DE4238037A1 - Paper web profile fault correction - uses mathematical model for current operation to eliminate residual faults on the lateral profile - Google Patents

Abstract

To eliminate residual faults on the lateral profile of web materials, esp. paper webs, during continuous mfg., the operation is divided into a learning and an operating phase. In the learning phase, a mathematic model is developed for the operating conditions, in a statistical process for the basic lateral profile measurements and the adjusting systems, such as the spindles at the upper lip of the stock inlet. The model is stored in a model archive, such as at a PC with a fixed panel, to hold models for the max. possible number of operating conditions. In the operating phase, the nearest model to the operation is selected from the archive for the application of a correction vector such as for the spindle setting, and used for the prodn. process. This is repeated until the lateral profile matches the model. In the operating phase, an adaption phase is repeatedly applied so that the adjustments applied according to the measured performance can be used as a learning phase, to improve the model being used. ADVANTAGE - The adjustment values during mfg. can be obtd. in a matter of mins. compared with hrs. from conventional data sources.

Description

1. General description

The invention relates to a method for eliminating the Residual defects in the cross profile of endlessly manufactured web-shaped Materials, especially paper webs.

In paper production u. a. compliance certain tolerances of the OTRO basis weight cross section required. (Note: The OTRO mass per unit area denotes the Grammage of the oven-dry paper).

There are two things for the quality of the cross section Evaluation criteria:

• - The mean square error of the whole Cross section.
• - The maximum error (amount) in one place Paper web.

The cross section is either set manually or using a controller that is usually very complex process control system is made available.

By and large, both procedures will work for the Operation achieved usable results. Stick to it significant in some areas (approx. 10% of the machine width) There are residual deviations in the profile.

These residual deviations are neither of the usual Control devices are still corrected satisfactorily balance them by hand.  

With the described method it becomes independent of the controller a process control system a minimization of the remaining Residual error enabled.

2. State of the art

The considered error can currently neither manually nor through the controllers available in the process control system be balanced.

The manual residual error elimination fails because the Operator the complex relationships between the up to 90 Input variables (= spindle positions) and up to 256 Output variables (= cross-section measured values, so-called data boxes) cannot survey and assess to the extent necessary there

• - a data box of several spindles in different ways (different strength, positive and negative sense of action) influenced becomes;
• - This influence varies from data box to data box distinguishes;
• - The assignment of the spindles to the data boxes (the so-called mapping) only experimentally determining function follows.

The errors when using the controller have their causes

• - in incorrect and not up to date Modeling in the process control system. The relationship between spindle <- <data box changes depending on numerous process parameters (Product, raw material, lip position, drying and drainage behavior) during operation. The determination of the relevant However, control parameters often only occur  when starting up the paper machine or after essential maintenance work.
• - in inappropriate regulatory concepts. There is an impression that the coupling of the Control loops are considered too little. As well dead time compensation will probably not adequately performed. Considering of filtering and periodically changing, location and traversing direction dependent Dead times usually appear for the Regulation used cycle times too short.

An example is the patent US 46 80 089 and the publication in the TAPPI-Journal 1987, Vol. 61, No. 1 Pages 77-80, PRACTICAL ALGORITHMS FOR CROSS-DIRECTION CONTROL referenced.

3. Object of the invention

The object of the invention is to present a method with which the residual errors in the cross section of a web-shaped Materiales, especially a paper web, the Use of known control devices arise can be eliminated.

4. Description of the process 4.1 Principle of the procedure

Fig. 1 shows the principle of the model identification and model-based correction.

The reduction of the residual error in the OTRO basis weight cross profile (abbr. OTRO-FM-QP) is model-based. For this purpose, a model M of the paper machine (input: spindle positions, output: OTRO-FM-QP) is created. An inverse model M ¹ (E: OTRO-FM-QP, A: spindle positions) is then determined from this model M, on the basis of which the spindle adjustment required for the best possible elimination of a cross profile error is determined.

