GB2267979A - Method of regulating a continuous process - Google Patents
Method of regulating a continuous process Download PDFInfo
- Publication number
- GB2267979A GB2267979A GB9312600A GB9312600A GB2267979A GB 2267979 A GB2267979 A GB 2267979A GB 9312600 A GB9312600 A GB 9312600A GB 9312600 A GB9312600 A GB 9312600A GB 2267979 A GB2267979 A GB 2267979A
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- 238000000034 method Methods 0.000 title claims abstract description 94
- 238000010924 continuous production Methods 0.000 title claims abstract description 7
- 230000001105 regulatory effect Effects 0.000 title claims abstract description 7
- 230000008569 process Effects 0.000 claims abstract description 74
- 238000005314 correlation function Methods 0.000 claims abstract description 6
- 230000004044 response Effects 0.000 claims description 13
- 230000004048 modification Effects 0.000 claims description 2
- 238000012986 modification Methods 0.000 claims description 2
- 238000005457 optimization Methods 0.000 description 10
- 238000013178 mathematical model Methods 0.000 description 8
- 238000010586 diagram Methods 0.000 description 5
- 230000008901 benefit Effects 0.000 description 2
- 101150002998 LCAT gene Proteins 0.000 description 1
- 241000153282 Theope Species 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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- Engineering & Computer Science (AREA)
- Software Systems (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Health & Medical Sciences (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
- Control Of Electric Motors In General (AREA)
- Stabilization Of Oscillater, Synchronisation, Frequency Synthesizers (AREA)
Abstract
A method of regulating a continuous process (P) includes a stage of optimizing a model (M) representative of the behaviour of said process (P), in which: a control magnitude (u) is applied both to the process (P) and to the model (M), each of which responds thereto by providing a signal; the two resulting signals are applied to a subtractor (13) to obtain an error signal ( sigma ); and the model (M) is corrected as a function of the error signal ( sigma ); and a subsequent regulation stage in which a control magnitude (u) is permanently applied to the process (P) and to the model (M). Correction is performed by generating discrete cross-correlation functions between the error signal ( sigma ) and the control magnitude (u) for different time offsets ( tau ) between the control magnitude (u) and the error signal ( sigma ), and in modifying the model (M) so as to minimise the sum of the squares of the cross-correlation functions over a time that the process is observed. <IMAGE>
Description
2267979 A METHOD OF REauLATING A CONTINUOUS PROCESS, THE METHOD INCLUDING
AN OPTIMIZATION STAGE AND.A REGULATIOX STAGE
The field of the invention is that of servocontrolling a continuous process, in particular an
5:Industrial process, and more particularly that processes identification enablIng a process to be modelled. Once- a process has been modelled, it is possible to regulate operation the=eof using mathematical models tha-t are optimized durIng:Ldent:L:Eicat:lon of the process.
in conventional mazmer, process identification performed for the purpose Of subsequent regulation of the process seeks to determine firstly the characteristics of the process, in particular such a listing causes and effects of external control magr.Litudes, and secondly in determining the Influence of the survound:Lngs constituted by non- measurable external causes that may disturb operation of the process. When completed, such IdentifIcatIon gives rise to a mathematical model which represents the resonse of the process firstly to external control magnituden (inputs) deliberately applied to the process and, referred to below as ncontrol magrLitudes" (which, magnitudes are applied by an operator, for example), and secondly to non-measurable input magn-itudes that disturb the process and that are- referred to below as ndisturbances". The input ma gnItudes to a process thus comprise control magnitudes and disturbances.
The identification stage of a process thus consists in determining its transfer function,, 1.e. Its static and dynamic characteristics, thus making it possible during the regulation stage to modify ^the control magnItudes so a to bring the operation of the process into s-cqxa-,LI:Ibr:Lum about precise values, and in spite of the presence of disturbances.
