Login| Sign Up| Help| Contact|

Patent Searching and Data


Title:
CONTROLLING CROSS MACHINE PROPERTIES OF A SHEET
Document Type and Number:
WIPO Patent Application WO/2001/075226
Kind Code:
A1
Abstract:
The invention relates to a method and an arrangement for controlling cross machine properties. A high resolution profile of a property is measured by measuring N points in the cross direction at two instants. A high resolution error profile of a property is formed by comparing the measured profile with the high resolution desired profile. A high resolution enhanced error profile comprising N spatial values is formed by subjecting the formed error profiles to a time-domain enhancement operation. Alternatively, a high resolution enhanced measured profile and a high resolution enhanced desired profile are formed by subjecting the profiles to a time-domain enhancement operation. Thereafter, a high resolution enhanced error profile of a property comprising N spatial values is formed by comparing the enhanced measured profile of each property with the enhanced desired profile. In order to control actuators, M actuator control signals are formed from the high resolution enhanced error profile comprising N spatial values, where M and N are positive integers greater than zero, M < N.

Inventors:
SHAKESPEARE JOHN (FI)
Application Number:
PCT/FI2001/000321
Publication Date:
October 11, 2001
Filing Date:
April 03, 2001
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
METSO PAPER AUTOMATION OY (FI)
SHAKESPEARE JOHN (FI)
International Classes:
D21G9/00; G05B15/02; (IPC1-7): D21G9/00; G05B13/00
Foreign References:
US4874467A1989-10-17
US6026334A2000-02-15
US5400247A1995-03-21
Attorney, Agent or Firm:
KOLSTER OY AB (Iso Roobertinkatu 23 P.O. Box 148 Helsinki, FI)
Download PDF:
Claims:
Claims
1. A method for controlling cross machine properties of a sheet during manufacture, comprising the steps of measuring a high resolution profile of at least one property from the sheet by measuring the sheet spatially from N points in the cross direction at least at two successive instants ; forming a high resolution error profile of each property comprising N spatial values for each measured instant by comparing the measured profile of each property with the desired high resolution profile comprising N spatial values ; forming a high resolution enhanced error profile comprising N spatial values by subjecting the formed error profiles to a timedomain enhancement operation ; forming M actuator control signals from the high resolution enhanced error profile comprising N spatial values, when M and N are positive integers greater than zero, M is smaller than N, and N denotes spatial high resolution ; and controlling actuators affecting the cross machine properties by means of the formed actuator control signals.
2. A method for controlling cross machine properties of a sheet during manufacture, comprising the steps of measuring a high resolution profile of at least one property from the sheet by measuring the sheet spatially from N points in the cross direction at least at two successive instants ; forming a high resolution enhanced measured profile comprising N spatial values by subjecting the measured profiles to a timedomain enhancement operation ; forming a high resolution enhanced desired profile comprising N spatial values by subjecting the desired profile to a timedomain enhancement operation ; forming a high resolution enhanced error profile of each property comprising N spatial values by comparing the enhanced measured profile of each property with the enhanced desired profile ; forming M actuator control signals from the high resolution enhanced error profile comprising N spatial values, when M and N are positive integers greater than zero, M is smaller than N, and N denotes spatial high resolution ; and controlling actuators affecting the cross machine properties by means of the formed actuator control signals.
3. A method according to claim 1 or 2, wherein the following steps are taken in order to perform a timedomain enhancement operation : the profile to be timedomainenhanced is decomposed into a plurality of components ; at least one component of the decomposition is subjected to a time domain enhancement operation ; and an enhanced profile is formed from at least one component after said enhancement.
4. A method according to claim 1 or 2, wherein the desired profile is a set point profile.
5. A method according to claim 3, wherein at least one component of the decomposition is subjected to a timedomain enhancement operation, which is different from the timedomain enhancement of at least one other component of the decomposition.
6. A method according to claim 3, wherein the decompositions are formed either by projection onto spatial frequency bands, spatial position or scale bands, or other supplied spatial basis functions, or by use of pattern matching spatial filters to extract specific spatial features.
7. A method according to claim 1 or 2, wherein the timedomain enhancement operation is as follows : where xi, j is the weighting coefficient at measuring point i in the sheet's cross direction at instant j, and the coefficients xi, j are not all equal, but at least two coefficients are nonzero, and their sum is nonzero and preferably positive.
8. A method according to claim 1 or 2, wherein the timedomain enhancement operation is as fomows in a velocity mode formulation : where wi, j is the weighting coefficient at measuring point i in the sheet's cross direction at instant j, and the coefficients xi, j are not all equal, but at least two coefficients are nonzero, and their sum is nonzero and preferably positive.
