CA1223943A - Method and installation enabling, on the one hand, the knowledge in advance at a given moment of the result to which a given developing chemical medium necessarily leads and, on the other hand, the regulation of this medium to arrive at a particular - Google Patents

Abstract

Method and installation enabling, on the one hand, the knowledge in advance at a given moment of the result to which a given developing chemical medium necessarily leads and, on the other hand, the regulation of this medium to arrive at a particular result fixed in advance, to be ensured.

ABSTRACT

Installation enabling the checking of a developing chemical medium and its regulation, to arrive at an opti-mal value of a predetermined function of physical or chemical parameters representative of the medium, the function Y being connected with the values of the para-meters by a relationship of the form :
Y = b0 + b1X1 + b2X2 ... + bkXk +...+ bnXn + b12X1X2 +...
+ bk-1,kXk-1Xk +...+ bkkXk2 +...+ bnnXn2 +...
said installation comprising: detectors intended to pro-vide the instantaneous value of each of said paramaters, a scanning member enabling the value of all of the parame-ters to be read periodically, a computer member enabling the determination of the modification to be applied to said parameters to give an optimal value to the function Y, and regulating means for said parameters actuated by said computer member to bring the value of said parameters to the optimum.
Figure 5

Description

method. ~n~--in~all~tion enable on ho One Hal thy Knowledge in adva~çe at a given moment of the result to which a oven develoP'nq chemical eddy necessarily leads and, on the other Honeywell the req~l~tiQn this tedium Jo arrive it_ Particular exult fixed in advance to be ensured .

It is an object of the invention to provide a me-trod enabling, on the one hand, the knowledge in advance at a given moment of the result to which a given develop-in chemical medium necessarily leads and, on the other hand, the regulation of this medium to arrive at a part-cuter result fixed in advance, to be ensured.
In industry numerous chemical media are changing through the variation of the parameters which characterize them, namely concentration of the various constituents, phi temperature and the like.
By way of examples of such media, may be mentioned - acid chemical conversion baths, - alkaline or acid baths for decreasing metals, - water contained in boilers and heating installations, and the like.
The use of these media leads to desired results in certain cases and undesired in other cases and Jay be us manifested in the above said examples respectively:
- by more or less favorable properties of coatings obtained by chemical conversion, - by a more or less thorough state of cleanliness of the decreased surfaces, - by variable scale deposition states of boilers or heating installations.
Now, it is important for the industrialist to Know at any moment if the result obtained at the moment con-corned by the use of the corresponding medium is indeed that which is expected.
However the response is often long and difficult to obtain. Thus, for example in the case of a chemical con-version bath, - 5 or 6 weeks must be available to know whether the resistance to salt fog of the coating obtained is 5 higher than 1000 hours or not, - expensive and bulky equipment must be available (electron scanning microscope) to know the crystalline structure of the coating obtained.
And it is indeed certain that once these tests have lo been carried out, that is to say, for example six weeks later, it is possible for the bath to have changed to an important extent, and its composition can then be very different from that which it had at the moment when the coating under test was obtained. It follows that a modify-lo cation which should possibly have been made in the bath at the moment concerned to arrange so that the result obtain-Ed is that desired, has in fact been overshot at the mow mint when the result is known as a result of the tests concerned.
methods for regulating changing chemical media at-ready exist. However, in these methods, it is customary to measure repetitively at least one of the parameters of such a medium, to compare each time the value measured with a reference value and to act on the parameter con-corned so as to modify the measured value according to the reference value, for example, by bringing, if the measured parameter is a constituent of the changing medium, the concentration of this constituent to the reference value my adding suitable regenerating substances.
And it is indeed certain that in a changing comma-eel medium of the type concerned, these operations cannot guarantee the constancy of the desired results.
The problem which Applicants therefore propose to resolve is that of perfecting a method suitable for enable in the user:
- on the one hand, to know, from the measurement of 394L~

