The principle of control by diagnosis as a result of the systematic application of fundamental control principles
The subject of study is the principle of management by diagnosis. The goal is to establish the principle of management by diagnosis as a result of the systemic application of fundamental management principles. The scientific novelty lies in the formulation of a new principle of management by diagnos...
Збережено в:
| Опубліковано в: : | Проблеми керування та інформатики |
|---|---|
| Дата: | 2023 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут кібернетики ім. В.М. Глушкова НАН України
2023
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210932 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The principle of control by diagnosis as a result of the systematic application of fundamental control principles / A. Kulik // Проблеми керування та інформатики. — 2023. — № 1. — С. 7–22. — Бібліогр.: 19 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860048244366639104 |
|---|---|
| author | Kulik, A. |
| author_facet | Kulik, A. |
| citation_txt | The principle of control by diagnosis as a result of the systematic application of fundamental control principles / A. Kulik // Проблеми керування та інформатики. — 2023. — № 1. — С. 7–22. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Проблеми керування та інформатики |
| description | The subject of study is the principle of management by diagnosis. The goal is to establish the principle of management by diagnosis as a result of the systemic application of fundamental management principles. The scientific novelty lies in the formulation of a new principle of management by diagnosis and the development of instrumental tools enabling the operability of automatic control objects under various destabilizing conditions.
Предметом вивчення є принцип керування за діагнозом. Мета полягає у формуванні принципу керування за діагнозом як результату системного застосування фундаментальних принципів керування. Наукова новизна полягає у формуванні нового принципу керування за діагнозом та розробці низки інструментальних засобів, застосування яких дозволяє забезпечити працездатність обʼєктів автоматичного керування в умовах дії різнотипних дестабілізуючих впливів.
|
| first_indexed | 2026-03-19T00:30:37Z |
| format | Article |
| fulltext |
© A. KULIK, 2023
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2023, № 1 7
ПРОБЛЕМИ ДИНАМІКИ КЕРОВАНИХ СИСТЕМ
УДК 62-52
A. Kulik
THE PRINCIPLE OF CONTROL BY DIAGNOSIS
AS A RESULT OF THE SYSTEMATIC APPLICATION
OF FUNDAMENTAL CONTROL PRINCIPLES
Anatoly Kulik
National Aerospace University «Kharkiv Aviation Institute»,
anatoly.kulik@gmail.com
The subject of study is the principle of control by diagnosis. The goal is to form
a control principle based on a diagnosis as a result of the systematic application
of fundamental management principles. Task: an excursion into history of mas-
tering the principles of control. Analysis of features, positive and negative quali-
ties of principles of control by setting influence, by disturbing influence and by
deviation. Description of the principle of control by diagnosis. Presentation of
diagnostic functional models of diagnostic objects. Giving an example of the ap-
plication of the principle of control by diagnosis. The methods used are: retro-
spective analysis, the method of constructing graphic functional schemes, the
method of the space of discrete states, the method of forming diagnostic func-
tional models, methods of bench research and simulation modeling. The follow-
ing results were obtained: the process of mastering control principles was de-
composed into three stages: intuitive understanding of principles, mastering
them in industry and scientific mastering. Features of the principles of control by
setting influence, disturbing influence and by deviation are described. The prin-
ciple of control by diagnosis and the functional scheme of a rational control sys-
tem are proposed. Diagnostic functional models are presented that reflect the re-
lationship between direct signs of destabilizing influences and indirect signs that
are directly available for measurement. The results of experimental studies are
presented, which testify to the possibility of rational control of the operability of
sensors of flight parameters, in particular, of angular movements, during the ac-
tion of various types of destabilizing influences. Conclusions. The scientific
novelty consists in the formation of a new principle of control based on diagno-
sis and the development of a number of tools, the use of which allows to ensure
the functionality of automatic control objects under the conditions of various
types of destabilizing influences.
Keywords: principle of control, automatic control object, control by diagnosis,
diagnosing, recovery of operability, state space, diagnostic functional model.
Introduction
The history of the development of automation is an integral part of the general his-
tory of the evolution of the material culture of mankind. The basic principles of automa-
tion are control principles. A principle (from lat. principium — beginning). The basic
beginning on which anything is built (any scientific system, theory, policy, device,
etc.) [1]. The mastery of the basic fundamental principles of automatic control continues
8 ISSN 2786-6491
throughout the history of the evolution of material culture, and this is evidenced by nu-
merous examples of tools, devices, machines and systems, with the help of which the
automation of certain technological processes was carried out in different periods of the
development of civilization.
Learning, mastering and applying of the fundamental control principles underlying
living and non-living nature is a long, complex, iterative process. The history of this
process allows us to trace the main trends in the development of scientific knowledge
and the ways of mastering and improving the fundamental principles of control by sys-
tematizing them to solve the current automation tasks caused by the challenges of scien-
tific and technological progress.
One of the basic ones is the trend related to the further implementation of the con-
trol processes of complex automatic control objects with long period of autonomous
functioning in conditions of uncertainty of influences that lead to impaired operability.
Improvement of control processes takes place through the development of new control
principles based on fundamental ones. Violation of the performance of automatic con-
trol objects occurs due to external influences: disturbance, noise, interference, and in-
ternal: malfunctions, failures and refusings. All these influences are uncertain events
that destabilize operability, in other words, they are destabilizing influences. The signif-
icant uncertainty of destabilizing influences makes it necessary to develop procedures
for identifying their specific physical types in order to make effective decisions how to
parry it for restoring the operability of the automatic control object. Fundamental prin-
ciples of control do not allow for the development of quality procedures for finding the
causes of performance degradation, and therefore one of the possible ways to identify
destabilizing influences is the development of a new principle of control based on diagnosis.
The article presents the results of research on the development of a new principle
of control by diagnosis based on further systematization of the fundamental principles
of control.
