CA2013454A1

CA2013454A1 - Control method for sheetmaking

Info

Publication number: CA2013454A1
Application number: CA002013454A
Authority: CA
Inventors: Ramesh Balakrishnan; George M. Butler
Original assignee: Ramesh Balakrishnan; George M. Butler; Measurex Corporation
Current assignee: Honeywell Measurex Corp
Priority date: 1989-03-31
Filing date: 1990-03-30
Publication date: 1990-09-30
Also published as: EP0390686A3; FI901623A0; US5121332A; EP0390686A2; JPH0320801A; KR900014239A

Abstract

ABSTRACT OF THE DISCLOSURE

A time delay compensation control system for use in controlling a sheetmaking process includes a controller operated according to the Smith Predictor control scheme and means to automatically adjust the closed-loop time constant of the controller in inverse relationship to the system error or to the signal-to-noise ratio of the system output signals.

Description

! ' ;- ~ ', ,., ~, ~` 20~3~

CONTROL SYSTEM FOR SHEETMAKING

BACXGROUND OF THE INVENTION

The present invention generally relates to tbe aontrol of hiyh-~peed ~heetmaking machines.

One Rhortcoming of conventional systems for controlling the operation of high-speed ~heetmaking ; machine L~ that the response times of the ~ystems are relatively slow following abrupt change6 in process condltions uch as caused by sheet breaks, reel or grade changes, or during start-up. The ~low reCponses of the control systems assure control stability under normal operating conditions but miay ~llow 6ubstantial quan~it~es of 6ubstandard ~heet~materiAl to be produced before efective corrective actions are implemented ; following abrupt proce~ohanges.

In the ~heetmak~ng art, it i8 well known to u~e the Smith Predictor control scheme~ This control BCheme i8 described in an article entitled "A Simple Adaptive S~ith--Predictor for Controlling Time-Delay Sy~tems,~ T. Bahill, IEEE Control Systems Magazine, .

-\ 2~3~

Vol. 3, No. 2 (May, 1983) pp. 16-22. The Smith Predictor control ~cheme is often employed in time delay compensation control sy~tems, which i8 to ~ay in systems having "dead times." Accordingly, the Smith-Predictor control 6cheme 1B appropriate for u6e insheetmaking systems because the.re are unavoidable delay~ between the times at which sheets are acted upon by manufacturing eguipment and the times at which sheet properties are measured.

In control 6ystem6 incorporating the Smith Predictor control scheme, error6 in estimating the gain6 and time constants o~ the ~y6tems can cause control ln6tab~1ities. Thu6, in conventional practice, controllers in 6y6tems based upon the Smith Pred~ctor control scheme ~re tuned to achieve long-ter~ stability ~t the expense of rapid responses to transient conditions. Another way of stating this is to say that, conventionally, controller parameters in S~lth Predictor sy~tems are selected 80 that the ~ystems re~pond relatively slowly, but stably, to detected variations in a property being controlled.

In view of the ~oregoing discussion, it can -~
be appreciatecl that there i~ a need for control systems that rapidly ~d~ust sheetmaking 6ystems when proces6 2013~

conditions change a~ruptly but, under normal condition6, provide 6mooth and ~table operation, Summary o~ the Invention The present inventiQn provides improvements in the control of high-speed sheetmaking operations after abrupt process changes and during ~tart-up period~. Generally speaking, the contr~l sy6tem of the invention comprises a time delay compensation control 8y8tem according to the S~ith Predictor control scheme wherein the closed-loop time conAtant of the controller ie automatically ad~usted. In the preferred embodiment, the control system of the invention comprises a time delay compensation control 6ystem of the Dahlin type whereln the closed-loop time constant 5 i8 automatically ad~usted in inverse relationship to system error or to the signal-to-noi6e ratio of the output eignals from the control system.

