FI115325B - Procedure and control arrangements for controlling a paper web manufacturing process - Google Patents

Abstract

A sheet-making process is controlled by forming at least two control action candidates based on the error by at least two process models, of which at least one is a perturbed process model. A control action is formed from the control action candidates to produce a sheet matching the desired values. Controlling a sheet-making process, in which sheet matching the desired values, comprises measuring to produce measurement value(s) representing the state of the process. Each measurement value is compared with corresponding desired value. On the basis of comparison, an error is formed representing the difference between a measurement value(s) and its desired value. At least two control action candidates based on the error are formed by at least two process models, of which at least one is a perturbed process model. A control action is formed from the control action candidates to control the sheet-making process, to produce a sheet matching the desired values. An independent claim is also included for a control arrangement for controlling a sheet-making process, which is adapted to make a sheet matching desired values, comprising a measuring unit; a comparator for comparing each measuring value with the corresponding desired value for forming an error representing the difference between measurement value(s) and its desired value; a control unit to utilize at least two process models, to form at least two control action candidates based on the profile; and a processing unit for forming a control action of the control action candidates, with which control action the control arrangement is adapted to control the sheet-making process to produce a sheet matching the desired values.

Description

115325

A method and control arrangement for controlling the web production process

Field of the Invention

The invention relates to a method for controlling the web production process and to a control arrangement for the web production process operating according to the method.

Background of the Invention

The quality of the sheet is typically measured across the web using cross direction (CD) measurements and other measurements. 10 Typical quantities for transverse measurements are moisture, thickness, basis weight and ash content. Other typical web quality measurements, which may be other than CD measurements, include color, opacity, gloss, and smoothness. The measurement results are compared with the setpoints and an error profile is created which describes the deviation between the measurement results and the setpoints. It is known that a process in a state corresponding to the set values produces a web of the desired quality, and therefore the process is intended to be kept as closely as possible in the state corresponding to the set values. By means of the error profile and the process nominal model, the controller generates a control command for one or more actuators that change the process according to the command. Changing the process caused: ·. 20 changes in the CD or other properties of the web, and this change

* «I

'comes in a time domain (TD) in a certain way. The nominal process model describes the TD and / or CD and / or other process response features for the actuator. In particular, in paper making, actuators may be the amount of material [or the total amount] or the mechanical load or heat applied to the web during the process. In order to maintain the quality of the paper being produced, the authorities are used to change or maintain the measured quantities. For each combination of actuator and web measured property, the process model comprises some or all of the following: (i) CD mapping, (ii) CD-w 'response, (iii) TD targeting, (iv) TD- response, (v) process validation; in addition to these, the process may comprise other features. One such web production system is described in U.S. Patent No. 5,539,634, which is incorporated herein by reference. The terms "targeting" and "response" are known per se to those skilled in the art; . helle, but they will be defined later in this presentation.

.: However, the process model used by the controller is always somewhat inaccurate. A highly advanced controller can work very well with a precision 115325 2 model, but the disadvantage is that the controller does not work well with an inaccurate model. Deterioration of the control function depends on the nature of the model's inaccuracy and the sensitivity of the controller to such an error.

BRIEF DESCRIPTION OF THE INVENTION The object of the invention is thus to provide a method and a control arrangement implementing the method so that the process can be well controlled also by means of an inaccurate nominal process model. For this purpose, the method and arrangement comprise a fail-safe or robust controller. This object is achieved by the method disclosed in the introduction for controlling a web-making process for producing a web of desired values, comprising: measuring a process state to obtain one or more process values; comparing the desired value corresponding to each measured value; generating, by comparison, an error representing at least one deviation between the measured value and the desired value; generating, by means of two process models, of which at least one is a deflected process model, at least two control action suggestions based on the error; generating, by means of control action proposals, a single control action controlling the web production process to produce a web of desired values.

The invention also relates to a control arrangement for controlling a web production process adapted to produce a web corresponding to the desired values, comprising: a measuring unit for measuring the process state, thereby obtaining one or more measurement values describing the process state; the comparator comparing I · to the desired value corresponding to each measured value and generating an error which represents at least one deviation between the measured value and the desired value; a control unit adapted to utilize at least two process models, at least one of which is a deflected process model, and the control unit adapted to generate at least two control action proposals based on: error; the processing unit is formed by one control operation from which the control arrangement is adapted to control. a web production process to produce a web corresponding to the desired values.

Preferred embodiments of the invention are claimed in the dependent claims.

The method and system of the invention provide several advantages. One important advantage is that the robust controller is well tolerated by errors in process models, so it also works well, even when its process model has (minor) errors. The controller works well because its operations are made up of process models that are more likely to contain the actual process model than a single nominal model.

5 Brief Description of the Drawings

The invention will now be described in more detail in connection with preferred embodiments with reference to the accompanying drawings, in which Fig. 1 illustrates an actuator error as a function of process model, Fig. 2 illustrates process control, Fig. 3 illustrates process control using multiple process templates, Figures 4A-4C Fig. 5A illustrates the generation of common control action suggestions for the validation process and the alignment process, Fig. 5B shows the generation of common control action suggestions for the validation process and the alignment process, Fig. 5C shows the generation of common control action suggestions for the validation process and generating alignment process proposals, FIG. 6A illustrates process behavior in the context of precise control when the nominal model has different levels errors, '' Figure 6B shows process behavior with moderate robust control when the nominal model has different levels of error, and Figure 6C shows process behavior with very robust control when the nominal model has different levels of error.

