Математична модель електричного калорифера для кіберфізичних систем
The article discusses the heat and mass transfer dynamic model for an electric heater with lumped parameters, which allows transient processes simulation for the main influences. The proposed model is recommended to be used in cyber-physical systems for forecasting and evaluating the effectiveness o...
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The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2021
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Репозитарії
System research and information technologies| _version_ | 1867334415861940224 |
|---|---|
| author | Pankratova, Nataliya Golinko, Igor |
| author_facet | Pankratova, Nataliya Golinko, Igor |
| author_institution_txt_mv | [
{
"author": "Nataliya Pankratova",
"institution": "Educational and Scientific Complex \"Institute for Applied System Analysis\" of the National Technical University of Ukraine \"Igor Sikorsky Kyiv Polytechnic Institute\", Kyiv"
},
{
"author": "Igor Golinko",
"institution": "The Faculty of Heat Power Engineering of the National Technical University of Ukraine \"Igor Sikorsky Kyiv Polytechnic Institute\", Kyiv"
}
] |
| author_sort | Pankratova, Nataliya |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2021-09-16T11:48:22Z |
| description | The article discusses the heat and mass transfer dynamic model for an electric heater with lumped parameters, which allows transient processes simulation for the main influences. The proposed model is recommended to be used in cyber-physical systems for forecasting and evaluating the effectiveness of control systems integrated into a single information management system. The developed model can be used by specialists for the analysis and synthesis of control systems for balanced ventilation systems or industrial air conditioners. As an example, a numerical simulation of transient processes along the action main channels for an electric heater HE 36/2 manufactured by VTS CLIMA was carried out. The significant advantage of the proposed model is the possibility for using it for the synthesis and analysis of multidimensional control systems. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2021.2.01 |
| first_indexed | 2025-07-17T10:27:23Z |
| format | Article |
| fulltext |
N. Pankratova, I. Golinko, 2021
Системні дослідження та інформаційні технології, 2021, № 2 7
TIДC
ПРОГРЕСИВНІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ,
ВИСОКОПРОДУКТИВНІ КОМП’ЮТЕРНІ
СИСТЕМИ
UDC 303.732.4, 519.226
DOI: 10.20535/SRIT.2308-8893.2021.2.01
ELECTRIC HEATER MATHEMATICAL MODEL
FOR CYBER-PHYSICAL SYSTEMS
N. PANKRATOVA, I. GOLINKO
Abstract. The article discusses the heat and mass transfer dynamic model for an
electric heater with lumped parameters, which allows transient processes simulation
for the main influences. The proposed model is recommended to be used in cyber-
physical systems for forecasting and evaluating the effectiveness of control systems
integrated into a single information management system. The developed model can
be used by specialists for the analysis and synthesis of control systems for balanced
ventilation systems or industrial air conditioners. As an example, a numerical simu-
lation of transient processes along the action main channels for an electric heater
HE 36/2 manufactured by VTS CLIMA was carried out. The significant advantage
of the proposed model is the possibility for using it for the synthesis and analysis of
multidimensional control systems.
Keywords: cyber-physical system, digital twin, mathematical model, state space,
electric heater.
INTRODUCTION
In the modern world, the managing technical systems tasks are closely inter-
twined with the social sphere of human activity. The growth and complexity of
management situations in technical systems requires the use of new scientific ap-
proaches to management. The computer-integrated control systems properties
study from the interaction view point of physical and computational component is
a priority in the modern science about cyber-physical systems [1]. To date, such
systems have not yet received a generally accepted definition, since they lie at the
intersection of several human spheres of activities. Their common characteristic is
the interaction between computing and physical processes, where the computing
system constantly receives data from the environment and uses them to further
optimize the physical processes control. Cyber-physical systems include, for ex-
ample, networked intelligent control of power supply or transport, automated con-
trol systems in production and agriculture, and much more.
While designing cyber-physical systems, it is necessary to solve a variety of
interrelated problems. One of the important tasks is the development of real ob-
ject’s digital twin based on mathematical modeling [2, 3]. A digital twin is a digi-
tal model obtained based on information from sensors installed on a physical ob-
ject, which allows you to simulate object’s behavior in the real world.
