Improving of electromechanical servo systems accuracy
Aim. Improving of accuracy parameters and reducing of sensitivity to changes of plant parameters of nonlinear robust electromechanical servo systems of guidance and stabilization of lightly armored vehicle weapons based on multiobjective synthesis. Methodology. The method of multicriterion synthes...
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irk-123456789-1479662019-02-17T01:24:00Z Improving of electromechanical servo systems accuracy Kuznetsov, B.I. Nikitina, T.B. Kolomiets, V.V. Bovdui, I.V. Електротехнічні комплекси та системи. Силова електроніка Aim. Improving of accuracy parameters and reducing of sensitivity to changes of plant parameters of nonlinear robust electromechanical servo systems of guidance and stabilization of lightly armored vehicle weapons based on multiobjective synthesis. Methodology. The method of multicriterion synthesis of nonlinear robust controllers for controlling by nonlinear multimass electromechanical servo systems with parametric uncertainty based on the choice of the target vector of robust control by solving the corresponding multicriterion nonlinear programming problem in which the calculation of the vectors of the objective function and constraints is algorithmic and associated with synthesis of nonlinear robust controllers and modeling of the synthesized system for various modes of operation of the system, with different input signals and for various values of the plant parameters. Synthesis of nonlinear robust controllers and non-linear robust observers reduces to solving the system of Hamilton-Jacobi-Isaacs equations. Results. The results of the synthesis of a nonlinear robust electromechanical servo system for the guidance and stabilization of lightly armored vehicle weapons are presented. Comparison of the dynamic characteristics of the synthesized servo electromechanical system showed that the use of synthesized nonlinear robust controllers allowed to improve the accuracy parameters and reduce the sensitivity of the system to changes of plant parameters in comparison with the existing system. Originality. For the first time carried out the multiobjective synthesis of nonlinear robust electromechanical servo systems of guidance and stabilization of lightly armored vehicle weapons. Practical value. Practical recommendations are given on reasonable choice of the gain matrix for the nonlinear feedbacks of the regulator and the nonlinear observer of the servo electromechanical system, which allows improving the dynamic characteristics and reducing the sensitivity of the system to plant parameters changing in comparison with the existing system. Цель. Повышение параметров точности и уменьшение чувствительности системы к изменениям параметров объекта управления нелинейной робастной электромеханической следящей системы наведения и стабилизации вооружения легкобронированной машины на основе многокритериального синтеза. Методология. Метод многокритериального синтеза нелинейных робастных регуляторов для управления нелинейными многомассовыми электромеханическими следящими системами с параметрической неопределенностью основан на выборе вектора цели робастного управления путем решения соответствующей задачи многокритериального нелинейного программирования, в которой вычисление векторов целевой функции и ограничений носит алгоритмический характер и связано с синтезом нелинейных робастных регуляторов и моделированием синтезированной системы для различных режимов работы системы, при различных входных сигналах и для различных значений параметров объекта управления. Синтез нелинейных робастных регуляторов и нелинейных робастных наблюдателей сводится к решению системы уравнений Гамильтона – Якоби – Айзекса. Результаты. Приводятся результаты синтеза нелинейной робастной электромеханической следящей системы наведения и стабилизации вооружения легкобронированной машины. Сравнение динамических характеристик синтезированной следящей электромеханической системы показало, что применение синтезированных нелинейных робастных регуляторов позволяет повысить параметры точности и снизить чувствительность системы к изменению параметров объекта управления по сравнению с существующей системой. Оригинальность. Впервые проведен многокритериальный синтез нелинейной робастной электромеханической следящей системы наведения и стабилизации вооружения легкобронированной машины. Практическая ценность. Приводятся практические рекомендации по обоснованному выбору матриц коэффициентов усиления нелинейных обратных связей регулятора и нелинейного наблюдателя следящей электромеханической системы, что позволяет улучшить динамические характеристики и снизить чувствительность системы к изменению параметров объекта управления по сравнению с существующей системой 2018 Article Improving of electromechanical servo systems accuracy / B.I. Kuznetsov, T.B. Nikitina, V.V. Kolomiets, I.V. Bovdui // Електротехніка і електромеханіка. — 2018. — № 6. — С. 33-37. — Бібліогр.: 12 назв. — англ. 2074-272X DOI: https://doi.org/10.20998/2074-272X.2018.6.04 http://dspace.nbuv.gov.ua/handle/123456789/147966 621.3.01 en Електротехніка і електромеханіка Інститут технічних проблем магнетизму НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Електротехнічні комплекси та системи. Силова електроніка Електротехнічні комплекси та системи. Силова електроніка |