I ·

DETAILED DESCRIPTION OF THE INVENTION The solution of the invention is particularly applicable to, but not limited to, the process of forming a web, such as paper and board, and plastic films.

Initially, let's get to know the processes through simple formulas.

, ..: The nominal model R of a process can be defined as: 115325 4 ΘΑ 'where θΡοη is the partial differential change of process relative to the partial differential change of the actuator ΘΑ. Generally, P is a vector of process values and A is a vector of actuator values which may be of different lengths than 5 P. In this case, R is a matrix whose size is determined by the lengths of P and A. This relation can also be expressed in transform modes using, for example, Laplace's transform P of P (s), A of A (s), and R of R (s), where the differential function is replaced by an algebraic function: R (s) = P (p) / A (s). The method according to the invention can be applied both in conversion modes and in direct calculations 10, but for the sake of clarity it is shown without modification.

A

lift. The nominal model R of the process is empirically estimated from previous measurements, which can be repeated, or the nominal model can be estimated using available information about the process, such as the size of the equipment and the nature of the physical processes it performs. The required actuator difference change ΔA at each time point can be calculated from the difference of the measured process conditions ΔΡ and the estimated nominal model R as follows: ΔA = R '1ΔΡ, 20 ·' "where ΔΡ is ΔΡ = Ph - Pm, Ph is the desired state of the process, Pm is the measured * Λ ···: state of the process and R'1 is the inverse matrix of the process nominal model estimate ΔΡ ^ :: can also be called an error signal.

Figure 1 shows an error in the operation of the actuator

* ♦ Λ A

·: 25 A A-AA, where ΔΑ is an institutional change based on the process name

I I · A

mallΑ is an institutional change based on the true process model R between the nominal process model R and the actual process model R * · '·. as a function of its difference. The greater the error in the estimated process model relative to the actual process model, the more the operation of the institution deviates from the desired operation. This type of error quickly leads to a completely incorrect process and a deterioration in the quality of the product being manufactured.

Referring now to Figure 2, a web production process known per se is considered. The process state is measured by transversely measuring the properties of the web 100 at N probes in the measuring unit 102 where N is a positive integer. Alternatively, a smaller number of probes may be used for traversing the web (measuring in the transverse direction), whereby measurements of these probes are obtained at N locations across the web. The measurement results Pm of the measuring unit 102 and the desired values Ph from the block 104 are supplied to the comparator 106, where an error signal ΔΡ is generated from the differences between the desired values and the measured values. By means of the error signal and the process model R obtained from block 110, the control unit 108 generates a control signal which Λ is intended to bring about the necessary change A in the operation of the actuator. The actuators 112, of which there are V, where V is a positive integer 10, which may be other than N, operate in accordance with the control signal and thus influence the web production process and the web quality.

Multiple actuators 112 are typically used in a web production apparatus to control one or more properties across the web. For example, the vapors fed to the dilution headbox of a papermaking machine may be combined in different proportions at each location over the headbox using controlled valves, whereby the properties of the combined material fed to the headbox can be modified in the transverse direction. Likewise, the headbox of the papermaking machine may have spindles that are attached to the headbox lip at multiple locations across the headbox, allowing the shape of the lip opening to be modified in the transverse direction, allowing the flow pattern to be modified at the headbox outlet. Other transverse actuators 112, such as steam boxes, re-irrigation equipment, coating machine scrapers, calender rolls, load-bearing shoes, zone-controlled rolls, etc., each with a plurality of its own adjustable elements, can be located in presses, other units in the papermaking process.

'*, * In other web production or web processing processes 100 such as' ·. for example, plastic film or layer extruders or laminators

i * I

processing equipment or printing presses, there are generally means for making transverse adjustments. These means comprise extruder bolts, '', load presses, various nozzles, heaters, humidifiers, and tensioners, and perform functions similar to those described for a paper machine.

: The properties of a web are generally measured at multiple locations across the web, normally having the same number of locations or more than '35 actuators 112. The set of property measurements performed across the web 102 is generally referred to as the profile of the property in question. Profiles can be measured with transducers across the web, or with groups of transducers fixed over the web. The properties of the web are generally measured by sensors based on radioactive, electromagnetic, thermal or mechanical mechanisms, and will be apparent to one skilled in the art. Important properties for the Pa-5 core fabrication are basis weight, moisture and ash content, thickness, gloss, color, opacity, fiber orientation distribution, tensile strength, smoothness, etc.

The effect of the actuator element on the measured web property profile is called the transverse response of the actuator. For example, the change in basis weight caused by moving one lip of the lip opening is the CD basis weight response of the mandrel. More than one property can be affected by each actuator so that movement of the spindles can also cause transverse moisture and thickness responses. The set of transverse locations on which the responses of the transverse actuator elements are concentrated is called the CD 112 mapping of the interlocutors 112.

Generally, a CD response does not occur instantaneously, but develops in a specific manner over time. This is called its TD response. Also, the TD response usually does not start immediately, but only after the dead time of the process due to various process delays, etc. In a manner similar to CD alignment, this delay is called the TD TD of the actuator.

Let us now examine the background of the invention. The process model has different errors for different properties or parameters and affects the operation of the process in different ways. The table below summarizes the expected model error, the sensitivity of the • 25 CD and TD algorithms used in conventional controls, and the robustness required. The table, · is primarily intended for dilution headbox CD control, but other CD processes are similar.