Brief Description of the Drawinas The present invention can be further understood by reference to the following description and ~ttached drawings which illustrate the preferred embodiments of the pre~ent invention. In the drawings:

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FIGURE 1 is a pictorlal view of an example of a conventional ~heetmaklng machine;

FIGURE 2 is a functional block diagram of a control Bystem known in the ar1:;

~IGURE 3 is a functional blocX diagram of a csntrol ystem according to the present invention;

~ , FIGURE 4 i6 a functional block diagram of an ::~
alternative e~bodiment of a control syste~ according to ~ -:
the present ~nvention; and FIGURE 5 1 n functional block diagram of yet : another alternative embodiment of a control system ~ ~;
accord1ng to the pre6ent inventionO

, . :.: .
Detailed Descrlption of the Pre~erred Embodiment FIGURE 1 6how~ an example of a conventional -machine for producing continuou~ sheet material. In the illu6trated embodiment, the ~heetmaking machine includes a feed box l9 which d~scharges raw material, such a~ paper pulp, onto ~ supporting web 13 trained :~
between roller6 14 and 15. Further, the ~heetma~ing :
'.

20~ 3~
`

machlne includes varioue processing ~tages, ~uch ~s a calendarlng ~tack 21, which operate upon the raw material to produce a finished ~heet 18 which is collected onto a reel 19. In modern high-speed S sheetmaking machine~, 6uch as papermaking machines, typical ~heet velocities are about ten to fi~teen inche6 per second.

In conventional sheetmaXing practice, the processing stages along the machine of FIGURE 1 each include actuator~ for controlling the properties of sheet 18 at ad~acent cross-directional locations, often referred to a~ "81ic~s. ~' Thus, for example, calendering stack 21 includes actuators 22 for controlling the compressive pressure applied to sheet 18 ~t variou6 sl~ce location~. In the following, the varlou~ actuator~ are referred to collectively ~6 profile ~ctuator6. The profile actuators normally are independently ad~ustable.

Further ln the ~yste~ of FIGU~E 1, at least one on-line ~ensor 30 is mounted on the Eheetmaklng ~achine to provide control information (i.e., ~easurements of ~ selected 6heet property) ~or operating the profile actuators. In the papermaking art, on-lins sensor6 ~re well known ~or detecting .,.. ~.. i~.... .

. ~ . :
'~:~ ~ '' ' `

;. .. .

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~5 -varlable sheet propertles such as basi~ weight, mol6ture content, and caliper. In the ~llustrated e~bodiment, on-line 6ensor 30 i~ a 6canning ~en60r which is mounted on a Lupportlng frame 31 whlch extends across the sheetmaking machine ln the cross direction.
Further, 6en60r 30 i8 csnnected, as by line 32, to prov$de ~ignals to a profile analyzer 33. The signals indlcate the magnitude of the measured sheet property at variou~ cro6s-directional measurement points. In turn, profile analyzer 33 i8 connected to control the proflle actuators at the various processing 6tages of the ~heetmaking ~achine. For example, line 34 carries ~;~
control signal~ from profile analyzer 33 to the profile actuator~ at calender stack 21, and llne 35 carries control 6ignals to profile actuators 36 at feedbox 10.

It 6hould be understood that profile analyzer 33 iB a conventlonal 6ignal processor that includes a control 6y6tem which operates in respon~e to ~heet ~-~
measurements. One example of 6uch an analyzer i~ the ~ini-Slic~ (TM) signal proces60r available fro~
Mea6urex Corpor~tion of Cupertino, C~lifornia.

In operat~on of the ~ystem of FIGURE 1, ~-6ensor 30 periodically traver6es 6heet 18 in the cross directlon at generally constant speed whlle ~ea~ureing .. , . :, .. ,, . ,. . ,: , ,., ., : . -: . ~. : ; ., --" 2013~5~

aheet properties. It 6hould be noted that there are unavaoidable delay6 between the time the ~heet i~
operated upon by the proflle ~ctuator6 and the ti~e the 6heet properties are measuredO In the case of the calender profile actuatorG 22, for initance, the delay i8 equal at leas~ to the time required for sheet 18 to travel from calender stack 21 to sensor 30.

