Volume 04 Issue 12-2024
47
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
04
ISSUE
12
Pages:
47-56
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
ABSTRACT
The advantages and disadvantages of numerous interconnected adaptive drying process control systems have been
analyzed. An adaptive system for the process has been developed that enables the calculation of hydrodynamics and
seed moisture content in a fluidized bed. This system is based on the separation of reactive zones, taking into account
the fluidized bed and dynamic models of the drying process within the fluidized bed.
KEYWORDS
Intensity, dynamic, model, adaptive, object, optimal, algorithm, parameter, microprocessor, concentration, material,
technology.
INTRODUCTION
Research Article
ADAPTIVE CONTROL SYSTEM FOR A FLUIDIZED BED DRYER
Submission Date:
December 13, 2024,
Accepted Date:
December 18, 2024,
Published Date:
December 23, 2024
Crossref doi:
https://doi.org/10.37547/ajast/Volume04Issue12-09
Bekkulov Jakhongir Sherbaevich
Department of "Automation and Control of Technological Processes," Doctor of Philosophy in Technical
Sciences, Karshi Institute of Engineering and Economics, Uzbekistan
Saidov Imam Hasan ugli
Master's student of the "Automation and Control of Technological Processes" Department, Karshi Institute of
Engineering and Economics, Uzbekistan
Akhemoda Sitora Askar kizi
Student of the Department of "Automation and Control of Technological Processes", Karshi Institute of
Engineering and Economics, Uzbekistan
Turaev Orzubek Amir ugli
Student of the Department of "Automation and Control of Technological Processes", Karshi Institute of
Engineering and Economics, Uzbekistan
Journal
Website:
https://theusajournals.
com/index.php/ajast
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 04 Issue 12-2024
48
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
04
ISSUE
12
Pages:
47-56
OCLC
–
1121105677
Publisher:
Oscar Publishing Services
Servi
The high intensity and instability of ongoing processes
make the fluidized bed a complex control object, with
process requirements becoming more stringent due to
significant nonlinear and stationary characteristics. As
a result, demands on the process control system are
increasing. The process control system should be
implemented at a modern level using means that
ensure high speed and accuracy [1-3]. Complex control
algorithms that differ from standard ones are being
developed, and principles of adaptation and industrial
algorithms are being utilized. The control system
should manage the adaptive main technological
parameters. Despite numerous theoretical and
practical works, the development of adaptive control
algorithms for interconnected objects remains a
relevant task today. Adaptive control algorithms for
fluidized bed objects are mainly used to control
temperature regimes, but they are rarely applied to
hydrodynamic regimes, which determine the efficiency
of heat and mass transfer and energy consumption. It
is necessary to ensure that the control system is
implemented using standard devices.
The development of microprocessor technology has
enabled its widespread use in improving the control of
the drying process. High speed, accuracy, reliability,
and compactness of microprocessor devices are
among the advantages of digital control systems.
Furthermore, digital control devices allow for the
implementation of complex control algorithms. The
use of mathematical models, optimal control
algorithms, as well as their advantages such as
flexibility and adaptability, are important factors. As a
result of these factors' influence, the following
methods are increasingly applied. The intensity of
processes leads to technological regimes approaching
the stability threshold. Ensuring such modes requires
the use of control systems based on mathematical
models. Extensive research in the field of adaptive
control is being conducted both domestically and
internationally[2]. Among the many adaptation
methods, three main ones are distinguished:
programmed control, adaptive control, and self-tuning
controllers. If a system has auxiliary variables that can
be measured and their relationship with the system's
dynamic characteristics is known, then these variables
can be used for programmed control of the regulator's
coefficients. The block diagram of such a system is
shown in Figure 1. When controlling technological
processes, the load (operating mode) of the control
object is chosen as such a variable.
Software Management
Control Object
Regulator
output
y
u
input
x
Figure 1. Program control of an adaptive system.
This method is used when a load is present, but it does
not always correspond to real conditions. This adaptive
control method is considered important; however, it
requires considerable time for modes associated with
complex processes. The adaptive system with a
guiding model is shown in Figure 2.