Waiting- CD-TD Algorithm Required Ro- !. * inbound optimizer sensitivity bust «; · '_model error sensitivity___ CD targeting_size_size_small_cd response_small medium to medium minor TDs to medium to medium to medium to medium * f -.1 ,,,. 11.,; TD Response_medium minor minor minor *

Process Confirmation Medium Low Minor Low Minor 115325 7

Of course, the control of non-CD processes does not include CD response or CD alignment, and thus is not sensitive to errors in CD alignment or CD response. However, there may be other features of the nominal process model in addition to or in place of the CD features, and ion-kinetic robustness is also required with respect to errors in these features of the nominal process model. Generally, processes always have TD responses and TD targeting, and some processes have a very high sensitivity to errors in TD targeting.

Because of the high sensitivity of CD controls to errors in CD alignment and the high degree of uncertainty in alignment, it is advisable to make the CD alignment robust. The sensitivity to the shape of the response is less, provided that sampling errors are avoided. A dead-time adjuster can have a high sensitivity to dead-time (TD focus) errors. The sensitivity to transient (TD response) 15 errors is lower. The equilibrium controller has low sensitivity to TD errors. The sensitivity to errors in process validation is low and relatively large errors can occur in process validation. Typical upper limits are: 20 CD Alignment ± 0.25 * Actuator Zone Width CD Response ± 0.1 * Model Response Width TD Alignment ± 1.0 * Spacing of Controls! Γ TD response ± 2.0 * control interval

Process Confirmation ± 0.2 * Model Process Confirmation.

"· 25

Let us now generally examine the method according to the invention with reference to Figure 3. The web 100 is measured in the same manner as in Figure 2 at block 102. In the same way as in Figure 2, the measurement result and the desired values obtained in the measuring unit 104 are compared in the comparator 30 106 and an error signal is generated. Thereafter, starting with the invention, '; ' important part. The offset process models of the nominal process model are formed into a set of process models in block 110. The set of process models can be pre-formed and stored in block 110. It is irrelevant to the invention whether the process set in block 110 is generated or dynamically stored in block 110. 110. What is important, on the other hand, is that the set of process models is available to the control unit 108. The control unit 108 implements each of these process models, at least one of which is a perturbed process model, and computes a control action proposal for each model.

The control unit 108 operates as follows, for example, in a process modeled by alignment and 5 response. For each combination of deflected alignment mapj and deflected response respj, a control action proposal is calculated from the error profile in a manner known per se using, for example, an optimizer: 10 stepsj = Optim (mapj, respj, error), j = 1, ..., m where mapj, respj, the error describes the process model and at least one profile error, and the action is a control action proposal. The offset response may include both gain offsets and offset response offsets. The optimizer normally calculates a control action proposal that minimizes a 2-margin or an infinity standard for the error profile. However, other goals can be included in the optimization by using weighting factors to combine the different goals into one optimization goal. For example, a 2-norm or an infinity norm of a control measure or control measure or an institution derivative or other functions based on an error or an institutional profile can also be minimized. In this example, control suggestions "were calculated using the optimizer, but other computational techniques can also be used, such as neural networks or fuzzy logic for various possible control purposes. One way to formulate control suggestions is to have the individual controller sequentially calculate the control suggestions for each process model. Another. ···. the way in which the control action proposals are generated is such that the control unit comprises control blocks, and each control block counts one control action proposal. In this way, 30 different control algorithms can be used with different process models. This is particularly useful if the different process models have different structures or complexities and are otherwise different from the values of the parameters of the models with the conventional structure only. Models can have different structures, for example, if the process is described as a Fourier plane cross-sectional model, which also uses a cross-sectional model that projects to orthogonal polynomials, or for some other reason such that the parameters of one model structure are irrelevant to the other. model structure. The set of control measure proposals (measure, measure2, .... toirnenpidem) is reduced to a single combined measure in processing unit 111: 5 control measure proposal = combined (measure, measure2, toirnenpidem).

This control operation is supplied to the actuators 112.

Let us now examine the process of the invention in more detail. At least two different process models are exported to and stored in the Robust CD Controller, comprising at least one offset process model and possibly a nominal model. Alternatively, the nominal model and the uncertainty predictions (or upper limit of expected error) contained in one or more parameters of the model are exported to a robust CD controller. In the latter case, the robust controller generates at least two different process models by deflecting the nominal model such that at least one variant is a deflected model and one variant is optionally a nominal model. A robust controller is a controller that gradually degrades in performance so that its process model begins to exhibit various errors, but is capable of maintaining robust performance despite the model's specific types and sizes of errors.

* 'The magnitude of the deviation is calculated from the property obtained or from the uncertainties of the parameter, Y. Each different model can only be deviated with respect to one or more parameters. Each deflected parameter ··: 25 can be deflected by a single quantity or by several quantities. The set of deflection rates for each parameter and the sum of deflection rates for different parameters. In each of the different models, the methods can be automatically calculated with the robust CD controller, or they can be generated by the amount exported to the robust CD controller. . according to the rag pattern. Not all different models need to have the same structure, and models with different structures need not have the same set of parameters. Naturally, different models can only be deviated from; * “! parameters. This generates a set of preliminary process templates which: "': may include a nominal process template.

The robust controller calculates the non-robust control action profile for each Ί 35 error profiles obtained from these initial process models or

• 'I I

for breads. This provides a set of control suggestion profiles. The robust 115325 10 control action profile is formed as a combination or consensus of a set of control action proposal profiles. The robustness of CD controllers can be of many types: they may be robust to errors in the CD response, to errors in CD alignment, to errors in TD response, to errors in TD alignment, or to errors in process validation. Because of the high sensitivity of CD controls to errors in CD alignment and the high degree of uncertainty in alignment, it is a good idea to make the CD controls robust with respect to CD alignment alone.