9. A method according to claim 1 or 2, wherein cross machine properties are controlled using differintegral operations of noninteger order.
10. A method according to claim 1 or 2, wherein cross machine properties are controlled using PID control.
11. An arrangement for controlling cross machine properties of a sheet during manufacture, comprising a measuring unit, a spatial unit, a temporal control unit which comprises an error unit and an enhancement unit, and at least one actuator, in which arrangement the measuring unit is arranged to measure from the sheet a high resolution profile of at least one property by measuring the sheet spatially from N points in the cross direction at least at two successive instants ; the error unit is arranged to form a high resolution error profile of each property comprising N spatial values for each measured instant by comparing the measured profile of each property with the high resolution desired profile comprising N spatial values ; the enhancement unit is arranged to form a high resolution enhanced error profile comprising N spatial values by subjecting the formed error profiles to a timedomain enhancement operation ; the spatial unit is arranged to form M actuator control signals from the high resolution enhanced error profile comprising N spatial values, when M and N are positive integers greater than zero, M is smaller than N, and N denotes spatial high resolution ; and the arrangement is arranged to control at least one actuator affecting the cross machine properties by means of the formed control signals.
12. An arrangement for controlling cross machine properties of a sheet during manufacture, comprising a measuring unit, a spatial unit, a desired profile enhancement unit, a temporal control unit which comprises an error unit and an enhancement unit, and at least one actuator, in which arrangement the measuring unit is arranged to measure from the sheet a high resolution profile of at least one property by measuring the sheet spatially from N points in the cross direction at least at two successive instants ; the enhancement unit of the control unit is arranged to form a high resolution enhanced measured profile comprising N spatial values by subjecting the measured profiles to a timedomain enhancement operation ; the desired profile enhancement unit is arranged to form a high resolution enhanced desired profile comprising N spatial values by subjecting the desired profile to a timedomain enhancement operation ; the error unit is arranged to form a high resolution enhanced error profile of each property comprising N spatial values by comparing the enhanced measured profile of each property with the enhanced desired profile ; the spatial unit is arranged to form M actuator control signals from the high resolution enhanced error profile comprising N spatial values, when M and N are positive integers greater than zero, M is smaller than N, and N denotes spatial high resolution ; and the arrangement is arranged to control at least one actuator affecting the cross machine properties by means of the formed control signals.
13. An arrangement according to claim 11 or 12, wherein the following steps are taken at least in one of said enhancement units in order to perform the timedomain enhancement operation : the profile to be timedomainenhanced is decomposed into a plurality of components ; at least one component of the decomposition is subjected to a time domain enhancement operation ; and an enhanced profile is formed from at least one component after said enhancement.
14. An arrangement according to claim 11 or 12, wherein the desired profile is a set point profile.
15. An arrangement according to claim 13, wherein at least one component of the decomposition in at least one of said enhancement units is subjected to a timedomain enhancement operation, which is different from the timedomain enhancement of at least one other component of the decomposition.
16. An arrangement according to claim 13, wherein the decompositions are based on a division comprising spectral bands, position or scale bands, feature extractions and arbitrary basis functions.
17. An arrangement according to claim 11 or 12, wherein the time domain enhancement operation is as follows : where xi, j is the weighting coefficient at measuring point i in the sheet's cross direction at instant j, and the coefficients xi, j are not all equal, but at least two coefficients are nonzero, and their sum is nonzero and preferably positive.
18. An arrangement according to claim 11 or 12, wherein the time domain enhancement operation is as follows in a velocity mode formulation : where xi, j is the weighting coefficient at measuring point i in the sheet's cross direction at instant j, and the coefficients wjj are not all equal, but at least two coefficients are nonzero, and their sum is nonzero and preferably positive.
19. An arrangement according to claim 11 or 12, wherein cross machine properties are controlled using differintegral operations of noninteger order.
20. An arrangement according to claim 11 or 12, wherein cross machine properties are controlled using PID control.
Description:
Controlling cross machine properties of a sheet Field of the invention The invention relates to a method for controlling a sheet-making process and to a control arrangement of the sheet-making process operating according to the method. The invention relates especially to regulating cross- directional properties of a sheet during the manufacture thereof.