Volume 04 Issue 12-2024
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American Journal Of Applied Science And Technology
(ISSN
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VOLUME
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Pages:
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OCLC
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Publisher:
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Directional model
Setting Parameters
Regulator
Control Object
u
input
x
output
y
Figure 2. Adaptive system with a guiding model.
The principle is that the system characteristics are
established in accordance with a guiding model, which
determines the exact response of the process to the
control signal. The scheme consists of two loops: an
internal loop, which includes the object and control,
and an external loop for adjusting control parameters,
which minimizes the difference between the output
data of the object and the model.
The guiding models used are generalized into
multidimensional systems. The self-tuning controller
does not directly update parameters that differ from
the aforementioned schemes; instead, this occurs as a
result of calculations. The structural diagram of the
self-regulation controller is shown in Figure 3.
Parameter calculation
regulator
Estimation of object
parameters
Regulator
Control Object
u
output
y
input
x
Figure 3. Self-tuning regulator of the adaptive system.
It can be considered that the self-tuning regulator
consists of two loops: an internal one, which includes
the object and the controller, and an external one,
comprising a parameter estimation device and a
computational regulator. The system can be viewed as
a device with automatic process modeling, where the
process model and control mode are continuously
updated. For periodic evaluation of process
parameters, various methods can be employed, such
as stochastic approximation[3-5].
The scope of application for adaptive methods is very
wide; however, when selecting an adaptation method,
it is necessary to consider the actual characteristics of
the control object. The hydrodynamics of the fluidized
bed does not provide previously considered models of
fluidized bed pulsations, and the understanding of
Volume 04 Issue 12-2024
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VOLUME
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macroscopic patterns does not allow for their use in
the design and operation of real devices for controlling
fluidized bed processes.
Thus, increasing porosity leads to a decrease in the
melting rate between particles, disrupting the
established equilibrium. However, if the layer is
compressed due to destruction, i.e., concentration,
then during its dissolution, the gas velocity between
particles increases, and the attraction force grows,
which also contributes to the layer returning to its
equilibrium state. In both cases, the layer moves while
possessing kinetic energy. The energy and resulting
inertia pass through the equilibrium position, after
which the motion occurs again in the opposite
direction. This model represents continuity equations
for solid matter and gas. The model assumes that when
disturbances or changes occur in the drying agent
reactant, the amount of material in the layer transitions
to a state of directed motion in the solid phase[5-8].
Furthermore, the dependence of the output
parameter on the input parameter is nonlinear, as the
moist concentrate is dried in a fluidized bed dryer at a
constant or decreasing rate (the degree of
characteristic equations can be two or more), and the
process under consideration has a stochastic
mathematical description. This is due to the fact that it
is continuously affected by external disturbing factors.
Figure 4 presents a functional diagram of the
relationship between the regulation of the potassium
chloride drying process in a fluidized bed dryer and the
technological
parameters
influencing
moisture
content.
Q
G
F
output
W
M
U
W
input
Figure 4. Functional diagram of the relationship
between product drying process regulation and
technological parameters affecting moisture content:
Q - drying agent flow rate [m3/hour]; G - primary air
flow rate [m3/hour]; F - secondary air flow rate
[m3/hour]; Winput - input material moisture content
[%]; M - material flow rate [m3/hour]; U - incoming air
humidity [%]; Woutput - output material moisture
content [%].
To simplify our reasoning, let's consider only two
channels; a more detailed scheme can then be
presented as shown in Figure 5. Here,
1
( )
вых
x
t
and
2
( )
вых
x
t
are the control signals, while
1
y
and
2
y
are
the actual values of the controlled variables. In a well-
designed system, the channels
1
( )
вых
x
t
and
2
( )
вых
x
t
are
independent,
meaning
that
the
output
1
1
( )
( )
вых
y t
x
t
→
is controlled only by the signal
1
( )
вых
x
t
, and
2
2
( )
( )
вых
y t
x
t
→
is controlled only by the signal
2
( )
вых
x
t
(the signal
1
( )
вых
x
t
does not affect
2
y
, and
2
( )
вых
x
t
does not affect
1
y
).