FIGURE 2 generally show6 a conventional control 6y~tem for use with a prof$1e analyzer for a 6heetmaking system such as the one shown in FIGURE 1.
The control 8y6te~ comprises the 6erial combination of a controller C, a simulator Gp which models the dynamics of the open-loop characteristics of the - ~heetmaking system, and a delay element Tp which simulates the dead time inherent in the sheetmaking ~y~tem. Further, the control sy~te~ of FIGURE 1 include~ A summing element S which receives negative feedbacX from the output of the 8y8tem. For 6implicity, the feedback qain is shown as unity.

The signals ass~ciated with the control system of ~IGURE 2 ~r~ des~gnated R, L and Y. The signal R represents a ~elected reference level, and the signal L represents a load disturbance. The signal Y

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-.- -. . :: ~ .
.. .. :- . . -.
: :
, .
... . .. .

:
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represent6 the actuating signal output provided by the control ~y~tem.

In general terms, the control system of FIGURE 2 can be characterized as a time delay compensation 6ystem with disturbance re~ection. The ~ystem generally operates such that output Y i~
relatively independent of input L but closely tracks any chan~es in reference signal level R: that i6, the ~y~tem generally operates to malntain the measured ~
~heet properties within 6pecified limits regardless of ~ -plant disturbances. In the preferred embodiment, the -system l~ one of the Dahlin design. The Dahlin design can be generally characterized by the followlng closed-loop transfer functlon, K, for discrete (i.e., digital) -~ ;
signal6 z~

~ .

In e~uation (l), T de lgnates time and ~ designates the inverse of the closed-loop tlme constant ~. Dahlin control ~y~tems are further de cribed in Industrial Diaital Contrc~l Sy~tem6, K. Warwick and D~ Ree~ (Peter Peregrinus, Ltd., London; 1986) pp. 76-82 and lO0. The 20~3~4 g clo~ed-loop time con~tan ~ , a parameter of the control sy~tem, i~ often referred to as the tuning factor.
Depending upon the order of the control ~ystem, there may be two or more tuning factors; for example, a third order system could have three tuning factors. The ~maller the value ~elected for a tuning factor, the more responsive or "tighter" She control system operates. In practice, tun~ng factors usually are under software control.

The dashed box labeled G8p in FIGURE 2 comprises circuitry and control algorithms according to the Smith Predictor control ~cheme. In functional ter~, the Smlth Predictor control scheme provides closed loop negative feedback to controller C. For example, the following transfer funct~on applies in the flrst order case:

G~p - (2) 1 + CGm(l ~ Tm) In equation (2), G~ represents ~ preselected model of the plant dynamics and Tm representfi a preselected model of the plant time delay.

.,... -. ~
~- ,..... ...
.: ,, ,- ~ ,., 2~3~
",~

The controller C in FIGURE 2 can be ~mplemented ln any one of several conventional embodiment~ ~nd still be eui~ble for use in a Smith Predictor control scheme. For example, the controller can be a PI (Proportional plu6 Integral) controller, ~
PD (Proport~onal plus Der~vative) controller, or a PID
(Proport~onal plus Integral plus Derivative) controller. Workers skilled in the art will recsgnize that the order of the controller will affect the tr~nsfer function expres~ion~

One embod~ment of ~ control system for ~-sheetmaking according to the pre6ent lnvention i~ shown ln ~IGURE 3. The ~ignals associated wlth the ~ystem o~
FIGURE 3 are designat~d Ri, Yi, L and-Ei. The input signals Ri represent 6elected reference levels for variou6 ~lice locations. In ~athe~atical terms, input signals Ri can be described a~ a vector whose $th component is the celected reference level of ~ sheet property at the ith 61ic~ locatlon. Th~ ~ignals Li repre~ent load disturbances. The output 6ignal6 Yi can be de6cribed ~8 a vector whose ith component is the actuator signal nssociated with the ith sllce location or with the ith zone of profile actuator. In practice, the signals Yi determine th~ 6etpoints of the profile ~5 actuators which operate upon the sheet during "::" :: ' . , ' ~ : . .

.

-;. 2013~5~

manufacture. The error B~ gnal~ E~ represent the difference between the output of the control ~y6tem and the reference slgnals ~t slice locationst that i8, ~i ' Ri ~ Yi- The error signals E1 each have trancient and steady-state components.