Background of the invention The quality of a sheet being manufactured is usually measured across the web by cross-directional (CD) measurements. Typical variables measured in CD measurements are moisture content, caliper and basis weight. The measurement results are compared with the set values and an error profile is formed to show the difference between the measurement results and the set values. A process which is in a state matching the set values is known to produce a sheet of a desired quality and, thus, the process should be kept in a state matching the set values as exactly as possible. By means of the error profile and a nominal process model, a controller gives a control command to one or more actuators, which alter the process according to the command. In papermaking in particular, nip pressure, steam quantity or other heat applied to the sheet during the process can be used as actuators.

The measurement variables are altered or maintained by means of the actuators to maintain good quality of the paper being made.

A drawback of the prior art arrangements is that the dynamics of the process cannot be handled at high spatial resolution. Moreover, the controller cannot respond to rapid disturbances.

Brief description of the invention An object of the invention is to provide an improved method and an arrangement implementing the method. This is achieved by a method for controlling cross machine properties of a sheet during manufacture, comprising the steps of measuring a high resolution profile of at least one property from the sheet by measuring the sheet spatially from N points in the cross direction at least at two successive instants ; forming a high resolution error profile of each property comprising N spatial values for each measured instant by comparing the measured profile of each property with the desired high resolution profile comprising N spatial values ; forming a high resolution

enhanced error profile comprising N spatial values by subjecting the formed error profiles to a time-domain enhancement operation ; forming M actuator control signals from the high resolution enhanced error profile comprising N spatial values, when M and N are positive integers greater than zero, M is smaller than N, and N denotes spatial high resolution ; and controlling actuators affecting the cross machine properties by means of the formed actuator control signals.

The invention also relates to a method for controlling cross machine properties of a sheet during manufacture, comprising the steps of measuring a high resolution profile of at least one property from the sheet by measuring the sheet spatially from N points in the cross direction at least at two successive instants ; forming a high resolution enhanced measured profile comprising N spatial values by subjecting the measured profiles to a time-domain enhancement operation ; forming a high resolution enhanced desired profile comprising N spatial values by subjecting the desired profile to a time-domain enhancement operation ; forming a high resolution enhanced error profile of each property comprising N spatial values by comparing the enhanced measured profile of each property with the enhanced desired profile ; forming M actuator control signals from the high resolution enhanced error profile comprising N spatial values, when M and N are positive integers greater than zero, M is smaller than N, and N denotes spatial high resolution ; and controlling actuators affecting the cross machine properties by means of the formed actuator control signals.

The invention further relates to an arrangement for controlling cross machine properties of a sheet during manufacture, comprising a measuring unit, a spatial unit, a temporal control unit which comprises an error unit and an enhancement unit, and at least one actuator, in which arrangement the measuring unit is arranged to measure from the sheet a high resolution profile of at least one property by measuring the sheet spatially from N points in the cross direction at least at two successive instants ; the error unit is arranged to form a high resolution error profile of each property comprising N spatial values for each measured instant by comparing the measured profile of each property with the high resolution desired profile comprising N spatial values ; the enhancement unit is arranged to form a high resolution enhanced error profile comprising N spatial values by subjecting the formed error profiles to a time-domain enhancement operation ; the spatial unit is arranged to form M

actuator control signals from the high resolution enhanced error profile comprising N spatial values, when M and N are positive integers greater than zero, M is smaller than N, and N denotes spatial high resolution ; and the arrangement is arranged to control at least one actuator affecting the cross machine properties by means of the formed control signals.

The invention also relates to an arrangement for controlling cross machine properties of a sheet during manufacture, comprising a measuring unit, a spatial unit, a desired profile enhancement unit, a temporal control unit which comprises an error unit and an enhancement unit, and at least one actuator, in which arrangement the measuring unit is arranged to measure from the sheet a high resolution profile of at least one property by measuring the sheet spatially from N points in the cross direction at least at two successive instants ; the enhancement unit of the control unit is arranged to form a high resolution enhanced measured profile comprising N spatial values by subjecting the measured profiles to a time-domain enhancement operation ; the desired profile enhancement unit is arranged to form a high resolution enhanced desired profile comprising N spatial values by subjecting the desired profile to a time-domain enhancement operation ; the error unit is arranged to form a high resolution enhanced error profile of each property comprising N spatial values by comparing the enhanced measured profile of each property with the enhanced desired profile ; the spatial unit is arranged to form M actuator control signals from the high resolution enhanced error profile comprising N spatial values, when M and N are positive integers greater than zero, M is smaller than N, and N denotes spatial high resolution ; and the arrangement is arranged to control at least one actuator affecting the cross machine properties by means of the formed control signals.

The preferred embodiments of the invention are disclosed in the dependent claims.

The invention is based on a time-domain enhancement operation of an error profile, which enables important high spatial resolution properties to be maintained in the profile for the formation of a control signal.