Such regulation Is pexformed by means of a mathematical model defined during the:Ldent:L:Eicat:Lon 2 stage of the process, which identification is performed as Shown in Figure 1. Figure 1 is a block diagram reDresft-snting the identification stage of a continuous process. 5 A process P that is to be. servo- controlled receives a cont=ol magrLitude that is applied on an input 10. The process P provides a respQnsa to said control magnitude on an output 11 and simultaneously a mathematical model M also receives the control magnitude and provides a response in the fo= of a signal on an output 12. Originally the mathematical model M is a model whose. response corresponds roughly to that of the process P. It is thus the result of a first selection made frOln among a certain number of available models. The signals from the, two outputs 11 and 12 are applied to a subtracter 13 which delivers a signal a co,.ist -t-u-tj-ng an error signal to the input 14 of a parameter optimization algor-thm POA. The error signal a corresponds to the difference between the. responses provided by the process P to be controlled and by the mathematical model M, and so far as possible It should be zero so that the. model M constitutes a good mathematical representation of the process P, i.e. of its transfer function- The model M is usually constituted by eauations chexac.,.--erizing the process P, with the paramatews of the differential equations being mod-4..,:Led by the algorithm PO.A via a link 15 so that t-he error signal a becomes as close as possible to zero.
This stage of S-dent.:LAO:Lcat:Lon of the process P lasts for as long as necessary, until a model M is obtained whose =espongic-. to the control magnitudes corresponds in satisfactory manner to the response the process P to the same control magnitudes. Model optimization thus consists in changing the parameters of differential equations until equations are obtalned that chare-cter;Lzethe process P as closely as poss:Lble.
3 in conventional manner, the FOA algorithm Is based on a function representative of the error and given by the relationship:
CFú2 j=CI where a:L corresponds to the between the magnitudes of outputs 11 and 12 at instant The error a is sampled n times while. the process P is under observation, and the algorithm FOA changes -theparameters of the differential equations of the model so as to bring the value of expresslon (1) to zero. This optlzdzat:Lon criterion thus consists in looking for the minimum of the sum of the errors squared, and thus corresponds to a least squares method.
Once. an acceptable model has been obtained, the. modal M 18 used for regulating the process P. A block d-Jagram. of this stage of regulation is given in Figure 2.
The user applies a reference- value corresponding to c. command on an input 23. ThIs command is applied to the input 21 of a corrector C which generates a control magnitude on its outl:)ut 22. The control magnitude is applied both to the process P and to the model M. The process P and the model M provide respective responses to said control magnitude on their respective outputs 11 and 12.
If the model M Is perfect, J. e. If it responds to the control magnitude in exactly the. same. way as the process P, i.e- if its transfer function is identical to that of the process, then the responses at the outputs 11 and 12 are likewise identical.
Rowever, in practice, such identity is never achieved,:Eirstly beoause the model M cannot be exactly representative of the behavior of the process P due to errors in modelling, and secondly because the process P Is subjected to disturbances to which the modal is not c-iso subjected (such disturbances are referenced 16 In 4 Figure 1) That is why the difference a avallable at the output 14 of the. subtracter 13 is in turn subtracted by means of a subtracter 20 from the reference value ava lable on input 23, thereby providing servo-control of 5 the operation of process P.
Rowever, since the optimization criterion used In the identification stage (Figure 1) is based an m:Ln:Lm:Lz:lng errors squared, the par;RTni- ters of the model M take account both o:E the behavlor of the process P and of the d-st=bances 16. Thus, the. optimization criterion used has the consequence of making it possIble. to achieve a model that does not correspond to the process that is to be servo-controlled since it takee account of the disturbances that modify the way the process operates.
The criterion Is thus not capable of distinguishing between modelling errors and disturbances, and as a Cable for providing a model that Is result It 15 not suit genuinely representative of the ope=ation of the. process. For example, the model obtained using the above criterion is not optimum, when disturbances are random. In order for the model to be able to reproduce the responses of the process to disturbances in the sate way as the process Itself, it is necessary for such dlsturbances themselves to be re-produced In identical manner. It the disturbances are. not the samar then the model must be subjected to a further identification stage.
Furthermore, the optimization criterion car-not be applied to processes that do not behave in l near manner. Consequently, the optimization criterion of equation (1) is not suitable under all c:Lrcums.9-.eLnce-, and the regulation achieved Is not optimal.
A particular object of the present. invention is to overcome the above drawbacks.