Figures 4A-4C show different prediction curves for process behavior after initial T0 when the process is controlled by three different control action suggestions. Each prediction is based on the different process models used by the controller. The horizontal dashed line represents the setpoint. The cross represents the average of the various space alternatives at the moment Ti. Generating an average of 15 from the various options generally results in a fairly good adjustment. In the case of Figure 4A, all three different control operations result in the same process state at time T 1. In this case, any control operation formed by the processing unit will direct the process to the prediction state. In the case of Fig. 4B, the process-20 states resulting from different control measures proposals are in the same direction, but at different distances from the setpoint at time Ti. The average of the various control suggestions also reaches quite far from the setpoint. In Fig. 4C, the process states caused by different control measure proposals at time Ti are far apart and at different points in the setpoint. Even if the average of the various control proposals is not far: ··· 25 setpoints, the individual control proposals are in opposite directions. j nissa. One control process controlling the web making process is created ···. thus using a simple average of the control measure proposals.

This situation can be further improved by using a more average control measure. How the control action is formed is not critical, as long as there is some known relationship between the control action that is formed and the control action suggestions that are generated. The control measure can be selected from the control measure proposals, or it can be formed from the control measure proposals as some combination, consensus, compromise, average, '[35 function, etc.]. as a signal sample set. The control measure suggestions can be arranged in a certain way so that they can be processed as samples of a signal (the order need not be the same every time the controller is used), or the control measure suggestions can be arranged in random or pseudorandom order.

There are various combinatorial methods employing digital filter processing formulas such as those known in the art (such as those of Ifeachor & Järvis in Digital Signal Processing, Addison Wesley), but applied to discrete sets rather than continuous samples.

Another way to form a composite control measure is to use the weighted average of the control measure proposals: m combined measure = weight measure (1) j = l 15 where weightj is the weighting factor. The sum total of the weighting factors is usually one. Ideally, each weight factor should be the relative probability at which the different model associated with it describes the process. In practice, these probabilities are not usually known, but near-20 predictions may be available.

Another simple combination method is to select a control measure proposal that has the lowest 2-norm or the lowest infinity norm. In other words, a control action proposal having the least sum of squares of its authors is selected, or a control action proposal is selected which '. _: The highest absolute value of the 25 Hansen factor is the lowest.

, ···) A biased standard can be used to generalize this method,

• I

whereby the control action proposal closest to the reference action is selected. In other words, a control measure proposal is selected whose reference

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• ;; t: Minimum deviation 2 or infinity norm for binding. Refe '; * · 30 the operation of the reference may be zero (giving a simple method), or it may be obtained by external logic. The reference operation may, for example. ; why not be a measure that leads the institutions to a safe space or a minimum cost.

: '* One particularly effective way to create a composite control action:: 35 is as follows. The rule-based composite method causes process 115325 12 to operate in an over-damped manner. The method is disclosed herein as a composite method of profile line control measures, but of course it can also be applied to other multivariate control measures or single-variable control measures.

5 For a set of m control candidate candidates, taking the reference control ref into account, a composite control is formed by the following three rules: j = m Rule 1: If ^ [{measurej> ref) is true, then> 1 combined measure = ref + min {measurej -ref} According to Rule 1, if all m of the control measures are larger than the reference measure, the combined measure is larger by the smallest number of draft measures remaining than the reference measure.

j-m Rule 2: If ^ {action; <ref} is true, then ./=1 15 combined action - ref - minjre / - action} Rule 2 states that if all m control measures are smaller than the reference action, the combined action is the smallest number of measures under the reference action. less than the reference measure.

^ 20 Rule 3: If neither Rule 1 or Rule 2 is activated, then · · 'combined action = ref »» »[Rule 3, if no set of control action suggestions': meets the conditions for either Rule 1 or Rule 2, combined :: operation is a reference operation.

25 Rule 1 and Rule 2 are clearly mutually exclusive, and Rule 3 complements both. Thus, these three rules are never in conflict and cover all possible scenarios. These Rules'. various calculations (comparisons, additions, subtractions, positions). l: * is accomplished by factor-by-factor calculations where each of the factors in the operation 30 of the compound is derived from these rules independently of other factors. Of the several control measures, these three rules. : A control measure calculated in accordance with this is called a consensus measure.

115325 13

Generally, the value of a reference measure in all its factors is zero. However, some or all of the authors of a reference operation may be non-zero and may be obtained by external logic. For example, the control intervention algorithm may attempt to bias the result of the controller to respond to ul-5 events. As another example, the reference operation may be a measure that returns the actuators to a minimum cost state, such as a state with the lowest energy or material consumption.

Alternatively, the control measure proposal calculated using the nominal process model can be used as a reference measure. In this case, the control rules suggestions calculated using only deviated process models are subject to the above rules.