The method and the arrangement according to the invention provide several advantages. An advantage of this invention is that the dynamics of the process can be handled at high spatial resolution. This allows a controller to be tuned to respond more rapidly to disturbances. Moreover, since disturbance dynamics tend to differ among different spatial frequency or

scale bands, each band can be enhanced individually for further improving controller performance. These advantages are realized especially when the present invention is combined with a high resolution controller.

Brief description of the figures The invention will be described below by means of preferred embodiments with reference to the accompanying drawings, in which Figure 1A shows a prior art CD controller, Figure 1 B shows a prior art CD controller, Figure 2A shows a CD controller utilizing time-domain enhancement, Figure 2B shows a CD controller utilizing time-domain enhancement, Figure 3A shows a manner of implementing a temporal control unit, Figure 3B shows a manner of implementing a temporal control unit, Figure 4A shows the effect of the enhancement operation on the measured profile or the error profile, and Figure 4B shows the effect of the enhancement operation on three components of a decomposition of the measured profile or the error profile.

Detailed description of the invention The present invention relates generally to the regulation of one or more properties of a sheet in the cross machine direction by modulation of actuators deployed across the sheet making apparatus. The solution of the invention can be applied especially to a sheet-making process, such as the manufacture of paper, board and plastic sheets, without being restricted to them, however.

Let us first examine the processes by means of simple formulae.

The nominal model R of the process can be defined as follows : ap aA where aP is the partial differential variation of the process in relation to the partial differential variation DA of the actuator. P and A are usually vectors representing a sheet property profile and an actuator profile respectively, and R is usually a matrix representing the process response characteristics. The

nominal model of the process is estimated empirically and using earlier measurements, thus providing the nominal model estimate R. In this manner, the required actuator difference variation hA at each moment of time can be calculated by means of the deviation #P of the measured process conditions and the estimated nominal model # as follows: AA = R' AP, where AP is AP = Ph-Pm, Ph is the desired state of the process, Pm is the measured state of the process and R 1 is the inverse of the nominal model estimate of the process. AP can also be called an error signal, which will be denoted hereinafter by EP.

Examine at first a prior art solution with reference to Figures 1A and 1B. A plurality of actuators 108 are commonly deployed across a sheet 100 in order to regulate one or more properties of the sheet 100 in the cross machine direction. Sheet properties are commonly measured by a measuring unit 102 at a plurality of locations (N measurements) across the sheet 100, where such plurality usually exceeds the plurality of actuators 108 (M actuators). The number of measurements N is often N : 3M. These N measurements form a measured profile. The measured sheet properties generally exhibit different deviations from desired values across the machine, and the purpose of regulation is to cause the measurements to approach the desired values, which form a desired profile.

The effect of an actuator on a measured sheet property is referred to as the response of the actuator. The magnitude and shape of responses can vary with operating conditions. The set of locations of the centres of responses for each actuator is referred to as the mapping of the actuators.

Shrinkage, stretching and other phenomena affecting the sheet as it moves from the actuators 108 to the measurement unit 102 can cause the mapping to be nonlinear and to be variable over time.

The actuators 108 need not be equally spaced across the machine, but they can be assumed to be so for the following discussion, without loss of generality. The pitch of the actuators 108 across the machine imposes a fundamental limit on the wavelengths which are theoretically controllable in a regulated sheet property. The spatial Nyquist wavelength, which equals twice the distance between two adjacent actuators, is the shortest wavelength over

which control is possible, and then only when the phase of the variation coincides favourably with an actuator mapping location. Wavelengths longer than about twice the spatial Nyquist wavelength and for which the response has non-zero spectral power density are substantially fully controllable at any phase with respect to the mapping locations. These issues are discussed by Duncan and Bryant [DB97], for example.