More precisely, one of the objects of nvf-hnt on is to mrovida a method of regulatS=gr a cont:l-nuous process, which method includes an optim-4zation stage and a regulation stage, and wb-ioh method makes it to obtain a mathematical model that Is Identical to the process without taking account of the disturbances that a-jEZect the Oparat on of the process.
Another obj ect of the Invention is to provide such a method that Is universally applicable, I.e. that can beused regardless of the process that Is to be regulated.
These objects, and others that appear below, are achieved by a method of regulating a continuous p=ocess, the method comprising a first stage of optini zlng a model representative of the behavlor of said process and in which:
a control magnitude is applied to said process and to said model. each of which provides a signal in respon.se thereto; the two resulting signals are applied to a subtracter to obtain an error sianal; and said model is corrected as a function of said error signal; and a second stage of regulation in which a control magnitude is permanently applied to said procLeass and said model, the control magnitude coming from a corrp-ator that has an irout receiving the difference between a xe,:Ett-rence value and the error signal obtained by taking the difference between the signals from said process and from said model. Said correction consists in generating discrete cross- correlation functions between said error signal and said control magnitude for different time offsets between said control magnitude and said e=or signal, and in modifying said model to achleva non- correlation between said error signal and said control magnitude- The optimization criterion is thus minjxdzing crosscorrelation between the control magnitudG and the error 8ignal. A model is thus obtained whose response to the control magnitude Is identical IL-1o that clE the process in tha absence of eiisturbances.
6 Preferably, said discrete cross-co=e-lat!Orl functions are generated by obtaixLing the value of the. following correlation coefficient 0,,cCT) for each tIme. offset T: 5 f cr(-t).u(t-,c)dt T where.:
T corresponds to the time offset between said control magnitude- and said error signal; a(t) corresponds to said error signal; u(t-c) corresponds to said control magnitude advanced by -c; T corresponds to the. duration over which said process is observed; and In obtaining the rum of the squares of the corresponding correlation coefficients; said modification consisting in correcting said model so as to Tni n J Tnize. sald sum.
Other characteristics and advantages of the invention appear on reading the. following description of a preferred implementation of the method of the. invention given by way of non- limiting illustration and made with reference to the accompanying drawings, in which:
Figure 1 is a block diagram showing the 25:Ldent:L;f:Lceit,:Lon stage. of a continuous process, said identification being:implemented in conventional manner using an o- otlzLizat:Lon criterion of minimizing errors squared; Figure 2 is a block diagram of regulation of tha process identified by means of the model as defined during the identification stage. of Figure l; and Figure 3 Is a block diagram showing an identification stage for a process as performed in a preferred implementation of the Invention. 35 Figures 1 and 2 are described above with reference to the state of the art.
7 Figure 3 is a block diagram showing a process identification stage In a preferred implementation of the method of the invention.
The process P to be identified and the mathematical model m to be defined both receive a control magnitude conveyed over a link 10, and they respond by providing respective signals which are subtracted from each other to constitute an error signal. The continuous error signal is supplied to the parameter optimization algorithm POA which modifies the parameters of the model M. The operation of the process P Is disturbed by disturbances 16 that are not measurable.
The method of the invention differs from that shown In Figure 1 in that the optimization criterion for the model M relies on the absence of correlation between the control magnitude, written u(t) and also applied to the algorithm POA, and the error signal written a(t). That is why a system 30 18 defined that includes the process P and the model M, which system has a control Input 10, a disturbance input 16, and an output 14.
So long as a correlation exi8ts between u(t) and a(t) for a given response time oC the system, the model is not optimized and the algorithm POA modifies the parameters of the model M.
The algorithm POA calculates in discrete steps:
1 95",(T) f a(t).u(t-'5)dt T 0 where:
so T corresponds to the time offset between said control magnitude and said error signal; a(t) corresponds to sald error signal; u(t-t) corresponds to the control magnitude advanced by,% relative to the error signal a(t); 0,(x) corresponds to the correlation coefficient for time offse? x; and 8 T corresponds to the observation duration of the process.
The period T l$ ChOSen SO as 4CO be =ePre-SentaLt:LVet Of the operation of the process, and, for example., it may be5 at least five times the response time of the process.
The value of the correlation coe:E:E:Lc:Lent O=Cr) Indicates whether there exists any relatloriship between the control magnitude and the error signal for the time offset value -r under consideration. The larger this coefficient, the greater the correlation and thus the worse the model.