| spellingShingle |
Електротехнічні комплекси та системи. Силова електроніка Електротехнічні комплекси та системи. Силова електроніка Kuznetsov, B.I. Nikitina, T.B. Kolomiets, V.V. Bovdui, I.V. Improving of electromechanical servo systems accuracy Електротехніка і електромеханіка |
| description |
Aim. Improving of accuracy parameters and reducing of sensitivity to changes of plant parameters of nonlinear robust
electromechanical servo systems of guidance and stabilization of lightly armored vehicle weapons based on multiobjective
synthesis. Methodology. The method of multicriterion synthesis of nonlinear robust controllers for controlling by nonlinear
multimass electromechanical servo systems with parametric uncertainty based on the choice of the target vector of robust control
by solving the corresponding multicriterion nonlinear programming problem in which the calculation of the vectors of the
objective function and constraints is algorithmic and associated with synthesis of nonlinear robust controllers and modeling of
the synthesized system for various modes of operation of the system, with different input signals and for various values of the
plant parameters. Synthesis of nonlinear robust controllers and non-linear robust observers reduces to solving the system of
Hamilton-Jacobi-Isaacs equations. Results. The results of the synthesis of a nonlinear robust electromechanical servo system for
the guidance and stabilization of lightly armored vehicle weapons are presented. Comparison of the dynamic characteristics of
the synthesized servo electromechanical system showed that the use of synthesized nonlinear robust controllers allowed to
improve the accuracy parameters and reduce the sensitivity of the system to changes of plant parameters in comparison with the
existing system. Originality. For the first time carried out the multiobjective synthesis of nonlinear robust electromechanical servo
systems of guidance and stabilization of lightly armored vehicle weapons. Practical value. Practical recommendations are given
on reasonable choice of the gain matrix for the nonlinear feedbacks of the regulator and the nonlinear observer of the servo
electromechanical system, which allows improving the dynamic characteristics and reducing the sensitivity of the system to plant
parameters changing in comparison with the existing system. |
| format |
Article |
| author |
Kuznetsov, B.I. Nikitina, T.B. Kolomiets, V.V. Bovdui, I.V. |
| author_facet |
Kuznetsov, B.I. Nikitina, T.B. Kolomiets, V.V. Bovdui, I.V. |
| author_sort |
Kuznetsov, B.I. |
| title |
Improving of electromechanical servo systems accuracy |
| title_short |
Improving of electromechanical servo systems accuracy |
| title_full |
Improving of electromechanical servo systems accuracy |
| title_fullStr |
Improving of electromechanical servo systems accuracy |
| title_full_unstemmed |
Improving of electromechanical servo systems accuracy |
| title_sort |
improving of electromechanical servo systems accuracy |
| publisher |
Інститут технічних проблем магнетизму НАН України |
| publishDate |
2018 |
| topic_facet |
Електротехнічні комплекси та системи. Силова електроніка |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147966 |
| citation_txt |
Improving of electromechanical servo systems accuracy / B.I. Kuznetsov, T.B. Nikitina, V.V. Kolomiets, I.V. Bovdui // Електротехніка і електромеханіка. — 2018. — № 6. — С. 33-37. — Бібліогр.: 12 назв. — англ. |
| series |
Електротехніка і електромеханіка |
| work_keys_str_mv |
AT kuznetsovbi improvingofelectromechanicalservosystemsaccuracy AT nikitinatb improvingofelectromechanicalservosystemsaccuracy AT kolomietsvv improvingofelectromechanicalservosystemsaccuracy AT bovduiiv improvingofelectromechanicalservosystemsaccuracy |
| first_indexed |
2025-07-12T18:12:09Z |
| last_indexed |
2025-07-12T18:12:09Z |
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1837465789934862336 |
| fulltext |
ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №6 33
© B.I. Kuznetsov, T.B. Nikitina, V.V. Kolomiets, I.V. Bovdui
UDC 621.3.01 doi: 10.20998/2074-272X.2018.6.04