In the prior art, sheet properties are regulated on the basis of the assumption that cross-directional profile measurements of the sheet P (x, t) can be distinguished spatially and temporally, P (x, t) describing the state of the sheet manufacturing process. This can be expressed in the following N mathematical form : P = P (x, t) = PCD (x) PTD (t), where PCD (x) represents spatial measurements and PTD (t) represents temporal measurements. This distinction is visible in the arrangement of Figure 1A in that a spatial control unit 104 constitutes a separate block before a temporal control unit 106. When N N measurement values P are transferred from the measuring unit 102 to the spatial control unit 104, the latter reduces the spatial accuracy to correspond M N to the number M of the actuators and forms a spatial error profile P* = CD (P), N N where CCD (P) is a spatial operation performed on the measured profile P. In N practice the spatial control unit 104 compares the measured profile P values N with the desired profile PD values which are defined by set values, and forms M a spatial control signal P* from the deviations. In other words, the spatial M N N N operation is for example of the form P* = CCD (P) = f (PD-P). The temporal M properties of this signal P* with a filtered spatial frequency are also processed in the temporal control unit 106, which provides a final actuator control signal M M a =CTp (P*). The variation SA of an actuator naturally corresponds to the M change determined by the actuator control signal a. Alternatively, a prior art controller may operate as shown in Figure 1 B. In this case, the spatial accuracy is reduced in unit 104 without reference to a desired profile, so that a M M N N control profile P is produced by block 104 as P = CCD (P) = f (P) The temporal control unit processes this control profile and provides a final M M M M actuator control signal a= CTD (P) = f (PD-P) by using the temporal M properties of the control profile's deviation from a desired profile PD that is defined by set values.

For many kinds of actuators, the response shape includes components of a higher spatial frequency than the aforementioned spatial Nyquist frequency. Manipulating the actuators will introduce or affect these frequencies in the measured profile. This can also occur as interference patterns between responses of nearby actuators. A cross machine disturbance which is equal to or higher than the spatial Nyquist frequency is not guaranteed to be controllable, but depending on its phase, it may be possible to attenuate it or at least to avoid introducing it.

There are many cross machine disturbances in sheet-making processes. The time-domain behavior of the cross machine disturbances is often different for low spatial frequency and high spatial frequency disturbances. One of the principal tasks of a cross machine controller is to compensate for these disturbances.

Moreover, separation of sheet properties P (x, t) into a single spatial component and a single temporal component may be inadequate. In other words, the decomposition P (x, t) = Pco (x) PTD (t) + â (x, t), in which 8 (x, t) represents the unseparable components of variation, may be too simple for controlling the process. Several patterns of spatial variation may have different patterns of temporal variation. Thus, a decomposition involving several independent components can better represent the process : P (x, t) = PcDi (x) ? TDi (t) + PcD2 (x) PTD2 (t) +... + 8 (x, t). Characteristic patterns of spatial and temporal variation in a process can be identified using spectral techniques, such as Fourier analysis, principal components analysis or wavelet analysis.

Examine below the arrangement according to the invention with reference to Figure 2A. Also in this arrangement properties of a sheet 100 are measured by a measuring unit 102 comprising N measurements in the cross N direction of the sheet 100. The measured profile P of each property, consisting of N measurements, is supplied in the inventive solution to a temporal control unit 200, which provides a temporally processed error profile N EP* that can be expressed shortly with the mathematical formula N N EP*=CTD (P). More precisely, the temporal control unit 200 compares the N N measured profile P with the desired profile PD in an error unit 2002 and it N forms a temporally processed error profile EP* from the difference between N N N N the measured profile and the desired profile P* = CTD (P) = f (PD-P) in an enhancement unit 2004. The difference between the desired profile and the

N N measured profile is called an error profile EP, which can be denoted by EP = N N PD-P. In this connection it should be noted that according to an advantageous feature of the invention a temporal control signal is formed with maximum accuracy of measurement, which means that all the N measurements formed across the sheet 100 are taken into account in the N temporally processed error profile EP*. In the temporal processing the N processed error profile EP* is subjected to a time-domain enhancement operation, which will be described in greater detail below. Thereafter the N temporally processed error profile EP* is also subjected to spatial processing M in a control unit 202, which forms an actuator control signal a. The spatial M control unit 202 forms the actuator control signal a from the temporally N M N processed error profile EP* by means of operation a=CcD (EP*),, where the N desired profile PDS is compared with the measured, temporally processed N M N N profile P*, i. e. a = CCD (EP*) = r (EP*), where r is the relation of the difference between the desired and the measured profile. In the relation operation r, the set of N values of the error profile is mapped onto a set of M values of the control signal, which means that more than one value of the error profile is M mapped onto one value of the control signal. The actuator control signal a is used to control the actuators 108, the number of which is M.

N In the inventive arrangement, a high resolution error profile EP is N formed from the high resolution measured profile P and the desired high N resolution profile PD, which is preferably a high resolution set point profile. The N N high resolution error profile EP can be formed for example as a difference EP N N N = PD-P. This high resolution error profile EP is subjected to a time-domain N enhancement operation CTD (EP) in order to form an enhanced high resolution N N N error profile EP*, i. e. EP* = CTD (EP). Thereafter the enhanced high resolution N error profile EP* is supplied to the spatial control unit 202 or a cross machine controller.