Structurally, the control system of FIGURE 3 iB 6imilar to the one o FIGURE 2 except that it includ2s a means for automatically ad~usting the closed-loop time constant ~ of the controller C in ~nver6e relationship to the 6ystem error. More particularly, the system in FIGURE 3 includes a means 37 which is connected between the summing element S and the controller C to receive error signals Ei ~rom the output of ~ummer S and to provide an QUtpUt which determine~ the clo~ed loop time constant ~as a function o~ the error Bignals; that i8~ (Ei)-In accordance with one embodiment of thepre~ent invention, the error signals Ei determine the value of the closed-loop time constantC~1 of the Smith Predictor controller via an inver~e functional rel~tionship. In other words, a relatively large value of an error signal Ei will produce a relative small value for the closed-loop time constant and, conver6ely, a rel~tively 6mall value of an error signal .
,.. .. .
.
.

~ ., . ; ^ . .

., . - .. ~ . . .
- ~

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Ei will produce a relatlvely large value ~or the ~: :
closed-loop time constant. The relationshlp between the error ~ignals and the clo~ed-loop time con~tant can al60 be expressed by 6aying that the closed-loop ti~e constant iB inver~ely adaptive to system error.

In the preferred embodiment of the system of FIGU~E 3, the functional relat~onship between the error 6ignals Ei and the closed-loop time constant6 ~i is as follows for any given ~lice location:
.:

~ i = ~ + ~ ~Tc (3 E~

In e~uation (3), Enom i8 the nominal error of the 5y8tem ~nd Tc iB the open-Ioop time constant of the lS 6y~tem. In practlce, the value of Enom i8 determined by statistlcal methods and, preferably, is set equal to about twice the standard deviation o~ the error signal~
Ei. For a given control 6ystem, the open-loop time constant, Tc, i6 ~ ~ixed and mea~urable guantity.

According to equation (3), the value of the closed-loop time constant 1 will approach the value o~ .
the open-loop time con~tant Tc when the error values Ei :-are relatively large. Conversely, for relatively 6mall "
. ,- . . , ,.- ~,, ;~ , ~ : : ' :

2 ~

~rror v~lues, the clo~ed-loop tlme constant could exceed the open-loop tlme constant~ However, when the nominal error, Enom~ i~ set equal to ~bout twice the standard deYiation of the srror signal~, the clo6ed-loop time constant typically will have the followingrelationship to the open-loop time constant:

Tc ~ ~i = 2Tc In the system of FIGURE 3, the algorithm of equat~on (3) i8 implemented in software so that the : 10 value ~f the tuning factor ~i i6 varied automatically : as system error change~. Normally, large values of the error ~ignals Ei are associated with abrupt process change6 such a6 are caused by shee~ breaks, reel or grade changes. Under such condition6, the algorithm o~ -equation t3) assures that the control 6ystem of FIGURE

3 will be tightly tuned and, hence, will respond rapidly to process disturbances. On the other hand, small values of the syfitem error Ei are normally associated with stable process conditions. For small values c~ the system error, the algorithm of ec~uation (3~ assure~ that the control sy6tem will be 1006ely tuned, and accordingly, will respond slowly and stably to proceæs changes.

.

, ~ , 2~34~

An alternatlve embodiment oP the present invention is illustrated in ~IGURE 4. In thl3 embodiment, a signal proce6~ing device 61 i~ connscted to recelve the actuator signalE~ Yi and to operate upon those signals to provide an output which determines the closed-loop time con~tant of the Smith Predictor controller C. More particularly, ~ignal processing device 61 operates such that the value o~ the closed loop time constant ~i~ iR inverfiely related to the magnitude of the 6ignal-to-noise ratio (S/N) of actuator 6ignals at the output of the control system.
In other words, a relatively large value of the 6iqnal-to-noise ratio of the actuator signals will produce a relatively ~mall value for the clo6ed-loop ti~e con6tant ~i and, converRely, a relatively small value of the ~ignal-to-noise ratio will produce a relatively large value of t~e clo~ed-loop time consta~t. Thus, for ~ relatively large 6ignal-to-noise ratio, the Smith Predictor controller will be tightly tuned and will respond quickly to process changes. Conversely, for relatively 6mall values of the 6ignal-to-noi~e ratio, the Smtih Predictor controller will be loosely tuned and will respond slowly.