1. Excursion into history of mastering control principles
In the history of mastering the principles of control, three stages can be condition-
ally distinguished. The first is related to an intuitive understanding of control principles
and their use in the simplest devices. The second stage is characterized by the further
development of the principles and their applying in industry. The third stage is the sci-
entific mastering of control principles, their formalization, solving the tasks of stabiliza-
tion and positioning of objects of various physical nature, including the states when they
are under uncertain operating conditions.
Man at the dawn of civilization realized his limited physiological capabilities in
comparison with the capabilities of nature. Various tools and devices became the first
means of expanding the physical capabilities of primitive people [2–4]. The need to
catch fish, animals and birds created a need for new devices and devices in which the
fishing process took place without direct human participation, i.e. automatically. The
impressive penetration of the first inventors into the principles of control and its imple-
mentation in various tools for daily life and hunting amazes the imagination. The analy-
sis of the first devices for fishing, from the point of view of the composition of func-
tional elements, shows that such functional elements as sensitive and executive per-
formed tasks without direct human participation, i.e., automatically, in accordance with
the principle of control by setting influence.
Great interest in the early period is shown in the invention of various toys and de-
vices used for entertainment and religious purposes. For example, the automatic signal-
ing device of the ancient Greek philosopher Platon, a water vending machine, a device
for opening temple doors, described by Heron of Alexandria, and a number of others
that used the principle of control by setting influence.
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2023, № 1 9
Twenty centuries ago, in ancient Greece, Heronʼs oil lamp was used for lighting —
it is a device that automatically feeds the wick when the oil level drops. The following
elements were used in the lamp: a float to determine the oil level, a rack and pinion to
transmit movement, a rack wrapped in wick to control the feed. In this device, the prin-
ciple of control by deviation was implemented.
So, the first stage is characterized by the following features. First, the wide applica-
tion of the principle of control by setting influence in various simplest automatic devic-
es. Secondly, the use of various physical phenomena to build automatic devices. Third-
ly, achieving an understanding of the main principle of building biological systems —
the principle of control by deviation, and its practical use in non-production spheres of
activity.
The second, most fruitful stage of the use of control principles was determined by
the need for further improvement of the technique of industrial use of wind, water and,
especially, steam. So, Agostino Romelli (1530–1590), an Italian military engineer, de-
veloped an automatic device that regulates the speed of rotation of the millstone when
grinding grain in a mill. This device used the principle of control by disturbance. The
appearance of the first steam engines by the Frenchman Papin, the Englishmen Sowery,
Thomas Newcomen and John Kelly contributed to the development of automatic stabi-
lization devices. In 1763, the outstanding Russian inventor I. Polzunov developed a pro-
ject of a universal steam engine, which used an automatic stabilizer of the water level in
the cauldron. In 1784, the Englishman James Watt received a patent for a centrifugal
regulator of the angular speed of rotation of the shaft of a steam engine. In this regula-
tor, the principle of control by deviation was used. In 1829, the French scientist J. Pon-
celet proposed a regulator of the angular speed of rotation of the shaft of a steam engine,
based on controlling the supply of steam depending on the amount of load, that is using
the principle of control by disturbance.
The inventions of I. Polzunov, J. Watt and J. Poncelet initiated a whole series of
inventions of new automatic devices designed to stabilize the operation of steam en-
gines using the principles of control by deviation and disturbance.
In 1676, the Dutch scientist Christian Huygene published a work on mechanics
called «The Pendulum Clock», in which a cycloidal pendulum was presented. It was
characterized by a constant oscillation period regardless of the amplitude due to the use
of an anchor mechanism. The anchor mechanism provided undamped oscillations with
the help of nonlinear negative feedback. This type of connection transforms the constant
force acting on the anchor wheel into a variable periodic effect on the pendulum, which
compensates for the effect of frictional forces. This invention started a new direction in
technology — the development of clock mechanisms for accurate time measurement.
At the same stage, various automatic devices were developed that use the principle
of control and by setting influence. For example, in 1929, the French inventor J. Jac-
quard proposed a device for a loom using a paper tape with holes — punched tape. The
automatic device, with the help of feelers, recognized the location of the holes on each
section of the punch tape and, in accordance with the received information, moved indi-
vidual threads of the fabric base up or down so that the weft passing between them cre-
ated the desired pattern programmed in the punch tape.
The second stage of the application of control principles is related to the creation of
industrial regulators for machines using wind, water and steam energy, as well as vari-
ous mechanisms and machines for the automation of technological operations of pro-
duction processes. Regulators at this stage were built only on the basis of the intuition
and experience of inventors who follow the path of trial and error. The importance of
this stage in mastering the principles of control is difficult to overestimate, since the
possibility of building various machines that perform their functions without human in-
tervention has been practically proven.
10 ISSN 2786-6491
The scientific development of control principles began at the third stage with the
works of the English physicist J.C. Maxwell «On Regulators» (1868) [5] and the Rus-
sian mechanical scientist I.O. Vyshnegradskyi «On direct-acting regulators» (1876) [6].
The works of the Swiss professor A.B. Stodola in the field of configuration and calcula-
tion of heat engines, steam and gas turbines complete the creation of the classic linear
theory of automatic regulation of the engines [7]. The scientific study of the possibilities
of the principle of control by deviation led to the emergence of a number of new scien-
tific tasks. Thus, a scientific approach to the mathematical description of transformation
processes in a steam engine and a centrifugal regulator was needed. As a result of the
conducted research, mathematical models of the first approximation were developed.