Fundamentally, a digital twin can be defined as an ever-changing digital profile
containing historical and most current data about a physical object or a production
N. Pankratova, I. Golinko
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 8
process. The digital twin is created to predict the real object’s behavior in the
“virtual space” and to adopt a control strategy. Sometimes the time required to
simulate a mathematical model can exceed the physical process flow, and the cal-
culated data becomes outdated. For this reason, the adequate mathematical mod-
els’ development for technical systems that can be used for calculations in “real
time” is an urgent task.
The heat power industry plays an important role in modern society as a tool
for creating material wealth and a means of servicing human life. The one of main
units in heat power engineering is a heat exchanger, which takes on “various
forms” in a particular human activity area. Heat exchangers include heaters,
which are designed to heat the air due to the heat flow from the primary heat
transfer fluid. In industry, air heaters are often used to heat air in heating, ventilation,
air conditioning systems, various dryers and other technical systems [4].
In the mining and coal industries, the most important underground mining
task is to organize the effective ventilation [5]. This problem has both technical
and economic aspects. In technical terms, the key issue in organizing the mine
ventilation is heating the air supplied to the mine to the temperature above 0 C
(from +2 °C to +5 °C). For many decades, the main technical solution for heating
the air supplied to the mine has been provided by the water heaters use. Despite
the design simplicity, using water heaters creates a variety of problems associated
with complex installation, water treatment, continuous maintenance, the danger of
water freezing in heaters and, as a consequence, the need to maintain the supplied
to the mine air temperature above the optimum level.
Recently, the industry began to use air heating systems, which have
established themselves as fast-acting systems with low specific capital
investments. For air heating of shopping and business centers, warehouses and
industrial buildings, centralized ventilation and air conditioning systems are used,
in which air heaters are the main equipment [6]. Residential air heating systems
use low-power electric heaters with a distributed automatic control system [7].
Considering the above, in recent years, electric heaters of high power (up to
30 kW) are increasingly used for heating air in various industries. Electricity
transportation has many advantages over other types of heat carriers, and the use
of thermoelectric heaters (TEH) can significantly increase the air heaters
efficiency and design air heaters with a wide heat output range. In addition,
electric heaters are efficient at outdoor temperatures down to –50 °C and do not
lose their functionality in the event of an emergency power outage.
RESEARCH PROBLEM STATEMENT
The aim of this publication is to develop the heat transfer process dynamic model
for an electric air heater, which can be used as a digital twin for a cyber-physical
system. An additional requirement for the mathematical model is its ease of use
by existing modeling tools on a personal computer.
HEAT TRANSFER PROCESS MATHEMATICAL MODELING
Heat transfer processes are discussed in many publications. To simulate the dy-
namic processes in heat exchangers, researchers use mathematical models with
lumped [8–10] and distributed [11, 12] parameters. Models with lumped parame-
ters provide an analytical solution to the heat transfer task. Models with distrib-
uted parameters describe the physical process more accurately, but in the analyti-
Electric heater mathematical model for cyber-physical systems
Системні дослідження та інформаційні технології, 2021, № 2 9
cal modeling of such processes, transcendental functions appear in the solution
[12], which complicates the calculations. In practice, numerical methods are used
to solve distributed heat transfer problems.
The existing dynamic models of air heaters [8–12] are based on the mathe-
matical description of the heat exchange process for devices where the primary
heat transfer fluid is steam or water, since these devices have long been used in
production as part of automatic control systems. For electric heaters, stationary
models are known, which are used to design the equipment. Considering that re-
cently, high-power electric heaters have been used in production as part of cyber-
physical systems, we will develop the electric heater dynamic model.
ELECTRIC HEATER MATHEMATICAL MODEL
The modern electric heaters designs are based on blowing the air through a bundle
of heating elements, while convective heat exchange is carried out between the
moving air and the heater surface. Considering surface heat exchangers used in
industrial systems, it is necessary to take into account that the air is intensively
mixed by fans. Practical research of unsteady heat transfer characterizes the air
heating process as clearly aperiodic [11], which is described with sufficient accu-
racy by second-order transfer functions. Thus, a lumped-parameter mathematical
model for a water cooler would be perfectly acceptable.