B.I. Kuznetsov, T.B. Nikitina, V.V. Kolomiets, I.V. Bovdui
IMPROVING OF ELECTROMECHANICAL SERVO SYSTEMS ACCURACY
Aim. Improving of accuracy parameters and reducing of sensitivity to changes of plant parameters of nonlinear robust
electromechanical servo systems of guidance and stabilization of lightly armored vehicle weapons based on multiobjective
synthesis. Methodology. The method of multicriterion synthesis of nonlinear robust controllers for controlling by nonlinear
multimass electromechanical servo systems with parametric uncertainty based on the choice of the target vector of robust control
by solving the corresponding multicriterion nonlinear programming problem in which the calculation of the vectors of the
objective function and constraints is algorithmic and associated with synthesis of nonlinear robust controllers and modeling of
the synthesized system for various modes of operation of the system, with different input signals and for various values of the
plant parameters. Synthesis of nonlinear robust controllers and non-linear robust observers reduces to solving the system of
Hamilton-Jacobi-Isaacs equations. Results. The results of the synthesis of a nonlinear robust electromechanical servo system for
the guidance and stabilization of lightly armored vehicle weapons are presented. Comparison of the dynamic characteristics of
the synthesized servo electromechanical system showed that the use of synthesized nonlinear robust controllers allowed to
improve the accuracy parameters and reduce the sensitivity of the system to changes of plant parameters in comparison with the
existing system. Originality. For the first time carried out the multiobjective synthesis of nonlinear robust electromechanical servo
systems of guidance and stabilization of lightly armored vehicle weapons. Practical value. Practical recommendations are given
on reasonable choice of the gain matrix for the nonlinear feedbacks of the regulator and the nonlinear observer of the servo
electromechanical system, which allows improving the dynamic characteristics and reducing the sensitivity of the system to plant
parameters changing in comparison with the existing system. References 12, figures 1.
Key words: electromechanical servo systems of guidance and stabilization of lightly armored vehicle weapon, nonlinear robust
system, multiobjective synthesis, dynamic characteristics.
Цель. Повышение параметров точности и уменьшение чувствительности системы к изменениям параметров
объекта управления нелинейной робастной электромеханической следящей системы наведения и стабилизации
вооружения легкобронированной машины на основе многокритериального синтеза. Методология. Метод
многокритериального синтеза нелинейных робастных регуляторов для управления нелинейными многомассовыми
электромеханическими следящими системами с параметрической неопределенностью основан на выборе вектора
цели робастного управления путем решения соответствующей задачи многокритериального нелинейного
программирования, в которой вычисление векторов целевой функции и ограничений носит алгоритмический
характер и связано с синтезом нелинейных робастных регуляторов и моделированием синтезированной системы для
различных режимов работы системы, при различных входных сигналах и для различных значений параметров
объекта управления. Синтез нелинейных робастных регуляторов и нелинейных робастных наблюдателей сводится к
решению системы уравнений Гамильтона – Якоби – Айзекса. Результаты. Приводятся результаты синтеза
нелинейной робастной электромеханической следящей системы наведения и стабилизации вооружения
легкобронированной машины. Сравнение динамических характеристик синтезированной следящей
электромеханической системы показало, что применение синтезированных нелинейных робастных регуляторов
позволяет повысить параметры точности и снизить чувствительность системы к изменению параметров объекта
управления по сравнению с существующей системой. Оригинальность. Впервые проведен многокритериальный
синтез нелинейной робастной электромеханической следящей системы наведения и стабилизации вооружения
легкобронированной машины. Практическая ценность. Приводятся практические рекомендации по обоснованному
выбору матриц коэффициентов усиления нелинейных обратных связей регулятора и нелинейного наблюдателя
следящей электромеханической системы, что позволяет улучшить динамические характеристики и снизить
чувствительность системы к изменению параметров объекта управления по сравнению с существующей системой.
Библ. 12, рис. 1.
Ключевые слова: электромеханическая следящая система наведения и стабилизации вооружения
легкобронированной машины, нелинейная робастная система, многокритериальный синтез, динамические
характеристики.
