Volume 04 Issue 03-2022
31
The American Journal of Engineering and Technology
(ISSN
–
2689-0984)
VOLUME
04
I
SSUE
03
Pages:
31-38
SJIF
I
MPACT
FACTOR
(2020:
5.
32
)
(2021:
5.
705
)
(2022:
6.
456
)
OCLC
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1121105677
METADATA
IF
–
7.856
Publisher:
The USA Journals
ABSTRACT
The article proposes solutions to the problem of using the theory of adaptive identification for automation of
multiply connected objects and shows the possibilities of applying the theory of adaptive identification of multiply
connected objects using the example of wastewater treatment plants.
KEYWORDS
Discrete systems, adaptive identification, matrix coefficients, compound vectors, block diagram.
INTRODUCTION
It is known that numerous tasks of managing
production processes and complex installations,
which include chemical and biological wastewater
treatment, are multi-connected objects that require a
transition from automation of individual processes to
automation of production complexes.
Automation of industrial complexes leads to the need
to take into account the interconnectedness of the
input and output coordinates of individual processes,
and, consequently, the structural links between them.
The lack of sufficiently complete a priori information
about the object, the laws of distribution of random
Research Article
THE POSSIBILITY OF APPLYING THE THEORY OF ADAPTIVE
IDENTIFICATION TO AUTOMATE MULTI-CONNECTED OBJECTS
Submission Date:
February 28, 2022,
Accepted Date:
March 20, 2022,
Published Date:
March 31, 2022 |
Crossref doi:
https://doi.org/10.37547/tajet/Volume04Issue03-05
Umid Kholmatov
Senior Lecturer, Andijan machine-building institute, Andijan, Uzbekistan
Journal
Website:
https://theamericanjou
rnals.com/index.php/ta
jet
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 04 Issue 03-2022
32
The American Journal of Engineering and Technology
(ISSN
–
2689-0984)
VOLUME
04
I
SSUE
03
Pages:
31-38
SJIF
I
MPACT
FACTOR
(2020:
5.
32
)
(2021:
5.
705
)
(2022:
6.
456
)
OCLC
–
1121105677
METADATA
IF
–
7.856
Publisher:
The USA Journals
parameters and random influences makes it necessary
to apply the theory of adaptive identification. In the
future, adaptive identification of multiply connected
objects will be understood as the determination of
the parameters and structure of objects under
conditions of initial uncertainty, based on the results
of monitoring the change in input and output values
during normal operation. From this point of view, of
particular interest are the electric power systems of
drainage and treatment facilities, in which the
frequency and voltage, active and reactive power
flows, the performance of turbocompressors of
pumping stations are simultaneously regulated, and
according to the technological mode they are treated
as multi-connected objects with separate control
channels, operating modes [1-2].
The parameters of the control object, for example,
water disposal and treatment facilities vary over a
wide range [1-3]. If we assume that only one factor
affects the change in the parameters of the object
(for example, the concentration of waste water),
while
neglecting
the
operating
modes
of
turbocompressors and pumping units, then it is not
possible to use the obtained parameters of the
control object without large errors. If we solve the
problem of identifying treatment facilities as a
multiply connected object, taking into account all the
indicated values during operation, then the
parameters of the object obtained in this case will be
determined much more accurately [4].
METHODS
The task of adaptive identification arises due to the
fact that, in the general case, the internal and external
influence that acts on the object is of a random
nature. For water treatment facilities as objects, this
randomness is due to the random nature of the
disturbing moments and other factors caused by the
uneven distribution of pump motor power, the
instability of pressure in turbocompressors from cycle
to cycle, the concentration of activated sludge, the
dose of active chlorine, etc [4, 6-8]. For treatment
facilities, such impacts are: filling of sedimentation
tanks and aerotanks, failure of one of the
symmetrically located engines and pumps, etc.
It is easy to determine the distribution laws for each
of these factors separately [5], but it is almost
impossible to determine the resulting distribution law
for the entire set of factors, and, accordingly, the
identifiable object parameters that depend on them.
In this regard, the problem of identifying multiply
connected objects is reduced to the problem of
adaptive identification.
Currently, there is no complete theory of adaptive
identification of multiply connected objects. In this
article, some questions of the theory of adaptive
identification
of
multiply
connected
objects
containing forward and reverse cross-links are
presented.
RESULTS AND DISCUSSION
Generalization of the equation of dynamics of multiply
connected objects.
Let us describe processes in multiply connected
objects of a system of linear inhomogeneous l-th
order differential equations with r unknown variables
x1, x2, . . . , xr of the argument t with constant
coefficients
Volume 04 Issue 03-2022
33
The American Journal of Engineering and Technology
(ISSN
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2689-0984)
VOLUME
04
I
SSUE
03
Pages:
31-38
SJIF
I
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FACTOR
(2020:
5.
32
)
(2021:
5.
705
)
(2022:
6.