The study of linear differential equations of the third order led to a new task — ensuring
the stability of processes in a closed-loop control system. And the first solutions were
the root criteria of stability. Then, the criteria of Raus-Hurwitz, Nyquist, Mikhailov,
Kharitonov and a number of others were developed. For a closed-loop control system,
in addition to the task of ensuring stability, which is a necessary condition of operation,
it is necessary to solve the task of quality of control — a sufficient condition of opera-
tion. As a result of solving the problem of the quality of regulation, and in the future —
the quality of control, a number of methods, theories, scientific directions appeared for
the purpose of ensuring the specified accuracy of control, optimization of the transition
process time, analytical design of regulators, dual control and others.
Further development of the principle of control by deviation in the class of nonlin-
ear systems led to new scientific results and the emergence of scientific trends in the
theory of stability, taking into account the fundamental results of O.M. Lyapunov.
The scientific development of the principle of control by disturbance, thanks to the
works of H.V. Shchypanov, V.S. Kulebakin, B.M. Petrov, A.G. Ivakhnenko and
A.I. Kukhtenko contributed to the creation of the theory of invariance. The further de-
velopment of the theory of invariance led to the formation of a new scientific direction —
combined control, which is based on the joint use of two principles of control — by de-
viation and by disturbance [8–11].
The trend of significant complication of control objects, caused by the expansion
of their functions, scale, energy intensity and criticality, contributed to the development
of many scientific directions regarding the joint use of fundamental principles of con-
trol. This trend has led to a revision of the classical approach to the design of control
systems. It was necessary to take into account cost, weight and size, energy limitations
and risks associated with the uncertainty of operating conditions, i.e. abnormal situa-
tions. Accidents and disasters in rocket and space engineering, nuclear technics and
chemical production challenged the theory of automatic control. The increase in the
structural and functional complexity of automation objects gives rise to the expansion of
a multitude of influences, both external (disturbance, interference, noise) and internal
(malfunctions, breakdowns, failures), which disrupt the performance of automatic con-
trol systems and lead to emergency situations. These disruptive actions, essentially de-
stabilizing actions, cannot be fully defined and described at the stage of the control sys-
tem design.
The problem of ensuring the guaranteed operability of autonomous control systems
at a given time interval can be solved in the intensively developing class of adaptive
systems. Thanks to the works of many scientists, such directions of automatic control
have been formed as extreme control, combined control, control with a reference model,
control with identification, control systems with self-adjustment and with the possibility
of self-organization and self-learning, and a number of others [12–14].
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2023, № 1 11
Known approaches of adaptive control use fundamental control principles, mathe-
matical models of automation objects, and a number of hypotheses regarding operating
conditions. Among all possible hypotheses about destabilizing influences, the most dif-
ficult for practical use is the hypothesis about the uncertainty of the moment of their ap-
pearance, place of their appearance, type and specific physical form; in other words, the
event uncertainty hypothesis.
The results of academician V.M. Kuntsevichʼs research on the use of fundamental
control principles for adaptation in conditions of uncertainty of a non-stochastic nature
initiated new scientific directions. Such directions expand the classes of automation ob-
jects up to objects of critical infrastructure and take into account more fully the peculi-
arities of their operation in order to ensure guaranteed operability over a long period of
autonomous operation [15].
Therefore, the third stage in mastering the fundamental principles of control,
thanks to the scientific approach, is characterized by a deeper penetration into the un-
derstanding of control processes in living and non-living nature and revolutionary au-
tomation of control processes of objects of various physical nature. This is accompanied
by the involvement of advanced mathematical tools both for describing the processes of
information transformation in control systems and for analytically solving the tasks of
analysis and synthesis. At the third stage, unique control systems for autonomous ob-
jects with advanced adaptation capabilities to changing operating conditions are created.
Intensive computer automation of the processes of analysis and synthesis of individual
classes of control systems is taking place.
Increasing requirements for the quality of operation of control systems for various
complex and critical objects and processes has contributed to the expansion of the front
of research on the joint use of fundamental control principles with the aim of obtaining
new system effects that provide more productive adaptation in uncertain operating con-
ditions.
Letʼs consider the functional features of the fundamental principles of control in re-
lation to modern and promising automation objects, the functioning of which is carried
out in conditions that change in an uncertain manner.
2. The principle of control by setting influence
It is advisable to consider the features of the principle of control by setting influ-
ence with the help of a functional scheme that reflects the informational features of
transformation processes (Fig. 1). The scheme uses the following notations: ( )SU t —
setting influence; ( )СU t — control signal; ( )y t — output parameter; MCD — micro-
processor control device; ACO — automatic control object; D — set of destabilizing
influences.
Fig. 1
The principle of operation of this automatic control system is obvious. When a set-
ting influence ( )Su t is applied to the MCD, a control signal ( )Сu t is formed, which is
sent to the actuators of the ACO. As a result, appropriate technological operations are
performed to obtain the desired value of the output signal ( ).y t
D is a set of disturbances, noises and failures that disrupt the operational efficien-
cy of the ACO. Failures mean malfunctions, refusings, degradations that lead to a sig-
( )Su t ( )Cu t
( )y t
MCD ACO
D
12 ISSN 2786-6491
nificant change in technical characteristics. All the destabilizing effects of the set D
lead to varying degrees of changes in the functional properties of the open-loop control
system, which is a sequential connection of the functional elements of the MCD and
ACO. A change in the functional properties of the control system is reflected in the re-
sult of its functioning — a signal ( ).y t
Among the positive features of the principle of control by setting influence can be
attributed:
— ideological and constructive simplicity;
— high operation speed of open-loop control system;
— preservation of operability under a number of destabilizing influences;
— satisfactory accuracy of output characteristics;
— ease of configuration and maintenance of open-loop control systems.
The negative features of this control principle include:
— high sensitivity to changes in open-loop control system parameters caused by
failures;
— impossibility of obtaining high accuracy of initial characteristics in case of un-
known disturbances and low accuracy of ACO models;
— impossibility of full compensation of disturbances for ACO with transport
delay;
— inoperability of the open-loop control system in case of catastrophic failures and
disturbances exceeding the design levels;
— impossibility of controlling an unstable ACO.