Volume 04 Issue 12-2024
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1
cd
W
2
cd
W
1
cc
W
2
cc
W
1
mch
W
2
mch
W
)
(
1
t
y
)
(
2
t
y
)
(
1
t
)
(
2
t
)
(
1
t
x
output
)
(
2
t
x
output
Fig. 5. Structural diagram of the two-dimensional system
In real systems (alongside the main channels
W
mch1
and
W
mch2
),
cross-connections
W
cc1
(where
signal
)
(
1
t
x
output
affects output
2
( )
y t
) and
W
cc2
(where
signal
)
(
2
t
x
output
affects output
1
( )
y t
) often occur.
When investigating such systems, as well as when
synthesizing regulators (correcting devices
W
cd1
and
W
cd2
), it is necessary to take these cross-connections
W
cc1
and
W
cc2
into account. An object is considered
autonomous if, through the application of additional
connections, the mutual influence between channels is
eliminated (i.e.,
W
cc1
and
W
cc2
are absent) [4].
The transfer function of each link represents an
aperiodic element with a delaying argument. Overall,
this is the case:
p
ij
ij
ij
ij
e
p
T
K
p
W
−
+
=
1
)
(
,
(1)
where
i
is the sequential number of the input,
j
is the sequential number of the output.
The dynamic characteristics of each dryer unit are
determined experimentally
Table 1
Channel designation
1-1
1-2
2-1
2-2
3-1
3-2
Channel/Parameter
Q
inp
-
W
out
Q
inp
–
T
out
W
inp
-
W
out
W
inp
-
T
out
T
inp
-
W
out
Т
inp
-
Т
out
K-gain coefficient
3
40
0,1
1
0,025
0,015
T-time constant
320
300
400
280
240
150
Volume 04 Issue 12-2024
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τ
-transport delay
240
90
380
80
120
30
When selecting the main signal transmission channel,
the dynamic characteristics of the object are evaluated.
A channel with two parameters -
T
and
τ
- is preferred.
In case these parameters are equal, a channel with a
low
τ
/T
ratio is selected, where the primary control
channel is the temperature of the drying agent at the
inlet - its temperature at the outlet (Fig. 6).
Regulator
Control Object
input
T
input
T
output
T
/
output
T
Fig. 6. Block diagram of an automatic control system
The adopted automatic control system does not
provide the required drying quality.
An adaptive control system is more preferable, the
model of which is presented in Figure 7. It is built on the
basis of a system that controls the main variable (
T
out
)
depending on the deviation.
Development of
optimal control
Compensator
nom
input
W
.
input
W
input
W
input
T
input
T
output
T
output
W
Adjustment
settings
Regulator
Object
Identifier
Figure 7. Model of an automatic control system for the drying process of mineral fertilizers.
The model parameters are estimated using a recurrent
method of stochastic approximation based on the
measured values of input and output variables. The
identification of model parameters is carried out in the
adjustment unit [5].
Volume 04 Issue 12-2024
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The model parameters consist of the object's dynamic
characteristics (
T, K, τ
) and the controller's tuning
coefficients (
K
p
, T
i
, T
N
)
The object under investigation - a drum dryer - can be
described in a linear form as difference equations:
1
1
( )
(
1) ...
(
)
(
1) ...
(
)
u
u
m
u
m
y K
a y K
a y K
m
b u K
d
b u K
d
m
+
− + +
−
=
− − + +
− −
,
(2)
where
d
and
m
are delay;
−
=
−
=
00
00
)
(
)
(
)
(
)
(
Y
K
Y
K
y
U
K
U
K
u
.
(3)
Here,
K
is the number of quantization cycles;
y(K)
and
u(K)
are variations, i.e., deviations;
U(K)
and
Y(K)
are
current values;
U
00
and
Y
00
are predefined parameter
values.
This linear differential equation corresponds to a
discrete function.
Applying the time shift operator
z
, defined by the
relation
y(k+i)=z
i
y(k)
, to the finite-difference equation
(2), one obtains the operator form of the discrete
model:
1
1
0
1
0
1
(
......
) ( )
(
......