various changing parameters of a developing chemical medium, the characteristics of the result to which the medium concerned leads at the selected moment, - on the other hand, in the case where the value found by this measurement shows that the result concerned does not correspond to that desired, to determine first a group ox modifications of the variables or parameters of the medium suitable to arrange that the result to which the so-modified medium will lead, corresponds to that desired, then to introduce this group of modifications into the developing chemical media concerned by action on the parameters concerned.
Applicant has had the merit of perfecting a method enabling this object to be achieved, this method being characterized by the fact - that, in the case of a given developing chemical me-drum and for at least one of the results to which this medium leads, a so-called provisional equation is eta-blushed of the type 0 1 1 b2X2 bkXk box by OX I
k-1,kX~_1Xk I---+ bkkXk +- Jo bnnxn2 +---in which - Y represents the result to which the medium leads, X1~ X2 --- Ok On represent variables or pane-meters of the developing chemical medium prom which the result Y depends and - boy by by bun are coefficients with respect to which the linearity of the equation is expressed, the value of these coefficients being determined by calculi-lions based on regression methods known in themselves, - that each of said variables or parameters is measured repetitively by as many probes or detectors and - that, on the one hand, at a given moment t, what is to say at the end of one of the repetitive measurements, the value of each of the equations Y is calculated by using the measured values for thy various variables at the moment t, - that, on the other hand, as the case may require and in the case where the value found for one or other of the s equations Y does not correspond to the desired result, there is determined by calculation a group of variations or modifications to be imparted to the variables or pane-meters, this group of variations giving far Y the de trod value and constituting among all the possible solutions of the provisional equation Y, that which is most economical and easiest to realize, and - that, on the other hand again, as many regulating members as independent available parameters are acted upon individually, providing to each of these regulating mom-biers a signal adapted to bring the variable or parameter associated therewith to the value corresponding to the above said solution of the provisional equation Y which is most economical and easiest to obtain.
In an advantageous embodiment, the calculations above mentioned are effected by means of a digital computer which is provided with appropriate data bases.
The invention also relates to other features which are preferably used at the same tire and which will be more explicitly considered below.
us It will, in any case, be well understood by means of the additional description, the drawing relating there-to and the examples, the said additional description and examples relating to advantageous embodiments.
Figure 1 of these drawings is a diagram relating 30 to an equation Y ; Figure 2 is a diagrammatic represent-lion of an installation suitable for practicing the method according to the invention.
Figures pa and 3b taken together, on the one hand, and pa, 4b and 4c taken together, on the other hand, each 35 represents a logigram relating to the practicing of the method according to the invention.

~Z239~s3 Figure 5 is a block diagram of an example of an installation enabling the invention to be put into pray-lice.
Figure 6 is an example of a projection of a hype-surface.
Figure 7 which is similar to Figure 5 shows an other example of the said installation.
In order, consequently, to provide the means enabling, on the one hand, to know in advance, at a given moment, the result to which an evolving chemical medium necessarily leads and, on the other hand, to ensure the regulation of this medium to arrive at a predetermined result fixed in advance, procedure is as follows or in equivalent manner.
For a given developing chemical medium, it may be necessary to know at any moment the result or property Ye to which it leads this result or property being the lung-lion ox a certain number of variables X1, X2, ..... Xi, of the medium and of which the result depends, Ye and the Ye-Z rubles X1, X2, ....... Xi being connected by the provision-at equation y = b -I b X + Buicks bit ~iXi it i in which boy by -- by -- are coefficients, unknown at the start and determined in the manner which will be India acted below, the effective value Ye translating at a given moment the result to which leads the medium taken in its composition corresponding to this same moment.
By assuming that the result concerned Ye must be, for example, equal or greater than the value N, it is no-Cicero that, for the medium at the moment envisaged to be considered as suitable, that at this moment the measure-mint of the variables X1, X2, ....... Xi should provide for I a value Ye N
the measurement of the variables X1, X2, ........ Xi being realizable by as many detectors or probes dipping into the medium and assigned respectively to each of the variables X1 l X2' ' Xi' If Ye so measured is 3 N, the medium leads to the desired result ; if not modifications must be introduced 5 into the medium.
However before anything else, it is necessary of course to establish the equation Ye and consequently, - to select the variables Xi that are considered as being relevant of the medium (these may be the concentration of certain constituents, the temperature, the pi and the like), - to determine the values of the coefficients by -- by The choice of the variables is determining for obtaining a provisional equation of good quality, the omission of an influerltial parameter resulting in the establishment of an erroneous equation. For each problem set, the choice of the parameters results from the prior knowledge of the technicians skilled in the art.
The determination of the coefficients by nieces i-tales recourse to calculations based on conventional regression methods (which will not be dwelt on here but whose principle is to be found in the work of L. LIBRA, A. MYRON, JO FENELON, "Possessing of statistical I data, methods and program, DUNNED) using the data provided by a certain number of experiments. From the practical point of view, this procedure is as follows:
- the one or more properties Y to be measured are selected, - the experimental parameters Xi or variables which will describe the equation are selected, - for each parameter Xi a range of variations is selected which is a function of the problem set and ox the prior knowledge of the experimentation, - a simple equation model is selected, it being noticed that the first model selected can be of the linear 3~3 type:
1 0 by X1 + - + by Xi +- --+ b X
or linear with interactions 1 0 1 1 Buicks + bjXj +--~ bnXn + + by X X +
or non linear with square terms:
n n n y by + Buicks bijXiXi I Buicks -- the number of experiments defined by the choice lo of the model is carried out and for each of them the value of the response Y obtained is collected, - the coefficients byway... of the model are eel-quilted.
The model is then tested. This model being chosen "a priori", it is in fact indispensable to test it to accept it and to use it or, on the contrary, to reject it.
With this object, some additional experiments are carried out for which the values of each of the parameters are fixed simultaneously at an equal distance from the ends of their range of variations and the response obtained is compared with the response calculated by the model. If the two results are neighboring, the model is accepted. In the contrary case, the model is made more elaborate by the addition of supplementary terms, for example, quadratic terms.
The provisional equation representing the new model is then written:
1 2 b1X1 I Buicks Jo bj~j +--+ bijXiXj+
+ bit Xi + by; Xj + --The additional experiments necessary for the eel-culation of the coefficients of the quadratic terms are carried out and the model is tested again.
Thus, by degrees, in sequential steps, the model is refined until the prediction is of good quality.
The equation so established is represented by a hypersurface in a space of no dimensions for n factors.