Introduction. Lightly armored wheeled and tracked
vehicles produced in Ukraine have high tactical and
technical characteristics and successfully compete with
foreign weapons [1]. The basis of combat in modern
conditions is firing off at a high speed and maneuvering
movement of the machine, so all modern lightly armored
vehicles in the world equipped with weapons stabilizers,
allowing to guide the target fire on the move. The
probability of fire engagement of the target at maximum
speeds, high maneuverability and effective evasion of the
machine against the enemy's fire damage is largely
determined by the accuracy of maintaining the specified
direction of the combat module on the target with intense
perturbations on the machine's side. Increasing the
accuracy has an important economic component. For
example, the practice of using the Protector combat
module in Kongsberg's Crows II version based on actual
operation data in 2007 made it possible to reduce the
consumption of 12.7-mm cartridges by 70 % due to a
sharp increase in the accuracy of the hit from the first
shot. Therefore, the issues of further improving the
accuracy of weapons stabilization are an urgent problem,
both in the development of new weapons systems and in
the modernization of existing systems in service.
To systems of guidance and stabilization of lightly
armored vehicles weapons, sufficiently stringent
requirements are set for the performance indicators in
34 ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №6
various modes. We bring a part of such requirements for
the light-armored vehicle presented to the guidance and
stabilization system [1]: time of working out of a given
angle of error; acceleration time to rated speed and
deceleration time to full stop; an error in working out a
harmonic signal of a specified amplitude and frequency;
stabilization error when moving along a normalized path
with a random profile change with a given speed;
maximum speed of guidance; minimum speed of
guidance; failure of guidance at minimum speed.
Naturally, this should take into account the voltage and
current limitations of the anchor chain of the drive motor,
as well as the speed of rotation of the drive motor.
The goal of this work is to improve of the accuracy
parameters and reduce of sensitivity to changes of plant
parameters for electromechanical servo system guidance
and stabilization of lightly armored vehicle weapons
based on multiobjective synthesis of nonlinear robust
control.
Problem statement. Stabilizers of armored vehicles
weapons in a vertical and horizontal plane are built
according to the same type of scheme [1-4]. With the help
of an optical sight, the sight mirror is mounted in the
direction of the target, respectively in the horizontal and
vertical planes. The specified direction is compared with
the actual direction of the armament block and the
voltages proportional to the discrepancy signals between
the specified directions of the shot lines and the axis of
the bore channel are fed to the inputs of the turret drives
in the horizontal guidance channel and the arming unit in
the vertical guidance channel. In addition, the absolute
speed of rotation of the turret in the horizontal plane and
the combat module in the vertical plane are measured
with the aid of gyroscopic angular velocity sensors
mounted on the arms block and used to develop control.
The turret in the horizontal plane and the combat
module in the vertical plane are driven by DC motors
driven from permanent magnets, whose armature circuits
are powered by pulse-width converters. The rotational
speed of the motors that drive the turret and the combat
module is measured using tachogenerators. The currents
of the motor armature anchors are measured by shunts
included in the motor armature circuits, converted and
also used for control purposes
The presence in the electromechanical servo systems
of elastic elements between the drive motor and the
operating element, the uncertainty of the parameters of
the control objects, the change in mass-inertial
characteristics, complex cinematic schemes, unknown
external and internal disturbances do not allow to obtain
potentially high dynamic characteristics inherent in
modern electromechanical systems with standard
regulators [2, 3]. The use of state control by complex
electromechanical systems containing nonlinear and
elastic elements allows obtaining acceptable quality
indicators. To reduce the sensitivity of synthesized
systems to changing the parameters and structure of the
control object and external influences, robust control is
used as the state control. Consider the design of such
system.
Let us consider the nonlinear model of a discrete
plant of robust control of a multimass system with a state
vector xk in the form of a difference state equation in the
standard form
kkkkk uxfx ,,,1 , (1)
where uk is the control vector, k and k are the vectors of
the external signal and parametric perturbations [5, 6], f is
a nonlinear function.
