JPS6165302A - Pid control method of photographic emulsion manufacture process - Google Patents

Abstract

PURPOSE:To perform multivariable control on PID basis by expressing the state of a process as a mathematical formula, and performing control arithmetic on the basis of the plant model expressed as the formula. CONSTITUTION:A manipulated variable feedback element 1 inputs the difference eU between UC.M obtained by correcting part of a pattern manipulated variable based upon a data base and a signal g(UC relating to a manipulated variable UC. An output value feedback element 2 inputs the difference eY between a control pattern YM that a process follows up and a signal f(Y) regarding an output Y. Output signals eU and eY of those two feedback elements are inputted to a comparator 3, which outputs one of them selectively. The comparator output (manipulated variable) UC is inputted to a controller 5 together with the output of a rate setting part 8 and its output U is inputted to an actual plant 6. When PID control on output pattern follow-up basis is performed, the output value feedback element 2 uses equations to calculate a manipulated variable UY(t), which is inputted to the plant 6 through the comparator 3 and controller 5.

Description

DETAILED DESCRIPTION OF THE INVENTION (Industrial Application Field) The present invention relates to a PID control method in a photographic emulsion manufacturing process, and more particularly to a PID control method in a photographic emulsion manufacturing process in which control amounts are multivariable.

(Prior Art) As photographic emulsions used in photographic paper, films, etc., those containing silver halide as a main component are used. Silver halide is a compound of silver and a halogen group element such as 3r, and is frequently used as a photographic emulsion. Such silver halides are produced by crystallization procedures. The crystallization operation involves adding silver nitrate <Ao N03) and potassium bromide <KBr) or potassium iodide (Kl) to cause reaction crystallization.

By the way, in this type of reactive crystallization process, it is not possible to directly measure the crystal diagnosis of silver halide itself.

So, silver in solution is associated with the growth of silver halide! Predict the growth of silver halide by 1 degree.

(Problems to be Solved by the Invention) By the way, in the silver halide crystal growth process, there are some parts of the crystal growth mechanism that have not been fully elucidated in terms of phenomena, and its control is largely based on experience. In addition, in this type of crystal growth process, the growth of silver halide crystals is influenced by various factors such as the silver concentration and halogen concentration in the solution, as well as the solution temperature and stirring speed. Changing one of these variables will affect the other process variables. In control (multivariable control) where changing one of these process variables also affects the other process variables, the process change ω that should be measured is measured, and each control variable is It has been impossible with conventional PrDII control to simultaneously and automatically control the respective manipulated variables so that the values are the desired values.

The present invention has been made in view of these points, and its purpose is to realize a control method that can perform PID control even in the case of multivariable control.

(Means for Solving the Problems) The present invention solves the above problems by converting the set IJ(t) of a plurality of process inputs into LJ(t)=! :LJ+ (t >, ++, t
Jn(t)1”=[UM”(t),
llc ” (L ) ]”The set Y([) of multiple process outputs is expressed as Y(j )=[Y+ (t >,...,YS(t
)] Pattern operation amount IJM(j
>.

LJc, -+T (t) respectively UM (t) = [UM, 1 (t >, ....

LJM, n −s (t) ]T turtle) O, M (
j)=[tJc, M, I,...

UO, Mt S (j)]T 1ltl)ill pattern to be followed by the process YM(
t) as YM (t) = [YM, t (t),
....

YM, 8 (t) ]T Furthermore, the set of P[) coefficients IKp, IK+, IKo
1Kp = [Kp, I (j >, ..., Kp, 5(
t) Ko1shiku; Army-[K+, t (t
＞, ... ,l(,,5(t)]IKo
= [KD, 1(t), ..., K
D, S (t)], and the difference between the process output Y(t) and the control pattern YM(j), and the difference between the pattern operation 111UC,M(j> and the set of manipulated variables IJc(t)) and calculate these differences as PA
This system is characterized in that the plant is driven by obtaining an optimal operating signal through D calculation and various calculation controls.

That is, the present invention formulates plant phenomena into a mathematical formula, and controls a plurality of control variables such as silver potential and llH based on this mathematical model, thereby allowing a plurality of factors to influence the growth of silver particles. The aim is to optimally control the crystal growth process.

(Example) Hereinafter, the present invention will be described in detail with reference to the drawings.

The figure is a block diagram showing an embodiment of a photographic emulsion manufacturing process for carrying out the present invention. In the figure, 1 is a signal (J
(UC), and 2 is an output amount feedback element that receives the difference ev between the control pattern YM to be followed by the process and the signal "(Y)" related to the output Y. .The manipulated variable feedback element 1 outputs a signal @tJ 11, and the feedback element 2 outputs a signal @%Jv.3 receives these two signals IJu and lJy and selects one of them. This is a comparator that outputs

4 is a filter that receives the output (operation amount>lJc) of the comparator 3, and its output (1 (IJc) is, as described above, the difference from the pattern operation 11JC, M. 5 is the operation A controller 6 which receives 1 kUc and a ratio value U'- is an actual plant which receives the output U of the controller 5 as an input.