456
)
OCLC
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1121105677
METADATA
IF
–
7.856
Publisher:
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(1)
where the set of coordinates
- vectors - columns of object state and
control, respectively;
i
- number of a separate channel;
D=d/dt
– differentiation operator;
- are
polynomials in
that have the form
(2)
Here
i, j=1,2, . . .,r; l, l
1
- the order of the polynomial of the coefficients a and b, respectively;
is the number
of separate channels of the controlled object. It is assumed that the number of direct cross-links is equal to the
number of reverse ones; the order of differential equations of reverse cross-links is equal to the order of
differential equations of direct cross-links. These assumptions do not reduce the generality of the problem, since
in the presence of any other options and combinations of cross-couplings, as well as the order of differential
equations, it is reduced to special cases. Let us introduce numerous matrices of operator coefficients [1-2]:
A(D)=
B(D)=
(3)
or expanded
;
(4)
Sloping
k
=0, 1, 2,. . . , l;
(5)
one can represent multiple matrices A (D) in B (D) as polynomials with matrix coefficients
A(D)=A
l
D
l
+A
l-1
D
l-1
+. . . +A
1
D+A
0
;
Volume 04 Issue 03-2022
34
The American Journal of Engineering and Technology
(ISSN
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2689-0984)
VOLUME
04
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03
Pages:
31-38
SJIF
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FACTOR
(2020:
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)
(2021:
5.
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)
(2022:
6.
456
)
OCLC
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1121105677
METADATA
IF
–
7.856
Publisher:
The USA Journals
B(D)=B
l1
D
l
1
+B
l-1
D
l1-1
+. . . +B
1
D+B
0
;
(6)
Then, in matrix form, the system of differential equations (1) takes the form
(7)
In expanded form, for any separate channel, one can write
(8)
Let us rewrite equation (8) in a difference form (in a recurrent form):
(9)
The matrix coefficients of the equations are interconnected by relations [1-2].
;
;
where
For a controlled object in the presence of only direct cross-links, equation (9) has the form
(9.а)
and in the presence of only inverses -
(9.б)
In some cases, some of the coefficients
and
may be equal, which corresponds to the absence of any
links.
General algorithm for adaptive identification of multiply connected stationary objects.
To solve the identification problem, we introduce a composite situation vector. By analogy with [4], we denote
the situation vector
, and the composite vector -
.
Consider a multiple composite vector of coefficients:
Volume 04 Issue 03-2022
35
The American Journal of Engineering and Technology
(ISSN
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2689-0984)
VOLUME
04
I
SSUE
03
Pages:
31-38
SJIF
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FACTOR
(2020:
5.
32
)
(2021:
5.
705
)
(2022:
6.
456
)
OCLC
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1121105677
METADATA
IF
–
7.856
Publisher:
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(10)
It should be noted that the dimension of the multiple composite vector
depends on the dimension of the
system and the order of the difference equation (9).
Let us express the composite situation vector
in terms of the vector
:
,
(11)
Where
The quality of identification is estimated using functionals from control errors, which are integral root-mean-
square estimates. Therefore, each of them is expressed through the mathematical expectation, taking into
account the stochastic nature of all influences [1-2]. In the general case, we write the optimality criterion in the
form
J(
) = M
The adaptive identification algorithm in this case will have the form
(13)
Where
– diagonal coefficient matrices
(k=x, u),
The block diagram of a discrete system corresponding to the identification algorithm (13) in vector form is
shown in Fig.1. Algorithm (13) can be expressed in expanded form in terms of composite vectors
(14)
Volume 04 Issue 03-2022
36
The American Journal of Engineering and Technology
(ISSN
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2689-0984)
VOLUME
04
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03
Pages:
31-38
SJIF
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FACTOR
(2020:
5.
32
)
(2021:
5.
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)
(2022:
6.
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METADATA
IF
–
7.856
Publisher:
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Where
v
=0, 1, 2, . . ., l; q. p=1, 2, . . ., l
1
;
=(
, . .
.
).
(15)
In expression (14), the functions
and
are
;
Taking into account the values of functions (15) for the quadratic functional, algorithm (14) is transformed to the
form
(16)
In expression (14), the functions
and
are
;
Taking into account the values of functions (15) for the quadratic functional, algorithm (14) is transformed to the
form
(16)
CONCLUSION
The above algorithms allow solving problems from
the transition of automation of individual processes to
automation of industrial complexes, and determine
the possibilities of applying the theory of adaptive
identification of multiply connected objects, as well as
consider complex issues of compiling identification
algorithms by using an iterative probabilistic method.
Volume 04 Issue 03-2022
37
The American Journal of Engineering and Technology
(ISSN
–
2689-0984)
VOLUME
04
I
SSUE
03
Pages:
31-38
SJIF
I
MPACT
FACTOR
(2020:
5.
32
)
(2021:
5.
705
)
(2022:
6.
456
)
OCLC
–
1121105677
METADATA
IF
–
7.856
Publisher:
The USA Journals
Fig.1.
A discrete system that implements an adaptive identification algorithm for multiply connected objects
in vector form.
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An object
BZ
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D
Г
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[n]
Г
x
[n]
BZ
Volume 04 Issue 03-2022
38
The American Journal of Engineering and Technology
(ISSN
–
2689-0984)
VOLUME
04
I
SSUE
03
Pages:
31-38
SJIF
I
MPACT
FACTOR
(2020:
5.
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(2021:
5.
705
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6.
456
)
OCLC
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1121105677
METADATA
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7.856
Publisher:
The USA Journals
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