Therefore, the principle of control by setting influence can be applied to stable
ACOs, the transforming properties of which are well studied and reflected in the corre-
sponding models. Under the uncertain conditions of operation of the ACO, the prin-
ciple of control by setting influence does not allow obtaining satisfactory output
characteristics.
Examples of the productive use of the principle of control by setting influence are
pneumatic and hydraulic valves, which open or close the supply of fuel, air or steam to
actuators when an electric signal is applied, vending machines, information boards of
stations and airports, and a number of others.
3. The principle of control by disturbance
There is much more information on the origins of the scientific development of the
principle of control by disturbance influence than by the first principle. With the help of
the simplest functional scheme, we will consider the features of this control principle
(Fig. 2).
Fig. 2
There are many destabilizing influences 1{ ,..., ,..., }i qD d d d on the ACO. Let
the impact id significantly affect the process of operation of the ACO and can be
measured, then with the help of a correction device (CD), it is converted into a correc-
( )Su t
( )Ku t
( )Su t ( )Cu t
MCD
CD
di
d1 dq
ACO
y(t)
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2023, № 1 13
tion signal ( )Ku t that enters the adder of the system. The corrected setting influence
( )Su t enters the MCD, where the control signal is formed ( ).Cu t This signal compen-
sates for the destabilizing impact id on the processes in the ACO and ensures the
corresponding output parameter of the system — signal ( ).y t So, the functional di-
agram shows a single-loop compensation system for one destabilizing impact .id
A fundamental point is the possibility of measuring destabilizing influences. Not all de-
stabilizing effects can be measured either because of the lack of appropriate sensors or
because of the complexity and cost of their measurement. It is not possible to provide a
measure of the magnitude of such destabilizing effects as failures. The formation of
several contours of compensation for destabilizing influences leads to difficulties in co-
ordinating their functioning and the complexity of technical implementation. For the or-
ganization of qualitative compensation of destabilizing influences, fairly accurate math-
ematical models of transformation processes in the ACO are required. Any changes in
the operating conditions lead to a change in the compensation conditions and, as a re-
sult, a deterioration of the output characteristics. For the formation of an effective com-
pensation circuit, knowledge of the maximum value of the destabilizing influence is re-
quired for the correct selection of the actuators in the ACO, which will ensure that the
control signal is worked out on the working area of static characteristics.
These circumstances lead to the fact that it is practically impossible to ensure high
accuracy of working out a setting influence in the conditions of destabilizing effects
from the set .D It is possible to ensure control accuracy only for a limited subset of in-
fluences that can be measured under the condition of stability of ACO characteristics
during operation.
The positive properties of the principle of control by disturbing influence in rela-
tion to the task of countering destabilizing influences are as follows.
1. Detection of all destabilizing influences only significant and measurable ones,
the impact of which on the processes in the ACO can be fully compensated.
2. The use of fairly simple compensation algorithms that do not create the need to
ensure the stability of the compensation loop.
3. Ensuring qualitative compensation of the impact of the measured destabilizing
influences on the output characteristics of the ACO.
4. The operation speed of the compensation loop is comparable to the operation
speed of the main ACO control channel.
5. The lack of complete information about the output characteristics of the ACO
excludes the need to solve the problem of management stability.
The following can be attributed to the negative properties of the principle of con-
trol by disturbance.
1. Elimination of the influence of only those destabilizing influences for which
compensation loops have been created.
2. The presence of a large number of uncontrolled destabilizing influences leads to
a low level of output characteristics of the ACO, that is, to a violation of the systemʼ s
operability.
3. When both the internal and external conditions of system functioning are changed,
the conditions for compensation of measurable destabilizing influences are violated.
4. Impossibility to applicate this principle in the ACO, the properties of which
change during operation.
5. There is a compensation for the impact of destabilizing influences on the opera-
tional efficiency of the ACO, rather than a countermeasure of the causes that gave rise
to abnormal situations in the control processes.
14 ISSN 2786-6491
The application of the principle of control by disturbance gives good results for stable
ACOs, the properties of which are adequately reflected in the corresponding models.
4. Principle of control by deviation
The scientific development of this productive principle of control has been started
with the fundamental works of J.K. Maxwell, I.A. Vyshnegradskyi and A.B. Stodola
and continues to the present day through implementation in various fields of human ac-
tivity. A graphic model in the form of the simplest functional scheme (Fig. 3) allows to
display visually the features of this principle in relation to the ACO.
Fig. 3
A set D of destabilizing influences , 1,id i q which change arbitrarily, acts on
the ACO. Information about the output parameter of the ACO is represented in the dia-
gram by a signal ( )Mu t from the sensor (S). In the given scheme, the «adder» function-
al element is removed from the MCD as a key element in the implementation of the
principle of control by deviation. A deviation signal ( ) ( ) ( ),S Mu t u t u t which con-
tains information about the consequences of destabilizing influences from the set ,D is
generated in the adder. The difference signal is converted into a control signal ( )Cu t in
the MCD. It is sent to the actuator, which changes the state of the control object (CO),
which is reflected in the output measurement signal ( )Mu t form the sensor. To imple-
ment this control principle, a signal from the system output to its input is used, that is,
feedback. As a result, a closed control loop or a closed-loop control system is formed.
The principle of control by deviation is universal, it is applicable to objects and disturb-
ances of any physical nature. This principle is quite effective, allows to achieve high-quality
compensation of destabilizing influences from the set ,D which are constantly changing.
The following are the positive properties of the principle of control by deviation.
1. The ability to detect the appearance of any destabilizing influences in the
control loop.
2. The ability to compensate for «small» deviations from the given behavior caused
by destabilizing influences.