When developing a mathematical model, the following simplifications were
adopted: there is no heat exchange with the environment; the model contains two
dynamic elements with lumped parameters – tubular electric heaters and the air
volume of heater. Physical properties of material flows and the heat exchange sur-
face are reduced to the average values of device’s operating range. The electric
heater design diagram is shown in Fig. 1.
To heat the air in the heater, electric heaters are used, which are connected to
the mains through a triac electrical converter. The electrical converter in propor-
tion to the regulator signal changes the electrical power )(tNE , due to which the
heating elements are heated to the temperature )(tE . All electrical power is used
to heat the air. Air is supplied crosswise to the electric heaters location with a
flow rate )(tGA . The inlet air temperature is )(0 tA , the outlet air temperature is
)(tA . The heater geometrical dimensions HCL ,, are the depth, width and
height, respectively. Let us analyze the heat balance in the dynamics for each dy-
namic element of the air heater.
The heat balance for heating elements is:
dt
d
cMFN E
EEAEE
)(00 , (1)
where Ec is the heat capacity of heating elements (heating elements contain metal
and dielectric parts, so their heat capacity is averaged in proportion to the mass
fraction of each part); EM is the total mass of heating elements; 0 is the heat
transfer coefficient between the air in the heater and the heating elements outer
surface; 0F is the heating elements surface ribbing total area. Let us present equa-
tion (1) in canonical form:
AEE
E
E kNk
dt
d
T
10 , (2)
N. Pankratova, I. Golinko
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 10
where 00 FKE ;
E
EE
E K
Mc
T ;
EK
k
1
0 ; 11 k .
Fig. 1. Design diagram for modelling an electric air heater
The heat balance for the air heater air space is:
dt
d
cMFcG A
AAAEAAAA
)()( 000 , (3)
where Ac is the air heat capacity; AM is the air mass in the heater volume
HCL . After linearization, let us transform equations (3) to the canonical form:
AAEA
A
A Gkkk
dt
d
T
4032 , (4)
where 00 FGcK AAA ;
A
AA
A K
Mc
T ;
AK
F
k 00
2
; 23 1 kk ;
A
AAA
K
c
k
)( 0
4
.
Electric heaters are often used in air conditioning systems. For such systems,
in addition to the temperature regime, it is also important to simulate the heated
air humidity characteristics. It is known from the physical properties of air that
with an increase in the vapor-air mixture temperature, its relative humidity de-
C
H
L
NE(t)
θA; dA; GA
θA0; dA0; GA
Electric heater mathematical model for cyber-physical systems
Системні дослідження та інформаційні технології, 2021, № 2 11
creases (an increase in temperature by 1 °C leads to a decrease in moisture by
about 3%), while the air moisture content remains constant [6]. In addition, at-
mospheric pressure affects humidity. For these reasons, we write the material bal-
ance for the air space of the heater in air moisture content terms:
dt
d
Vdd
G A
AAA
A
)(
1000 0 , (5)
where )(0 tdA and )(tdA are the air moisture content at the air inlet and outlet,
respectively; A is the air density; AV is the heater air space volume. The humid
air density is determined from the equation [13]:
1000
1 A
A
d
, (6)
where is the dry air density under normal conditions. Taking into account (6),
equation (5) after mathematical transformations will take the form:
AAA
A
d Gkdkd
dt
dd
T
605 , (7)
where
A
A
d G
V
T
; 15 k ;
A
AA
G
dd
k
0
6 .
Equations (2), (4) and (7) represent a dynamic model of heat and mass trans-
fer processes when humid air is heated by an electric heater:
.
;
;
605
4032
10
AAA
A
d
AAEA
A
A
AEE
E
E
Gkdkd
dt
dd
T
Gkkk
dt
d
T
kNk
dt
d
T
(8)
Mathematical model (8) in the state space has the form:
BUAXX , (9)
where
E
A
A
dX ;
EE
d
AA
TTk
T
TkT
10
010
01
1
2
A ;
E
A
A
dX ;
E
d
A
d
A
Tk
Tk
Tk
Tk
Tk
0
6
4
5
3
0
0
00
0
0
0B ;
E
A
A
A
N
G
d 0
0
U .’ (10)
Let us solve the system of differential equations (8) with respect to the
sought variables using the Laplace transform:
)13(.)1(
)12(;)1(
)11(;)1(
605
4032
10
AAdA
AAEAA
AEEE
GkdkpTd
GkkkpT
kNkpT
N. Pankratova, I. Golinko
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 12
From (11) we find )( pE , then we substitute it in (12), and after grouping
similar ones we obtain:
])()[(
1
1
423001
1
2
2
EAAA NbGbpbbpb
papa
, (14)
where
21
2 1 kk
TT
a AE
;
21
1 1 kk
TT
a AE
;
21
3
0 1 kk
k
b
;
21
3
1 1 kk
Tk
b E
;
21
4
2 1 kk
k
b
;
21
4
3 1 kk
Tk
b E
;
21
20
4 1 kk
kk
b
.