Signal processing device 61 can operate in ~ -various way6 to determine the signal-to-noi6e ratio of .. ' ';

20~3~

the actu~tor ~ignals. In the preferred embodiment, the ratio of low-frequency to high-frequency components in the actuator ~ignals provid2s l~ proxy for the ~lgnal to noise ratio. The low and high freguency componPnts o~
the actuator signals can be determined by, for example, Fast Fourier Transform techniques. Also, United States Patent 3,610,899 teaches a method for obtaining long-term machine direction and short-term machine direction variances of a prede~ermined characteristic of a ~heet material being manufactured. The methodology taught in that patent can be used by signal processor 61.
Further, United States Patent 4,707,779 teaches a method for obtainin~ short-term and long-term machine direction variation~ in sheet properties by a particular filtering technique; such methods al80 can be used by signal processor 61.

In normal operation of the 6ystem of FIGURE

4, the closed-loop time constant ~i i8 under 60ftware control ~ia signal processor 61 and i8 varied automatically as the ~lgnal-to-noise ratio of the ~ctuator signals chang~s. In practice, large Yalues of the signal-to--noise ratio are associa ed with abrupt proce6s change~s and 6malI values of the 6ignal-to-noise ratio are a6sociated with stable process conditions.
Accordingly, t:he ~ystem of FIGURE 4 will respond ~ 2 ~ 5 ~

rel~tively rapidly to rapidly changing process conditions and will re~pond relatively more slowly when the proces i5 operatlng ~tably.

Another alternative embodiment o~ the present invention i6 illustrated ~n FIGURE 4. In ~his embodiment, a signal processing device 67 i8 connected to receive the error signals Ei and to provide an output which determines the closed-loop tlme constant i f the Smith Predictor controller C a~ a ~unction of the error signals Ei. More particularly, signal proce66ing device 67 operates 6uch that the value of the closed loop time constant,o~ B lnver6ely related to the Dagnltude of the signal-to-noi6e ratlo ~S/N) oP
the errox s$gnals. Here again, a relatlvely large value cf the ~lgnal-to-nol6e ratlo of the ~ctuator ~ignal~ vill produc- a relat~vely small value for the closed-loop ti~e constant ~i and, conYersely, a relatlvely 8mall value o~ the ~lgnal-to-noise ratio will produce ~ relatlvely large value of the clo6ed-loop tlme constant. It ehould be appreciated that theembodi~ent6 of FIGURES ~ and 5 are sub6tantially equivalent, in accordance with the relationsh~p Ei ' ~i - Yi~

~, 2 ~

Although the foregolng has described preferrad embodiments of systems accordinq to the present invention, those 6killed in the art will ~ppreciate that additions, mod.l~icatlons, ~ubstitutions and deletions which are not specifically described in the foregoing may be ~ade without departing from the spirit and scope of the present invention as defined by the following claimc. For example, ~lthough the present invention i8 preferably employed in con~unction wlth ~ystems having a Smith Predictor controller, it is generally applicable to other types of time delay compensation control systems.

-, . ,

Claims

1. In a system for controlling a sheetmaking process using a time delay compensation control system such as a Smith Predictor control scheme, the improvement comprising: adjustment means to automatically vary the closed-loop time constant of the system as a function of the system error.

2. The improvement according to claim 1 wherein the adjustment means operates such that the closed-loop time constant is related inversely to system error.

3. The improvement according to claim 1 wherein the system error is measured by the magnitude of the difference between the control system output signals and preselected reference input signals.

4. The improvement according to claim 3 wherein the adjustment means operates such that the closed-loop time constant ?i is determined substantially according to the following functional relationship:

where Enom is the nominal error of the system and Tc is the open-loop time constant for the system.

5. The improvement according claim 4 wherein the nominal error is determined by the standard deviation of the system error signals.

6. The improvement according to claim 4 wherein the nominal error is equated to about twice the standard deviation of the system error signals.