7 is a filter that receives the output Y of the plant 6, and as described above, the difference between the output f (Y) and the control pattern YM to be followed by the process is taken. Reference numeral 8 denotes a ratio setting section which changes the ratio in response to the difference ev and the pattern operation input weight based on the database, and its output UM' is input to one input of the controller 5 described above. The present invention will be explained in detail using the process configured as described above.

Now, a set of multiple process inputs U (
t) is expressed by the following formula.

υ(t)−[LJ+(t), ・−, Un
(t)]”=(lJM'(t), (Jc
T <t >1" where T is the notation S indicating the repurchase matrix]
It is. Matrix element U+(t
), . . . UnB) indicates the comprehensive element of the input, and is represented by a 0-by-1 column vector. (2) Expressed by formula This is a set of pattern data extracted from the most suitable pattern data used in the process, and is input to the arithmetic control unit 1 as a pattern operation unit.

1Jc(t) is a set for operation, and is added to plan 1-0 via controller 5. As these manipulated variables, for example, the addition amount of KBr or acetic acid is used. The pattern operation amount ■M(t) and the operation unit 11c (t) are expressed by the following equation.

LJM (t) = [LJM, 1(t),...
.

LJM, n-5(t)]T (3) tic(t)-[Uc, 1(Y>, ++
.

1Jc,s(t)]T(4)
Here, the operation ILIc (t) is an 8-by-1 column vector represented by S elements, and UM(t) is (1)
The operation amount [Jc(
It is a column vector of (n −s ) rows and one column, which is represented by the number (n −s ) elements obtained by subtracting the number S of t).

Next, a set UO,M(t) of partially modified pattern operation amounts based on the database is expressed by the following equation.

uc l M < t > = [uC* M+ s +
....

Uc+M+s(t>1'') Here, the pattern operation (IUO, M (j)) is an 8-by-1 column vector represented by S elements.

Next, the output Y(t) of the plant 6 is expressed by the following equation.

Y(t)−[Y+(t>,...,YS(t)
]T Here, Y(t) is a column vector of 8 rows and 1 column, similar to LJC(t).

Next, the set γM(t) of multiple target values (control patterns to be followed by the process) such as silver potential is calculated using the following formula % Formula % Here, the target value YM(t) is expressed by S elements 8
It is a column vector with one row and one column, and its elements are obtained experimentally or empirically in advance.

Next, the row PJY' of the output @Y(t) with careful consideration of changes over time
(t) and input fi[J (t) (7) Matrix [1' (t) are respectively expressed by the following equations.

Y' (t) = [Y(t), Y(-Δ1),
....

y<t-zy ・Δt)] (8) Turtle J' (t
) = [U (t >, tJ (-Δ1),...
・.

IJ(t-zu-Δt)] (9) Here, Y'(
t) goes to S! IJ'(t) is a matrix of columns, and IJ'(t) is n
line! It is a matrix of columns.

Next, the output error %ev (t) and the input error 6u (
t) are respectively expressed by the following formulas.

ev (t) = f (Y (t)) −Y
M (i)ell (t)=<1 (tic
(t>) −Kame JC, M(t) where, ey
, ell are both column vectors with 8 rows and 1 column.

Next, each tI for implementing PTD control according to the present invention
The D coefficients IKII, IK+, and lKo are each defined in matrix form as follows.

K11 = diao[Kp, t N >, ・, Kp,
s (t >1IK + =diaO [K+ , +mouth>, ++, K+ ,
s(t)]IK.

=diaO[Ko, +N>, ++, K(
1, S (i)] Here, diag indicates, for example, a diagonal matrix, and IKI'l.

Both lK+ and IKo are matrices with S rows and S columns.

Next, a matrix Ey of the output difference ev(t) that takes into account changes over time.
(t) is expressed by the following formula.

Ev (t)−[ey (t>, ev (t−△
t).

..., eY(t −nt ・Δ1)]=[ey+
r+ IT (t)+ ev, r, 2” (t >, ++.

eY, r, ST (j >] I T16> However, ev, r,, i (t) = [ev, i (t), ev, i (-Δt) +
”'+ev, i (t-nt-Δ1)]i=1・
...S Here, Ey is a matrix with 8 rows (111 to 1) columns.

Each culm of one process shown in the figure is expressed mathematically as described above, and arithmetic control as shown in 1 below is performed to perform PID control, limit control, ratio change, etc.

