The method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm
Problem. Most research on the design of nonlinear electromechanical tracking systems has been conducted using typical proportional-differential controllers, but there is no methodology for designing nonlinear electromechanical tracking system based on neural network controller to meet different requ...
Saved in:
| Date: | 2026 |
|---|---|
| Main Authors: | , , , , , |
| Format: | Article |
| Language: | English |
| Published: |
National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine
2026
|
| Subjects: | |
| Online Access: | https://eie.khpi.edu.ua/article/view/366076 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Electrical Engineering & Electromechanics |
| Download file: |  |
Institution
Electrical Engineering & Electromechanics| _version_ | 1869562804910948352 |
|---|---|
| author | Kuznetsov, B. I. Nikitina, T. B. Bovdui, I. V. Voloshko, O. V. Kolomiets, V. V. Kobylianskyi, B. B. |
| author_facet | Kuznetsov, B. I. Nikitina, T. B. Bovdui, I. V. Voloshko, O. V. Kolomiets, V. V. Kobylianskyi, B. B. |
| author_institution_txt_mv | [
{
"author": "B. I. Kuznetsov",
"institution": "Anatolii Pidhornyi Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine"
},
{
"author": "T. B. Nikitina",
"institution": "Bakhmut Education Research and Professional Pedagogical Institute V.N. Karazin Kharkiv National University"
},
{
"author": "I. V. Bovdui",
"institution": "Anatolii Pidhornyi Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine"
},
{
"author": "O. V. Voloshko",
"institution": "Anatolii Pidhornyi Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine"
},
{
"author": "V. V. Kolomiets",
"institution": "Bakhmut Education Research and Professional Pedagogical Institute V.N. Karazin Kharkiv National University"
},
{
"author": "B. B. Kobylianskyi",
"institution": "Bakhmut Education Research and Professional Pedagogical Institute V.N. Karazin Kharkiv National University"
}
] |
| author_sort | Kuznetsov, B. I. |
| baseUrl_str | http://eie.khpi.edu.ua/oai |
| collection | OJS |
| datestamp_date | 2026-07-01T21:42:56Z |
| description | Problem. Most research on the design of nonlinear electromechanical tracking systems has been conducted using typical proportional-differential controllers, but there is no methodology for designing nonlinear electromechanical tracking system based on neural network controller to meet different requirements that are imposed on the operation of the system in different modes. Goal. To develop the method of multi objective design of nonlinear electromechanical tracking system based on neural network controller to satisfy different requirements that are imposed on the operation of the system in various modes. Methodology. The designed nonlinear electromechanical tracking system based on neural network controller implements the dynamics of a reference model by training a neural network controller for a given model of a nonlinear control object. Multi objective design of the reference model reduces to solving a vector nonlinear programming problem, in which the components of the vector objective function are direct different requirements that are imposed on the operation of the system in various modes. The solution to the vector nonlinear programming problem is calculated using a hybrid heuristic optimization algorithm, incorporating particle swarm optimization and stochastic sequential quadratic programming. Results. The results multi objective design of two-mass nonlinear electromechanical tracking systems based on neural network controller in which different requirements that are imposed on the operation of the system in various modes were satisfied are given. Based on the results of modeling and experimental studies it is established, that with the help of synthesized neural network controllers, it is possible to improve of quality indicators of two-mass nonlinear electromechanical tracking system in comparison with the system with standard regulators. Scientific novelty. For the first time the method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller to satisfy different requirements that are imposed on the operation of the system in various modes is developed. Practical value. From the point of view of the practical implementation the possibility of solving the problem of multi objective design of nonlinear electromechanical tracking systems based on neural network controller to satisfy different requirements that are imposed on the operation of the system in various modes is shown. References 43, figures 8. |
| doi_str_mv | 10.20998/2074-272X.2026.4.03 |
| first_indexed | 2026-07-02T01:00:29Z |
| format | Article |
| fulltext |
Electrical Engineering & Electromechanics, 2026, no. 4 17
© B.I. Kuznetsov, T.B. Nikitina, I.V. Bovdui, O.V. Voloshko, V.V. Kolomiets, B.B. Kobylianskyi
UDC 621.3.013 https://doi.org/10.20998/2074-272X.2026.4.03
B.I. Kuznetsov, T.B. Nikitina, I.V. Bovdui, O.V. Voloshko, V.V. Kolomiets, B.B. Kobylianskyi
The method of multi objective design of nonlinear electromechanical tracking systems based
on neural network controller using hybrid metaheuristic optimization algorithm
Problem. Most research on the design of nonlinear electromechanical tracking systems has been conducted using typical proportional-
differential controllers, but there is no methodology for designing nonlinear electromechanical tracking system based on neural network
controller to meet different requirements that are imposed on the operation of the system in different modes. Goal. To develop the method
of multi objective design of nonlinear electromechanical tracking system based on neural network controller to satisfy different
requirements that are imposed on the operation of the system in various modes. Methodology. The designed nonlinear electromechanical
tracking system based on neural network controller implements the dynamics of a reference model by training a neural network controller
for a given model of a nonlinear control object. Multi objective design of the reference model reduces to solving a vector nonlinear
programming problem, in which the components of the vector objective function are direct different requirements that are imposed on the
operation of the system in various modes. The solution to the vector nonlinear programming problem is calculated using a hybrid heuristic
optimization algorithm, incorporating particle swarm optimization and stochastic sequential quadratic programming. Results. The results
multi objective design of two-mass nonlinear electromechanical tracking systems based on neural network controller in which different
requirements that are imposed on the operation of the system in various modes were satisfied are given. Based on the results of modeling
and experimental studies it is established, that with the help of synthesized neural network controllers, it is possible to improve of quality
indicators of two-mass nonlinear electromechanical tracking system in comparison with the system with standard regulators. Scientific
novelty. For the first time the method of multi objective design of nonlinear electromechanical tracking systems based on neural network
controller to satisfy different requirements that are imposed on the operation of the system in various modes is developed. Practical value.
From the point of view of the practical implementation the possibility of solving the problem of multi objective design of nonlinear
electromechanical tracking systems based on neural network controller to satisfy different requirements that are imposed on the operation
of the system in various modes is shown. References 43, figures 8.
Key words: nonlinear electromechanical tracking system, neural network controller, multi objective design, computer
simulation, experimental research.