From (13) we obtain a solution for the variable Ad :
][
1
1
706 AA
d
A Gkdk
pT
d
.’ (15)
Applying the inverse Laplace transform, it is possible to find an analytical
solution for (14) and (15) by the influence channels. We represent (14) and (15)
by a multidimensional model in the Laplace domain
ZWY , (16)
where
A
A
d
Y ;
0
0
0
14
23
13
22
11 W
W
W
W
W
W ; (17)
EAAA NGd 00
TZ ;
11
2
2
01
11
papa
bpb
W ;
11
2
2
23
13
papa
bpb
W ;
11
2
2
4
14
papa
b
W ;
1
6
22
pT
k
W
d
;
1
7
23
pT
k
W
d
.
The proposed electric heater dynamic model in the differential equations
system form (8), in the state space (9), or in the Laplace region (16)–(17), when
modelling mass transfer processes, uses the air moisture content, which by defini-
tion is expressed as:
A
W
A М
М
d , (18)
where WМ is the water steam mass in the air mixture; AM is the dry air mass in
the air mixture. Often, when synthesizing and analysing industrial air conditioners
control systems, it is necessary to use the relative humidity of air, which is de-
fined as:
S
P
A P
P
, (19)
where SP is the saturated steam pressure; PP is the water steam partial pressure.
The water steam partial pressure of humid air is uniquely determined by the mois-
ture content and does not depend on the steam temperature [14]
Electric heater mathematical model for cyber-physical systems
Системні дослідження та інформаційні технології, 2021, № 2 13
A
AB
P d
dP
P
623
. (20)
where BP is the barometric air pressure. The saturated steam pressure can be de-
termined by the approximating dependence of N.I. Filneem [15]
A
A
SP
236
12,8156
103,133 . (21)
If the air temperature A and its relative humidity are known, using
dependencies (18)–(21), it is possible to determine the air mixture moisture content d
A
A
A
A
AB
A
A
P
d
236
12,8156
236
12,8156
103,133
1083045,9 . (22)
Moisture content recalculation into relative humidity can be carried out according
to the inverse relationship
A
A
A
AB
A
d
dP
236
12,8156
10)623(3,133
. (23)
It is worth noting that the moisture content (22) and relative humidity (23) are
calculated in absolute values, and in models (8), (9), and (16), variables in-
crements are considered, and this feature must be taken into account during mod-
elling.
AIR HEATER DYNAMIC MODE SIMULATION
As an example, let us carry out dynamic processes’ simulation modelling for the
eclectic heater НЕ 36/2 of the central air conditioner CV-P 2L N-63B/F-N manu-
factured by VTS CLIMA. In Table the thermal and physical parameters for mod-
elling the air heater НЕ 36/2 are shown.