To materialize the incidence of the various lag-ions, the hypersurface is projected successively on Jo sub spaces of three dimensions of which two are constituted by two variables thaw it is desired to study and the third S by the response Y, the remaining variables being fixed at constant values ; this is translated by contollr lines in the plane of the two variables, the response being mate-realized by the values of the contour lines; thus it is possible to contemplate projecting the hypersurface repro-setting the equation Ye on the plane of the parameters Xanadu X4; by way of example, it may be imagined that Ye represents the resistance to salt fog of a metal surface which has been previously subjected to a chemical convert soon treatment and to a paint coating, X3 representing, for example, the content of the developing medium, that is to say of the conversion bath, of Zen ions and X4 the content of the same bath of P04 ions, the remaining Ye-rubles X1 and X2 being fixed at constant values.
There will be as many sets of lines Y = f(X3, X4) as selected pairs X1, X2.
In this case, the hypersurface is translated in the plane defined by X3, X4 by a certain number of lines eel-led "isoresponse lines" or contour lines and denoted by C1, C2 Con each of these lines corresponding to a given value of the resistance to salt fog and each point of each of the lines representing a pair of values of X3 and X4 which results in a metal surface having the resistance to salt fog corresponding to the line.
In Figure 1 is shown a diagram projection of the hypersurface on the plane X3, I showing the following isoresponse lines:
line C1 : resistance to salt fog: 80 h line C2 : resistance to salt fog: 100 h line C3 : resistance to salt fog: 400 h line C4 : resistance to salt fog: 500 h line C5 : resistance to salt fog: 800 h line I : resistance to salt fog: 900 h line C7 : resistance to salt fog: 9S0 h line C8 : resistance to salt fog: 1000 h.
If it is assumed that, to be sati~factcry, the 5 resistance to salt fog of the treated surfaces must be from 950 to 1000 h, all the pairs of values of X3 and I
corresponding to points situated on one of the lines C7 and C8 or in the surface comprised between these lines lead to the desired result.
lo In other words if, at a given moment, the measure-mint of X3 and X4 results in a point Pi corresponding Jo this condition, the resistance to salt fog of the treated part will be satisfactory; if, on the contrary, it results in a point Pi not corresponding to this condition, that is lo to say located outside of the area defined by the lines C7 and I , the result will not be satisfactory an it will be necessary to introduce into the developing tedium, that is to say into the conversion bath, a modification of the concentrations X3 and X4 which brings back within said area the point situated outside of the latter.
And the modification taken among all the possible modifications leading to this result must be that which is easiest and Yost economical to realize.
This determination is carried out at each moment by us effecting the necessary calculations to determine, for each of the different variables concerned and no only X3 and X4, of each of the provisional equations Ye, Ye -Y
... the simplest and most economical modification among all the possible modifications leading to a satisfactory result.
For example, calculations may be carried out by means of a calculator provided with necessary data bases, particularly data relating to the provisional equations Ye' 2 '' n To enable all of the calculations to be carried out, there should be available at the given moment for 3~3 each provisional equation all of the values of the cores-pounding parameters, which can be produced by way of toe repetitive measurements considered above by detectors or probes dipping into the changing chemical odium con-corned.
The modification is then produced by the dispatch to one or several devices of a group of devices adapted to act on the various parameters, of signals suitable for triggering a group of responses on the part of these 0 devices, which responses are translated at the level of each parameter by a specific change, this set of changes resulting in the above said modification, selected and determined by the calculations.
For convenience of description, it is assured in lo the following and in particular in the examples that the developing chemical medium taken into consideration is a sequence of phosphatation treatments of a chemical convert soon bath with zinc, it being understood that the prince-pies which will be developed with respect to this part-cuter example of a developing chemical medium are easily transposed to any other developing chemical medium taking into account the preceding more general considerations.
It is known that the conversion baths concerned comprise nickel, zinc, phosptlate ions and are accelerated us by nitrates and/or chlorates.
In addition, the sequence of treatments can come prose conventionally, for example, a prior conditioning treatment of the surface and a subsequent treatment con-sitting of a passivating rinse; it goes without saying that the sequence can comprise other treatments, but the latter are not taken into consideration here for convey niece of the description.
Figure 2 shows diagrammatically an installation suitable for practicing the method according to the invention.
This installation comprises - three vessels shown diagrammatically at 1, 2 and 3 and containing respectively the conditioning, conversion proper and passivating rinse baths, - six probes or detectors shown diagrammatically at 5 4 to 9, constituted by pH-meters, selective electrodes, thermometers and the like and dip respectively, as regards probe 4, into the vessel 1, as regards probes 5, 6 and 7, into the vessel 2 and, as regards the probes 8 and 9, into the vessel 3, - a computer ox processor RAM PROM 10 into which have been introduced on the one hand in the form of a pro-gram the algorithms for resolving the various contemplated equations Yin, on the other hand stored therein the per ma-next data and coefficients, this processor being connected to the probes 4 to 9 from which it can consequently no-chive the measured values through interfaces comprising converters A/N, - a control channel or device 11 connected to the processor 10 and adapted to control, under the influence of signals emitted by the processor and through devices shown diagrammatically by arrows 12, 13 and 14, the supply of substances particularly suitable chemical products to the various vessels 1, 2 and 3 and - as the case may require, a printer 15 providing us as a print-out the variations of the various equations Yin on which it is intended to operate and of which the data have been provided to the processor.
I\ In respect of the above said processor, there are indicated in Figures awoke and awoke logigrams or flow-sheets showing one of the possible approaches to, firstly charge into the memory PROM of the processor isoresponse lines as digital samples, on the other hand, to search for the optimum of the response Y my the method of the gray dint.
Plotting and memorizing of the isores~onse lines The case illustrated by the logigram of Figures pa-3c corresponds to that of a polynomial equation of which certain terms are linear functions of one of the parade-lens an other functions of two parameters.
The start is by indicating, to the scratch pad or RAM of the processor, the number N of experimental factors Xi which take part in thy determination of Y. I and J are then introduced, which are the two values of i each cons-tituting pairs for which isoresponse curves will be plot-ted. In the course of the progress of the program, I and J
will obviously take all the pairs of values possible bet-wren 1 and N, with the exception of the pairs for which IT and for each pair (ZOO), K) there will be applied, to the N-2 remaining variables, all the sets of constant values within a determined finished list.
Once this loading of the program has been carried out, there is introduced (frame 20) the equation of the response function which, for simplification, has been assumed to be of linear form with interactions:
ion N
20 Y = by E b. K + b...... K X(j~
it 1 i-l joy Before tracing the curves, the value of Y for all points of a rectangular matrix corresponding to values of us K and K distributed regularly, will be determined.
Preferably, so that the matrixes corresponding to all the pairs of values may have the same number of points, it is necessary to carry out a standardization and a centering taking into account the range of possible variations for each of the parameters or factors X. This amounts to varying the number representing each parameter X between -1 and I which involves the introduction of a scale factor. For this, there are introduced into the Mom limiting values of the parameters (frame 22) and then there is determined, for each pair of parameters corresponding to an isoresponse curve, the scale factor.
The frame 24 corresponds to a matrix with P points for K and Q points for XtJ), corresponding to a first set of constant values of all the Us other than K and K.
The tracing of the curves can then be done from the minimal values X(I)MIN and X(J)MI~ provided for K
and X(J~ (for example ambient temperature, on the one hand, concentration of one constituent nil, on the other hand). After initialization of these values at 26, the calculation of all the points in sequence is done, by employing two loops one of which is included in the other.
The frame shown at 28 corresponds to the determination of all the points of the matrix corresponding to a given value of one of the parameters before passing to a new value of this parameter to recommence the calculation.
Thus the values taken by Y for all the points of the matrix are determined. The isoresponse curves are then traced by an interpolation whose parameters are introduced at 30. The spacing pitch or step of the isoresponses (Ye-lutes of Y for which it is desired to have curves avail-blew will be chosen as a function of the fineness of adjustment desired.
The operation will be carried out from the points of the matrix, using an interpolation program which may be classical.
At the end of the operation, diagrammatically shown at 32, all the isoresponse values for each couple of stank dardized values of K and ZOO will be displayed and memorized.
The same operation will be repeated for all the pairs or couples of parameters XtI), K with all the N
sets of constant values applied to the fixed parameters (N
being a predetermined number).
Once the data are thus stored in the processor, the latter can be used to optimize the function Y by the mathematical gradient method, used for finding a maximum or minimum value of a function.