Проблема. Більшість досліджень по проєктуванню нелінійних електромеханічних систем стеження виконані на основі
використання типових пропорційно диференційних регуляторів, але відсутня методологія проєктування нелінійних
електромеханічних систем стеження на основі нейромережевого контролеру для задоволення різноманітних вимог, які
пред’являються до роботи системи у різних режимах. Метою роботи є розробка методу багатокритеріального проєктування
нелінійних електромеханічних систем стеження на основі нейромережевого контролеру для задоволення різноманітних вимог,
які пред’являються до роботи системи у різних режимах. Методологія. У спроєктованих нелінійних електромеханічних систем
стеження на основі нейромережевого контролеру реалізується динаміка еталонної моделі в результаті навчання
нейромережевого контролеру для заданої моделі нелінійного об’єкта управління. Багатокритеріальне проєктування еталонної
моделі зводиться до вирішення проблеми векторного нелінійного програмування, в якій компонентами цільової векторної функції
є різноманітні вимоги, які пред’являються до роботи системи у різних режимах. Вирішення проблеми векторного нелінійного
програмування обчислюється за допомогою гібридного евристичного алгоритму оптимізації, що включає оптимізацію роєм
частинок і послідовне стохастичне квадратичне програмування. Результати. Наведено результати багатокритеріального
проєктування двомасової нелінійної електромеханічної системи стеження на основі нейромережевого контролеру, в якій були
задоволені різноманітні вимоги, які пред’являються до роботи системи у різних режимах. На основі результатів моделювання
та експериментальних досліджень встановлено, що за допомогою синтезованих нейромережевих контролерів можна підвищити
якісні показники двомасової нелінійної електромеханічної системи стеження у порівнянні із системою зі стандартними
регуляторами. Наукова новизна. Вперше розроблено метод багатокритеріального проєктування нелінійних електромеханічних
систем стеження на основі нейромережевого контролеру для задоволення різноманітних вимог, які пред’являються до роботи
системи у різних режимах. Практична значимість. З точки зору практичної реалізації показана можливість вирішення задачі
багатокритеріального проєктування нелінійних електромеханічних систем стеження на основі нейромережевого контролеру
для задоволення різноманітних вимог, які пред’являються до роботи системи у різних режимах. Бібл. 43, рис. 8.
Ключові слова: нелінійна електромеханічна система стеження, нейромережевий контролер, багатоцільове
проєктування, комп’ютерне моделювання, експериментальні дослідження.
Introduction. Most existing electromechanical
tracking systems are based on DC motors due to their low
cost and ease of design and setup [1, 2]. Furthermore,
brushless DC motors are also becoming widespread in
modern electromechanical tracking systems [3]. Despite the
need for a valve commutator for the windings of a
brushless DC motor, the subsequent control algorithms are
equivalent to those of a brushed DC motor. Due to the
rapid development of converter technology, modern
electromechanical tracking systems are also designed on
the basis of AC motors – synchronous or asynchronous –
due to their higher reliability despite their higher cost [4, 5].
Electromechanical tracking systems are often
installed on a moving base, which imposes additional
requirements for compensating for disturbances when the
moving base moves over rough terrain. The use of
permanent magnet synchronous motors for such systems
instead of traditional hydraulic motors, together with
modern control systems instead of standard regulators,
allows for a more than tenfold increase in the control
accuracy of such electromechanical tracking systems.
Electromechanical tracking systems have different
accuracy requirements for various operating modes.
Therefore, the design of electromechanical tracking
systems is a multi objective problem [6–8].
The potential accuracy of electromechanical tracking
systems is often limited by the presence of nonlinear friction
characteristics on the drive motor and working mechanism
shafts, as well as elastic elements between the drive motor
and working mechanism shafts, which lead to uneven
movement up to the so-called «stick-slip» solution when
moving at low speeds. Therefore, existing electromechanical
tracking systems use standard proportional-differential
controllers, which limits the potential accuracy of such
18 Electrical Engineering & Electromechanics, 2026, no. 4
systems. Often, it is the operating accuracy of systems in
these modes that determines their potential accuracy of
electromechanical tracking systems.
When driving at high speeds and with high
acceleration, the dynamic characteristics of
electromechanical tracking systems are limited by the
maximum voltage of the on-board network and the
maximum torque of the actuator motor [9, 10].
In addition, the parameters of electromechanical
tracking systems, firstly, are not known precisely and,
secondly, can change significantly during operation,
therefore the designed electromechanical tracking system
must be robust [11, 12].
The presence of complex nonlinear dependencies,
uncontrolled disturbances and interference, uncertainties
in parameters, and possibly the structure, models of the
control object and external disturbances in
electromechanical tracking systems complicates the
implementation of traditional control strategies, since
both modern, in particular the theory of adaptive and
optimal control, and classical control theory are largely
based on the idea of linearization of systems.
Currently, neural networks controllers based on
artificial neural networks (ANN) are widely used to
control various objects, which make it possible to
effectively control complex nonlinear objects under
conditions of uncertainty. Most research on the design of
nonlinear electromechanical tracking systems has been
conducted using typical proportional-differential
controllers, but there is no methodology for designing
neural network control by nonlinear electromechanical
tracking system to meet different operating requirements
in different modes.
The goal of the work is to develop the method for
multi objective design of nonlinear electromechanical
tracking systems based on neural network controller to
satisfy different requirements that are imposed on the
operation of the system in various modes. This goal
proposed to achieve based on hybrid metaheuristic
optimization algorithm.
Problem statement. Recently, ANN has become a
very promising alternative to classical methods of
constructing control systems for nonlinear objects. Neural
network control technologies allow us to overcome many of
the challenges that arise when working with nonlinear
objects or objects of unknown structure and that are
intractable using conventional adaptive control methods.
The ability of ANN to implement complex nonlinear control
laws is due to the use of sigmoid activation functions or
other nonlinear functions for neurons in hidden layers.
The ability of ANN to self-learn allows the use of
neural controllers even in conditions of significant
uncertainties, while for the implementation of traditional
adaptive control methods, a necessary condition is the
presence of a large amount of a priori information about
the control object. The high performance and reliability of
neural controllers is due to the high degree of parallelism
of ANNs. The ease of implementation of neural networks
on modern computing hardware and their ability to learn
make them particularly attractive for controlling complex
nonlinear systems in real time.
The diagram of the neural network system with a
reference model is shown in Fig. 1.
Model
error
Plant model
neural network
Reference
model
Controller
neural network
PLANT
Control
error
Reference
Plant
output Control
Fig. 1. Diagram of the control system with a reference model
Let us consider a mathematical model of a nonlinear
control object of an electromechanical tracking system in the
form of a state space adopted in classical control theory
kkkk φuzΨz ,,1 , (1)
kkkk φuzFy ,, , (2)
where Tk kzkzkzk
z
,...,, 21z is the system state
vector; Tk kukukuk
u
,...,, 21u is the vector of
input signals Tk kykykyk
y
,...,, 21y is the vector
of output; Ψ[ꞏ], F[ꞏ] are some static nonlinear functions;
φ(k), ϕ(k) are the process noise and measurement noise,
respectively.