First, speed-type PID control will be explained.

Now, output Y(t) at time t (actually filter 7
The differential error ev(t) between the output f(Y)) and the target pattern YM(t) and the differential error eY
If the deviation from (−Δt) is Δev(j>, then Δey
(t) is expressed by the following formula.

Δev (t) =ev ・(t) −ev (t
-Δ1) Next, if the deviation between Δev at @time ( and Δev at (t-Δt) is Δ2ev(t), then Δ2e
Y (t) is expressed by the following formula.

Δ2ev (t) −ΔeY (t > −Δev (−Δt) (
18) The output amount feedback element 2 is (17).

The deviation amount expressed by equation (18) and (12) to (14)
An operation deviation amount ΔLJv(t) expressed by the following equation is calculated from each PAD coefficient expressed by the equation.

ΔUy (t) ==lKp <t) (△e
Y (t)+lK+ (j) ・ev ([)
+1Ko(t)・Δ2ev(t)) After calculating ΔLJv (t), operation at time (E−Δ[) before by Δt! HJC(t-Δ[), (
The operation deviation amount Δ(Jv(t>) calculated using equation 19) is inputted to the plant 6 via the comparator 3 and the controller 5 as a new operation -tLJy(t).

That is, tJIl (t) is expressed by the following equation.

Tortoise 1v (t) = Llc (t
−−Δ t ) 10 Δ l1y(t) or more”:
, the output pattern following type PID il control has been explained. The same thing can be said about the input cover turn following type P10.
It can also be applied to control.

Now, the input %Jc (t) (actually the output of filter 4 (IiIC)) at time t and lT14! pattern lc.

The deviation between the differential error eu(t) with M(1) and the differential error et+(t-Δt) at (−Δt) is expressed as ΔBu(t)
Then, Δ6t+(t) is expressed by the following formula.

Δeu (t) = et+ (t) −e++
(t-Δt) Next, Δeu at time t and (t-Δt)
If the deviation from Δ6u at t) is Δ2eLl(t), Δ2eu(t) is expressed by the following equation.

Δ2eu(t) −Δeu(t)−Δeu (t−Δt) (22
>The operation amount feedback element 1 is (21>).

The deviation amount expressed by equation (22) and (12) to (14)
An operation bias amount ΔIJU(t) expressed by the following equation is calculated from each PrD coefficient expressed by the equation.

ΔUu (t)=lKp (t) (Δeu
(t)+lK+ (t) ・ell (t)+
lKo (E)・Δ2eu(t)) After calculating Δ(Ju(t), set the time (−) before by Δt
The sum of the manipulated variable IC(t-Δt) at Δt) and the manipulated variable mΔUu(t) calculated by equation (23) is set as a new manipulated variable 11u(t), and the comparator 3. Plans 1-6 are input via the controller 5. That is, L.J.
u(t) is expressed by the following formula.

lJu (t) −1jc (t−Δt)+ΔU
u(t) Next, the positional type P■DIIIl] will be explained. First, output pattern following type PID control will be explained. Now, the difference error ev
If the sum of (t) and a predetermined peak Sy (t-Δt) at a time Δ1 before (t-Δt) is 5v(1),
5v(t) is expressed by the following formula.

Sv <t> = Sv (-Δt) 1-eY
<t>The output feedback element 2 calculates the operation 1tUv (t) as expressed by the following equation using equation (25) and equations (12) to (14), and outputs the operation 1tUv (t) to the comparator 3. Input 1 to the plant 6 via the controller 5! Ru.

Turtle Jv (t) = Kp ('t > ・ev
(t)+lKI(t)·sY ([)′+IKm·Δev(t) Here, ΔeY is the differential error expressed by equation (17).

=15- Next, the input cover turn following type PID control will be explained. Now, the difference error eu(t) at time t and the predetermined amount 5u (t-
When the sum of Δt) is 5u(t), 5u(t) is expressed by the following equation.

Su (t)=Su (−Δt)+eu
(t) The manipulated variable feedback element 1 calculates the manipulated variable Uu(t) as expressed by the following formula using equation (27) and equations (12) to (14), and comparator 3. It is input to the plant 6 via the controller 5.

LJu (t)=IKp (t) −ell
(t)+lK+(t)・Su(t)
+lKD·Δ6u(t) Here, Δ6u is the differential error expressed by equation (21).゛Accommodation As variously explained above, according to the method of the present invention, multivariable PID control can be performed for each of the velocity type and position type, and therefore, the silver halide crystal growth process can be optimally controlled. be able to.

Next, the limiter operation will be explained. As described above, according to the present invention, even when the control layer has multiple variables, by using a mathematical model for each state of the process, it is possible to perform multivariable control of PID, which was impossible with conventional methods. It becomes possible. Operation it to drive the plant 6 (input ati>u
As for <20>.

