Method for computer-assisted determination of an optimum-fuel control of nozzles
Method for the computer-assisted determination of an optimum-fuel control of nozzles according to a control instruction b=Ax. A defined matrix transformation of starting constraints for the mass flow of the nozzles and of the minimization criterion thereby takes place in a computer-assisted manner, a data processing representation of a geometric description of the matrix-transformed starting constraints, a computer-assisted determination of limiting point sets of the geometric description of the starting constraints through a computer-assisted geometric search procedure in the vector space and the application of the matrix-transformed minimization criterion to the points of the limiting point sets.
1. A method for controlling nozzles based upon computer-assisted determination of an optimum-fuel control of the nozzles according to a control instruction b=Ax, whereby
b represents a desired m-dimensional forces/torque vector,
A represents an m×n-dimensional nozzle matrix, and
x represents a sought n-dimensional nozzle control vector and the nozzle control vector meets a minimization criterion of
J
:=
∑
i
=
1
i
=
n
x
i
→
min
,
the method comprising:
computer generating a defined matrix transformation of starting constraints for a mass flow of the nozzles and of the minimization criterion;
data processing a representation of a geometric description of the matrix transformation of starting constraints;
searching, with a computer-assisted geometric search procedure in vector space, limiting point sets of the geometric description of the starting constraints;
applying the matrix transformation of minimization criterion to the points of the limiting point sets; and
controlling the nozzles.
2. The method according to claim 1 , wherein the matrix transformation of the starting constraints for the mass flow of the nozzles includes a homogenous solution of the control instruction according to x ho =A o r, whereby
A o : represents the n×(n−m) dimensional zero space matrix of A, and
r: represents an (n−m) dimensional vector of any real numbers, the method further comprising:
calculating, within a scope of a use of the matrix transformation of the minimization criterion, scalar products of a vector representation of points of the limiting point set and the vector
v
d
T
:=
[
∑
j
=
1
n
A
0
j1
∑
j
=
1
n
A
0
j2
…
∑
j
=
1
n
A
0
jp
]
,
p
:=
n
-
m
and
calculating an optimum-fuel solution with the aid of the vector r whose scalar product is minimal with the vector v d .
3. The method according to claim 1 , further comprising:
converting the matrix transformation of the starting constraints for the mass flow of the nozzles in a computer-assisted manner into allowable multi-dimensional value regions;
forming, to determine the limiting point sets, at least one multi-dimensional cut set of individual allowable multi-dimensional value regions; and
determining the limiting point sets as those point sets that limit the at least one cut set.
4. The method according to claim 3 , further comprising:
repeatedly projecting the allowable multi-dimensional value regions of the dimension p on a dimension p−1, until a projection of the allowable value regions on limiting intervals of a dimension p=1 has been achieved; and
subsequently searching, with a computer-assisted search procedure, determination of limiting point sets as a cut set of limiting intervals.
5. A computer control method for controlling nozzles based upon an optimum-fuel usage for the nozzles based on a m-dimensional forces/torque vector, m×n-dimensional nozzle matrix, and a n-dimensional nozzle control vector that meets a minimization criterion, the method comprising:
generating a defined matrix transformation of starting constraints for a mass flow of the nozzles and of the minimization criterion;
data processing a representation of a geometric description of the matrix transformation of starting constraints;
searching, with a geometric search procedure in vector space, limiting point sets of the geometric description of the starting constraints;
applying the matrix transformation of minimization criterion to the points of the limiting point sets; and
controlling the nozzles.
6. The method according to claim 5 , wherein the control instruction is b=Ax, whereby
b represents the desired m-dimensional forces/torque vector,
A represents the m×n-dimensional nozzle matrix, and
x represents the sought n-dimensional nozzle control vector and the nozzle control vector satisfies the minimization criterion of
J
:=
∑
i
=
1
i
=
n
x
i
→
min
.
7. The method according to claim 6 , wherein the matrix transformation of the starting constraints for the mass flow of the nozzles includes a homogenous solution of the control instruction according to x ho =A o r , whereby
A o : represents the n×(n−m) dimensional zero space matrix of A, and
r: represents an (n−m) dimensional vector of real numbers, the method further comprising:
calculating, within a scope of a use of the matrix transformation of the minimization criterion, scalar products of a vector representation of points of the limiting point set and the vector
v
d
T
:=
[
∑
j
=
1
n
A
0
j1
∑
j
=
1
n
A
0
j2
…
∑
j
=
1
n
A
0
jp
]
,
p
:=
n
-
m
and
calculating an optimum-fuel solution with the aid of the vector r whose scalar product is minimal with the vector v d .
8. The method according to claim 6 , further comprising:
converting the matrix transformation of the starting constraints for the mass flow of the nozzles into allowable multi-dimensional value regions;
forming, to determine the limiting point sets, at least one multi-dimensional cut set of individual allowable multi-dimensional value regions; and
determining the limiting point sets as those point sets that limit the at least one cut set.
9. The method according to claim 8 , further comprising:
repeatedly projecting the allowable multi-dimensional value regions of the dimension p on a dimension p−1, until a projection of the allowable value regions on limiting intervals of a dimension p=1 has been achieved; and
subsequently searching a determination of limiting point sets as a cut set of limiting intervals.