Figures 5A-5D illustrate examples of methods for forming a plurality of different patterns involving two-parameter deflection, alignment, and gain. Three parameter variations are used for alignment: nominee-15 alignment and two deflected alignments M1 and M2. There are also three parameter variations in the gain: nominal gain and two deviated gain G1 and G2. In Fig. 5A, all permutations of these parameter variations are used, resulting in a set of nine different models, one of which is a nominal model. Figure 5B shows five different types of models, one of which is a nominal model and four are deflected models, where both parameters are deflected simultaneously. Figure 5C also shows "five different models, one of which is a nominal model and four are deflected models, each with only one parameter deflected. Figure -: ... · * In section 5D there are six different models, none of which are Nominal model In Figure ·. · *: 25 of the 5D models, two combine the nominal gain with the offset alignment and the remaining four models combine the offset simultaneously in both parameters. Usually if the W parameter is offset and the nominal mode and two offsets are used for each parameter -; to indicate an increase or decrease compared to the nominal state), the total number of possible different models is 3 W. This is the case in Fig. 5A, where 'W = 2, so there are nine different models. is the product of the number of different states of each deviated parameter, that is, if akin with the parameter parm, is K, different thi. 'Laa (one of which may be the nominal state of the parameter), the possible different models are:' * · w,,: 35 is the total. Thus, if W is a large number, or if one of the numbers K, i = 1 is large, a large number of possible different models can be found.

115325 14

If more than one model structure is used, the total number of possible models depends on the number of parameters to be offset in each model structure and the number of different states of each parameter.

However, the number of 5 different models among the various models used by the Robust controller, and thus the number of control measures proposed, can be reduced. Generally, it is not necessary to use all possible different designs, such as in Figure 5A. A subset of the possible different models is usually sufficient to ensure robustness, and often a few subsets are sufficient when some parameters have many parameters or many mah-10 dollars. For example, if each W parameter has a nominal state and two deflected states and the parameter deflections are not combined, 2W + 1 different models (one of which is a nominal model) will be obtained, as in Figure 5C. Figure 5B illustrates a similar situation except that the parameters are linearly offset in independent combinations, which also results in a different model used in 2W + 1. Figures 5B and 5C thus illustrate two simple ways of sampling a set of possible different designs. Many other ways are also possible, depending on how much the interaction between the exceptions affects the various parameters. For example, Figure 5D illustrates a different subset that does not have different designs with nominal space for targeting at all.

A subset of all possible different models can be defined as a sampling pattern or sampling algorithm. If more than one model structure is used, the sampling method need not be the same for all model structures. If there is a priori information about the effects of the differences: ··· 25 interactions on different parameters, the sampling pattern can be: *, · predefined. For example, the parameters can be offset by one. · * ·. bogies, as in Figure 5C, or in certain combinations, as in Figure 5B. If the parameters are offset by combinations, the combinations need not be linear; / t independent. If the effects of the interactions between exceptions on 30 different parameters depend on the current state of the process being controlled (or · respectively the current nominal process model), the sampling *: · *: can be determined as an algorithm. If such a priori information is not available, '' ': random sampling may be used, which may vary from one control to another.

Random sampling can follow a prescribed statistical pattern. For example, a uniform probability density may be used for the whole set of possible exceptions, or it may have different densities for some parameters. Alternatively, random probability density or other commonly known statistical distribution can be used for random sampling. Naturally, each particular set of parameters should occur at most once in the set of variable models 5 in use, so that sampling is performed without compensation.

Fig. 6A illustrates a simulated operation of a conventional minimal variance CD controller, which uses optimization of least squares to minimize variance, and hence error standard deviation ΔΡ. The CD actuator has 70 elements, each 6 cm wide, while 10 errors have 421 elements, each an average of 1 cm wide web. For the sake of clarity, only the CD portion of the control algorithm is taken into account and the process is expected to rapidly reach equilibrium in the TD. The nominal process model consists of a nominal transverse response and a Λ nominal CD alignment, which are combined into a response matrix R with 15,421 rows and 70 columns. Each column of the response matrix has a nominal response of an individual institution relative to the entire error, so that its response is centered on a row representing the position of that institution's nominal alignment in the profile. Similarly, each column of the response matrix R indicates the effect of each actuator on the individual element in the error.

20 The optimal control for minimizing variance, ΔΑ, is thus formed as follows: Λ λΝ-1 ·: · AA = | R RJ R ΔΡ '** Figure 6A shows how the standard deviation of error changes from an initial value of less than one. , with this minimal variation CD! The 25 standard controls are used ten times in a row and once the process has fully responded to each operation before calculating the next operation. The bottom line 600 represents the performance when the nominal process model Λ · R is exactly the same as the actual process model. Its asymptotic. * Value (after multiple controls) is 0.6713. The following two lines 602,: 30 604 from the bottom, respectively, represent the performance when the nominal alignment has an error of 1 cm and 2 cm for the actual process alignment: · '(when the nominal response moves 1 cm and 2 cm respectively in the transverse direction) process response). Overall, model performance is still quite good (asymptotic values of 0.6743 and 0.6872, respectively), 35 even though performance is slightly inferior to the exact process model 115325 16. The following line 606 represents performance with a nominal alignment error of 3 cm. In this case, although the first two control operations produce a better result, the controller causes a steady process deterioration. Top line 608 represents performance-5 with a nominal alignment error of 4 cm. The first control operation produces a slightly better result, but is followed by a rapid and continuous deterioration such that after three operations the performance is lower than in the initial state and deteriorates at an ever accelerating rate. In the latter two cases (10 errors of 3 cm and 4 cm in alignment), the controller has become unstable, thus increasing the error variance indefinitely (in practice, the process would limit the increase of error variance when the error variance has increased sufficiently). In the first three cases, the controller is stable and operates satisfactorily. From this it can be inferred that this particular minimum variance regulator is inherently robust with respect to errors of about 2 cm in targeting when controlling this particular process.