This correlation is, in fact, measured for a plurality of values of T, w:L-thz va=y-;Lngr between a lower value and an upper value corresponding to the response t me of the process P to the control magnitude under consideration. A plurality of succes8:Lva correlatIon coefficients Ow(t) are thus obtained.
Since correlation is performed in discrete steps,!.c. after sampling the control magnitude and the error signal, a pair of values Is avallable. at each Instant. A first value corresponds to the control magnitude at time t-t, end the second value corresponds to the error signal at time t. The two values in each pair are multiplied together and the results of the multiplications are averaged. The average value obtained corresponds to the.
correlation coefficient for time offset t.
These various coefficients obtained for different time offsets c are then squared and summed,!.a. the following value S is calculated:
so S = E O.rCe) 2 This value S is representative of the difference that exists between the. model M and the. process P. The algorithm POA modifies the parameters of the model M n order to minimize this value S.
When S Is substantially ze=o, the model M is takerL to be suitably representative of the behavlor of the process P and the regulation stage shown in Figure 2 can then be undertaken.
In this regulation stage, if the model-does indeed correspond to the process, then the system operates as an open loop,!.a. error signals are due solely to disturbances. Open loop operatIon, makes it possible to obtain a system that is stable. Dur ng this regulation stage, the cross-correlation function can be calculated on a permanent basis without changing the parameters of the model. if a non-zero correlation between the signals u and g is observed to a meaningful extent during this regulation stage, then a new Identification stage is undertaken in order to eliminate the correlation.
The process identification method of the present invention Is applicable to any type of system, whether linear or non-l near. It makes it possible to obtain a model whose parameters do not take disturbances Into account and which is therefore an accurate reflection of the way the process operates.
Naturally, some other criterion capable of measuring correlation between the control magnitude and the error signal could be used, taking advantage of statistical tools that are more sophisticated. For example, it Is possible to give different weights to the coa=cients of the correlation function so as to weight certain porClons of the response characteristics of The process.
Claims (1)
- CLAIMS 1/ A method of regulating a continuous process (P), the methodcomprising a first stage of optimizing a model (M) representative of 'the behavlor of said process (P) and in which: a control magnitude (u) Is applied to said crocess (P) and to said model (M), each of which provides a signal In response thereto; the two resulting signals are applied to a subtractear (13) to obtain an error signal (a); and said model (M) Is corrected as a function of said error signal (a); and a second stage of regulat:Lon ln whi-ch a control magnitude (22) is permanently applied to said process (P) and said model (M), the control magnitude. (22) coming from a co=ector (C) that has an Input receiving the, difference between a reference value (23) and the error signal (a) obtained by taking the difference between the signals from said process (P) and from said model (M); the method being characterized In that said correction consists in generating discrete cross correlation functions between said error signal (a) and said control magnitude (u) for different time c--Fisets (,r) between said control magnitude (u) and said error signal (cr), and In modifying said model (M) to achleve. noncorrelation between said error signal (a) and said conecol magnitude (u).2/ A method according to claim 1, characterized in that said discrete cross-corralation functions are generated by obtaining the value of the. following correlat4on coaf:E:Lc:Le.nt for each time offset C.0.(T) 1 f cr(t).u(t-z)clt 3.5 T 0 where: t corresponds to the time offset between said control magnitude and said error signal; cr(t) corresponds to said error signal; 5 u(t-T) corresponds to said control magnitude advanced by T; T corresponds to the duration over which said process (P) is observed; and in obtaining the sum (S) of the scuazes of the corresponding correlation coefficients; and n that said modification consists In correcting said model (m) so as to minimize said sum (S) of the squares of the corresponding correlation coefficients.3/ A method of regulating a cont:Lnuous process, substantially as herein described with reference to figure 3 of the- accompanying drawings.