3~3 OPtimiz~tion,of yo-yo the q~adient,_~et,,hod The logigram shown in Figures pa to 4c takes up again a fraction of the preceding logigram. However it does not put into operation this common portion for the s totality of the field of variation of the parameters X, but only around the experimental point, instead of recomb mincing from the minimal values.
An installation working according to the logigram of Figures pa to 4c hence constitutes an autonomous unit.
o This logigram provides constraints, in order to reduce the duration of the calculations and to avoid too frequent adjustments of the parameters. The passages of the cowlick-lotion loops is stopped when the improvement in Y obtained by an additional traversal is less than a predetermined value. In addition, the values of the responses must remain within a field of validity defined by a radius R.
Figure pa shows the initialization operations of the programs. N and the equation of the response function Y, that is to say data identical with those used at the beginning of the program of curve tracing are introduced.
To apply the gradient method, the partial derivatives D~X(i)] = yucca of Y with respect to a first parameter Xi frame 34) are then introduced and then the limiting values and the algorithm of the gradient frame 36) with a predetermined value, the same for all the Us. Then at 38 (Figure 4b) there is determined the direction of the in-fluency on Y of a first variation of the set of parameters before carrying out the search for the optimum, by the application of the algorithm of the gradient. It is import lent to note that the logigram reduces the multiplier coefficient applied to the derivative when the preceding latter iteration lends to exceeding the validity radius R
and recommences the same calculation, but with the reduced value. In the example shown, this reduction is done in a ratio 2. If the new calculation leads again to exceeding the radius R, a further reduction in the same ratio is us applied: the accuracy is thus very much increased.
The logigram limits, in addition, the number of passages through the loop by stopping the iterations as soon as the proximity of the optimum is reached, which is manifested by the fact that the difference between two successive results is less than a threshold DYE or that, at the same time, the radius R has been exceeded and that the coefficient L applied to the derivative in the algorithm of the gradient has fallen below a predetermined value (test 44, Figure 4c).
Figure 5 shows, by way of simple example, an ins-tallation capable of performing the process which has just been defined. In this Figure, the members corresponding to Figure 2 are denoted by the same reference numeral.
In the embodiment shown in Figure 5, a periodic scanning circuit 46 samples, for example, once hourly, the parameters X, which in the case illustrated are two in number and are provided respectively by the probes 5 and 6. The sampled value is applied to an analog-digital or A/D-converter 48 and sent to a calculating unit 10, which can be a microcomputer or a programmable controller. The new set values of the parameters X completed by thy cowlick-feting unit 10 are sent to circuits 50 and 52 (each on a printed card) for regulating the parameters. In systems with slow kinetics, lending themselves poorly to regular lion, the circuit 50 could be provided to complete, from data known on the system, of the set value which has just been provided by the calculating unit 10 and of the actual value provided by the probe 5, the amount of reagent to be I added to the system to obtain the set value. The regulate in operation can then be carried out by actuating the opening of a valve 54 for a predetermined time. In the case where the kinetics are faster, it is possible to use a circuit 52 which also receives, for a servo regulation, an output signal coming from the converter 48, the scan-nine circuit 46 then providing constantly the value of the corresponding parameter, in order to permit the change thereof to be followed. The circuit 52 then stops the opening of the corresponding valve 54 as soon as the reference value is reached.
It is by employing the method and installation according to the invention that the following examples have been produced.
EXAMPLE 1 - Determination of provisional equations repro-setting two properties of a metal surface 0 treated in a chemical conversion bath.
In this example, it has been chosen to form a model and hence to provide two properties Ye and Ye of a convert soon coating currently measured as a check in phosphate-lion treatments, namely:
- the layer weight Ye expressed in g/m2, - the crystalline structure density Ye expressed as number of crystals per unit surface and measured by means of a photograph taken with a scanning electron microscope with a magnification of 1500 times.
Five variables X1 to X5 of the conversion bath have been taken into consideration:
X1 : concentration of nickel ions X2 : concentration of chlorate ions X3 : concentration of zinc ions X4 : concentration of phosphate ions X5 : value of the free acidity or Awl it being understood that, by Awl, is meant the value ox-twined expressed in ml of N/10 Noah on a sample of 10 ml of the bath determined by N/10 Noah on the color change of methyl orange.
Samples of cold-rolled steel sheet of current quality are submitted to treatments by immersion using products marketed by Compagnie Frowns de Products Industries and currently employed in the automobile in-dusty for the preparation of car bodies before painting.
The steps and products employed comprise I