Figure 2B shows an alternative manner of controlling the actuators by means of the inventive arrangement. The high resolution measured profile N P is subjected to a first time-domain (TD) enhancement operation in an N enhancement unit 2010 in order to form an enhanced measured profile P*,

N and the desired high resolution profile Po, which corresponds to the high resolution set point profile, is subjected to a second time-domain enhancement operation in an enhancement unit 2012 in order to form the N desired enhanced high resolution profile PD. This can be expressed with the N N N N mathematical formula : P* = CTD (P) and PD-= CTD (PD). The second time- domain enhancement operation CTD can be the same as or different from the first time-domain enhancement operation CTD. An enhanced high resolution N N error profile EP* is formed from the enhanced measured profile P* and the N enhanced set point profile Po* in an error unit 2014 for example in the form of N N N a difference EP* = PD-P*.

In the following, the time-domain enhancement operation will be described in greater detail. In both these methods, a range of time-domain error enhancement algorithms can be employed, embodied in time-series operations on successive high resolution profiles. For example, in the first method, the enhanced error profile EP at instant (time) to is calculated from a series of at least two high resolution error profiles EP at instants (times) to, ti, ... tL using corresponding weighting factors wo, wi,... w. In a positional formulation, this is : where xi, j is the weighting coefficient at measuring point i at instant j, where i = 1,..., L. This calculation can alternatively be carried out in a velocity mode formulation : The change in the enhanced error is calculated from changes between successive high resolution error profiles. This is beneficial if the controller to which the enhanced error is supplied is a velocity mode controller. Suitable initialization, such as setting unavailable previous values to zero or to the first available value, must be used for the first L-1 calculations. However, in many cases the weighting coefficient xi, j is not dependent on the measuring point i, but xi, j is only variable in time, which means that the coefficient can be denoted by w and the enhanced error profile can be expressed in the form

The weighting coefficients cannot be selected freely, but the following rules apply to the coefficients wj. In either formulation, the coefficients xi, j are not all equal, but at least two coefficients are non-zero, and their sum is non-zero and preferably positive. Thus, this time-domain enhancement amplifies and attenuates the components of the cross machine error on the basis of their dynamics, rather than attenuating essentially all components as is the case with the filtering employed at high resolution in prior art cross machine controllers. In particular, the filtering in prior art methods suppresses rapid variations more than gradual variations, while in the present solution rapid variations can be amplified. Note that a boxcar average requires that all the coefficients w be equal in a positional formulation, while an exponential filter can be represented in a velocity formulation with only wo being non-zero, so that these prior art methods lie outside the scope of the present solution.

In particular, PI or PID algorithms (P = proportional, I = integral, D = derivative) and commonly known variations thereof are especially useful as error enhancement algorithms. PID algorithms and related issues are as such commonly known to the man skilled in the art. Let KP, Kl and Ko be gains for the proportional, integral and derivative terms, respectively, whereupon the enhanced error EP is as follows in a velocity mode formulation : EP ; (tO) = EP ; (t,) + (Kp + K1 + KD)EPi(t0) - (Kp + 2KD)EPi (t,) + KDEPj (t2), where the weighting coefficients w are : wo = KP + Kl + Ko, WR =- (KP + 2kip) and w2 = Ko, and the aforementioned rules apply to the coefficients.

Other time-series error enhancement algorithms can also be employed, such as the fractional order operations disclosed for use in a controller in US Patent 09/348, 413, which is incorporated herein by reference.

In this enhancement, time-series coefficients w are derived to provide finite approximations to a weighted sum of time differintegrals of the error profile.

Let us examine the differintegral operations set forth in the aforementioned patent. A method employing the fractional order operations for forming a control signal from a control input signal to regulate a process comprises the following method steps. The real state of the process is measured, whereafter a control input signal is formed as a difference between the desired state and the real state of the process. And the control signal from the control input

signal is formed by at least one differintegral operation of non-integer order.

The control signal 0 is formed by formula : where j is an index, M is the number of terms of differintegral operations, XQj represents an approximation to the differintegral operation, Qj is the order of the differintegral operation, Kj is the gain factor, E is the control input signal ; and for at least one term KjX , where 1 < the order ! is the non-integer and Kj is non-zero. The term"non-integer"means"not a pure integer". Thus any complex number which has a non-zero imaginary part is a"non-integer", even if its magnitude is an integer, or its real part or imaginary part is an integer, or both real and imaginary parts are integers."Non-integer"also means quaternion or Hamiltonian numbers. Quaternion numbers are also known as hypercomplex numbers. A non-integer is any number which is not a real integer, but which is a member of a finite-dimensional field for which a division algebra exists. The term"integer"includes both positive and negative integer real numbers, as well as zero. Moreover, the term"arbitrary" encompasses integer and non-integer quantities, including complex numbers and quaternion numbers.