The mathematical model (1) takes into account the
nonlinear frictional dependencies on the shafts of the
drive motor, the rotating parts of the reducer and the
operating element, the play between the teeth of the
driving and driven gears, the control constraints, current,
torque and engine speed, as well as the moment of inertia
of the plant.
Method of synthesis. The task of synthesis is the
determination of such a regulator [7, 8] which, based on
the measured output of the initial system
kkkk uxYy ,, (2)
forming control uk using a dynamic system described by
the difference state equation and output
);,,ξ
(,,,
3
1
1
kkk
i
kikkkkk
uY
yGuf
(3)
3
1
,
i
kkik yUu , (4)
where i is the order of the forms Gi and Ui.
The synthesis of the regulator (4) is reduced to
determining the matrix of the forms of the regulator gain
Ui by minimizing the norm of the target vector
4
2
,,,,
i
kkkikkk uxZuxz (5)
on control vector of uk and maximization of the same
norm on a of plant uncertain vector k for the worst case
disturbance.
The synthesis of the observer (3) is reduced to
determining the observer gain coefficients Gi by
minimization of the error vector of the recovery of the
state vector xk of the initial system and maximization of
the same norm of the error vector along the plant
uncertainty vector k and the vector of external signal
influences k, which also corresponds to the worst case
disturbance.
Matrices of the regulator Ui and observer Gi gain
coefficients are found from approximate solutions of the
Hamilton-Jacobi-Isaacs equations [7, 8], in which the
matrices of linear forms being found from the four Riccati
equations solutions. This approach corresponds to the
standard 4-Riccati approach to the synthesis of linear
robust or anisotropic regulators [9].
To determine the regulator (4) for plant (1) with
target vector (5) consider Hamiltonian function
,,,,,
,,,,
kkkkkk
T
x
kkkkkk
uxfuxV
uxzuxH
(6)
where Vx are partial derivatives with respect to the state
vector xk of the infinite-horizon performance functional
(Lyapunov function)
ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №6 35
ki
iiikkk uxzuxV ,,,, . (7)
To determine the robust regulator (4) it is necessary
to find the minimum norm of the target vector (5) along
the control vector uk and the maximum of this norm in
the external perturbations vector k, which reduces to
solving the minimax extremal problem of Hamiltonian
function [7]
kkk
du
k uxHxH
kk
,,maxmin* . (8)
The necessary conditions for the extremum of the
Hamiltonian function (8) both in the control vector uk and
in the external perturbation vector k are these equations
0,, ** kkku xxuxH ; (9)
0,, ** kkk xxuxH , (10)
which are Hamilton-Jacobi-Isaacs equations. Here Hu and
H are the partial derivatives of the Hamiltonian function
with respect to the control vector uk and with respect to
the external perturbations vector k.
Note that these equations (9) – (10) are also
necessary conditions for optimizing a dynamic game, in
which the first player –the regulator which minimizes the
target vector, and the second player – external
disturbances which maximizes the same target vector.
The difficulty of obtaining a nonlinear discrete
control law is due to the fact that the difference Hamilton-
Jacobi-Isaacs equations (9) – (10) is a nonlinear algebraic
equation, while the Hamilton-Jacobi-Isaacs equations for
a continuous system is a partial differential equation.
Therefore, the difference Hamilton-Jacobi-Isaacs
equations is not a quadratic equations in the control and
perturbation.
In this paper we use an approximate solution of the
Hamilton-Jacobi-Isaacs equation (9) – (10) assuming the
analytical dependences of the nonlinearities of the
original system (1), (2), (5) in the form of the
corresponding series [8]. Then the linear approximation of
the Hamilton-Jacobi-Isaac equation (9), (10) are the
algebraic Riccati equations
PAE
PAB
IPEEPAE
PEBPBBI
PEAPBARPAAP
T
T
TT
TT
TTT
1
2
. (11)
Here, the matrices A and B in (11) are the
corresponding matrices of the linear system obtained by
linearizing the original nonlinear system (1), (2), (5).
Similarly matrices of the observer Gi gain
coefficients (3) are found from approximate solutions of
the Hamilton-Jacobi-Isaacs equations type (9) – (10).