Model (1), (2) takes into account the presence of
nonlinear friction characteristics on the shafts of the drive
motor and the working mechanism, as well as elastic
elements between the shafts of the drive motor and the
working mechanism.
Process noise also includes uncertainties in the
control object model and external influences.
Let us write a mathematical model of a nonlinear
control object of an electromechanical tracking system
(1), (2) in the form of a Nonlinear Autoregressive-Moving
Average (NARMA) – model
ke
nkekenku
kunkyky
fky
eu
y
,...,1,
,...,1,,...,1
, (3)
where 1 MRky is the output signal of the object;
1 NRku is the input signal of the object;
1 MRke is the measurement error; f [ꞏ] is the
nonlinear transformation function:
11
: MMkNkMk euyf RR ,
where ny, nu, ne are the orders of magnitude of the delay in
the output and input signals of the object and the
measurement error, respectively.
Representations of objects as NARMA models play
a fundamental role in the study of nonlinear objects using
ANN. It is important to consider a generalization of
model (3) that takes into account various types of
nonlinearities in input and output variables.
The NARMA neural network controller uses a
NARMA model of the controlled object. When
synthesizing the controller in question, a discrete
nonlinear model of the nonlinear controlled object is
constructed as NARMA model in the form
1,...,1,
,1,...,1,
mkukuku
nkykyky
Ndky , (4)
where y(k) is the model output; d is the number of
prediction cycles; u(k) is the model input.
Electrical Engineering & Electromechanics, 2026, no. 4 19
At the identification stage, a neural network is
constructed for the NARMA model. This procedure is
similar to the identification procedure described above
with a predictive controller.
If it is necessary to design a tracking system that
ensures movement along a given trajectory
dkydky r . (5)
Then the controller calculates the control in the
following form:
1,...,1
,1,...,1,
1,...,1
,1,...,1,
1
mkuku
nkykyky
g
mkuku
nkykyky
fdky
ku
r
. (6)
After the network is created, it is trained using the
trainlm function, which corresponds to the Levenberg-
Marquardt algorithm. Currently, genetic algorithms and
hybrid heuristic algorithms are widely used to train neural
networks, which allow finding a global optimum.
Multi objective design of reference model. When
operating electromechanical tracking systems, the following
accuracy requirements are typically imposed in various
modes. The range of control objects angles with a stepwise
input. The time it takes to process the specified control object
angles with a stepwise input.
This time typically characterizes the system’s response
time when transferring the control object’s position and
when compensating for large errors during initial
positioning. Limitations on reducing this time are the energy
limitations of the drive motor’s rotation speed and torque.
The minimum rate of increase and decrease of the
controlled object’s angles with a linearly varying input signal
is. Typically, limitations are set on the roughness of the
working element’s motion at low guidance speeds. The main
limitations here are the nonlinear friction characteristics on
the drive motor and working mechanism shafts. These
limitations often determine the potential accuracy of the
electromechanical tracking system.
Error in processing harmonic changes in the set angles
of the controlled object and set frequencies [13, 14]. These
requirements are typically based on the accuracy of
compensation for disturbances acting on the
electromechanical tracking system mounted on a moving
base as it moves over rough terrain [15, 16]. All these
requirements must be satisfied using a single neural network
controller. Naturally, it is necessary to take into account the
uncertainties in the controlled object [17–19]. The neural
network controller implements the system’s dynamics.
Let’s consider a nonlinear electromechanical tracking
systems based on neural network controller with a
reference model shown in Fig. 1. Using an object’s neural
controller, the system dynamics defined by the reference
model are implemented for a given model of the control
object [20–22]. Naturally, the reference model is defined as
an NARMA system [23–25]. To train the NARMA model
with a reference model, it is first necessary to design a
reference model in NARMA model form.
We introduce the vector χ of the reference model’s
parameter in the state space form (1), (2) adopted in
classical control theory [26, 27]. Then, for a given value
of the desired vector χ of the reference model’s
parameters, the performance indicators that are imposed
on the electromechanical tracking system in various
operating modes can be calculated. We introduce the
vector objective function
TmFFF χχχχF ..., 21 , (7)
in which the components of the vector target function Fi()
are direct quality indicators that are presented to the system
in various modes of its operation such as the time of the
first matching, the time of regulation, overshooting, etc. To
calculate the vectors objective function (7), the initial
nonlinear electromechanical tracking system (1), (2) based
on neural network controller (6) is modeled in various
modes of operation, with different input signals [28–30].
Then, the process of training the reference model
(1), (2) in the NARMA model form (6) is reduced to
minimizing the vector objective function (7) with respect
to the desired vector X of reference model parameters.
Hybrid heuristic optimization algorithm. This
multi objective nonlinear programming problem (7) is
solved on the basis on hybrid heuristic optimization
algorithm, which includes multi-swarm stochastic multi-
agent optimization algorithms and stochastic sequential
quadratic programming optimization algorithms [31–33].
For this purpose minimum for multi objective
nonlinear programming problem (7) desired parameters
vector X calculated by multi-swarm stochastic particle
swarm optimization algorithm in following procedure
[34–36]. Particle i swarm j movement described by
11 tvtxtx ijijij , (8)
where
,
1
*
2222
1111
txty
tpHtrctxty
tpHtrctvwtv
ijj
jjjjijij
jjjjijjij
(9)
where xij(t), νij(t) are position and velocity vectors
components of the particle i of the swarm j for multi
objective nonlinear programming problem (7) minimum
for desired parameters vector χ calculated.
This optimization algorithm (8), (9) works
effectively at initial stages of iterations, when movement
speeds have significant values. When entering quasi-
stationary range of multi objective nonlinear
programming problem (7) motion speeds tend to zero. To
speed up global optima calculating process in stationary
range, it is advisable second-order methods used based on
second derivatives. One of simplest and quite effective
second-order optimization methods is sequential quadratic
programming algorithm. The of the initial parameters
values of desired parameters vector χ obtained with
optimization algorithm (8), (9) help are initial values for
refining solutions in quasi-stationary range.
To calculate multi objective nonlinear programming
problem (7) minimum for desired parameters vector χ by
stochastic sequential quadratic programming optimization
algorithms formulated minimization problem with
quadratic objective function [37–39]
).()(
)())(()(
2
1
))((
tt
tttt
ijx
T
ijx
ijxijijx
T
ijxijr
dJ
dXHdXH
(10)
Jacobian matrices Jijx(t) and Hessian matrices Hijx(t)
components along vector X calculated from particle i of
20 Electrical Engineering & Electromechanics, 2026, no. 4
swarm j movement velocities νij(t) and accelerations
aijx(t), which calculated based on velocities νij(t)
tvtvta ijijijx 11 .