For the best possible correction, there are the following correction options for n actuators (e.g. headbox spindles) and m measuring elements or measuring information elements (data boxes):
n <m optimization according to an optimization criterion (usually Gauss criterion, conceivable e.g. Chebyshev criterion). Complete compensation to 0 for all data boxes is usually not theoretically possible.
n = m Complete compensation is theoretically possible.
n <m Complete compensation is possible in several ways.

4.2 Phases of the correction process

Fig. 2 shows how the individual phases are linked. The correction process takes place in 4 phases.

a. Learning phase
Determination of the model for the process using statistical methods based on measurements. Storage of the calculated model in the model archive.

b. Search phase
Search for a suitable model in the model archive.

c. Adaptation phase
Improvement of a model after the search phase (forward) or in connection with the adjustment phase (feedback). Storage of the improved model in the model archive.

d. Adjustment phase
Determination of a correction vector for the spindle profile. Introduction of the correction vector into the process (spindle adjustment) and comparison of the reaction obtained with the predicted reaction.

The learning phase is usually of the other phases decoupled in time. Depending on the convergence of the Results and the temporal consistency of the process individual phases are also carried out iteratively.

4.3 Learning phase

Fig. 3 shows the block diagram of the learning phase.

In the learning phase, the situation model of the process Paper machine (E: spindle profile, A: OTRO-FM-QP) determined.

This situation model consists of the mathematical Model of the process and a collection characteristic operating data that the respective Describe the operating situation.

Such operational data can include:

• - paper type
• - production speed
• - lip position
• - raw material data
• - medium spindle profile
• - medium OTRO-FM-QP
• - other medium profiles (LUTRO, moisture, ash, Kaolin)
• - characteristic data of the substance supplied.

To determine the transmission model, you need to take time corresponding values of the spindle positions and the OTRO-FM QP are considered. The timely paired assignment the spindle positions and the data box values are taken over by Time compensator. With this assignment, the dead times, that of

• - Machine design / production speed
• - respective location of data box and spindle and
• - Current traversing direction of the measuring frame depend, compensated.

By suitable filtering in the input and output branch ensures that short-period disturbances are suppressed are the same on the input and output side Signal delays occur.

4.4 Search phase

Fig. 4 shows the block diagram of the search phase. In the search phase, the model archive searches for a transfer model suitable for this situation using data that describe the current operating situation (so-called actual operating data).

The assessment is initially based on Pattern comparisons and weighted distances.

With longer use and increasing enlargement of the Model archives also become expert knowledge brought in. This expert knowledge serves z. B. for Description of cases according to the analytical Data can be expected to be suitable for the model, however proven problematic in practice or vice versa.

If a sufficiently suitable model is not available, it must from the search phase to the learning phase.  

If only a model that is suitable to a limited extent is available, must this before use in the adjustment phase in a Adaptation phase can be improved.

It turns out in the setting phase that this is in the model archive existing model for operating situation A also the new one Operating situation B with sufficient accuracy the model archive is closed accordingly complete.

The advantage of introduction and careful design The search phase lies in the significant reduction in the Response times. While the full editing of the Learning phase for a variety-specific model a few hours takes up and the adaptation (4.5) in many cases will take an hour or two, the direct takes archive-supported setting of the spindle profile only a few Minutes.

4.5 Adaptation phase

Fig. 5 shows the adaptation phase. The adaptation phase serves to improve existing transmission models. As a rule, this improvement should take place using signals occurring during operation and not on the basis of special test signals. Usually only the models of individual MISO processes are adapted, rarely their entirety.

The data box discriminator determines that which MISO processes need improvement and whether these can really be improved. Improvement arises when for data boxes relatively large errors between model and process output occur. Mathematically closed There is room for improvement if everyone is on a data box (note: these are definitely  those spindles, which according to the current model the considered data box are effective. If a suspicion arises If there are mapping errors, the next ones will come Neighboring spindles) acting significantly and change independently. The one with the Regulation of common mode changes that occur frequently (Note: observed on the paper machine and Metrologically proven, in my opinion with good Control concept does not occur) of neighboring spindles do not represent independent adjustments. They lead to insoluble systems of equations (ideal case) or too incorrect solutions (real case, due to the Noise).