The enhanced error EP'can thus be formed by formula : where the gain factor Kj is also the same as the weighting coefficient wj, to which apply the same conditions as described above. Weights w for error enhancement using fractional order differintegrals can be calculated from the formulae set forth in US Patent application 09/348, 413 disclosing the fractional order controller. For example, if the enhancement uses a differintegral of the error of order q, then a Z transform representation can be expressed in the form : which results in the weighting coefficients wj = ##########. In practice, the error enhancement would usually comprise a combination of terms. For example, a differintegral of order q could be combined with a differintegral of

order p, using respective weighting factors wq and wr. In this case, the weights to be applied to individual errors are : <BR> <BR> rG-G) rG-P)<BR> <BR> <BR> <BR> wj = wq# (j+1)#(-q) +wp #(j+1)#(-p).

Figure 3A shows one manner of implementing a temporal control unit, where the error profile is decomposed into components. The high resolution error profile is formed in an error unit 300 and is divided into a plurality of components by means of bands A (p-A (p, where K is the number of the components, in a high resolution decomposition unit 302. Each component of the decomposition is subjected to a time-domain enhancement operation in enhancement units 304-308. The components of a decomposition can be for example frequency bands, position or scale bands, feature extractions, projections onto arbitrary basis functions, etc. If the components of a decomposition are frequency bands, the decomposition unit 302 can subject the error profile for example to a Fourier transform producing the Fourier coefficients representing the error profile, and each component of the decomposition is formed from a subset of the Fourier coefficients.

Similarly, for decomposition using wavelets or other basis functions, the error profile is transformed to the corresponding coefficient space, and each component of the decomposition is formed from a subset of the coefficients.

This method can also be applied using arbitrary basis functions which have been identified from previous measurements using principal components analysis or functional principal components analysis, as described for example in [SSK99a] and [SSK99b]. Decomposition into position and scale bands corresponds to extraction of particular subsets of coefficients in a wavelet transform. Decomposition by feature extraction can be accomplished for example by applying a suitable pattern-matching filter to the error profile, thereby extracting the feature and calculating the residual by subtracting the extracted feature from the error profile. The time-domain enhancement operations of the components of a decomposition need not all be identical. For example, some components of a decomposition may be suppressed or set to zero. Similarly, the enhancement applied to one component of a decomposition may differ from that applied to another component of the decomposition. An enhanced profile is then formed by combining at least one enhanced component of at least one decomposition in a combiner 310. The combiner performs the inverse operation of the corresponding decomposition

operation on the enhanced components of the decomposition, and thus forms an enhanced error profile corresponding to the error profile.

Figure 3B shows another manner of implementing a temporal control unit, where the measured profile is divided in a decomposition unit 320 into components by means of bands A (PB-A ;, where K is the number of the components, at high resolution. Each component of the decomposition is subjected to a time-domain enhancement operation in enhancement units 322 -326. Similarly as in the case of Figure 3A, the components of a decomposition can be for example frequency bands, position or scale bands, feature extractions, projections onto arbitrary basis functions, etc. If the components of a decomposition are frequency bands, the decomposition unit 320 can subject the error profile for example to a Fourier transform. The time- domain enhancement operations of the components of a decomposition need not all be identical. For example, some components of a decomposition may be suppressed or set to zero. Similarly, the enhancement applied to one component of a decomposition may differ from that applied to another component of the decomposition. An enhanced profile is then formed by combining at least one enhanced component of at least one decomposition in a combiner 328. The combiner performs the inverse operation of the corresponding decomposition operation on the enhanced components of the decomposition, and thus forms an enhanced measured profile corresponding to the measured profile. The combined enhanced measured profile is compared in an error unit 332 with the enhanced desired profile formed in an enhance unit 330 from the desired profile.

The decomposition into components is accomplished for example by dividing the measured profile or the error profile into several spatial frequency bands by means of a Fourier transform, or by dividing the measured profile or the error profile into several spatial scale bands by means of a Wavelet transform, or projecting onto other orthogonal or nonorthogonal spectral bases at high resolution. Suitable bases for such projections can be obtained, for example, by PCA (Principal Component Analysis) or Functional PCA of a set of previously measured high resolution profiles, as described by Shakespeare et al [SSK99a, SSK99b], thus obtaining a high resolution decomposition of the error profile which reflects the innate patterns of spatial and dynamic variation in the process. Fourier and Wavelet transforms and

their applications are described in Chapters 2 and 10 respectively of Poularikas [Pou96], among many others.