During stochastic sequential quadratic programming
optimization algorithms process (10) step size dijx(t)
calculated, which used to calculated multi objective
nonlinear programming problem (7) minimum by desired
parameters vector X
)(1 tdttxtx ijxijxijij .
Simulation results. Let us now consider the dynamic
characteristics of the nonlinear electromechanical tracking
system with the designed neural network controller. The
design of neural network controller is implemented in the
Neural Network Toolbox application package of the
MATLAB system.
The parameters adopted for neural network controller
design for nonlinear electromechanical tracking system are:
rated voltage of the drive motor Un=27 V rated motor
current; In=31 A; armature winding resistance of the motor
Ra=75 m; motor design factor cf=0.062; moment of inertia
of the motor rotor Jr=27ꞏ10–5 kgꞏm2; electromagnetic time
constant of the armature chain Т=4.5ꞏ10–3; power amplifier
transmission coefficient k=27; gear ratio of the kinematic
coupling device N=377; dry friction moments in the motor
bearings Мb=0.15 Nꞏm; frictional torque on the working
mechanism shaft Мs=200 Nꞏm; load moment of inertia
Jm=250 kgꞏm2; transmission element stiffness coefficient
с=3ꞏ105 Nꞏm; gap between the teeth of the drive and driven
gears σ=1,5.
One of the most demanding operating modes of the
system is the mode of processing specified rotation angles
of the actuator with a stepwise input signal. This mode
largely determines the speed of processing the reference
values and compensating for disturbances. Figure 2 shows
the implementations of the state variables of the nonlinear
electromechanical tracking systems based on neural
network controller in this operating mode.
Figure 2 shows the following state variables: a) plant
rotation angle φ(t); b) plant rotation speed ωp(t); c) elastic
moment Мe(t); d) motor speed ωm(t); e) motor current Im(t);
f) voltage on the motor circuit Um(t). As can be seen from
these figures, the main limitation is the on-board network
voltage, which changes practically in a relay manner from
the minimum to the maximum value. Note that this operating
mode approximately corresponds to a maximum-speed
controller, which approximately implements the minimum
transient process time. Thus, the use of a neural network
controller allows for a more than 2-fold reduction in the
system’s transition time in this operating mode of the
nonlinear electromechanical tracking system.
Another stressful operating mode is the low-speed
guidance mode. In this mode, friction nonlinearities on the
actuator and working mechanism shafts are most
pronounced, resulting in uneven movement of the working
element in the «stick-slip» mode. Technical requirements for
electromechanical tracking systems in this mode typically
impose restrictions on the unevenness of the working
element’s motion at low, creeping speeds. Figure 3 shows
the implementation of the state variables of an
electromechanical tracking system in this operating mode.
Figure 3 shows the same state variables as in Fig. 2.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.01
0.02
0.03
0.04
0.05
0.06
φ, rad
t, s
a
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7 p, s
–1
t, s
b
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-10
-5
0
5
10 Me, Nm
t, s
c
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-150
-100
-50
0
50
100
150
200
250
t, s
d
m, s–1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-150
-100
-50
0
50
100
150
t, s
e
Im, A
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-30
-20
-10
0
10
20
30
t, s
f
Um, V
Fig. 2. Transition process when working out angle
As can be seen from these figures, the movement of the
working element is accompanied by oscillations at a
frequency of approximately 6 Hz and stops. Note that for
many electromechanical tracking systems, the requirement
for uneven movement of the working element at low,
creeping speeds determines the potential accuracy of the
electromechanical tracking system in one of its most critical
Electrical Engineering & Electromechanics, 2026, no. 4 21
operating modes. One of the system’s stressful operating
modes is high-speed movement. This mode determines the
system’s response time when firing behind fast-moving
targets and also defines the system’s key technical
characteristics in this mode.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-2
0
2
4
6
8
10
12
x 10
-3
φ, rad
t, s
a
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
p, s
–1
t, s
b
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-10
-8
-6
-4
-2
0
2
4
6
8
Me, Nm
t, s
c
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-150
-100
-50
0
50
100
150
t, s
d
m, s–1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-80
-60
-40
-20
0
20
40
60
80
100
t, s
e
Im, A
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-30
-20
-10
0
10
20
30
t, s
f
Um, V
Fig. 3. Transition process during guidance at low speeds
Figure 4 shows the implementation of the state
variables of an electromechanical tracking system in this
operating mode. Figure 4 shows the same state variables as
in Fig. 2. As can be seen from Fig. 4,a, the system exhibits a
steady-state velocity error. As can be seen from Fig. 4,b,
even when moving at high speed, the system exhibits «stick-
slip» sections where the velocity becomes zero, resulting in
uneven motion of the controlled object. In this case, the
control voltage, as can be seen from Fig. 4,f changes
practically according to the relay law from the minimum to
the maximum voltage of the motor.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.02
0.04
0.06
0.08
0.1
0.12
φ, rad
t, s
a
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
p, s
–1
t, s
b
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-6
-4
-2
0
2
4
6
8
Me, Nm
t, s
c
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-100
-50
0
50
100
150
t, s
d
m, s–1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-80
-60
-40
-20
0
20
40
60
80
t, s
e
Im, A
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-30
-20
-10
0
10
20
30
t, s
f
Um, V
Fig. 4. Transition process during guidance at high speeds
22 Electrical Engineering & Electromechanics, 2026, no. 4
In conclusion, we note that similar results can be
obtained with vector control of permanent magnet
synchronous motor [40] or induction motor [41–43].
Experimental research. To conduct experimental
studies of the effectiveness of the designed neural network
controller a laboratory setup for a two-mass
electromechanical tracking system was developed, the
schematic of which is shown in Fig. 5.
Fig. 5. Laboratory setup for a two-mass electromechanical
tracking system
The setup consists of two motors M1 and M2, the
shafts of which are connected by an elastic coupling. The
diagram shows the power amplifiers PA1 and PA2 and
motor position sensors PS1 and PS2. Figure 6 shows the
appearance of the laboratory setup.
Fig. 6. The appearance of the laboratory setup
Let’s consider experimental transient processes in
the mode of working element rotation angle testing. In
this operating mode, the limitations on state and control
variables are most pronounced. Figure 7 shows the
realizations of the state variables of the electromechanical
servo system in this operating mode.