- a hot alkaline decreasing with the use ox de-greasing agents based on alkaline salts and on surface active agents marketed by Compagnie Frowns de Products Industries respectively under the trademarks REDLINE
s 1550 CF/23" and "RIDOSOL 550 OF", - a cold rinse in running water, - a surface conditioning with the use of a refining agent based on titanium salt marketed by Compagnie Fran-raise de Products Industries under the trademark "FIX-I DINE 5", - a chemical conversion treatment with the use of an acid solution based on zinc phosphate and other convent tonal ions marketed by Compagnie Frowns de Products Industries under the trademark "GRENADINE 908", lo - a cold rinse, - a passivating rinse with the use of an agent based on chromium ions marketed by Compagnie Frowns de Products Industries under the trademark "DEOXYLYTE 41", - a staving treatment.
The five variables of the chemical conversion bath which are taken into account are measured by any convent tonal means currently used: chemical determination, pi measurement, potentiometryl ionic conductivity and the like.
16 experiments are carried out to determine the constants of the corresponding provisional equation which is written for Ye:
1 0 1 1 b2X2 + b3X3 = box + b5X5 + b~2X1X2 13 1 3 b14X1~4 + b15X1X5 b23X2X3 + b24X2X4 25X2X5 + b34X3X4 + b35X3X5 + b45X4X5 and or each experiment there are measured - the layer weight of each sample treated, by disk solving the coating in a hot chronic acid solution ( 10% r 60~C, 15 minutes), - the number of crystals present within a window of 7.5 cm diameter of each specimen treated, these crystals being counted on a photograph taken with the scanning electron microscope with a magnification of 1500 times.
To determine the characteristics of these export-mints so as to be able to determine the above said cons-s tents, the procedure is as follows:
For each of the five factors taken into account, a field of variation is defined as follows:
0.8 g/l Zen 1.4 g/l g/l P04 23 g/l lo 0.3 g/l Coo - 0.9 g/l +.?~
0.5 g/l No 0.8 g/l 0.9 ml Noah N/10 Awl 1.3 ml Noah N/10.
Taking into account the preceding equation, it is necessary to determine p Pi coefficients connected with lo the terms of the sty degree and with the rectangular terms (p representing the number of parameters with, in the pro-sent case p = 5), to which has been added the constant term. This leads to carrying out the 16 experiments shown in the hollowing table for which each of the parameters takes only the extreme values of its range of variation.