Figure 4A shows the effect of the enhancement operation on the measured profile or the error profile. The horizontal axis shows frequency co in the time domain, while the vertical axis shows gain on an arbitrary axis. The lowest frequency on the horizontal axis is normally ce=0. The curve shows the gain of the enhancement operation as a function of frequency in the time domain. The maximum gain for the enhanced profile does not occur at the highest or lowest time-domain frequency. Figure 4B shows the effect of the enhancement operation on three components of a decomposition of the measured profile or the error profile. The curves show the gain of the enhancement operation for each of the three components labeled (pi, (p2, and p3, denoting the characteristic value of (p for each component. The variable (P is for example spatial frequency, spatial position or spatial scale or some other parameter which distinguishes the components of the decomposition from one another. The shape of each curve depends on the weighting factors w used in the corresponding time-domain enhancement. In Figure 4B, the maximum gain does not occur at the highest or lowest time-domain frequency for the two components (pi and (p2, but occurs at the lowest frequency for the third component (p3. In case the measured profile or error profile is decomposed into a plurality of components, where not all components are subjected to the same time-domain enhancement, the maximum gain of each component can occur at any frequency, including the highest or lowest frequencies, provided at least two frequency response curves are different and contain non-zero amplitudes at some frequencies.

The present invention may be extended or combined in several ways with the prior art. The measured profile may be adjusted to compensate for the pending effects of previously enforced control actions. This should occur before the time-domain enhancement operation, so that the enhancement operation is applied to time domain disturbances in the profile, rather than on the time domain effects of previously enforced control actions.

The formation of the error profile from the measured profile and the set point profile, whether before or after the time-domain enhancement, may incorporate nonlinear operations in addition to linear operations. As an example of a nonlinear operation, an error profile EP, of squared magnitude

may be calculated for each measurement cell i from the set point profile p*D and the measured profile P ; : EP ; _ (P ; °-P ;) IP ; °-P ; Alternatively, a time-domain enhanced error EP ; * of squared magnitude may be calculated from the time-domain enhanced set point and measured profiles : EPi* = (PiD*-Pi*)#PiD*-Pi* The cross machine controller may incorporate transformation of the enhanced high resolution error profile to actuator resolution in the same manner as prior art mapped controllers. Alternatively, the cross machine controller may use the high resolution profile directly, in the same manner as the optimizing controller. An optimization-type controller may include the actuator state in its optimization objective. Examples of optimization-type controllers incorporating the control action in the optimization objective can be found in [Gen97], while examples including the actuator state in the optimization objective can be found in [SK97].

The several spatial bands of the high resolution error profile enhanced according to the third method of this invention may be supplied to separate cross machine controllers which control different sets of actuators.

Alternatively, the several spatial bands of the enhanced high resolution error profile may be separately supplied to a cross-machine controller which controls several sets of actuators. Alternatively the numerous spatial bands of the high resolution error profile may be supplied to separate cross-machine controllers whose actions are combined to control a single set of actuators.

Even though the invention is described above with reference to an example according to the accompanying drawings, it is clear that the invention is not restricted thereto but it can be modified in several manners within the scope of the inventive idea disclosed in the appended claims.

References [DB97] S. Duncan, G. Bryant."The Spatial Bandwidth of Cross-directional Control Systems for Web Processes", Automatica 33 (2) 129-153, 1997.

[Pou96] A. Poularikas (ed.). The Transforms and Applications Handbook, CRC Press, 1996.

[SK97] J. Shakespeare, J. Kniivila."Quality Control with Dilution Headboxes", Proc. 1St Intl. CD Symp. at XIV IMEKO World Congress (1-6 June 1997, Tampere Finland), vol. XB p 86-91.

[SSK99a] J. Shakespeare, T. Shakespeare, A. Kaunonen."Functional Data Analysis in Paper Machines, Part 1-Theory", Proc. TAPPI Engineering'99 (12-16 Sept., Anaheim California), vol. 2 p. 555-562.

[SSK99b] J. Shakespeare, T. Shakespeare, A. Kaunonen."Functional Data Analysis in Paper Machines, Part 2-Applications", Proc. TAPPI Engineering'99 (12-16 Sept., Anaheim California), vol. 2 p. 563-569.

[Gen97] S. Gendron,"A Class of Algorithms for Solving CD Control Problems : convergence results and simulated examples", Proc 1St Intl. CD Symp. at XIV IMEKO World Congress (1-6 June 1997, Tampere Finland), vol. XB p. 68-85