The actuator response and original profile used in this simulation are taken from a real paper machine, but for the sake of clarity the alignment was slightly simplified. In practice, the nominal model is never completely accurate, 20 and many, if not all, institutions have misalignments. However, targeting errors are not the same for the entire profile: '··, and vary over time. Local errors in alignment are generally greater than 2 cm. Many actuators can sometimes have misalignments larger than 2 cm, especially when process ·: ··· 25 moves back and forth between balanced modes. This is typical for correct processes where the width of the web can be more than 1000 cm and, ··! which can have more than 300 actuators, making it difficult and costly to focus each institution within 2 cm. It should be noted that the curves and numerical results are for double mean · ·; / 30 curl and not so much for standard deviation or variance. This is a common way of expressing the amount of transverse variation in a profile.

Figure 6B shows the same minimum variance control algorithm; simulated operation modified in accordance with the present invention.

The simulation uses the same response and alignment information, so the nominal '35 model R is similar and uses the same original error ΔΡ. In this case, alignment deviations of ± 1 cm are used to derive two deflected patterns whose response matrices can be represented as + Λ in the form R + 5Ri and R + 6R2. Exceptions are made only to the nominal alignment, not to the nominal response. Thus, for each control, three control suggestions are generated from the error ΔΡ, where ΔΑ0 uses 5 nominal process models and ΔΑ, and ΔΑ2 uses two deviated process models: Λ / Λ T AN ”1 λΤ ΔΑ0 = Ι R RJ R ΔΡ

AA ^ R + ÖR. ^ R + SR,)) (R + 6R,) TAP

Λ / Λ Λ \ −1 Λ

AA2 = [(R + 5R2) t (R + 6R2) J (R + 5R2) tAP

10 These proposals for action are then combined into a joint action. The combination method of this example employs the three rules described above, where all the factors of the reference operation are zero, whereby the three control action proposals form a consensus action.

Figure 6B shows how the standard deviation of error changes from an initial value of slightly less than one when this robust CD controller is used several times in succession and when the process has fully responded to each operation before calculating the next operation. Lowest

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"line 610 represents performance when the nominal process model R is exactly the same <I · 20 as the true process model. It has an asymptotic value of 0.6776. The following three lines 612, 614, 616 represent the bottom, respectively, when the nominal alignment has errors size is 1 cm, 2 cm and 3 cm compared to the actual process alignment. Asymptotic values are "0.6793, 0.6858 and 0.7077, respectively, although performance is slightly lower compared to the minimal variance standard with the exact process model. controller performance. In these four cases, performance is still] '[overall] very good. In particular, the system is stable and performs quite well with a 3 em error in alignment, which does not: stabilize the operation of a conventional controller. The top line 618 represents the performance,,! 30 when the nominal alignment has a 4 cm error. The first two control measures will produce a slightly better result, but after that. followed by a gradual decline towards the asymptotic value of 17.65. Although the regulator is stable, its performance is poor for a 4 cm error I »115325 18. It can be concluded that when the parametric variations in alignment are 1 cm, the robust control is about 1 cm more robust than the conventional control in terms of misalignment.

Figure 6C shows a simulated operation of the Robust Minimum Variance Control Algorithms-5 min using the same robust minimum variance control algorithm, the same process data, and the same nominal process model as in Figure 6B. However, in this case, the alignment deviations of ± 2 cm are used to derive two deflected patterns. Otherwise, the procedure is the same as in Figure 6B.

Figure 6C shows how the standard deviation of the error changes from an initial value of slightly less than one, when this robust minimum variance CD controller is used several times in succession and when the process is fully responsive to each operation before the next operation is calculated. The lowest line 620 represents performance when the nominal process model R 15 is exactly the same as the actual process model. It has an asymptotic value of 0.6894. The next two lines 622, 624 from the bottom show the performance, respectively, with nominal alignment errors of 1 cm and 2 cm relative to the actual process alignment (when the nominal response shifts 1 cm and 2 cm, respectively, to the actual process response ver-20). Asymptotic values are 0.6906 and 0.6933, respectively. Performance is slightly reduced compared to the minimum variance of the exact process model: '·· its standard controller, but overall performance is still very good in these three cases. The following line 626 represents performance when a nominal alignment error of 3 cm occurs.

•: ·: 25 Although performance is degraded, control is stable and the potential improvement is almost complete with an asymptotic value of 2 * sigma of 0.7055. ·· *, Top line 628 represents performance with a nominal alignment error of 4 cm. In this case, the control is stable and the asymptotic value is 0.7243.

. . The system is stable and performs quite well with a misalignment of up to 4 cm, thus causing the traditional controller to become unstable rapidly. It can be concluded that when targeting; the parametric variations occurring are about 2 cm, the robust control is about 2 cm more robust than the traditional control for alignment errors.

'35 Controller performance is usually represented by a Harris-type index. Such an index can be defined herein as the exact ratio of the simulated performance of the minimum variance control using the 115325 19 model to the simulated performance of each controller using its own process model, multiplied by 100. An ideal index is 100, with values lower than this indicating lower performance; so zero means full-5 instability. The results of the simulations shown in Figures 6A, 6B and 6C are summarized in the following table:

Error in nominal Oem 1 cm 2 cm 3 cm 4 cm alignment______

Nominal Alignment of the Standard 100 99.55 97.68 0.0 0.0 Controller______

Robust Control 99.07 98.82 97.89 94.86 3.80 Nominal Alignment ± 1 cm______

97.37 97.21 96.83 95.15 92.68 Robust Adjuster Nominal Alignment ± 2 cm______

The benefits of the present invention will be readily apparent.