lo 3 E:xp. No C103- Zen Pickle Ye p do Ye no (s/m2 ) __ O.Sg/l 0.3g/1 Ogle 15g/1 1.3ml 1.74147

2 0.5g/1 O.9g/1 0.8g/1 15g/1 0.8ml1.14 160

3 0.8g/1 O.9g/1 1:).8g/115g/1 1.3ml1.19 168 _ . .. . . _

4 0.5g/1 0.3g/1 1.4g/1 15g/1 0.8ml 1.61 117 . _ _ . .
0.5g/1 O.9g/1 1.4g/1 15g/1 1.3ml 1.78 91 1 o . . . _ _ .
6 0.8g/1 0.3g/1 0.8g/1 23g/1 1.3ml 1.39 128 . _ . _ .
7 0.5g/1 0.3g/1 1.4g/1 23g/1 1.3ml 1.86 101 _ _ . .. _ _ 8 0.8g/1 O.9g/1 1.4g/1 15g/1 0.8ml 1.29 I
. _ _ _ _ . _ . . _ _ . _. . _ _ 9 0.8g/1 O.9g/1 0.8g/1 23g/1 0.8ml 1.1g 205 . _ _ , . . .. . _ 0.8g/1 0.9g/1 1.4g/1 23g/1 1.3~1 1.41 66 11 0.5g/1 0.9g/1 1.4g/1 23g/1 0.8ml 1.61 I
_ . . . _ . . _ _ .
12 0.5g/1 0.9g/1 0.8g/1 23g/1 1.3ml 1.36 157 . _ _ _ . _ _ . _ 20 13 0.5g/1 0.3g/1 0.8g/1 23g/1 0.8ml 1.34 126 .. .... .. _ ..
14 0.8g/1 0.3g/1 O.Bg/l 15g/1 `0.8ml 1.39 181 . . _ _ 0.8g/1 0.3g/1 1.4g/1 23g/1 0.8ml 1.81 97 . = . . _ _ , . _ . . _ . . _ 16 0.8g~1 0.3g/1 0.8g/1 1~/1 0.8ml 1.91 90 .. ---- _ __ To be independent of the factor units, to simplify the calculations and the interpretations end to compare the effects of the factors with one another, the values of each factor are centered and reduced.
The calculation of the coefficients b. is then done by the method of least squares described in detail in the previously cited book. Only the most influential goof-fishnets are taken into account in the equation.
After processiTIg of the data, the equations of the two properties of the coating, namely respectively the layer weight pdc and the number of crystals no per unit surface area, are:

Y pdc = 1,~0 0,16 X3- 0,13 X2+ 0,079 X5- 0,070 X~X5 (I) 3 2 X3 14 X1X3~10 X2 X4 (II) EXAMPLE 2 - Determination of the provisional equation no-preventative of a property of metal surface treated in a chemical conversion bath.
The property taken into consideration is again the yen weight.
For the determination of the corresponding equal lion, one may take into account not only the chemical constituents but also physical factors such as tempera-lure, stirring speed and the like, or discrete parameters, i.e. digital samples such as the nature or surface state of a substrate.
In the present case, the equation Ypdc was deter-mined from seven variables.
Six of these variables, respectively X1, I X3, X4, X5 and X7, relate to the chemical conversion bath, namely, X : concentration of zinc ions X2 : concentration of chlorate ions X3 : concentration of phosphate ions X4 : accelerator proportion sodium nitrite) X5 : temperature of the bath X7 : value of the free acidity the seventh, X6, representing the concentration of the surface conditioning bath relative to the step which pro-cedes the chemical conversion treatment proper.
my operating a in Example 1 as to the operational method, the equation Ypdc obtained is written:
Y pdc = 2,15 - 0,19 X6 + 0,16 X1 - 0,13 X2 + 0,13 X5 0,11 X3 - 0,10 X4 + 0,07 X7 (III).
EXAMPLE_ - Practical examples of use.
A chemical conversion coating such as that obtained with the conversion event marketed by Compagnie Frenzies de Products Industries under the trademark "GRENADINE 908" must meet the following requirements:

12~23~3 - its thickness or layer weight must be suffix Jo ciently small, in the region of 2 to 2.5 g/m2, to permit good adherence of the paint, - its crystalline structure must be the densest S and most regular possible to minimize porosity and to improve the protection that it confers against corrosion.
It is this requirement "paint adherence-density of crystalline structure" which it is proposed to resolve by means of the equation indicated in Example 2.
lo In general, the parameters of such a bath vary according to the ranges below:
0.8 g/l Zen 1.4 g/l 15 g/l P043 23 g/l 0.3 g/l Coo - 0.9 g/l 0.5 g/l I 0.8 g/l 0.9 ml Noah N/10 S Awl 1.3 ml Noah N/10 50-C < temperature of the conversion bath < 60-C
1.0 ml accelerator proportion 2.0 ml 1.0 g/l < concentration of the "FIXODINE 5"
surface conditioning bath < 3.0 g/l.
Each of the parameters X1-X7 are measured at successive moments, for instance at intervals of half an hour For instance:
a) Measurement at the moment to:
Concentration of the surface conditioning bath: 2 g/l Parameters of the chemical conversion bath:
Zen++ : 0.8 g/l Clue- : 0.6 g/l pox : 19 g/l accelerator proportion: 1.5 ml temperature: 55-C
free acidity: 0.9 ml.
This set of values is introduced into the equation (III) Y pdc, once the said values have been centered and reduced:
Y pdc = 2.15 - 0.19 X6 + 0.16 X1 0 13 I + 0.13 I +
0.11 X3 - 0.10 X4 + 0.07 X7.