The following state variables are shown in Fig. 7:
a) the angle φ2(t) of the second motor; b) the speed ω1(t)
of the first motor; c) the elastic moment Me(t); d) the
voltage U1(t) on the chain of the first motor.
As can be seen in Fig. 7,b, the second motor’s rate
of change transiently reaches a limit. As can be seen in
Fig. 7,c, the first motor’s rate of change transiently
doubles, which is typical for forcing transient processes in
two-mass electromechanical systems.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
φ2, rad
t, s
a
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-1
0
1
2
3
4
5
6
t
φ1, rad
t, s
b
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-2
0
2
4
6
8
10
x 10
-4
Me, Nm
t, s
c
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-4
-2
0
2
4
6
8
10
12
t, s
d
U1, V
Fig. 7. Experimental transient processes during the development
of large rotation angles
Let us now consider the experimental transient
processes in the low-speed mode of the working element.
Figure 8 shows the realizations of the state variables
of the electromechanical servo system in this operating
mode.
Transient processes in the mode of movement of the
working element at low speed: a) the angle φ1(t) of
rotation of the first motor; b) the angle φ2(t) of rotation of
the second motor; c) the speed ω1(t) of the first motor;
d) the speed ω2(t) of the second motor; e) the moment of
elasticity Me(t); f ) the voltage U1(t) on the anchor chain
of the first motor.
The nature of the transient processes in this low-speed
operating mode is largely determined by the presence of
nonlinear friction relationships on the shafts of the drive
motor and the operating element.
0 1 2 3 4 5 6 7
0
0.2
0.4
0.6
0.8
1 φ1, rad
t, s
a
0 1 2 3 4 5 6 7
0
0.5
1
1.5
φ2, rad
t, s
b
Electrical Engineering & Electromechanics, 2026, no. 4 23
0 1 2 3 4 5 6 7
0
0.5
1
1.5
2
2.5
3
t, s
c
1, s
–1
0 1 2 3 4 5 6 7
-1
0
1
2
3
t, s
d
2, s
–1
0 1 2 3 4 5 6 7
-3
-2
-1
0
1
2
3
Me, Nm
t, s
e
0 1 2 3 4 5 6 7
-60
-40
-20
0
20
40
t, s
f
U1, V
Fig. 8. Transient processes in the mode of movement
of the working element at low speed
The transient process of the second motor exhibits
characteristic stops and, naturally, zero speeds at those
points in time when the elastic moment between the shafts
of the drive motor and the operating element does not
exceed the dry friction moment on the shaft of the
operating element.
Conclusions.
1. For the first time the method of multi objective
design of nonlinear electromechanical tracking system
based on neural network controller is developed, which
allows to satisfy different requirements that are imposed
on the operation of the system in various modes.
2. The new solution method of reference model multi
objective design problem for nonlinear electromechanical
tracking system based on neural network controller is
formulated as vector nonlinear programming problem
solution, in which the components of the vector objective
function are different requirements that are imposed on
the operation of the system in various modes.
3. The new solution method of vector nonlinear
programming problem is developed based on hybrid
heuristic optimization algorithm, incorporating particle
swarm optimization and stochastic sequential quadratic
programming, which allows to reduce the computation time.
4. Based on the results of modeling and experimental
studies of designed two-mass nonlinear electromechanical
tracking system based on neural network controller it is
established, that with the help of designed neural network
controller, it is possible to reduce the control error the angle
of rotation of the shaft of the second motor more than 2 times
in comparison with the system with standard regulators.
5. Based on the results of modeling and experimental
studies of designed two-mass nonlinear electromechanical
tracking system based on neural network controller it is
established, that designed control system is robust. When
the moment of inertia of the working mechanism is varied
by a factor of two, either upward or downward, relative to
the average value adopted during the multi-criteria design
of the reference model, the dynamic characteristics of the
designed system with a neural network controller change
only slightly compared to the dynamic characteristics of a
system with standard controllers.
6. It is planned to practically realization of developed
method of multi objective design of nonlinear
electromechanical tracking system based on neural
network controller to satisfy different requirements that
are imposed on the operation of the system in various
modes of real electromechanical tracking system.
Conflict of interest. The authors declare that they
have no conflicts of interest.
REFERENCES
1. Amieur T., Taibi D., Kahla S., Bechouat M., Sedraoui M. Tilt-
fractional order proportional integral derivative control for DC motor
using particle swarm optimization. Electrical Engineering &
Electromechanics, 2023, no. 2, pp. 14-19. doi:
https://doi.org/10.20998/2074-272X.2023.2.03.
2. Nguyen X.C., Le D.T. Adaptive finite-time synergetic control for
flexible-joint robot manipulator with disturbance inputs. Electrical
Engineering & Electromechanics, 2025, no. 3, pp. 45-52. doi:
https://doi.org/10.20998/2074-272X.2025.3.07.
3. Alnaib I.I., Alsammak A.N., Mohammed K.K. Brushless DC motor
drive with optimal fractional-order sliding-mode control based on a
genetic algorithm. Electrical Engineering & Electromechanics, 2025, no.
2, pp. 19-23. doi: https://doi.org/10.20998/2074-272X.2025.2.03.
4. Srinivas G., Durga Sukumar G., Subbarao M. Total harmonic
distortion analysis of inverter fed induction motor drive using neuro fuzzy
type-1 and neuro fuzzy type-2 controllers. Electrical Engineering &
Electromechanics, 2024, no. 1, pp. 10-16. doi:
https://doi.org/10.20998/2074-272X.2024.1.02.
5. Khatir A., Bouchama Z., Benaggoune S., Zerroug N. Indirect
adaptive fuzzy finite time synergetic control for power systems. Electrical
Engineering & Electromechanics, 2023, no. 1, pp. 57-62. doi:
https://doi.org/10.20998/2074-272X.2023.1.08.
6. Liu Z., Reynolds A. Robust Multiobjective Nonlinear Constrained
Optimization with Ensemble Stochastic Gradient Sequential Quadratic
Programming-Filter Algorithm. SPE Journal, 2021, vol. 26, no. 4, pp.
1964-1979. doi: https://doi.org/10.2118/205366-PA.
7. Han H.-G., Chen C., Sun H.-Y., Qiao J.-F. Multiobjective Integrated
Optimal Control for Nonlinear Systems. IEEE Transactions on
Cybernetics, 2023, vol. 53, no. 12, pp. 7712-7722. doi:
https://doi.org/10.1109/TCYB.2022.3204030.
8. Wang Q., et. al. Multi objective optimization and evaluation
approach of prefabricated component combination solutions using
NSGA-II and simulated annealing optimized projection pursuit method.