) ( )
n
m
n
m
a
a z
a z
y k
b
b z
b z
u k
−
−
−
−
+
+
=
+
+
(4)
From (4), under zero initial conditions, we can derive a
discrete transfer function of the linear system,
representing the ratio of
z
-transforms of the input
signal to the output signal:
1
0
1
1
0
1
......
( )
( )
( )
......
m
m
n
n
b
b z
b z
y z
W z
u z
a
a z
a z
−
−
−
−
+
+
=
=
+
+
,
(5)
)]
(
);
(
);
(
);
(
);
(
);
(
[
)
(
3
2
1
3
2
1
k
b
k
b
k
b
k
a
k
a
k
a
k
j
j
j
j
j
j
j
=
.
The proposed algorithm for evaluating model
parameters:
1.
y
j
(k)
and
u
i
(k)
,
j=1,2;
A measure
i=1,3;
2. Calculate the equation error
)
1
(
)
(
)
(
−
−
=
k
k
y
k
e
j
T
j
j
j
, where
)
(
k
e
j
is the
equation error,
)
(
k
y
j
is the new measurement, and
)
1
(
−
k
j
T
j
is the predicted value;
3. Calculation of new parameter values
)
(
)
(
)
(
)
(
k
e
l
k
l
k
k
j
j
j
j
−
−
−
=
,
(6)
Volume 04 Issue 12-2024
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American Journal Of Applied Science And Technology
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VOLUME
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Publisher:
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where:
)
(
k
j
- new value;
)
(
l
k
j
−
- previous value;
)
(
l
k
j
−
- correction vector;
)
(
k
e
j
- error.
4. New data vectors
)]
(
);
(
);
(
);
(
);
(
);
(
[
)
1
(
3
2
1
3
2
1
ij
ij
ij
j
j
j
T
j
d
k
u
d
k
u
d
k
u
k
y
k
y
k
y
k
−
−
−
−
−
−
=
+
,
(7)
T
i
i
k
y
k
y
k
P
k
P
k
P
k
P
k
k
P
j
j
j
j
j
j
j
j
T
j
j
=
=
−
−
=
+
6
1
6
1
66
61
16
11
)
(
)
(
)
(
)
(
)
(
)
(
)
1
(
)
(
.
(8)
5. Calculation
The measurable output
у
(
K
) contains an additive
random noise
n
(
K
). The noise signal is considered an
autoregressive process with a shifting mean value:
)
(
...
)
(
)
(
)
(
...
)
(
)
(
1
p
K
V
d
l
K
V
d
K
V
p
k
n
C
l
K
n
C
K
n
p
r
p
−
+
+
−
+
=
−
+
+
−
+
,
(9)
where
V(K)
is a sequence of statistically independent, randomly distributed values following a normal distribution.
Noise transfer function:
m
p
m
p
v
p
c
p
c
p
d
p
d
p
C
p
D
p
V
p
n
p
G
−
−
−
−
−
−
+
+
+
+
+
+
=
=
=
...
1
...
1
)
(
)
(
)
(
)
(
)
(
1
1
1
1
1
1
.
(10)
Thus, the model of the object involved in the external
noise is:
)
(
)
(
)
(
)
(
)
(
)
(
)
(
1
1
1
1
p
V
p
C
p
D
p
u
p
p
A
p
B
p
y
d
+
=
−
−
−
−
−
.
(11)
The task of parametric identification is to obtain an
estimate of the model parameters, i.e., the coefficients
of the polynomials
)
(
1
−
p
A
and
)
(
1
−
p
B
, as well as
)
(
1
−
p
C
and
)
(
1
−
p
D
.
To implement such approaches, it is necessary to apply
or identify special methods based on transient process
calculations. For high-quality drying in the automatic
control system, an adaptive control system is the most
optimal solution. Adaptive control is built on a system
that manages the main regulated parameter (
W
output
)
based on deviations, adaptively compensating for the
drying agent flow rate (
Q
), primary air flow rate (
G
),
secondary air flow rate (
F
), and external disturbances
related to the moisture content of the incoming wet
concentrate, material flow rate, and incoming air
humidity [6-8]. Figure 8 presents the structure of the
adaptive control system for the drying process.