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| FR9207502A FR2692688B1 (en) | 1992-06-19 | 1992-06-19 | Method for regulating a continuous process comprising a phase of optimization of a model and a phase of regulation. |
Publications (3)
| Publication Number | Publication Date |
|---|---|
| GB9312600D0 GB9312600D0 (en) | 1993-08-04 |
| GB2267979A true GB2267979A (en) | 1993-12-22 |
| GB2267979B GB2267979B (en) | 1995-08-23 |
Family
ID=9430950
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| GB9312600A Expired - Fee Related GB2267979B (en) | 1992-06-19 | 1993-06-18 | A method of regulating a continuous process, the method including an optimization stage and a regulation stage |
Country Status (7)
| Country | Link |
|---|---|
| BE (1) | BE1006423A3 (en) |
| DE (1) | DE4319926C2 (en) |
| ES (1) | ES2076088B1 (en) |
| FR (1) | FR2692688B1 (en) |
| GB (1) | GB2267979B (en) |
| IT (1) | IT1261062B (en) |
| NL (1) | NL9301068A (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0660208A1 (en) * | 1993-12-27 | 1995-06-28 | Yamatake-Honeywell Co. Ltd. | Controller |
| US6085183A (en) * | 1995-03-09 | 2000-07-04 | Siemens Aktiengesellschaft | Intelligent computerized control system |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE4429191A1 (en) * | 1994-08-18 | 1996-02-22 | Licentia Gmbh | Algorithm for modelling status changes e.g. in electrical power transmission networks |
| DE19932945A1 (en) * | 1999-07-14 | 2001-01-25 | Siemens Ag | Process, arrangement and computer program for preprocessing |
| DE19939973A1 (en) * | 1999-08-24 | 2001-03-01 | Volkswagen Ag | Regulation of a gasoline engine |
| DE10030294B4 (en) * | 2000-06-27 | 2008-04-30 | Ennovatis Gmbh | Method for recording the energy consumption and the need for refurbishment of a building |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB1257319A (en) * | 1968-11-20 | 1971-12-15 | ||
| JPH0625930B2 (en) * | 1985-09-24 | 1994-04-06 | 株式会社東芝 | Plant diagnostic equipment |
-
1992
- 1992-06-19 FR FR9207502A patent/FR2692688B1/en not_active Expired - Fee Related
-
1993
- 1993-06-15 BE BE9300605A patent/BE1006423A3/en not_active IP Right Cessation
- 1993-06-16 DE DE4319926A patent/DE4319926C2/en not_active Expired - Fee Related
- 1993-06-18 GB GB9312600A patent/GB2267979B/en not_active Expired - Fee Related
- 1993-06-18 IT ITTO930445A patent/IT1261062B/en active IP Right Grant
- 1993-06-18 NL NL9301068A patent/NL9301068A/en not_active Application Discontinuation
- 1993-06-18 ES ES09301364A patent/ES2076088B1/en not_active Expired - Lifetime
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0660208A1 (en) * | 1993-12-27 | 1995-06-28 | Yamatake-Honeywell Co. Ltd. | Controller |
| US5537310A (en) * | 1993-12-27 | 1996-07-16 | Yamatake-Honeywell Co., Ltd. | Internal Model Controller with automatically correcting gain of the internal model controller |
| US6085183A (en) * | 1995-03-09 | 2000-07-04 | Siemens Aktiengesellschaft | Intelligent computerized control system |
Also Published As
| Publication number | Publication date |
|---|---|
| DE4319926C2 (en) | 1996-02-29 |
| GB2267979B (en) | 1995-08-23 |
| NL9301068A (en) | 1994-01-17 |
| ITTO930445A1 (en) | 1994-12-18 |
| FR2692688A1 (en) | 1993-12-24 |
| FR2692688B1 (en) | 1994-08-19 |
| ES2076088A2 (en) | 1995-10-16 |
| ITTO930445A0 (en) | 1993-06-18 |
| DE4319926A1 (en) | 1993-12-23 |
| IT1261062B (en) | 1996-05-08 |
| ES2076088B1 (en) | 1997-10-16 |
| GB9312600D0 (en) | 1993-08-04 |
| ES2076088R (en) | 1997-03-16 |
| BE1006423A3 (en) | 1994-08-23 |
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| 711B | Application made for correction of error (sect. 117/77) | ||
| 711L | Appl. made for correction of error (sect. 117/77) now open to opposition | ||
| PCNP | Patent ceased through non-payment of renewal fee |
Effective date: 19980618 |