Scientific Reports, 2024, vol. 14, no. 1, art. no. 16688. doi:
https://doi.org/10.1038/s41598-024-65319-3.
9. He R., Hao J., Zhou H., Chen F. Multi-Objective Collaborative
Optimization of Distribution Networks with Energy Storage and Electric
Vehicles Using an Improved NSGA-II Algorithm. Energies, 2025, vol.
18, no. 19, art. no. 5232. doi: https://doi.org/10.3390/en18195232.
10. Li J., Tang H., Li P., Li Z., Liang C. An Improved NSGA-II Based
Multi-Objective Optimization Model for Electric Vehicle Charging
Station Selection. Mathematics, 2025, vol. 13, no. 23, art. no. 3855. doi:
https://doi.org/10.3390/math13233855.
11. Kolavennu S., Cockburn J.C., Palanki S. Synthesis of robust
controllers for nonsquare multivariable nonlinear systems. Proceedings of
the 2001 American Control Conference, 2001, vol. 5, pp. 4032-4037. doi:
https://doi.org/10.1109/ACC.2001.946323.
12. Looye G., Joos H.-D. Design of Autoland Controller Functions with
Multiobjective Optimization. Journal of Guidance, Control, and
Dynamics, 2006, vol. 29, no. 2, pp. 475-484. doi:
https://doi.org/10.2514/1.8797.
13. Rozov V.Y., Reutskiy S.Y., Pelevin D.Y., Kundius K.D. Magnetic
field of electrical heating cable systems of the floors for residential
premises. Electrical Engineering & Electromechanics, 2024, no. 5, pp.
48-57. doi: https://doi.org/10.20998/2074-272X.2024.5.07.
24 Electrical Engineering & Electromechanics, 2026, no. 4
14. Rozov V.Y., Zavalnyi A.V., Zolotov S.M., Gretskikh S.V. The
normalization methods of the static geomagnetic field inside houses.
Electrical Engineering & Electromechanics, 2015, no. 2, pp. 35-40. doi:
https://doi.org/10.20998/2074-272X.2015.2.07.
15. Rozov V.Y., Reutskiy S.Y., Kundius K.D. Protection of workers
against the magnetic field of 330-750 kV overhead power lines when
performing work without removing the voltage under load. Electrical
Engineering & Electromechanics, 2024, no. 4, pp. 70-78. doi:
https://doi.org/10.20998/2074-272X.2024.4.09.
16. Rozov V.Y., Pelevin D.Y., Reutskiy S.Y., Kundius K.D.,
Vorushylo A.O. The complex influence of external and internal
electricity networks on the magnetic field level in residential premises of
buildings. Electrical Engineering & Electromechanics, 2025, no. 4, pp.
11-19. doi: https://doi.org/10.20998/2074-272X.2025.4.02.
17. Popov A., Tserne E., Volosyuk V., Zhyla S., Pavlikov V.,
Ruzhentsev N., Dergachov K., Havrylenko O., Shmatko O.,
Averyanova Y., Ostroumov I., Kuzmenko N., Sushchenko O., Zaliskyi
M., Solomentsev O., Kuznetsov B., Nikitina T. Invariant Polarization
Signatures for Recognition of Hydrometeors by Airborne Weather
Radars. Computational Science and Its Applications – ICCSA 2023.
Lecture Notes in Computer Science, 2023, vol. 13956, pp. 201-217. doi:
https://doi.org/10.1007/978-3-031-36805-9_14.
18. Sushchenko O., Averyanova Y., Ostroumov I., Kuzmenko N.,
Zaliskyi M., Solomentsev O., Kuznetsov B., Nikitina T., Havrylenko O.,
Popov A., Volosyuk V., Shmatko O., Ruzhentsev N., Zhyla S., Pavlikov
V., Dergachov K., Tserne E. Algorithms for Design of Robust
Stabilization Systems. Computational Science and Its Applications –
ICCSA 2022. ICCSA 2022. Lecture Notes in Computer Science, 2022, vol.
13375, pp. 198-213. doi: https://doi.org/10.1007/978-3-031-10522-7_15.
19. Maksymenko-Sheiko K.V., Sheiko T.I., Lisin D.O., Petrenko N.D.
Mathematical and Computer Modeling of the Forms of Multi-Zone Fuel
Elements with Plates. Journal of Mechanical Engineering, 2022, vol.
25, no. 4, pp. 32-38. doi: https://doi.org/10.15407/pmach2022.04.032.
20. Hontarovskyi P.P., Smetankina N.V., Ugrimov S.V., Garmash
N.H., Melezhyk I.I. Computational Studies of the Thermal Stress State
of Multilayer Glazing with Electric Heating. Journal of Mechanical
Engineering, 2022, vol. 25, no. 1, pp. 14-21. doi:
https://doi.org/10.15407/pmach2022.02.014.
21. Kostikov A.O., Zevin L.I., Krol H.H., Vorontsova A.L. The
Optimal Correcting the Power Value of a Nuclear Power Plant Power
Unit Reactor in the Event of Equipment Failures. Journal of Mechanical
Engineering, 2022, vol. 25, no. 3, pp. 40-45. doi:
https://doi.org/10.15407/pmach2022.03.040.
22. Rusanov A.V., Subotin V.H., Khoryev O.M., Bykov Y.A.,
Korotaiev P.O., Ahibalov Y.S. Effect of 3D Shape of Pump-Turbine
Runner Blade on Flow Characteristics in Turbine Mode. Journal of
Mechanical Engineering, 2022, vol. 25, no. 4, pp. 6-14. doi:
https://doi.org/10.15407/pmach2022.04.006.
23. Kurennov S., Smetankina N., Pavlikov V., Dvoretskaya D.,
Radchenko V. Mathematical Model of the Stress State of the Antenna
Radome Joint with the Load-Bearing Edging of the Skin Cutout. Lecture
Notes in Networks and Systems, 2022, vol. 305, pp. 287-295. doi:
https://doi.org/10.1007/978-3-030-83368-8_28.
24. Kurennov S., Smetankina N. Stress-Strain State of a Double Lap
Joint of Circular Form. Axisymmetric Model. Lecture Notes in
Networks and Systems, 2022, vol 367 LNNS, pp. 36-46. doi:
https://doi.org/10.1007/978-3-030-94259-5_4.
25. Smetankina N., Merkulova A., Merkulov D., Misiura S., Misiura I.
Modelling Thermal Stresses in Laminated Aircraft Elements of a
Complex Form with Account of Heat Sources. Lecture Notes in
Networks and Systems, 2023, vol. 534 LNNS, pp. 233-246. doi:
https://doi.org/10.1007/978-3-031-15944-2_22.