:.

I

Consequently, at the moment to:
Y pdc = 2.06 g/m2.
This value of the coating weight is situated bet-wren the limits of the range, i.e. 2 and 2.5 g/m2, which has been recommended for the obtention of a good adherence of the paint.
Consequently, it is not necessary to modify the parameters.
b) Measurement at the moment I
0 Concentration of the surface conditioning bath: 1 g/l Parameters of the chemical conversion bath:
Zen : 1.4 g/l (X1) Clue- : 0.3 g/l (x2) P04 : 19 g/l (X3) accelerator proportion: 1.0 ml temperature: 55'C
free acidity: 1.0 ml.
The result thus obtained by introducing this set of values into the equation (IV), is Y pdc = 2.77 g/m .
This calculated layer weight value is outside of the acceptable range. This is the result of the drifting of one or of several parameters, which it is necessary to correct by way of the most economical adjustment.
To this purpose, one uses the projections of the hypersurface having eight dimensions and representing the equation (III) on the planes of which each one corresponds to two parameters. For example, the Figure 6 shows, for constant values of X2, X3, X4, X5 and X7 corresponding to the measurement at the moment to, the isoresponse curves Jo or level curves in the plane X1, X6, wherein:
X1 is the content of the conversion bath in Zen ions, X6 is the content of the surface conditioning bath in FIXODINE 5.
Each level curve corresponds to a same value of the layer weight Y (in g/m2). The values of the other parameters are:

I : 0 3 g/l of Cloy-X3 : 19 g/l of POX
X4 : 1 ml of accelerator X5 : 55-C
S X7 : 1.0 ml of free acidity.
The processor will then calculate, starting from the value of X, the optimum variations to be imparted to the chemical conversion bath and/or the conditioning bath to bring the value of Y within the acceptable range, for lo instance to a value close to 2 g/m2.
To this purpose, at each investigation, all the values of X are introduced into the working memory, either automatically, or manually at the end of an analysis of a bath sample. The processor then determines by way of the gradient method, the optimum variations of each of the parameters leading to the obtention of the desired value of the layer weight.
When using the gradient method, it is possible to make movements over the hypersurface at each point per pen-dicularly to the isoresponse curves, the gradient being the direction which permits the most rapid shifting towards an optimum.
One calls the gradient of a function u = f(x,y,z), the vector whose projections on the coordinate axes are the corresponding partial derivatives of the given lung-lion.

grad u = dud i + duo j + duo k i, j, k representing unit values of the reference system chosen.
The gradient of a function of three variables is directed, at each point, along the normal to the surface passing through this point. The direction of the gradient of a function at a given point is the direction along which the function has the greatest growth speed at this point, that it to say for 1 = grad u the derivative duo do reaches its greatest value which is equal to:
Dow + Dow + duo 2 do dye do In the same way the gradient of a function with n variables u = f(x,y,z, no is defined as grad u = duo i + duo j + duo k + ... + duo n do dye do dun The latter is at each point directed along the normal to the hypersurface passing through this point.
After the treatment, the processor provides the optimum values:
X1 1.09 g/l of Zen+
X2 : 0.56 g/l ox Cloy X3 : 16 g/l of POX
I : 1.33 ml X5 : 51 C
X6 : 2.25 g/l X7 : 0.91 ml corresponding to Y - 1.94 g/m (selected lower than the optimum due to the fact that the developing continues).
It is then assumed that the adjustment should be made by - providing FIXODINE 5 into the conditioning bath, in the form of an aqueous premix containing 3 g/l of active components, - providing of phosphatizing product starting from two concentrated aqueous solutions:
one of these solutions, A, giving the possibility of regeneration of -the conversion bath during nor-I met working, containing the ions Zen , P043 , No , for instance in the following formulation (OWE
by weight) 3.0 < Zen++ < 6.5 < H3PO4 < 45 0.1 < No < 1.9 the free acidity of which is comprised between 3 I
and 11 ml of N Noah (test sample to 1 ml), the total acidity being comprised between 9.8 and 13.4 of N Noah (test sample: 1 ml), . the other solution, B, providing the possibility of correcting the increases in the free acidity and of the zinc concentration of the bath, and containing the ions P04 , No , for instance in the following formulation:
2~+4 lo 0.1 < No <
4.2 < pi < 3.8 3 < Act < 5 ml Noah N to 1 ml) - providing accelerators in the chemical conversion bath obtained separately starting from concentrated aqueous lo solutions:
one of these solutions, C, containing the nitrite ions in a formulation comprised for instance bet-wren 16 and 20%1 . the other solution, D, containing chlorate ions in a formulation comprised for instance between 20 and 30%.
The adjustment of the preparation bath may be car-fled out in a very simple way. The processor 10 sends to the corresponding control card a value representative of us the increase in contents to be obtained, i.e. 2.25 - 1 =
1.25 g/l. The circuit comprises a microprocessor or merely a coding ROME. tread Only Memory) which determines, starting from that value and from the volume of the bath, the volume of premix to be added and opens an electrovalve with constant flow-rate proper to introduce the premix during the necessary time.
The adjustment of the surface conditioning bath is somewhat more complicated. The processor determines the amounts of solutions A, I, C and D introduced and nieces-spry to bring the bath to the required composition and sends the corresponding information to the operating control cards 56. Each one of these cards comprises a circuit for the determination of the time during which the introduction is necessary from a corresponding tank 58 as well as a power circuit which opens the appropriate electrovalve 60 during the necessary time.
Another card 62 r capable to being addressed alike cards 56, receives the temperature information and con-trots a switching circuit 64 which regulates the electric eel power applied by a source 66 on a heating resistor 58, in the direction of a decrease in the case under consider ration.
* *
It is also possible to regulate a bath of the type concerned by effecting a compromise between several pro-parties.
Thus, it is possible to use simultaneously the provisional equations Y pdc (I) and Y no (II) of example 1. The system then permits the parameters to be developed simultaneously to obtain the best compromise between the layer weight and the structure density.
As is self-evident and as emerges already from the foregoing, the invention is in no way limited to those of its types of application and embodiments which have been more especially envisaged; it encompasses thereof, on the contrary, all modifications.