To what extent in need of improvement of the model and insufficient input data search method for solutions could lead, should be checked.

Results of the adaptation phase are generally Correction of the model archive (see 4.4) used. Also Cases where there is no model improvement by switching on the adaptation phase was possible are noted there (Bringing in experience).

4.6 Adjustment phase 4.6.1 Basic design of the adjustment phase

Fig. 6 shows the block diagram for the basic design of the adjustment phase. In the setting phase, the spindle profile change required for the best possible QP error compensation is determined on the basis of the transmission model and OTRO-FM-QP error, and the expected new cross profile error is predicted.

This results after the proposed adjustment has been carried out an OTRO-FM-QP that comes very close to the calculated one, so the setting process is completed.  

In the event of minor deviations, the setting process is carried out with repeated the same model.

If the result of the setting is clearly from predicted value deviates is an adaptation phase (4.5) and then connect a new adjustment phase.

4.6.2 Setting with a reduced number of spindles or limited correction range 4.6.2.1. Setting with reduced number of spindles

A simultaneous adjustment of all spindles is over psychological reasons only after intensive testing of the Procedure makes sense. Unexpected results due to a such adjustment, which at least initially not quite can rule out confidence in the process interfere sensitively.

In the first phases of use, should only be a manageable number be operated by spindles at once, so that the Effects remain manageable and the operator Can assess the adjustment proposal at least qualitatively. Over time, the number of simultaneously operated can Spindles can be increased.

Adjustment suggestions for operation are corresponding to generate a reduced number of spindles. The goal is now the optimal profile improvement when operating some fewer spindles (e.g. 8).

The adjusted spindles are either operated by the operator predefined or determined automatically. Mixed forms, at which individual spindles are specified by the operator and others are determined by the computer are also conceivable.  

Are the spindles to be adjusted by the operator given, then only needs to be calculated the value by which the selected spindles are added are adjusted.

With automatic spindle adjustment with intelligent search method those n spindles (n will specified, value 1 to approx. 8) selected, their common Adjustment a maximum improvement of the OTRO-FM-QP can be expected.

4.6.2.2 Limitation of the correction range

Limiting the correction range can then make sense be if within a zone (= about 10 or more consecutive data boxes) only minor Faults ("noise") occur. In this area the QP error then declared 0 and the correction value for the spindle profile is calculated accordingly.

5. Mathematical outline 5.1 Learning phase

The system is modeled in the learning phase Spindle positions - <data box values. The transmission behavior of this system on the Basis of a technically common and meaningful Compensation procedure determined.

This comes into consideration for. B. the method of the smallest Squares (Gaussian compensation) or the uniform Approximation (Chebyshev compensation).

In the following, the model formation according to the Least squares method explained. The The operating point of the system is known as  provided and the calculation for (small) deviations represented from the working point.

Model approach

The measured value of the OTRO basis weight on a data box i be linear from the position of the k + l + 1 spindles o-k to 0 + l dependent.

In this case:

The coefficients aj are initially unknown, while bi and si can be measured. The spindle o is the spindle that the data box i influenced to the maximum. It results from the Cross correlation between spindle positions and Data box values.

If there are m independent measurements of the data box values b _i and the spindle positions s _j (m k + l + 1), the unknowns a _ÿ can be determined as follows:

b _i = S ₀ · ª _i (2)

S oT · b i = S · S oT o · ªi (3)

Equation (3) represents a linear system of equations that with the known methods (e.g. Gaussian Elimination procedure) can be solved. The single ones Symbols have the following meaning:

b _i : vector, dimension m1
Box i data box values from m measurements (ordered)
S ₀: matrix, dimension m · (k + l + 1)
Columns: Spindle positions of the spindles ok to o + l
Lines: measurements 1 to m (ordered)
The superscript T denotes the assigned transposed matrix.
ª _i : vector, dimension (k + l + 1) · 1
Coefficients (results)
ª _{i, 1} contains the coefficient assigned to the spindle ok.

Instead of (1), a non-linear approach can also be chosen will. In principle, the procedure remains the same, it increases just the number of unknowns.