The manipulated variables shown in equations (24>, (26), and (28) are used. However, depending on the state of the process, these manipulated variables may become too large, so they cannot be input into process 6 as is. Otherwise, the process may become unstable.

Therefore, in the present invention, a certain limit is placed on the magnitude of the operation m.

The comparator 3 outputs the operation input from the operation amount feedback element 1 and the output feedback element 2.
It operates to receive h u and UY, compare jju and UY, and output the smaller one as operation IUC. That is, the output 10(t) of the comparator 3 is expressed by the following equation.

Ua (t) = lJY (t) (lJy(t)
≦1Ju (t)) lJc (t) −, lJu (t) (lJy
(t) > lJu (t)) As a result, a small manipulated variable is input to the controller 5, so that unstable operation of the plant 6 can be prevented. Furthermore,
Regarding the manipulated variable that has passed through the comparator 3, a level clamp circuit is provided in the controller 5 or the filter 4 to clamp the upper limit of the manipulated variable to a predetermined level.

Next, the ratio changing operation will be explained. The ratio changing operation is performed by the ratio setting section 8. That is, the ratio setting section 8 receives the difference error ev and the pattern operation amount UM and outputs the optimal ratio UM'. Now, ley, r, i (t )l>γ/i/i = 1 for all elements.
...'+ IT f -1+ '''* For Ili that satisfies 8, the set β of ratio elements that is accepted as follows
Consider γ.

βr−[βr A' l+βr/2 + river+βr
/Sl'' Here, βr is a column vector of S rows and 1 column with 8 elements.

Now, βr r r for βT shown in the above equation (30)
=Cs・βr=[βr,r,1,...

βy, r, n-8]” Consider a second set of ratio elements represented by .

Here, βγ, r are column vectors with (n −s ) rows and 1 column. However, C# is a transformation matrix. Next, consider the diagonal matrix expressed by the following equation.

βy, c = diag(βr+ 'l'l''
'1βr, r, n 5) Here, βj, C is a square matrix with (n −s ) rows and (n −s ) columns.

As described above, the ratio setting unit 8 outputs the changed ratio U Mr expressed by the following equation.

UM' = (If(n-s)(n-s)+βr,C)・
LJM(j) However, IF(n-s)(n-s) is (n-s) row (
n −s ) column identity matrix. In the above explanation, we took the case of a diagonal matrix as an example for the PID coefficients IKp, +, and lKo, but it is not necessary to limit it to a diagonal matrix (if we consider the mutual interference of plant outputs, we can use elements other than diagonal elements). There may be cases where the elements of are not required to be O either.

- (Effects of the Invention) As explained in detail above, according to the present invention, the state of the process is expressed mathematically, and control calculations are performed based on the mathematically expressed plant model, thereby achieving improvements that were impossible with conventional methods. It is possible to perform multivariable control of PID.

Therefore, according to the present invention, the silver halide crystal growth process can be optimally controlled.

[Brief explanation of the drawing]

The figure is a block diagram showing an embodiment of a photographic emulsion manufacturing process for carrying out the present invention. 1... Manipulated amount feedback element 2... Output amount feedback element 3... Comparator 4.7... Filter 8...
・Comparison Setting Department Patent applicant Roku Konishi Photo Industry Co., Ltd. Agent Patent attorney Fuji Ijima 1 person

Claims (1)

[Claims] A set of multiple process inputs ■(t) is defined as ■(t) = [U_1(t),..., U_n(t)]^
T = [■_M^T(t), ■_C^T(t)]^T Set of multiple process outputs ■(t) = [Y_1(t), ..., Y_S(t )] ＾
Pattern operation amount based on T database ■_M(t),
■_C, _M^T(t), respectively ■_M(t) = [U_M, _1(t), ..., U_M
,_n_-_S(t)]^T ■_C,_M(t)=[U_C,_M,_1,...,
U_C,_M,_S(t)]^T The control pattern that the process should follow ■_M(t) is
M(t)=[Y_M,_1(t),...,Y_M,_
S(t)]^T Furthermore, the set of PID coefficients ■_p, ■_I, ■_D are respectively ■_p=[K_p, _1(t), ..., K_p, _S
(t)]■_I−[K_I,_1(t),...,K_
I,_S(t)]■_D-[K_D,_1(t),...
・, K_D, _S(t)], the difference between the process output ■(t) and the control pattern ■_M(t), and the pattern operation amount ■_C, _M(t) and the set of operation amounts ■_C (t), and calculate these differences as P
A PID control method in a photographic emulsion manufacturing process, characterized in that an optimum operation signal is obtained by ID calculation and various calculation controls to drive a plant.