10 Robust controller performance suffers only slightly with minor model errors, but it is stable for larger model errors. In addition, the robust controller achieves almost the same performance with both large and small model errors. In addition, the robust controller “! • The increase in robustness compared to a non-robust controller is obtained by: • the amount of deflection used in the • robust controller.

Note that, in practice, the ideal situation with zero misalignment will hardly ever occur.

: Let's now briefly look at the * 'bodies used in the webmaking process. The actuators are commonly used in the web production process for feed-; 20 material. For example, the relationship between the various raw materials may be altered so as to obtain the desired properties of the web.

; In papermaking, the ratios of hardwood pulp to softwood pulp, or the amounts of resins or kaolins, can be varied to provide the desired mechanical or compositional properties to the web, such as smoothness or ash content. Likewise, additives such as dyes or pigments may be added to the streams fed into the process, thereby affecting the color or opacity of the web being produced.

Optical and composition properties are generally measured by spectroscopic sensors such as absorption, reflectance, emission or fluorescence spectra in the X-ray, ultraviolet, infrared, microwave or visible regions, or by some combination of such methods. Such measurements can be made in one transverse location to provide a measurement that is assumed to represent the entire width of the web. Alternatively, spectral measurements may be made at multiple locations across the web to provide a spectral profile or a combined average spectrum for the amount of web sampled by the sensors.

Spectroscopic and spectrophotometric measurements are known for being made at each of several wavelength ranges, which is why they are called wavelength domain (WD) measurements. Here, any property that is directly measured as a spectroscopic spectrum is a WD measurement. Because properties measured as WD measurements, such as reflectance or transmittance, can also change over time or can be measured as spectral profiles, these properties may also have time-domain and cross-directional characteristics.

Any characteristic that is indirectly measured from one or more spectroscopic measurements, but is not necessarily a spectral, is thus a characteristic of the wavelength plane in the context of the present invention. For example, color is a WD property that is indirectly measured by spectral measurements of visible area reflectivity and can be expressed in any of several non-spectral coordinates, such as CIELAB or tristimulus. Similarly infrared ···. composite measurements derived from absorption spectra or X-ray fluorescence spectra are also WD properties, although they are often expressed as mass; _.t fraction. Techniques for spectrophotometric color measurement and spectroscopic quantitation are well known per se and will not be further discussed herein.

A: The effect of an institution on spectroscopic measurement is called the WD response of the institution. For example, increasing the amount of red dye in the feed material causes the web's reflectivity to decrease in the blue, [green and yellow] wavelength range, making the web reddish. The shape of the change in reflectance is the response of the red toner to the WD reflectance.

Similar to the process of controlling the profile, there may be uncertainty about the TD and CD models, as well as the process of adjusting the WD property, there may be uncertainty about the WD model of the process. In papermaking, for example color adjustment, one or more dyes or pigments are fed to the paper forming pulp fed to the process. WD response to dyes paper absorption! the spread spectra change with changes in substrate characteristics.

For example, the shape and magnitude of the pigment response of the spread spectrum depends on the geometry of the fibers (diameter, roughness, etc.) and the amount of filler (kaolin, chalk, precipitated CaCCV, TiCl2, etc.) in the web. It may also depend on the temperature at the site of administration and the chemical environment (pH, presence of anions and cations) at the site. In some cases, the shape of the spectroscopic response is not clearly erroneous, but shifted at wavelength, similar to the misalignment in the profile.

The present invention is thus advantageously applicable to the control of WD properties such as color and composition. A color control using WD gauges and a nominal process model of WD is described in "An Optimizing Color Controller" by Shakespeare & Shakespeare: * ·· TAPPI Journal 81 (9), pp. 171-179, September 1998. WD- the controller is made more robust to errors in its nominal process model by using at least two different process models, at least one of which is a deviation of the 25: 1 minimum process model. WD controllers nominal process model offsets can be generated using one or more offset • ». ···. occurring in one or more WD process model parameters.

. It is clear that although the inventive idea has been described primarily in the context of control using CD-based process models, it can equally be applied to control using i-WD process models, regardless of whether: CD features available or not. Replacing the spectra with profiles makes the control problems of WD and CD the same. Although the examples and claims show robustness primarily in connection with CD controllers, they should also be construed as referring to the robustness of WD controllers.

22 115325 CD and WD processes are special cases of multi-variable processes. Thus, the replacement of measurement vectors with profiles renders the problems of the ordinary multivariate controller and the problems of the CD controller equal. Although an example of alignment is not essential here, the process structure can be expressed in the same matrix form as the CD process, and the robustness of the multivariate controller can be improved by incorporating variations in the process model according to the present invention. Although the examples and claims show robustness primarily in connection with a CD controller, they should also be construed as referring to the robustness of a general multi-10 variable controller.

Robustness can also be achieved by combining WD and TD features of control, WD and CD features of control, CD and TD features of control, or CD, TD, and WD features of control. The application of the present invention to these combinations will be apparent to those of ordinary skill in the art of CD or TD or WD control, and such applications are within the scope of the present invention.

Although the invention has been described above with reference to the example of the accompanying drawings, it is to be understood that the invention is not limited thereto, but that it can be modified in many ways within the scope of the inventive concept of the claims.