Parameters of the electric heater НЕ 36/2
N Parameter name Symbol Numerical value Dimension
1 Electric heater dimensions LCH 4,0138,0 m
2 Heating element material density ρE 7900 kg/m3
3 Heating element material heat capacity сE 460 J/(kg оС)
4 Heating element material mass МE 0,6 kg
5 Air flow through the electric heater GA 0,43 kg/s
6 Dry air density 1,2 kg/m3
7 Air heat capacity сA 1010 J/(kg оС)
8 Air mass in the heater МA 0,182 kg
9 Heat exchange area between heating
elements and air F0 0,306 m2
10 Heat transfer coefficient between
heating elements and air α0 161 W/(m2оС)
11 Input air temperature θA0 11 оС
12 Output air temperature θA 15 оС
13 Input air moisture content dA0 9 g/kg
14 Output air moisture content dA 9 g/kg
15 Heater power NE 3300 W
N. Pankratova, I. Golinko
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 14
The elements for the matrices A and B of the electric heater model (9) were
calculated according to the dependencies (10) in the MatLab environment using
the program module:
H=0.38; C=1; L=0.4;
A0=161; F0=0.306; Ga=0.43; w=1.2;
Ma=0.182; ca=1010; Me=0.6; ce=460;
TetA0=11; TetA=15; dA0=9; dA=9;
Ke=A0*F0; Te=ce*Me/Ke; k0=1/Ke; k1=1;
Ka=ca*Ga+A0*F0; Ta=ca*Ma/Ka; k2=A0*F0/Ka; k3=1-k2;
k4=ca*(TetA0-TetA)/Ka;k=1-k1*k2;
Td=w*H*L*C/Ga; k5=1; k6=(dA0-dA)/Ga;
A=[-1/Ta,0,k2/Ta;0,-1/Td,0;k1/Te,0,-1/Te];
B=[k3/Ta,0,k4/Ta,0;0,k5/Td,k6/Td,0;0,0,0,k0/Te];
According to the calculations, the following numerical values were obtained
for the matrices:
178,00179,0
0357,20
268,00631,2
A ;
0036,0
0
0
0
0
98,21
0
358,2
0
0
0
362,2
B .
The dynamic mode simulation for the HE 36/2 electric heater was carried
out in the Simulink MatLab environment using the State Space function block.
Fig. 2, a–c show the research results for transient processes in the electric heater
for the perturbation channels, and Fig. 2, d – shows such results for the control
channel.
From the conducted research, it can be concluded that a change in the inlet
temperature 0A does not affect the air moisture content at the electric heater
outlet Ad (Fig. 2, a). A change in the air moisture content at the inlet 0Ad
does not affect the outlet temperature (Fig. 2, b). A change in the steam-air mix-
ture flow rate 0AG affects the heated air temperature A (Fig. 2, c). Control
actions EN do not affect the heated air moisture content Ad (Fig. 2, d). The
considered effect of heating the steam-air mixture on air heaters is recommended
to be used in the artificial microclimate control systems development. The air
moisture content use as a control variable (relative humidity instead) can signifi-
cantly reduce the mutual influences of the temperature and humidity control loops
in the air conditioner and improve the control system dynamic properties.
The resulting transients are aperiodic without delay. The control channel in-
ertia is greater than the disturbance channels inertia. This dynamic is explained by
the small heater airspace volume VA=0,152 m3 with a relatively large flow rate of
heated air GA=0,43 kg/s. For this reason, if necessary, it is recommended to calcu-
late the relative humidity at the output of the electric heater according to depend-
ence (23). The transient processes inertia in the electric heater is comparable to
the temperature sensor inertia, therefore, the dynamic sensor properties must be
taken into account when developing a control system. From practical recommen-
dations in control systems with electric heaters, it is sufficient to use control
PI-law. Using the more complex control law is not justified for these devices.
Electric heater mathematical model for cyber-physical systems
Системні дослідження та інформаційні технології, 2021, № 2 15
CONCLUSIONS
The article proposes a mathematical description of heating the steam-air mixture
by an electric heater. The mathematical model is obtained in the equivalent de-
pendencies form: the system of differential equations (8); in the state space (9); in
the Laplace domain (16). The mathematical model can be used as a digital twin
for a digital controller with a reference model. In addition, the proposed model is
recommended to be used for the synthesis and analysis of control systems for bal-
anced ventilation systems or industrial artificial microclimate systems. The math-
ematical description makes it possible to obtain the air heater dynamic character-
istics for the main channels of control and disturbance. An example for the
transient processes simulation for an electric heater HE 36/2 is given.