If equation (3) has been solved for all data boxes, the coefficients aÿ obtained can be summarized in a matrix A.

the equation

b = A · s (4)

then describes the transmission behavior of the Paper machine across the entire width (= all data boxes).

b : All data box values, line i = value of data box i
s : All spindle values, line o, value of the spindle o
A : Model matrix, row i: columns ok to columns o + l: ª _i , otherwise 0

As a rule, A is not quadratic, so the inverse model M _i is not obtained by inversion, but as

M _i = (A · A ^T) ⁻¹ · A ^T (5)

If you want a determined cross profile error b _i , the necessary spindle adjustment is obtained when all spindles are adjusted

s ₁ = - M _i · b _i (6)

5.2. Search phase Formation of the distance measure

All the characteristic features of one in the archive stored operating case are in a vector a; the Dimension n · 1 filed. n is the number of considered properties.

A newly recorded operating case is in vector b (also Dimension n · 1) filed.

The meaning of each vector component is indicated by the components of the vector k (k _i large = meaning of the i th component large). k is determined experimentally.

A distance dimension d can then, for example, be as

d = | ( k ^T · (ª _i - b ) |

To be defined.

Small distance dimension d means great agreement between two operating cases.

5.3. Adaptation phase

Mathematical basics analogous to the learning phase.

5.4. Adjustment phase Setting with a reduced number of spindles

The example below shows one adjusted spindle. The procedure for several spindles follows by summarizing the results for individual spindles.  

If only the spindle o is actuated, only those data boxes b _{j are} affected which depend on the position of this spindle, that is to say those for which a _jo << 0 in the model matrix.

If the spindle position o affects the data boxes k to l, only the lines k to l of A have to be taken into account.

Only those are to be taken into account in columns correspond to the actuated spindle (s).

In this way, the model matrix A is reduced to the reduced model matrix A _r . From A _r , the inverse reduced model M _ir follows, as described in the learning phase.

The models A _r and M _ir only describe the relationship between the moving spindles and the data boxes influenced by them.

6. Extended area of application

The invention described above has been in the field papermaking / papermaking operations Elimination of residual errors in the OTRO basis weight cross profile developed. However, it is in the making of others relevant web-shaped products (e.g. film production), provided the following conditions exist:

a. The aim of litigation is to adhere to a predetermined cross section of a certain size (in the original OTRO basis weight, also conceivable Thickness etc.).

b. The size under consideration becomes continuous or in periodically at several locations across the Web width measured.  

c. The material inflow or distribution is about a number across the web width distributed actuators influenced.

d. The process is stable in the medium term.

e. The process can be done through a mathematical model are reproduced with sufficient accuracy.

7. Figure overview

Fig. 1 shows the principle of the model identification and model-based correction.

Fig. 2 shows how the individual phases are linked.

Fig. 3 shows the block diagram of the learning phase.

Fig. 4 shows the block diagram of the search phase.

Fig. 5 shows the adaptation phase.

Claims (2)

1. Method for eliminating residual errors in the cross profile of a material web, in particular paper web, produced in continuous operation, with the following method steps:

• 1.1 learning phase
  • 1.1.1 For an operating state, a mathematical model for the production process is created by means of statistical methods on the basis of measurements of the cross profile and the state of the adjusting devices (e.g. the spindles on the upper lip of a headbox of a paper machine);
  • 1.1.2 the determined model is stored in a model archive (e.g. a PC with a hard disk);
  • 1.1.3 Items 1.1.1 and 1.1.2 are carried out for as many operating states as possible;
• 1.2 Operating phase
  • 1.2.1 Search phase
    On the basis of the measured operating state, a model that is as close as possible is selected from the model archive;
  • 1.2.2 Adjustment phase
    Using the selected model, a correction vector (e.g. for the spindle settings) is determined and introduced into the production process;
  • 1.2.3 Repetition
    The points 1.2.1 and 1.2.2 are repeated iteratively until the cross profile is adjusted in the desired manner.

2. The method according to claim 1, characterized in that an adaptation phase is repeated in the operating phase is incorporated so that based on the measured Results after a setting has been made Learning phase is carried out and a new improved Model is stored in the model archive.