Claims (4)

C L A I M S

1. Method adapted to enable:
- on the one hand, knowledge, from the measurement of various developing parameters of a developing chemical medium, the particularities of the result to which the medium concerned leads at the moment selected, - on the other hand, in the case where the value found by this measurement shows that the result concerned does not correspond to that desired, determination first of all of a set of modifications of the variables or para-meters of the medium, adapted to arrange so that the re-sult to which the thus modified medium will lead, corres-ponds to that desired, then to apply this set of modifica-tions to the developing chemical medium concerned, by action on the parameters concerned, this method being characterized by the fact - that, for at least one of the results to which this medium leads, a so-called provisional equation of the type Y = b0 + b1X1 + b2X2 ... + bkXk + ...+ bnXn + b12X1X2 +...
+ bk-1,kXk-1Xk +...+ bkkXk2 +...+ bnnXn2 +...

is established in which - Y represents the result to which the medium leads, - X1, X2 .... Xk, ...Xn represent variables or pa-rameters of the developing chemical medium from which the result Y depends and - bo, b1 ...bk,..., bnn are coefficients with res-pect to which the linearity of the equation is expressed, the value of these coefficients being determined by calculations based on regression methods known in themselves, - that each of said variables or parameters is measured repetitively by as many probes or detectors and - that, on the one hand, at a given moment, that is to say on the conclusion of one of the repetitive measure-ments, the value of each of the equations Y is calculated by using the measured values for the various variables at the moment t, - that, on the other hand, as the case may require and in the case where the value found for one or other of the equations Y does not correspond to the desired result, there is determined by calculation a set of variations or modifications to be imparted to the variables or parame-ters, this set of variations giving for Y the desired value and constituting, among all the possible solutions of the provisional equation Y, that which is most econo-mical and easiest to carry out, and - that, on the other hand also, action is applied indi-vidually to as many regulating members as parameters, providing each of these regulating members with a signal adapted to bring the variable or parameter associated therewith to the value corresponding to the abovesaid solution of the provisional equation Y which is most economical and easiest to obtain.

2. Method according to claim 1, wherein the set of the calculations is carried out by means of a digital computer which is supplied with suitable data bases.

3. Method according to claim 1, wherein the modifi-cations to be imparted to the variables or parameters are calculated by the process represented in Figures 4a-4c.

4. Installation enabling the checking of a deve-loping chemical medium and its regulation, to arrive at an optimal value of a predetermined function of physical or chemical parameters representative of the medium, the function Y being connected with the values of the para-meters by a relationship of the form :

Y = bo + b1X1 + b2X2 ... + bkXk + ...+ bnXn + b12X1X2 +...
+ bk-1,kXk-1Xk +...+ bkkXk2 +...+ bnnXn2 +...

in which - Y represents the result to which the medium leads, - X1, X2 .... Xk, ...Xn represent the variables or parameters of the developing chemical medium from which the result Y depends and - bo, b1 ...bk,..., bnn are coefficients with respect to which the linearity of the equation is expressed, the values of these coefficients being determined by calcula-tions based on regression methods known in themselves, said installation comprising:
- detectors designed to provide the instantaneous value of each of said paramaters, - a scanning member enabling the value of all of the parameters to be read periodically, - a computing member enabling the modification to be applied to said parameters to give an optimal value to the function Y, to be determined, and - regulating means for said parameters actuated by said computer member to bring the value of said parameters to the optimum.