3. The ability to adjust the dynamic properties of the ACO using appropriate algo-
rithms in order to ensure the necessary reserves of stability and quality indicators.
4. Low sensitivity to changes in parameters of functional elements in a closed-loop
control circuit.
5. Low requirements for the adequacy of the mathematical description of the trans-
formation processes in the functional elements of the system.
In the presence of such positive properties, the use of the principle of control by
deviation does not allow to ensure fully the necessary and sufficient conditions for the
operability of modern and promising control systems of long-term and autonomous
functioning. The main reasons are as follows.
1. There is compensation for the consequences of destabilizing influences, rather
than parrying the causes of influences that can be eliminated.
2. The internal inconsistency of the principle is due to the need to allow destabili-
zation and then compensate for it.
( )Su t ( )Am t ( )Mu t ( )Cu t
MCD
D
CO
ACO
y(t)
A S
( )u t
–
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2023, № 1 15
3. When compensating for destabilization, workable functional elements are forced
to work simultaneously with non-functional ones, and in costly, intensive modes, while
spending additional energy and resources.
4. Destabilizing influences that lead to a significant change in system parameters
and structure are not compensated.
5. It is impossible to localize destabilizing influences and target, flexibly and con-
cretely neutralize them.
6. The period of detection and compensation of destabilizing influences is deter-
mined by the transition period of the closed-loop control system.
7. Destabilizing influences are uncontrollable and unmeasured inputs to the control
system.
The application of the principle of deviation control allows to develop automatic
control systems that have the ability to adapt in the «small». Such adaptation occurs due
to the property of the system to detect and compensate for the limited effects of arbitrar-
ily changing, uncontrolled destabilizing influences.
Further development and improvement of the considered control principles are
possible in their systematic combination. Such a union should preserve their positive
properties and eliminate their shortcomings in such a way as to ensure the possibility of
adaptation in the «big» to real destabilizing influences. Such a systematic combination
of basic principles is called the principle of control by diagnosis.
5. Principle of control by diagnosis
The development of the first instrumental means of signal-parametric diagnostics
of automatic control systems [16] and means of restoration of operability [17] led to the
need to find a control principle that allows adaptation to arbitrarily changing uncon-
trolled various types of destabilizing influences on a unified ideological basis in order to
ensure the desired behavior of an autonomous control objects.
As a result of further research, it was possible to formulate the principle of control
based on the diagnosis, which can be presented using the functional scheme shown
in Fig. 4.
Fig. 4
The rational control object (RCO) is an object that has the properties of being di-
agnosed and restored. Diagnosability is the possibility of establishing the causes of de-
stabilizing influences in finite time according to states available for measurement. Re-
coverability is defined as the possibility of transferring the RCO from an inoperable
state to an operable one by neutralizing destabilizing influences id D in a finite time
interval. Two types of signals are received by the MCD diagnostic module from the ra-
tional control object: 0( )Mu kT — discrete signals for measuring RCO parameters from
sensors; 0( )Pu kT — signals from check points; 0,1,2,...k ; 0T — period of discre-
tion. With the application of a setting influence 0( )Su kT in the diagnostic module, a di-
agnosis D̂ is formed in the form of estimates of direct signs of destabilizing influences.
The received diagnosis is sent to the control module, in which control actions are formed
0( )Su kT 0( )Mu kT
D̂
MCD
Diagnostic
module
D
0( )Ru kT
0( )Pu kT
Control
module
Rational
control
object
Diagnosis
0( )Cu kT
16 ISSN 2786-6491
that restore operability of RCO: 0( )Сu kT — signals that parry the destabilizing influences
revealed as a result of diagnostics, and 0( )Ru kT — signals that control the reconfiguration
of hardware by disconnecting failed and connecting backup devices.
In the diagnostic module, the tasks of detecting destabilization are solved sequen-
tially using the principle of control based on the deviation of the current signal
0( )Mu kT relative to the reference behavior of the object. Next, the place of occurrence
of destabilization is localized using local deviations of signals from their reference val-
ues. Identification of the type and kind of destabilization in accordance with the princi-
ple of control by disturbance allows to obtain estimated values of the magnitude of de-
stabilizing influences. Thus, the diagnosis consists in estimating the moment of time
when destabilization was detected, finding a specific structural part of the object where
destabilization occurred, identifying the type of destabilization, and determining the es-
timated value of the destabilizing effect.
The positive properties of the principle of control by diagnosis include the fol-
lowing.
1. Ability to diagnose specific destabilizing influences and parry them.
2. Possibility of more accurate compensation of destabilizing influences on control
processes.
3. The principle makes it possible to develop perfect adaptive systems that ensure a
more accurate working out of a setting influence ( )SU t during longer operation.
4. This principle is applied to diagnosed objects with incomplete or even missing
information about destabilizing influences.
5. The principle of control by diagnosis helps to actively increase the resource and
duration of active functioning of autonomous control systems.
The negative features of this principle are as follows.
1. The difficulties of creating scenarios of abnormal situations in control systems and
the impact of their consequences on the performance of autonomous control functions.
2. The formation of the set D requires a deep knowledge of the features of the
functioning of the automatic controling object.
3. The complexity of developing algorithms and programs for the processes of di-
agnosing and restoring the operability of objects.
4. At the current stage of mastering this principle, it is not possible to automate the
development of diagnostic and recovery processes.
5. The work intensity of the formation of means of operability restoration, balanced
with a set of destabilizations .D
So, in the principle of control by diagnosis, the principle of control by disturbance
is applied in terms of obtaining information about destabilizing influences and in terms
of compensating the action of destabilizing influences on the control process. The prin-
ciple of control by deviation is applied to detect the fact of destabilization, detect the
destabilized structural part of the object, and form stabilizing control influences. The
principle of control setting effect is used in the part of the formation of control effects
during the reconfiguration of hardware.