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Claims (32)

A method for controlling a manufacturing process of a web, wherein a web corresponding to the desired values is produced: the state of the process (100) is measured, whereby one or more measurement values describing the state of the process (100) are obtained; each measured value is compared with a corresponding desired value; on the basis of the comparison, an error is represented representing a deviation in relation to each other between at least one measurement value and the desired value, characterized by at least two suggestions for control measures being formed using at least two process models, at least one of which is a deflected process model , which control proposals are based on the error; by means of the proposals for control measures, a control measure is formed, by means of which the process (100) for producing a web is controlled to produce a web corresponding to the desired values. 2. A method according to claim 1, characterized in that the control measure is formed by using a rule-based combination of proposals for control measures. 3. A method according to claim 2, characterized in; In the rule-based combination, the following three rules are used: 0 Rule 1: if all proposals for control measures for an actuator are greater than a reference action value obtained for the actuator, then combine - *** \ the actuation value of the actuator greater than the reference action value with a minimum part exceeding the reference action value for the proposals for control measures; in rule 2: if all proposals for control measures for an actuator are:: less than a reference action value obtained for the actuator, the combined actuator value of the actuator is less than the received reference setpoint value with a minimum part that falls below the reference action deficit. : the proposal for governance measures; Rule 3: If the proposals for control measures for the control device do not meet the conditions set for activating the nondescript of rules 1 or 2, the combined measure value is the reference reference value obtained. 4. A method according to claim 3, characterized in that the reference reference value obtained for at least one actuator is zero. 115325 29 5. A method according to claim 3, characterized in that the obtained reference measure value for at least one actuator is the measure value which controls the actuator to a minimum cost condition. 6. A method according to claim 1, characterized in that the control measure is formed by calculating the average value of the proposals for control measures. 7. A method according to claim 6, characterized in that the calculation of the mean is weighted calculation of the mean. 8. A method according to claim 1, characterized in that the control measure is formed so that a control measure is selected from the proposals for control measures. 10 Method according to claim 8, characterized in that the selected control measure is the proposal for a control measure with the minimum 2 standard or the minimum infinity standard of all proposals for control measures. Method according to claim 1, characterized in that the desired values are predetermined setpoints. 15 Method according to claim 1, characterized in that several deflected process models are formed by a nominal process model and a obtained deflection amount. The method according to claim 1, characterized in that at least one deflected process model has been deflected by a random amount. 20 13. A method according to claim 1, characterized in that -. at least two process models have different structures. The method according to claim 1, characterized in that the method is used in multivariate control. Method according to claim 1, characterized in that the method is used in transverse control. i.i j Method according to claim 1, characterized in that the method is used in controlling a spectroscopically measured quantity. : i A control arrangement for controlling a manufacturing process of a: web, which process is arranged to produce a web that corresponds to desired values, comprising: a measuring unit (102) for measuring the state of the process (100), wherein one or more several metrics describing the state of the process (100) are obtained; A comparator (106) for comparing the respective measurement value to a corresponding desired value and to form an error representing a deviation in relation to each other between at least one measurement value and the desired value, the characteristic water arrangement comprises a control unit (108) arranged to utilizing at least two process models, of which at least one is a deflected process model, and the controller is arranged to form at least two suggestions for control measures, which are based on the profile; a processor unit (111) for forming a control measure by the proposals for control measures, by means of which the control arrangement is arranged to control the process of producing a web to produce a web corresponding to the desired values. Arrangement according to claim 17, characterized in that the processor unit (111) is arranged to form the control measure by using a rule-based combination of suggestions for control measures. 19. Arrangement according to claim 18, characterized by! the rule-based combination uses the following three rules: Rule 1: if all suggestions for control measures for an actuator are greater than a reference action value obtained for the actuator (112), the combined action value of the actuator (112) is greater than the reference action value. with a minimum part exceeding the reference measure value of the proposals for control measures; rule 2; if all proposals for control measures for an actuator (112) are less than a reference action value obtained for the actuator (112), then,. The combined action value of the actuator (112) is less than the reference reference measure value with a minimum proportion that falls short of the deficit of the reference measure for the proposals for control measures; rule 3: if the proposals for control measures for the actuator (112) do not j meet the conditions set for activating the neogondera of rules 1 or 2, '' ': 30, the combined measure value is the received reference measure value. ,; An arrangement according to claim 19, characterized in that the reference reference value obtained for at least one actuator (112) is zero. An arrangement according to claim 20, characterized in that in the received reference measure value for at least one actuator (112), the actuation value which controls the actuator (112) is at a minimum cost condition. 22. Arrangement according to claim 17, characterized in that the processor unit (111) is arranged to form the control measure by calculating the average value of the proposals for control measures. 23. Arrangement according to claim 22, characterized in that the calculation of the mean is weighted calculation of the mean. Arrangement according to claim 17, characterized in that the processor unit (111) is arranged to select a proposal for control measures from the proposals for control measures. 25. Arrangement according to claim 17, characterized in that the selected control measure is the proposal for a control measure with the minimum 2 standard or the minimum infinity standard of all proposals for control measures. Arrangement according to claim 17, characterized in that the desired values are predetermined setpoints. Arrangement according to claim 17, characterized in that the processor unit (111) is arranged to form several deflected process models of a nominal process model and a given deflection amount. 28. Arrangement according to claim 17, characterized in that the processor unit (111) is arranged to form at least one deflected process. Model using a random or pseudo-random deflection. flow volumes. An arrangement according to claim 17, characterized in that at least two process models have different structures. An arrangement according to claim 17, characterized in that the control arrangement is used in multivariate control. , 31. Arrangement according to claim 17, characterized by: the control arrangement is used for transverse control. » 32. Arrangement according to claim 17, characterized by the control arrangement used in controlling a spectroscopically measured magnitude.