Method and device for controlling production of a mixture of components, in particular a mixture with pre-mix dead volumes
The invention relates to a method and a device for controlling the production of a mixture of components, especially a mixture with premix dead volumes. The method and the device according to the invention ensure multivariable regulation feedback by a dynamic observer providing an estimate in real time of the properties of the components of the mixture, said estimate being sufficient to guarantee the effectiveness of the feedback loop. Thus, the desired properties of the mixture are guaranteed despite large uncertainties in the properties of the components on the one hand, and partial knowledge of the mixing process on the other.
1. A method for controlling production of a mixture M of n components, the method making it possible to determine proportions u of the components involved in the mixture so as to obtain values for a number m of predetermined properties y of the mixture, the values lying between predetermined minimum and maximum thresholds and/or, for m′ of them (where m′≦n−1), are substantially equal to predetermined target values, characterized in that the method comprises the following steps:
(i) at time t=0:
(1) a matrix B representing the number m of properties y of the n components is determined,
(2) a reference recipe ū is determined from the predetermined minimum and maximum thresholds and/or from the predetermined target values, such that properties Bū of the mixture lie between said predetermined thresholds and/or, for m′ of them, are equal to said predetermined target values,
ū, being a vector of dimension n, representing the proportions of the components involved in the composition of the mixture, where Σ i=1 n ū i =1, and
(3) the recipe ū is applied to the components so as to produce the mixture M;
(ii) at time t′=t+Δt:
(1) properties y mes of the mixture M obtained by applying the recipe ū are measured,
(2) a corrected matrix {circumflex over (B)}, representing an estimate of the properties of the components, is deduced therefrom,
(3) a new recipe u is determined in such a way that the properties {circumflex over (B)}u of the mixture lie between said predetermined thresholds and/or, for m′ of them, are equal to said predetermined target values, and
(4) the new recipe u is applied to the components;
(iii) at time t″=t′+Δt, operations (1) to (4) of the preceding step (ii) are repeated; and
(iv) step (iii) is repeated throughout the duration of production of the mixture.
2. The method according to claim 1 , in which the properties y mes of the mixture that are measured during operation (1) of step (ii) are measured by means of a continuous measurement procedure on the mixture produced.
3. The method according to claim 1 , in which, at a predetermined time during the production of the mixture, one or more properties of the components are measured and the matrix B representing the properties of the components is updated.
4. The method according to claim 1 , characterized in that, during operation (2) of step (ii), the corrected matrix {circumflex over (B)} is determined using the following equation:
ⅆ
B
^
j
t
ⅆ
t
=
-
β
j
H
u
(
y
j
-
y
j
mes
)
,
(
1
)
where
the matrix H is a positive definite symmetric matrix having the objective of ensuring normalization taking into account the measurement-prediction deviation, allowing component quality prediction deviation calculation;
B j t is the transpose of B j and
β j , a strictly positive real number, is a constant for setting the convergence time, allowing the rate of convergence of the estimate to be differentiated property by property.
5. The method according to claim 1 , for the production of the mixture of components, in which at least one premix of at least two of the components is produced before production of the mixture, characterized in that the recipe u determined during operation (3) of step (ii) takes into account the delays due to dead volumes present in premixing zones.
6. The method according to claim 5 , characterized in that, during operation (2) of step (ii), the matrix {circumflex over (B)} is determined using the following equation:
ⅆ
B
^
j
t
ⅆ
t
=
-
β
j
H
U
(
t
)
(
y
j
(
t
)
-
y
j
mes
(
t
)
)
,
(
2
)
where U(t) (U 1 (t), . . . U n (t)) t , at time t, the recipe vector taking into account the dead volumes, and
y
(
t
)
=
∑
i
=
1
n
U
i
(
t
)
b
i
,
b i being the vector of the properties of component i.
7. The method according to claim 6 ,
characterized in that the control and output quantities involved in equation (2) are synchronized in order to take into account the premixing delay and measurement delay.
8. The method according to claim 1 , characterized in that the recipe u determined in substep (3) of step (ii) is determined by using an optimization procedure comprising the following steps:
(a) determination of the solution of a complete regulation problem P 0 , the solution consisting of recipe u taking into account the constraints on the proportions of the components and constraints on the properties of the mixture, and
application of the recipe u if the complete regulation problem P 0 is solvable;
(b) determination of recipe u for which a minimal regulation problem P 1 is solved, if the complete regulation problem P 0 is not solvable, which takes into account only constraints on the problem P 0 that are defined as priority constraints; the problem P 1 involving a succession of normally feasible optimization problems, the criteria of which consist in penalizing the violation of the priority constraints so as to define achievable new values for the priority constraints;
(c) determination of recipe u for which a regulation problem P 2 is solved, if the minimal regulation problem P 1 is solvable, which takes into account said achievable new values of the priority constraints of the problem P 0 and also non-priority constraints of the problem P 0 ; the problem P 2 involving an optimization problem, the criteria of which consist in penalizing the violation of non-priority constraints so as to define achievable new values for the non-priority constraints, or
application of the current recipe u if the minimal regulation problem P 1 is not solvable;
(d) determination of recipe u for which a regulation problem P 3 is solved, if the regulation problem P 2 is solvable, which takes into account said achievable new values of the priority constraints of the problem P 0 obtained in step (b), the achievable new values of the non-priority constraints obtained in step (c) and also all other non-priority constraints of the problem P 0 not treated by the problems P 1 and P 2 ; the problem P 3 involving a succession of normally feasible optimization problems, the criteria of which consist in penalizing the violation of the other non-priority constraints so as to define achievable new values for the other non-priority constraints, or
application of the recipe obtained by the problem P 1 if the regulation problem P 2 is not solvable; and
application of recipe u that is the solution of the problem P 3 if the regulation problem P 3 is solvable, otherwise application of recipe u that is the solution of the problem P 2 .
9. The method according to claim 8 ,
characterized in that it comprises an additional step during which, if the regulation problem P 3 is solvable, recipe u is determined for which the regulation problem P 0 is solved taking into account said achievable new values determined during steps (b), (c) and (d).
10. The method according to claim 8 ,
characterized in that the priority constraints taken into account for solving the problem P 1 are constraints on the proportions of the components and constraints on the properties of the mixture.
11. The method according to claim 1 , for a plant for producing a mixture of n components and of additives, characterized in that, for a property j of the mixture on which an additive has an influence, the method takes into account the effect d of the additive addition during operations (2) and (3) of step (ii) according to: y j ={circumflex over (B)} j u+d.