The application of the principle of control by diagnosis opens up the possibility
of implementing better adaptive automatic control of objects with incomplete a pri-
ori information about destabilizing influences in the process of development, pro-
duction and operation, and even in the absence of such information. Such adaptive
control will allow in the future reduce ignificantly various resource costs for devel-
opment, production and operation and significantly increase the periods of active
functioning of autonomous control objects.
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2023, № 1 17
6. Diagnostic functional models
In the practical application of the principle of control by diagnosis, there is a need
for mathematical models that reflect the relationship between the characteristics of de-
stabilizing influences and the signals available by measurement. Such specific models
are diagnostic functional models (DFM) [18]. Letʼs consider the main provisions re-
garding these models.
The process of functioning of the linearized diagnostic object in the time domain
can be represented by the following system of equations:
0 0 0 0 0 0
0 0
[( 1) ] ( ) ( ); (k ) ;
( ) ( ),
x k T Ax kT Bu kT x T x
y kT Cx kT
(1)
where 0( )x kT — state vector of the control object, 0( ) ;nx kT X 0( )u kT — control
vector, 0( ) ;ru kT U 0( )y kT — vector of measured parameters, 0( ) ;my kT Y
, і A B C — matrices of appropriate dimensions; 0, 1, 2,...k — discrete number; 0T —
period of discretion.
A set of possible destabilizing influences 1{ ,..., ,..., }i qD d d d is used in the con-
struction of the DFM. Each destabilizing influence is matched by a parameter i whose
value changes in the interval [ , ].i i i The perturbed motion of the diagnostics ob-
ject for the parameter i will take the following form:
0 0 0 0 0 0
0 0
[( 1) ] ( ) ( ) ( ) ( ); ( ) ;
( ) ( ) ( ),
i i i i i i
i i
x k T A x kT B u kT x k T x
y kT C x kT
(2)
where 0( )x kT — the state vector of the object destabilized by the event ;id
( ), ( ) і ( )i i iA B C — matrices of the corresponding dimensions, the coefficients of
which depend nonlinearly on the parameter .i
Equations of additional movements of the object caused by the appearance of de-
stabilizing influence id can be obtained by applying reference models. Having chosen
the simplest reference model in the form of the system of equations (1) for 0 0( ) 0x k T
and performing analytical linearization of nonlinear dependencies, we obtain
0 0 0 0 0 0
i 0 0
[( 1) ] [ ( ) ( )] ; ( ) ;
( ) ( ); 1, ,
i i i i i i
i i
x k T A x kT B u kT x k T x
y kT C x kT i q
(3)
where
( ) ( ) ( )
, ,i i i
i i i
i i i
A B C
A B C
— sensitivity functions of the corre-
sponding matrices by parameter ;i i — a slight change in the parameter ,i such
as
2.i i
The system of equations (3) reflects the functional relationship of the unmeasura-
ble direct sign i of the destabilizing influence id with the measurable indirect sign
0( ).iy kT Such a system of equations is the DFM for the direct sign i of the desta-
bilizing influence .id
Diagnosability criteria are used to assess the diagnosability using DFM.
18 ISSN 2786-6491
Criteria of structural diagnosability. For the structural diagnosability of the ob-
ject according to the DFM, it is necessary and sufficient that the matrices , 1,iL i q
are linearly independent in all pairwise combinations.
0
i i
i
i
A B
L
C
. (4)
Criteria of signal diagnosability. For signal diagnosability of an object by DFM,
it is necessary and sufficient that the vectors * , 1,i iL v i q are linearly independent in all
pairwise combinations.
Matrices *, 1,iL i q are matrices of an object that has the property of structural di-
agnosability. Vector
0
0
0
( )
( ) ,
( )
x kT
v kT
u kT
(5)
where 0( )x kT — state vector of the reference model.
The criteria of structural and signal diagnosability make it possible to form a DFM
with an unambiguous connection of direct signs of destabilizing influences i with
indirect signs i 0( )y kT and to determine the signal conditions for the manifestation of
these connections.
7. An example of the application of the principle of control by diagnosis
As an object of research, letʼ s consider a fragment of a block of gyroscopic sensors,
which was used on flying models. Flying models are a research tool for obtaining reliable in-
formation about the behavior of the future aircraft in all designed flight modes [19]. The
general view of the stand for the study of sensors in the course channel is shown in Fig. 5.
An angle sensor (AS) and two angular velocity sensors (AVS) were used in this channel. In
order to work out the models, algorithms and programs of the principle of managing the per-
formance of sensors by diagnosis, a stand was developed according to the functional scheme
shown in Fig. 6.
Fig. 5
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2023, № 1 19
Fig. 6
Signals from the angle sensor (AS) and angular velocity sensors (AVS1 and AVS2)
through the ADC are sent to the corresponding blocks of simulators of destabilization
types SDT , 1, 3.i i The blocks SDTi work according to commands from the generator
of types of destabilizing influences (GTDI). Blocks SDTi together with GTDI carry out
deformation of signals from sensors according to defined scenarios specified by the
command 1 0( ).С kT Deformed signals, which reflect the result of the current destabiliz-
ing effect on the sensor, are sent to the unit for diagnosing the sensor operability (DSO).
In this block, the cause of impaired operability is revealed by indirect signs and a diag-
nosis ˆ
id is formed. The DSO unit is activated by the command 2 0( ).С kT The result of
diagnosing — the diagnosis is sent to the unit, which performs the function of recover-
ing the sensor operability (RSO). In the RSO block, according to the diagnosis and with
the help of available means, the deformed signal distorted by the destabilizing influence
is restored, and the estimated values of the signals 0ˆ ( )u kT and 0ˆ ( )u kT are calculated.