26. Krot P.V., Korennoy V.V. Nonlinear Effects in Rolling Mills
Dynamics. Proceedings of the 5th International Conference on Nonlinear
Dynamics ND-KhPI2016, September 27-30, 2016, Kharkov, Ukraine.
27. Kugi A., Schlacher K., Novak R. Nonlinear control in rolling mills: a
new perspective. IEEE Transactions on Industry Applications, 2001, vol.
37, no. 5, pp. 1394-1402. doi: https://doi.org/10.1109/28.952515.
28. William M. McEneaney. Max-plus methods for nonlinear control
and estimation. Birkhauser Boston Basel Berlin, 2006. 256 p. doi:
https://doi.org/10.1007/0-8176-4453-9.
29. Wilson J. Rugh. Nonlinear System Theory: The Volterra/Wiener
Approach. The Johns Hopkins University Press, 2002. 330 p.
30. Ray S., Lowther D.A. Multi-Objective Optimization Applied to the
Matching of a Specified Torque-Speed Curve for an Internal Permanent
Magnet Motor. IEEE Transactions on Magnetics, 2009, vol. 45, no. 3,
pp. 1518-1521. doi: https://doi.org/10.1109/TMAG.2009.2012694.
31. Ren Z., Pham M.-T., Koh C.S. Robust Global Optimization of
Electromagnetic Devices With Uncertain Design Parameters:
Comparison of the Worst Case Optimization Methods and Multiobjective
Optimization Approach Using Gradient Index. IEEE Transactions on
Magnetics, 2013, vol. 49, no. 2, pp. 851-859. doi:
https://doi.org/10.1109/TMAG.2012.2212713.
32. Shoham Y., Leyton-Brown K. Multiagent Systems: Algorithmic,
Game-Theoretic, and Logical Foundations. Cambridge University Press,
2009. 504 p.
33. Ummels M. Stochastic Multiplayer Games Theory and Algorithms.
Amsterdam University Press, 2010. 174 p.
34. Yang X.-S., Cui Z., Xiao R., Gandomi A.H., Karamanoglu M.
Swarm Intelligence and Bio-Inspired Computation: Theory and
Applications. Elsevier, 2013. 450 p. doi: https://doi.org/10.1016/C2012-
0-02754-8.
35. Deb K., Pratap A., Agarwal S., Meyarivan T. A fast and elitist
multiobjective genetic algorithm: NSGA-II. IEEE Transactions on
Evolutionary Computation, 2002, vol. 6, no. 2, pp. 182-197. doi:
https://doi.org/10.1109/4235.996017.
36. Xiaohui Hu, Eberhart R.C., Yuhui Shi. Particle swarm with extended
memory for multiobjective optimization. Proceedings of the 2003 IEEE
Swarm Intelligence Symposium. SIS’03, 2003, pp. 193-197. doi:
https://doi.org/10.1109/SIS.2003.1202267.
37. Pulido G.T., Coello C.A.C. A constraint-handling mechanism for
particle swarm optimization. Proceedings of the 2004 Congress on
Evolutionary Computation, 2004, pp. 1396-1403. doi:
https://doi.org/10.1109/CEC.2004.1331060.
38. Hamadneh, T., et. al. Optimization of Reconfiguration and Resource
Allocation for Distributed Generation and Capacitor Banks Using
NSGA-II: A Multi-Scenario Approach. Computer Modeling in
Engineering & Sciences, 2025, vol. 143, no. 2, pp. 1519-1548. doi:
https://doi.org/10.32604/cmes.2025.063571.
39. Parsopoulos K.E., Vrahatis M.N. Particle swarm optimization
method for constrained optimization problems. Frontiers in Artificial
Intelligence and Applications, 2002, vol. 76, pp. 214-220.
40. Guezi A., Bendaikha A., Dendouga A. Direct torque control based
on second order sliding mode controller for three-level inverter-fed
permanent magnet synchronous motor: comparative study. Electrical
Engineering & Electromechanics, 2022, no. 5, pp. 10-13. doi:
https://doi.org/10.20998/2074-272X.2022.5.02.
41. Aib A., Khodja D.E., Chakroune S. Field programmable gate array
hardware in the loop validation of fuzzy direct torque control for
induction machine drive. Electrical Engineering & Electromechanics,
2023, no. 3, pp. 28-35. doi: https://doi.org/10.20998/2074-
272X.2023.3.04.
42. Darsouni Z., Rezgui S.E., Benalla H., Rebahi F., Boumendjel
M.A.M. Ensuring service continuity in electric vehicles with vector
control and linear quadratic regulator for dual star induction motors.
Electrical Engineering & Electromechanics, 2025, no. 2, pp. 24-30. doi:
https://doi.org/10.20998/2074-272X.2025.2.04.
43. Bounab A., Chaiba A., Belkacem S., Chariete A. Performance
improvement of parallel dual-star permanent magnet synchronous
machines via type-2 fuzzy direct torque control with a single six-phase
inverter. Electrical Engineering & Electromechanics, 2026, no. 1, pp. 28-
37. doi: https://doi.org/10.20998/2074-272X.2026.1.04.
Received 12.12.2025
Accepted 16.02.2026
Published 03.07.2026
B.I. Kuznetsov1, Doctor of Technical Science, Professor,
T.B. Nikitina2, Doctor of Technical Science, Professor,
I.V. Bovdui1, PhD, Senior Research Scientist,
O.V. Voloshko1, PhD, Junior Research Scientist,
V.V. Kolomiets2, PhD, Associate Professor,
B.B. Kobylianskyi2, PhD, Associate Professor,
1 Anatolii Pidhornyi Institute of Power Machines and Systems of
the National Academy of Sciences of Ukraine,
2/10, Komunalnykiv Str., Kharkiv, 61046, Ukraine,
e-mail: kuznetsov.boris.i@gmail.com (Corresponding Author)
2 Bakhmut Education Research and Professional Pedagogical
Institute V.N. Karazin Kharkiv National University,
9a, Nosakov Str., Bakhmut, Donetsk Region, 84511, Ukraine.