The choice of a mathematical model (8), (9) or (16) is determined by the ap-
proach to designing a cyber-physical system. The model in the state space (9) has
a number of advantages over the notation in the transfer functions form (16). For
example, it allows to describe the internal model structures using a minimum
number of parameters. An additional argument in favor of vector models is a
large number of software packages for the computer analysis of technical systems
in the state space, which allow complex mathematical research to be carried out
with little time.
dA
E
A
X
t,s
dA
A, E
t,s
X
dA
E
t,s
X
A,
dA
E
t,s
X
A,
a b
c d
Fig. 2. Transient processes modelling in the heater HE 36/2 for the action main
channels: а — X 0A , 10 A
оС; b — X 0Ad , 10 Ad g/kg; c —
X 0AG , 1,00 AG kg/s; d — X EN , 1000 EN W
N. Pankratova, I. Golinko
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 16
A separate direction in the technical systems modeling is the identification of
dynamic model coefficients and the resulting model adequacy assessment. The
electric heater model coefficients were calculated according to the parameters
given in Table. Thermal and physical parameters for the considered model are
determined with a high accuracy from reference books, except for the heat trans-
fer coefficient 0 . This coefficient depends on many factors [16]. Therefore, the
heat transfer coefficient should be attributed to the proposed model parametric
uncertainty, which affects almost all elements in matrices A and B of model (9).
The heat transfer coefficient can be determined with a high accuracy based on
experimental studies. Thus, there is a need for the proposed model parametric ad-
aptation to the specific conditions of air preparation on the experiment basis. This
research will be the topic for the next publication, where the model coefficients
will be identified based on an active experiment using computer technology.
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Received 01.05.2021
Electric heater mathematical model for cyber-physical systems
Системні дослідження та інформаційні технології, 2021, № 2 17
INFORMATION ON THE ARTICLE
Nataliya D. Pankratova, ORCID: 0000-0002-6372-5813, Educational and Scientific
Complex “Institute for Applied System Analysis” of the National Technical
University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail:
natalidmp@gmail.com
Igor M. Golinko, ORCID: 0000-0002-7640-4760, National Technical University
of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail: conis@ukr.net
МАТЕМАТИЧНА МОДЕЛЬ ЕЛЕКТРИЧНОГО КАЛОРИФЕРА ДЛЯ
КІБЕРФІЗИЧНИХ СИСТЕМ / Н.Д. Панкратова, І.М. Голінко
Анотація. Розглянуто динамічну модель тепло- і масообміну для електричного
калорифера із зосередженими параметрами, яка дозволяє проводити імітаційне
моделювання перехідних процесів за основними каналами впливу. Запропоно-
вану модель рекомендується використовувати в кіберфізичних системах для
прогнозування та оцінювання ефективності систем управління, інтегрованих в
єдину інформаційну систему управління. Розроблену модель можуть викорис-
товувати фахівці для аналізу та синтезу систем управління припливно-
витяжної вентиляції або промислових кондиціонерів. Як приклад виконано чи-
слове моделювання перехідних процесів за основними каналами впливу для
електрокалорифера HE 36/2 виробництва VTS CLIMA. Суттєвою перевагою
запропонованої моделі є можливість використання її для синтезу та аналізу ба-
гатовимірних систем управління.
Ключові слова: кіберфізична система, цифровий двійник, математична мо-
дель, простір станів, електричний калорифер.
МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ЭЛЕКТРИЧЕСКОГО КАЛОРИФЕРА ДЛЯ
КИБЕРФИЗИЧЕСКИХ СИСТЕМ / Н.Д. Панкратова, И.М. Голинко
Аннотация. Рассмотрена динамическая модель тепломассообмена для элек-
трического калорифера с сосредоточенными параметрами, которая позволяет
проводить имитационное моделирование переходных процессов по основным
каналам воздействия. Предложенную модель рекомендуется использовать в
киберфизических системах для прогнозирования и оценки эффективности сис-
тем регулирования, которые интегрированы в единую информационную сис-
тему управления. Разработанную модель могут использовать специалисты для
анализа и синтеза систем регулирования приточно-вытяжной вентиляции или
промышленных кондиционеров. В качестве примера проведено численное мо-
делирование переходных процессов по основным каналам воздействия для
электрического калорифера НЕ 36/2 производства фирмы VTS CLIMA. Суще-
ственным преимуществом предложенной модели является возможность ее ис-
пользования для синтеза и анализа многомерных систем управления.