With this approach the strategy that is best for one of
the players is at the same time the worst for the other
player. This is the so-called saddle point principle, which
corresponds to the condition of equilibrium: the minimum
guaranteed loss of the first player is equal to the
maximum guaranteed win of the second, so that none of
the players is interested in changing the optimal strategy
of behavior.
According to the modern concept of guaranteed
result, a mathematical model of uncertainty is constructed
on the basis of the hypothesis of the «worst» behavior of
perturbing factors. The essence of this hypothesis,
overcoming the uncertainty in the control problem,
consists in interpreting uncontrolled perturbing factors as
some hypothetical deterministic perturbation, of which
only the ranges of its change are known. This perturbation
is introduced into the model of the dynamics of the
control object with the assumption of its most unfavorable
(extreme) effect on the control process. In other words, it
is considered that in the a priori a given range of
perturbation change, those values are realized that ensure
the lowest quality of the control process.
It should be noted that the perturbation introduced
into the study admits a very broad interpretation and does
not appear as a physical, but as an abstract mathematical
concept, symbolizing the influence of disturbing factors.
Thus, not only the «external» perturbations applied to the
object from the side of the environment, but also all sorts
of «internal» disturbances (for example, noise and
measurement errors) can be attributed to it. It is also
possible to include here also uncertain factors related to
the inaccuracy of the mathematical description of the
object: unknown parameters of the object, unaccounted
inertial and nonlinear links, errors in linearization and
discretization of the object model.
Robust control target vector choice. A synthesized
system including a nonlinear plant (1) that is closed by a
robust controller (3) – (4) has certain dynamic
characteristics that are determined by the control system
model of the system (1), the parameters of the measuring
devices (2), the target vector (5).
The most important stage in the formalization of the
problem of optimal control is the choice of the quality
criterion, determined both by the functional purpose of
the control object and by the capabilities of the
mathematical apparatus used.
The problem of a reasonable choice of the quality
criterion, despite its relevance, is still unresolved. The
choice of the quality criterion is a very complex,
ambiguous and, often, contradictory task. It is known [7]
that any asymptotically stable control system even with
unsatisfactory quality of transient processes is optimal in
the sense of some criterion of this type.
From the engineering point of view, it seems natural
to construct optimal criteria that directly take into account
the direct indicators of the quality of the management
process, such as steady errors, regulation time, overshoot,
magnitude of oscillations, etc., which are physically most
clear and have clear limits of permissible values, based on
a rich experience in the design of systems. However, in
methods of designing control systems, indirect quality
indicators are more widely used, which, as a rule, are
easier to calculate and more convenient in analytical
research.
For the correct definition of the target vector (7), we
introduce the vector of the unknown parameters =
= {Zi(xk, uk, k)}, the components of which are the
required weight matrices of the norm Zi(xk, uk, k). We
introduce the vector target function
36 ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №6
TmFFFF ..., 21 (10)
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 (10) and
constraints on state variables and control, the initial
nonlinear system (1), (2) is modeled by a closed
synthesized nonlinear regulator (3), (4) in various modes
of operation, with different input signals and for various
values of the plant parameters [10, 11]. This
multiobjective nonlinear programming problem is solved
on the basis of multi-swarm stochastic multi-agent
optimization algorithms [12].
Computer simulation results. We present the
results of research of dynamic characteristics and
sensitivity to the plant parameters change of a nonlinear
two-mass electromechanical servo system of lightly
armored vehicle weapons [1] with synthesized nonlinear
robust regulators. In the existing system, PD regulators
are used, which are realized with the aid of a gyroscopic
angle sensor and a gyroscopic angular velocity sensor.
The introduction of the integral control law leads to the
emergence of undamped oscillations in the mode of
working out the given angles of the combat module
position, due to the presence of dry friction on the shafts
of the drive motor and the working member. With the
help of robust controllers it was possible to ensure a stable
operation of the system taking into account all the
essential nonlinearities inherent in the elements of this
system when two integrating links are introduced into the
control loop.
As an example, Fig.1 shows the transient processes of
state variables: a) the combat module angle; b) the combat
module speed; c) the elasticity moment and d) motor speed
in the guidance mode with a low speed 0.5 grad/s in the
synthesized system. As can be seen from Fig.1,b and
Fig.1,d, the drive motor and the combat module are
moving in a «stick-slip» mode. As can be seen from
Fig.1,a, the established error in the processing of the
linearly changing driving force of the gun barrel angle of
the combat module of a lightly armored machine is
practically zero.