7. The improvement according to claim 1 wherein the time delay compensation control system is one according to the Dahlin design.

8. The improvement according to claim 7 wherein the time delay compensation control system has the following transfer function, k, in the case of discrete signals, z:

where T designates time, .lambda. designates the inverse of the closed-loop time constant ?, and ? is the base of the natural logarithm.

9. The improvement according to claim 1 wherein the time delay compensation control system is characterized by a transfer function substantially as follows:

where Gm represents a preselected model of the plant dynamics, Tm represents a model of the plant time delay, and C represents the controller in the control system.

10. In a system for controlling a sheetmaking process using a time delay compensation control system such as a Smith Predictor control scheme, the improvement comprising: adjustment means to automatically adjust the closed-loop time constant of the system as a function of the signal-to-noise ratio of signals related to the output signals of the control system.

11. The improvement according to claim 10 wherein the adjustment means operates such that the closed-loop time constant is related inversely to the signal-to-noise ratio of the signals related to the output signals.

12. The improvement according to claim 11 wherein the ratio of low-frequency to high-frequency components in the signals related to the output signals provides a proxy for the signal to-noise ratio.

13. The improvement according to claim 10 wherein the time delay compensation control system is one according to the Dahlin design.

14. The improvement according to claim 13 wherein the time delay compensation control system has the following transfer function in the case of discrete signals:

where T designates time, .lambda. designates the inverse of the closed-loop time constant ?, and ? is the base of the natural logarithm.

15. The improvement according to claim 10 wherein the time delay compensation control system has a transfer function substantially as follows:

where Gm represents a preselected model of the plant dynamics, Tm represents a model of the plant time delay, and C represents the controller in the control system.

16. The improvement according to claim 10 wherein the signals related to the output signals are equated to the output signals.

17. The improvement according to claim 10 wherein the signals related to the output signals are error signals, Ei, as determined by the relationship Ei = Ri - Yi where Ri are reference signals and Yi are output signals from the control system.

18. A system for controlling a continuous sheetmaking machine comprising:
a time delay compensation control system; and adjustment means to automatically adjust the closed-loop time constant of the time delay compensation control system as a function of the system error.

19. The improvement according to claim 18 wherein the adjustment means operates such that the closed loop time constant is related inversely to system error.

20. The improvement according to claim 18 including summing means connected to provide input to the adjustment means equal to the difference between the control system output signals and preselected reference input signals.

21. The system according to claim 20 wherein the adjustment means operates such that the closed-loop time constant is determined according to the following functional relationship:

where Enom is the nominal error of the system and Tc is the open-loop time constant for the system.

22. The system according to claim 18 wherein the time delay compensation control system is one according to the Dahlin design.

23. The system according to claim 22 wherein the system has the following transfer function in the case of discrete signals;

where T designates time, .lambda. designates the inverse of the closed-loop time constant ? , and ? is the base of the natural logarithm.

24. A system for controlling a continuous sheetmaking machine comprising:
a time delay compensation control system; and adjustment means to automatically adjust the closed-loop time constant of the time delay compensation control system as a function of the signal-to-noise ratio of signals related to the output signals of the control system.

25. The system according to claim 24 wherein the adjustment means operates such that the closed-loop time constant is related inversely to the signal-to-noise ratio of the output signals.

26. The system according to claim 24, wherein the ratio of low-frequency to high-frequency components in the actuator signals provides a proxy for the signal-to-noise ratio.

27. The system according to claim 24 wherein the time delay compensation control system is one according to the Dahlin design.

28. The system according to claim 27 wherein the time delay compensation control system has the following transfer function in the case of discrete signals:

where T designates time, .lambda. designates the inverse of the closed-loop time constant ?, and ? is the base of the natural logarithm.

29. The system according to claim 28 wherein the time delay compensation control system has a transfer function substantially as follows:
where Gm represents a preselected model of the plant dynamics, Tm represents a model of the plant time delay, and C represents the controller in the control system.

30. The system according to claim 24 wherein the signals related to the output signals are error signals, Ei, as determined by the relationship Ei = Ri - Yi where Ri are reference signals and Yi are output signals from the control system.