Ключевые слова: киберфизическая система, цифровой двойник, математиче-
ская модель, пространство состояний, электрический калорифер.
|
| id | journaliasakpiua-article-239826 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:27:23Z |
| publishDate | 2021 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/17/fde07c53ff4c30b05b49be4771f5c217.pdf |
| spelling | journaliasakpiua-article-2398262021-09-16T11:48:22Z Electric heater mathematical model for cyber-physical systems Математическая модель электрического калорифера для киберфизических систем Математична модель електричного калорифера для кіберфізичних систем Pankratova, Nataliya Golinko, Igor киберфизическая система цифровой двойник математическая модель пространство состояний электрический калорифер cyber-physical system digital twin mathematical model state space electric heater кіберфізична система цифровий двійник математична модель простір станів електричний калорифер The article discusses the heat and mass transfer dynamic model for an electric heater with lumped parameters, which allows transient processes simulation for the main influences. The proposed model is recommended to be used in cyber-physical systems for forecasting and evaluating the effectiveness of control systems integrated into a single information management system. The developed model can be used by specialists for the analysis and synthesis of control systems for balanced ventilation systems or industrial air conditioners. As an example, a numerical simulation of transient processes along the action main channels for an electric heater HE 36/2 manufactured by VTS CLIMA was carried out. The significant advantage of the proposed model is the possibility for using it for the synthesis and analysis of multidimensional control systems. Рассмотрена динамическая модель тепломассообмена для электрического калорифера с сосредоточенными параметрами, которая позволяет проводить имитационное моделирование переходных процессов по основным каналам воздействия. Предложенную модель рекомендуется использовать в киберфизических системах для прогнозирования и оценки эффективности систем регулирования, которые интегрированы в единую информационную систему управления. Разработанную модель могут использовать специалисты для анализа и синтеза систем регулирования приточно-вытяжной вентиляции или промышленных кондиционеров. В качестве примера проведено численное моделирование переходных процессов по основным каналам воздействия для электрического калорифера НЕ 36/2 производства фирмы VTS CLIMA. Существенным преимуществом предложенной модели является возможность ее использования для синтеза и анализа многомерных систем управления. Розглянуто динамічну модель тепло- і масообміну для електричного калорифера із зосередженими параметрами, яка дозволяє проводити імітаційне моделювання перехідних процесів за основними каналами впливу. Запропоновану модель рекомендується використовувати в кіберфізичних системах для прогнозування та оцінювання ефективності систем управління, інтегрованих в єдину інформаційну систему управління. Розроблену модель можуть використовувати фахівці для аналізу та синтезу систем управління припливно-витяжної вентиляції або промислових кондиціонерів. Як приклад виконано числове моделювання перехідних процесів за основними каналами впливу для електрокалорифера HE 36/2 виробництва VTS CLIMA. Суттєвою перевагою запропонованої моделі є можливість використання її для синтезу та аналізу багатовимірних систем управління. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2021-09-14 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/239826 10.20535/SRIT.2308-8893.2021.2.01 System research and information technologies; No. 2 (2021); 7-17 Системные исследования и информационные технологии; № 2 (2021); 7-17 Системні дослідження та інформаційні технології; № 2 (2021); 7-17 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/239826/238229 |
| spellingShingle | кіберфізична система цифровий двійник математична модель простір станів електричний калорифер Pankratova, Nataliya Golinko, Igor Математична модель електричного калорифера для кіберфізичних систем |
| title | Математична модель електричного калорифера для кіберфізичних систем |
| title_alt | Electric heater mathematical model for cyber-physical systems Математическая модель электрического калорифера для киберфизических систем |
| title_full | Математична модель електричного калорифера для кіберфізичних систем |
| title_fullStr | Математична модель електричного калорифера для кіберфізичних систем |
| title_full_unstemmed | Математична модель електричного калорифера для кіберфізичних систем |
| title_short | Математична модель електричного калорифера для кіберфізичних систем |
| title_sort | математична модель електричного калорифера для кіберфізичних систем |
| topic | кіберфізична система цифровий двійник математична модель простір станів електричний калорифер |
| topic_facet | киберфизическая система цифровой двойник математическая модель пространство состояний электрический калорифер cyber-physical system digital twin mathematical model state space electric heater кіберфізична система цифровий двійник математична модель простір станів електричний калорифер |
| url | https://journal.iasa.kpi.ua/article/view/239826 |
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