How to cite this article:
Kuznetsov B.I., Nikitina T.B., Bovdui I.V., Voloshko O.V., Kolomiets V.V., Kobylianskyi B.B. The method of multi objective
design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization
algorithm. Electrical Engineering & Electromechanics, 2026, no. 4, pp. 17-24. doi: https://doi.org/10.20998/2074-272X.2026.4.03
|
| id | eiekhpieduua-article-366076 |
| institution | Electrical Engineering & Electromechanics |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-02T01:00:29Z |
| publishDate | 2026 |
| publisher | National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | eiekhpieduua/cc/30d11d09f0633c2d3062bdc68c5008cc.pdf |
| spelling | eiekhpieduua-article-3660762026-07-01T21:42:56Z The method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm The method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm Kuznetsov, B. I. Nikitina, T. B. Bovdui, I. V. Voloshko, O. V. Kolomiets, V. V. Kobylianskyi, B. B. nonlinear electromechanical tracking system neural network controller multi objective design computer simulation experimental research нелінійна електромеханічна система стеження нейромережевий контролер багатоцільове проєктування комп’ютерне моделювання експериментальні дослідження Problem. Most research on the design of nonlinear electromechanical tracking systems has been conducted using typical proportional-differential controllers, but there is no methodology for designing nonlinear electromechanical tracking system based on neural network controller to meet different requirements that are imposed on the operation of the system in different modes. Goal. To develop the method of multi objective design of nonlinear electromechanical tracking system based on neural network controller to satisfy different requirements that are imposed on the operation of the system in various modes. Methodology. The designed nonlinear electromechanical tracking system based on neural network controller implements the dynamics of a reference model by training a neural network controller for a given model of a nonlinear control object. Multi objective design of the reference model reduces to solving a vector nonlinear programming problem, in which the components of the vector objective function are direct different requirements that are imposed on the operation of the system in various modes. The solution to the vector nonlinear programming problem is calculated using a hybrid heuristic optimization algorithm, incorporating particle swarm optimization and stochastic sequential quadratic programming. Results. The results multi objective design of two-mass nonlinear electromechanical tracking systems based on neural network controller in which different requirements that are imposed on the operation of the system in various modes were satisfied are given. Based on the results of modeling and experimental studies it is established, that with the help of synthesized neural network controllers, it is possible to improve of quality indicators of two-mass nonlinear electromechanical tracking system in comparison with the system with standard regulators. Scientific novelty. For the first time the method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller to satisfy different requirements that are imposed on the operation of the system in various modes is developed. Practical value. From the point of view of the practical implementation the possibility of solving the problem of multi objective design of nonlinear electromechanical tracking systems based on neural network controller to satisfy different requirements that are imposed on the operation of the system in various modes is shown. References 43, figures 8. Проблема. Більшість досліджень по проєктуванню нелінійних електромеханічних систем стеження виконані на основі використання типових пропорційно диференційних регуляторів, але відсутня методологія проєктування нелінійних електромеханічних систем стеження на основі нейромережевого контролеру для задоволення різноманітних вимог, які пред’являються до роботи системи у різних режимах. Метою роботи є розробка методу багатокритеріального проєктування нелінійних електромеханічних систем стеження на основі нейромережевого контролеру для задоволення різноманітних вимог, які пред’являються до роботи системи у різних режимах. Методологія. У спроєктованих нелінійних електромеханічних систем стеження на основі нейромережевого контролеру реалізується динаміка еталонної моделі в результаті навчання нейромережевого контролеру для заданої моделі нелінійного об’єкта управління. Багатокритеріальне проєктування еталонної моделі зводиться до вирішення проблеми векторного нелінійного програмування, в якій компонентами цільової векторної функції є різноманітні вимоги, які пред’являються до роботи системи у різних режимах. Вирішення проблеми векторного нелінійного програмування обчислюється за допомогою гібридного евристичного алгоритму оптимізації, що включає оптимізацію роєм частинок і послідовне стохастичне квадратичне програмування. Результати. Наведено результати багатокритеріального проєктування двомасової нелінійної електромеханічної системи стеження на основі нейромережевого контролеру, в якій були задоволені різноманітні вимоги, які пред’являються до роботи системи у різних режимах. На основі результатів моделювання та експериментальних досліджень встановлено, що за допомогою синтезованих нейромережевих контролерів можна підвищити якісні показники двомасової нелінійної електромеханічної системи стеження у порівнянні із системою зі стандартними регуляторами. Наукова новизна. Вперше розроблено метод багатокритеріального проєктування нелінійних електромеханічних систем стеження на основі нейромережевого контролеру для задоволення різноманітних вимог, які пред’являються до роботи системи у різних режимах. Практична значимість. З точки зору практичної реалізації показана можливість вирішення задачі багатокритеріального проєктування нелінійних електромеханічних систем стеження на основі нейромережевого контролеру для задоволення різноманітних вимог, які пред’являються до роботи системи у різних режимах. Бібл. 43, рис. 8. National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine 2026-07-02 Article Article application/pdf https://eie.khpi.edu.ua/article/view/366076 10.20998/2074-272X.2026.4.03 Electrical Engineering & Electromechanics; No. 4 (2026); 17-24 Электротехника и Электромеханика; № 4 (2026); 17-24 Електротехніка і Електромеханіка; № 4 (2026); 17-24 2309-3404 2074-272X en https://eie.khpi.edu.ua/article/view/366076/351646 Copyright (c) 2026 B. I. Kuznetsov, T. B. Nikitina, I. V. Bovdui, O. V. Voloshko, V. V. Kolomiets, B. B. Kobylianskyi http://creativecommons.org/licenses/by-nc/4.0 |
| spellingShingle | nonlinear electromechanical tracking system neural network controller multi objective design computer simulation experimental research Kuznetsov, B. I. Nikitina, T. B. Bovdui, I. V. Voloshko, O. V. Kolomiets, V. V. Kobylianskyi, B. B. The method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm |
| title | The method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm |
| title_alt | The method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm |
| title_full | The method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm |
| title_fullStr | The method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm |
| title_full_unstemmed | The method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm |
| title_short | The method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm |
| title_sort | method of multi objective design of nonlinear electromechanical tracking systems based on neural network controller using hybrid metaheuristic optimization algorithm |
| topic | nonlinear electromechanical tracking system neural network controller multi objective design computer simulation experimental research |
| topic_facet | nonlinear electromechanical tracking system neural network controller multi objective design computer simulation experimental research нелінійна електромеханічна система стеження нейромережевий контролер багатоцільове проєктування комп’ютерне моделювання експериментальні дослідження |
| url | https://eie.khpi.edu.ua/article/view/366076 |
| work_keys_str_mv | AT kuznetsovbi themethodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT nikitinatb themethodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT bovduiiv themethodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT voloshkoov themethodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT kolomietsvv themethodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT kobylianskyibb themethodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT kuznetsovbi methodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT nikitinatb methodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT bovduiiv methodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT voloshkoov methodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT kolomietsvv methodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm AT kobylianskyibb methodofmultiobjectivedesignofnonlinearelectromechanicaltrackingsystemsbasedonneuralnetworkcontrollerusinghybridmetaheuristicoptimizationalgorithm |