Such system with second-order astatism, taking into
account all the non-linearities and the moment of inertia
of the working element that changes during operation,
made it possible to improve the smoothness of the motion
of the control object by more than 3.7 times when
hovering at low speeds. We note that this indicator largely
determines the potential accuracy of the operation of the
electromechanical servo system in one of the most
important modes of its operation.
The use of synthesized nonlinear robust controllers
has also made it possible to reduce the time of transient
processes in the regime of working out small angles by
more than 5.3 times in comparison with the existing
system. Moreover, when the moment of inertia of the
working mechanism changes within the given limits, the
transient processes change insignificantly and satisfy the
technical requirements imposed on the system.
0 0.5 1 1.5 2 2.5 3
0
0.005
0.01
0.015
0.02
0.025
0.03
a
0 0.5 1 1.5 2 2.5 3
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
b
0 0.5 1 1.5 2 2.5 3
-5
-4
-3
-2
-1
0
1
2
3
4
5
c
0 0.5 1 1.5 2 2.5 3
-80
-60
-40
-20
0
20
40
60
80
d
Fig. 1. Transient processes of state variables:
a) the combat module angle and b) combat module speed;
c) elasticity moment and d) the motor rotation speed in the
guidance mode at a rate of 0.5 grad/s
The synthesized system also allowed to increase the
accuracy of working out harmonic influences of a given
ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №6 37
range of frequencies in 2.7 – 3.3 times, which increased
the efficiency of the system installed on a mobile base
moving along an uneven road at a given speed and given
parameters of road irregularities.
Experimental researches results. For carrying out
of experimental researches the model of a two-mass
electromechanical system is developed. The layout
consists of two electric machines, the shafts of which are
connected by an elastic element whose parameters are
chosen so that the natural frequencies of the mechanical
elastic vibrations of the layout coincide with the
experimentally obtained oscillations of the real system.
Experimental research of model of electromechanical
servo system confirmed the correctness of computer
simulation results and experimental research.
Conclusions.
1. For the first time the multiobjective synthesis of
nonlinear robust regulators for controlling by non-linear
multi-mass electromechanical servo systems of lightly
armored vehicles weapons with parametric uncertainty
based on the choice of the target vector of robust control by
solving the corresponding multiobjective nonlinear
programming problem. Calculation of the vectors of the
objective function and constraints of nonlinear
programming problem are algorithmic character and are
connected with synthesis of nonlinear robust controllers
and modeling of the synthesized system for various
operating modes of the system, with different input signals
and for different values of the plant parameters is given.
2. Synthesis of nonlinear robust regulators and
nonlinear robust observers reduces to solving the system
of Hamilton-Jacobi-Isaacs equations.
3. Based on the analysis of the dynamic characteristics
of the synthesized servo electromechanical system of
lightly armored vehicles weapons have shown that the use
of synthesized nonlinear robust controllers has allowed to
improve the accuracy parameters and to reduce the
sensitivity to plant parameters changes in comparison
with the existing system.
4. Further increase of accuracy can be obtained by
restoring, with the observer of plant parametric
uncertainty vector and of external signal disturbances
vector and basis on their design of feed forward control
system. In addition, to further improve accuracy, it is
expedient to replace the DC drive motor with a high-
torque motor and realize a gearless drive with separate
stabilization of the aiming and aiming lines.
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Received 14.07.2018
B.I. Kuznetsov1, Doctor of Technical Science, Professor,
T.B. Nikitina2, Doctor of Technical Science, Professor,
V.V. Kolomiets2, Candidate of Technical Science,
I.V. Bovdui1, Candidate of Technical Science,
1 State Institution «Institute of Technical Problems
of Magnetism of the NAS of Ukraine»,
19, Industrialna Str., Kharkiv, 61106, Ukraine,
phone +380 50 5766900,
e-mail: kuznetsov.boris.i@gmail.com
2 Kharkov National Automobile and Highway University,
25, Yaroslava Mudroho Str., Kharkov, 61002, Ukraine,
е-mail: tatjana55555@gmail.com
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