kompensationssignal (u_{LMS})
überlagert werden.

Verfahren nach einem der Ansprüche 1 bis 6, dadurch gekennzeichnet, dass
das Kompensationssignal für eine bestimmte Frequenz ω gemäß der Gleichung
u_{LMS,k} = U_{1,k} sin(kωT_{a}) + U_{2,k}
cos(kωT_{a}) mit der Abtastzeit T_{a} und dem Abtastschritt
k gebildet wird, wobei die Faktoren U_{1,k} und U_{2,k} durch ein
Verfahren, welches zur Lösung eines allgemeinen quadratischen Optimierungsproblems
geeignet ist, bestimmt werden.

Verfahren nach einem der Ansprüche 1 bis 7, dadurch gekennzeichnet, dass
die durch das Kompensationssignal (u_{LMS}) korrigierte Eingangsgröße
(u) zusätzlich einer nichtlinearen Regelung (9) unterworfen wird.

Vorrichtung zur aktiven Kompensation periodischer Störungen mit bekannter Frequenz
beim Warm- oder Kaltwalzen, wie Walzenexzentrizitäten, unter Verwendung einer Regelungseinheit,
dadurch gekennzeichnet, dass die Regelungseinheit einen linearen dynamischen
Regler (2) aufweist, der ein Modell (P_{u}) für einen Teil der Vorgänge
auf einer Regelstrecke (1) umfasst und der aus einer Eingangsgröße (u) aufgrund
einer Führungsgröße (r) eine Ausgangsgröße (y) ermittelt, und
dass der Regler (2) mit einem Störregler (16), der aus der Differenz einer gemessenen
Ausgangsgröße (y) der Regelstrecke (1) und der ermittelten Ausgangsgröße
(y) ein Kompensationssignal (u_{LMS}) erzeugt, verbunden ist, und
dass der Störregler (16) mit dem Eingang der Regelstrecke (1) zur Zuführung des
Kompensationssignals (u_{LMS}) zur Eingangsgröße (u) verbunden ist.

Anspruch[en]

Method for the active compensation of periodic disturbances of known frequency
during hot or cold rolling, such as roll eccentricities, by means of a control system,
characterized in that with the aid of a linear dynamic controller (2) which
comprises a model (P_{u}) that describes one part of the dynamic
behaviour of the controlled system (1), an output variable (y) is determined
from an input variable (u) on the basis of a reference variable (r), and
in that a compensation signal (u_{LMS}) is generated on the basis
of said output variable and a measured output variable (y) of the controlled system
(1) and is impressed on the input variable (u) fed to the controlled system (1).

Method according to Claim 1, characterized in that in the frequency domain
of the disturbances (d) the model (P_{u}) describes the dynamic behaviour
of the undisturbed controlled system (P_{u}).

Method according to Claim 1 or 2,characterized in that a compensation
signal (u_{LMS}) is generated on the basis of the difference (y_{LMS})
between calculated output variable (y) and measured output variable (y) and
on the basis of at least one frequency of a disturbance (d).

Method according to one of Claims 1 to 3,characterized in that the angular
velocity (ω_{roll}) of a roll (5, 6) is measured for the purpose of
determining the frequency of a disturbance (d).

Method according to Claim 4, characterized in that the frequencies of
other disturbances(d) are determined with the aid of the geometrical data of the
rolls (5, 6) from the measured angular velocity (ω_{roll}) of a roll
(6).

Method according to one of Claims 1 to 5,characterized in that, in the
case of a plurality of frequencies which occur, one compensation signal each is
generated for each frequency, these compensation signals being superimposed to form
one compensation signal (u_{LMS}).

Method according to one of Claims 1 to 6,characterized in that the compensation
signal is formed for a specific frequency ω in accordance with the equation
u_{LMS,k} = U_{1,k} sin(kωT_{a}) + U_{2,k}
cos(kωT_{a}) with the sampling time T_{a} and the sampling
step k, the factors U_{1,k} and U_{2,k} being determined by a method
which is suitable for solving a general quadratic optimization problem.

Method according to one of Claims 1 to 7,characterized in that the input
variable (u) corrected by the compensation signal (u_{LMS}) is additionally
subjected to non-linear control (9).