The set of types of destabilization were generated for each sensor. For example, for
AS the set 1 2 10{ , ,..., },D d d d where 1d — positive zero drift with the possibility of
compensation, 2d — negative zero drift with the possibility of compensation, 3d —
positive zero drift without compensation, 4d — negative zero drift without compensa-
tion, 5d — reduction of the conversion factor with the possibility of compensation, 6d —
reduction of the conversion factor with and without compensation, 7d — break in the
signal wire of the sensor, 8d — break in the negative power wire, 9d — break in the
positive power supply wire, 10d — unknown type of destabilization.
For the stand, which contains three gyroscopic sensors, 30 scenarios of emer-
gency situations were formed and algorithms and software were developed for diag-
nosing and restoring sensor operability. Graphs of processes during destabilization
in AVS2, which is caused by a rediction in the conversion factor is shown in Fig. 7.
At the 5th second, a distortion of the sensor signal appeared due to destabilization
from a reduction in the conversion factor with the possibility of compensation. The
graph shows the distortion of the time characteristic of the signal compared to the
time characteristic of AVS1. From this moment, destabilization in the functioning of
the sensors is detected. Then, as a result of the search, a faulty sensor is found. It is
AVS2. The type of destabilizing effect is established — reduction of the conversion
factor, and the type of destabilizing effect — reduction of the conversion factor
with the possibility of compensation is determined. At the 10th second, the diagnos-
tic process was completed, and at the 12th second, the process of restoring meas-
urements from AVS2 by signal tuning was completed.
( )u t
AS
0ˆ ( )u kT
1 0( )u kT
2 0( )u kT
2 ( )u t
1( )u t
( )t
( )t
AVS1
AVS2
ADC
STD1
STD2
STD3
GTDI DSO
1 0( )С kT
2 0( )С kT
ˆ
id
2 0( )u kT
1 0( )u kT
0( )u kT
0ˆ ( )u kT
RSO
0( )u kT
20 ISSN 2786-6491
a
b
Fig. 7
Therefore, for each scenario, the graphs of the processes of diagnosing and restor-
ing measurements of gyroscopic sensors were obtained. This indicates the fundamental
possibility of adapting to various types of destabilizing influences and ensuring high-
quality measurement of flight parameters, for example, yaw angle and angular speed,
using the principle of control by diagnosis.
Conclusion
The presented description of the fundamental principles of control and the history
of their scientific development testifies to their continuous development and improve-
ment. One of the productive directions of development consists in their systematic com-
bination and obtaining a new systemic effect.
Angle sensor Estimation of angular velocity value from AS
Estimation of yaw angle value from AVS1
Recovered value of yaw angle
Angular velocity sensor AVS1
Angular velocity sensor AVS2
, grad ˆ
, grad/s
, grad/s
1̂ , grad
, grad/s 2̂ , grad
0 20 40 60 t, s
– 150
0
150
0 20 40 60 t, s
– 15
0
15
0 20 40 60 t, s
– 15
0
15
0 20 40 60 t, s
– 150
0
100
0 20 40 60 t, s
– 150
0
100
0 20 40 60 t, s
– 15
0
15
0 20 40 60 t, s
– 15
0
15
, grad
ˆ
, grad/s
20 40 60 t, s
– 100
0
100
0
Recovered value of angular velocity
Estimation of yaw angle value from AVS2
Міжнародний науково-технічний журнал
Проблеми керування та інформатики, 2023, № 1 21
Systematic combination of fundamental principles of control with the aim of obtaining
information about uncontrolled destabilizing influences that change arbitrarily led to a new
principle of control by diagnosis. In this control principle, it was possible to preserve the posi-
tive properties of the fundamental control principles, the combination of which made it possi-
ble to obtain a new property that ensures the controllability of destabilizing influences and the
possibility of parrying them. This circumstance opens up new opportunities for the develop-
ment of advanced control systems with wider adaptive properties for autonomous objects
with a long period of active operation in harsh, not fully defined operating conditions.
А.С. Кулік
ПРИНЦИП КЕРУВАННЯ ЗА ДІАГНОЗОМ
ЯК РЕЗУЛЬТАТ СИСТЕМНОГО ЗАСТОСУВАННЯ
ФУНДАМЕНТАЛЬНИХ ПРИНЦИПІВ КЕРУВАННЯ
Кулік Анатолій Степанович
Національний аерокосмічний університет ім. М.Є. Жуковського «Харківський
авіаційний інститут»,
anatoly.kulik@gmail.com
Предметом вивчення є принцип керування за діагнозом. Мета полягає у фор-
муванні принципу керування за діагнозом як результату системного застосу-
вання фундаментальних принципів керування. Зроблено екскурс в історію
освоєння принципів керування. Проаналізовано особливості, позитивні та не-
гативні якості принципів керування за задавальним впливом, за збурювальним
впливом та за відхиленням. Описано принцип керування за діагнозом. Подано
діагностичні функціональні моделі обʼєктів діагностування. Наведено приклад
застосування принципу керування за діагнозом. Використано ретроспективний
аналіз, метод побудови графічних функціональних схем, метод простору дис-
кретних станів, метод формування діагностичних функціональних моделей,
методи стендових досліджень та імітаційного моделювання. Отримано такі ре-
зультати — проведена декомпозиція процесу освоєння принципів керування на
три етапи: інтуїтивного розуміння принципів, освоєння їх у промисловості та
наукового освоєння. Описано особливості принципів керування за задаваль-
ним впливом, збурювальним впливом і за відхиленням. Запропоновано прин-
цип керування за діагнозом та функціональну схему раціональної системи ке-
рування. Представлено діагностичні функціональні моделі, що відображають
звʼязок прямих ознак дестабілізуючих впливів із непрямими ознаками, які без-
посередньо доступні для вимірювання. Наведено результати експерименталь-
них досліджень, які свідчать про можливість раціонального керування працез-
датністю датчиків параметрів польоту, зокрема кутових рухів, під час дії різно-
типних дестабілізуючих впливів. Наукова новизна полягає у формуванні
нового принципу керування за діагнозом та розробці низки інструментальних
засобів, застосування яких дозволяє забезпечити працездатність обʼєктів авто-
матичного керування в умовах дії різнотипних дестабілізуючих впливів.