Volume 04 Issue 12-2024
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American Journal Of Applied Science And Technology
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VOLUME
04
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OCLC
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Publisher:
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Figure 8. Structure of the improved adaptive control
system for the drying process: 1 - task formation unit, 2,
3, 4 - comparative elements, 5, 6, 7 - flow sensors, 8, 9 -
summing units, 10 - controlled object, 11 - moisture
analyzer, 12 - compensator, 13 - functional unit, 14 -
identification unit, 15 - parameter adjustment unit, 16 -
adaptive control unit, 17 - external disturbances.
The drying process for the proposed moist product is
characterized by an improved adaptive control method
and the fact that during the operation of the control
system, the regulated parameters remain unchanged
and conform to the settings. During the operation of
the improved adaptive control system, the time
constant T of the compensating device [5-8] changes
in response to variations in the parameters of the
controlled object. This change occurs only when the
result of altering the characteristics of the controlled
object leads to a deterioration in the quality of
regulation. This ensures the necessary stability margin
for the system. The structural and functional diagram
of the proposed improved drying drum control system
is shown in Figure 9.
Pri mary a ir
Seco nd ary a ir
Dryi ng
ag en t
Natu ra l g as
2
3
Mo ist mate ri al
Fin al
p ro d uc t
8
Spent drying agent
10
АТ02
ТТ 01
FТ 03
FТ 02
L Т01
М 01
ТТ 02
FТ 01
Progr amma ble Logic
Controller (PLC)
Персанал
компютер
Frequency converter
(inverter)
Analog output block
(module)
6
7
1
4
9
14
15
16
17
18
1- 1
1 -2
1- 3
М02
WT
12
19
11
13
5
АТ 01
Personal
computer
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Figure 9. Structural and functional diagram of the
improved fluidized bed dryer control system: 1 - wet
material feed conveyor; 2 - wet material hopper; 3 -
feeder; 4 - frequency regulator (frequency converter);
5 - feed conveyor; 6 - heater; 7 - mixer; 8 - dryer; 9, 10 -
cyclones; 11 - dust collector; 12 - storage hopper; 13 -
conveyor for feeding dried material to the cooler; 14 -
programmable logic controller (PLC), 15 - analog input
module and 16 - analog output modules; TT01, TT02 -
temperature sensors; FT01 - gas flow sensor; FT02 -
primary air flow sensor; FT03 - secondary air flow
sensor; FT04 - drying agent flow rate sensor; FT05 - wet
concentrate flow sensor; LT01 - level sensor; M01, M02
- electric motors.
CONCLUSION
The model accounts for the main parameters of the
layer: gas velocity, solid phase velocity, and solid phase
concentration. Based on the gravitational-vibrational
model, it is possible to determine the final height of the
layer and its pulsation. The technological process of
seed drying in fluidized bed dryers and methods for
modeling control objects have been analyzed.
Shortcomings of existing control systems have been
identified. When considering the technological process
as a control object, reactive flows are defined, which
enables the formulation of a control task that takes
into account the identified monitoring requirements.
REFERENCES
1.
Sherbоevich, B. Z. (2023). Advanced control system
for the drying process of potassium chloride in a
drum dryer. PEDAGOGS, 46(2), 48-54.
2.
Nurullаеviсh, K. S., & Sherboyevich, B. J. (2024).
Abstract boiling on the example of an improved
control system for the combustion of natural gas
(potassium chloride) in the calorifier of the dryer.
American Journal of Innovation in Science
Research and Development, 1(7), 18-27.
3.
Zhuraev, F. D., & Bekkulov, J. S. (2018). Analysis of
membership functions and assessment of the
condition of the management object. Scientific
Knowledge of Modernity, (6), 31-35.
4.
Zhuraev, F. D., & Bekkulov, J. S. (2018). Tasks Of
Calculation And Design Of Automatic Control
Systems. Scientific knowledge of Modernity, (6),
24-30.
5.
Sherboyevich, B. J. (2022). Virtual analyzers used in
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