Device for the active compensation of periodic disturbances of known frequency
during hot or cold rolling, such as roll eccentricities, using a control unit,
characterized in that the control unit has a linear dynamic controller (2)
which comprises a model (P_{u}) that describes one part of the dynamic
behaviour of the controlled system (1) and which determines an output variable (y)
from an input variable (u) on the basis of a reference variable (r), and
in that the controller (2) is connected to a disturbance controller (16)
which generates a compensation signal (u_{LMS}) from the difference between
a measured output variable (y) of the controlled system (1) and the determined output
variable (y), and in that the disturbance controller (16) is connected
to the input of the controlled system (1) for the purpose of feeding the compensation
signal (u_{LMS}) to the input variable (u).

Anspruch[fr]

Procédé pour la compensation active de perturbations périodiques de fréquence
connue pendant le laminage à chaud ou à froid, telles que des excentricités de cylindre,
au moyen d'un système de commande, caractérisé en ce que, à l'aide d'un dispositif
de commande dynamique linéaire (2) qui comprend un modèle (P_{u})
qui décrit une partie du comportement dynamique du système commandé (1), une variable
de sortie (y) est déterminée à partir d'une variable d'entrée (u) sur la base d'une
variable de référence(r) et en ce que un signal de compensation (u_{LMS})
est généré sur la base de ladite variable de sortie et une variable de sortie mesurée
(y) du système commandé (1) et est inscrit sur la variable d'entrée (u) donnée au
système commandé (1).

Procédé selon la revendication 1, caractérisé en ce que le domaine de
fréquence de perturbations (d), le modèle (Pu) décrit le comportement dynamique
du système commandé non-perturbé (P_{u}).

Procédé selon la revendication 1 ou 2, caractérisé en ce qu'un signal
de compensation (u_{LMS}) est généré sur la base de la différence (y_{LMS})
entre la variable de sortie calculée (y)et la variable de sortie mesurée
(y) et sur la base d'au moins une fréquence d'une perturbation (d).

Procédé selon l'une des revendications 1 à 3, caractérisé en ce que la
vitesse angulaire (&thetas;_{roll}) d'un cylindre (5 et 6) est mesurée dans
le but de déterminer la fréquence d'une perturbation (d).

Procédé selon la revendication 4, caractérisé en ce que les fréquences
d'autres perturbations (d) sont déterminées à l'aide de mesure géométrique des cylindres
(5 et 6) à partir de la vitesse angulaire mesurée (&thetas;_{roll}) d'un
cylindre (6).

Procédé selon l'une des revendications 1 à 5, caractérisé en ce que,
dans le cas d'une pluralité de fréquences se produisant, un signal de compensation
est généré pour chaque fréquence, ces signaux de compensation étant superposés de
façon à former un signal de compensation (u_{LMS}).

Procédé selon l'une des revendications 1 à 6, caractérisé en ce que le
signal de compensation est formé pour une fréquence spécifique &thetas; selon l'équation
u_{LMS,k} = U_{1,k} sin(k&thetas;T_{a}) + U_{2,k}
cos(k&thetas;T_{a}) avec la durée d'échantillonnage T_{a} et l'étape
d'échantillonnage k, les facteurs U_{1,k} et U_{2,k} étant déterminés
par un procédé qui est approprié pour résoudre un problème d'optimisation quadratique
général.

Procédé selon l'une des revendications 1 à 7, caractérise en ce que la
variable d'entrée (u) corrigée par le signal de compensation (u_{LMS}) est
soumise en plus à une commande non-linéaire (9).

Dispositif pour la compensation active des perturbations périodiques de fréquence
connue pendant le laminage à chaud ou à froid telles que des excentricités de cylindre,
utilisant une unité de commande, caractérisé en ce que l'unité de commande
possède un dispositif de commande dynamique linéaire (2) qui comprend un modèle
(Pu) qui décrit une partie du comportement dynamique du système commandé (1) et
qui détermine une variable de sortie (y) à partir d'une variable d'entrée (u) sur
la base d'une variable de référence (r), et en ce que le dispositif de commande
(2) est couplé à un dispositif de commande de perturbation (16) qui génère un signal
de compensation (u_{LMS}) à partir de la différence entre une variable de
sortie mesurée (y) du système commandé (1) et la variable de sortie déterminée (y),
et en ce que le dispositif de commande de perturbation (16) est couplé à
l'entrée du système de commandé (1) dans le but de transmettre le signal de compensation
(u_{LMS}) à la variable d'entrée (u).