Ключові слова: принцип керування, об’єкт автоматичного керування, ке-
рування за діагнозом, діагностування, відновлення працездатності, простір
станів, діагностична функціональна модель.
REFERENCES
1. Большой словарь иностранных слов. (Large dictionary of foreign words. https://gufo.me>
dict>foreign_words. 18.10.2022.)
2. Романенко, Д. И. Забытые изобретения Герона Александрийского. (Romanenko D.I. Forgot-
ten inventions of Heron of Alexandria. https:// romanenko.biz. 20.10.2022.)
3. Черепнев А.Н. Истоки автоматизации. М. : Наука, 1975. 200 c. (Cherepnev A.N. The origins
of automation. M. : Science, 1975. 200 p.)
22 ISSN 2786-6491
4. Косса П. Кибернетика. М. : Изд-во иностр. лит., 1958. 130 c. (Kossa P. Cybernetics. M. : For-
eign Lit. Publ., 1958. 130 p.)
5. Максвел Д.К., Вышнеградский И.А., Стодола А. О регуляторах: В кн. Теория автоматиче-
ского регулирования (линеаризованные задачи). Редакция и комментарии академика
А.А. Андронова и члена-корреспондента АН СССР И.Н. Вознесенского. М. : Изд-во АН
СССР, 1949. С. 43–95. (Maxwell D.K., Vyshnegradsky I.A., Stodola A. On regulators. In book:
Theory of automatic control (linearized problems). Edited and commentary by Academician
A.A. Andronov and Corresponding Member of the USSR Academy of Sciences I.N. Voznesen-
sky. М. : USSR Academy of Sciences Publ., 1949. P. 43–95.)
6. Андронов А.А. И.А. Вышнеградский и его роль в создании теории автоматического регу-
лирования (100 лет со дня опубликования работ И.А. Вышнеградского по теории автома-
тического регулирования). Автоматика и телемеханика. 1978. № 4. С. 5–17. (An-
dronov A.A. I.A. Vyshnegradsky and his role in the creation of the theory of automatic control
(100 years since the publication of the works of I.A. Vyshnegradsky on the theory of automatic
control). Automation and telemechanics. 1978. N 4. P. 5–17.)
7. Максвел Д.К., Вышнеградский И.А., Стодола А. О регулировании турбин: В кн.: Теория
автоматического регулирования (линеаризованные задачи). Редакция и комментарии ака-
демика А.А. Андронова и члена-корреспондента АН СССР И.Н. Вознесенского. М. : Изд-
во АН СССР, 1949. С. 101–176. (Maxwell D.K., Vyshnegradsky I.A., Stodola A. On the regula-
tion of turbines. In book: Theory of automatic control (linearized problems). Editing and com-
ments by Academician A.A. Andronov and Corresponding Member of the USSR Academy of
Sciences I.N. Voznesensky. М. : USSR Academy of Sciences Publ., 1949. P. 101–176.)
8. Щипанов Г.В. Теория и методы построения автоматических регуляторов. Автоматика и
телемеханика. 1939. № 4. С. 4–37. (Shchipanov G.V. Theory and methods for constructing au-
tomatic controllers. Automation and telemechanics. 1939. N 4. P. 4–37.)
9. Кунцевич В.М. Памяти друга и учителя. Индуктивное моделирование сложных систем.
2013. Вып. 5. С. 21–25. (Kuntsevich V.M. In memory of a friend and teacher. Inductive model-
ing of complex systems. 2013. Vol. 5. P. 21–25.)
10. Ивахненко А.Г. Теория комбинированного автоматического управления. К. : Изд-во КПИ,
1954. 121 c. (Ivakhnenko A.G. Theory of combined automatic control. K. : KPI Publ., 1954. 121 p.)
11. Ивахненко А.Г. Электроавтоматика. К. : Гостехиздат, 1954. 292 c. (Ivakhnenko A.G. Electro-
automatics. K. : Gostekhizdat, 1954. 292 p.)
12. Ивахненко А.Г. Связь теории инвариантности с теорией стабильности измерительных си-
стем. Автоматика. 1960. № 5. С. 35–40. (Ivakhnenko A.G. Communication of the theory of in-
variance with the theory of stability of measuring systems. Automation. 1960. N 5. P. 35–40.)
13. Кухтенко А.И. Проблема инвариантности в автоматике. К. : Гос. изд-во технической лите-
ратуры УССР, 1963. 376 с. (Kukhtenko A.I. The problem of invariance in automation. K. : State
publishing house of technical literature of the Ukrainian SSR, 1963. 376 p.)
14. Кухтенко А.И. Основные этапы формирования теории инвариантности. Часть 1. Автома-
тика. 1984. № 2. С. 3–13. (Kukhtenko A.I. Main stages of the formation of the invariance theo-
ry. Part 1. Automation. 1984. N 2. P. 3–13.)
15. Кунцевич В.М. Управление в условиях неопределенности: гарантированные результаты в
задачах управления и идентификации. Київ : Наукова думка, 2006. 261 с. (Kuntsevich V.M.
Control under uncertainty: guaranteed results in control and identification problems. Kyiv : Nau-
kova dumka, 2006. 261 p.)
16. Kulik A.S. Fault diagnosis in dynamic systems via signal-paramitric approach. IFAC/IMACS
Symposium of Fault Detection, Supervision and Safety for Technical Processes – SafeProcess’91.
Sept. 10-13, Baden-Baden, FRG, 1991. Vol. 1. P. 157–162.
17. Kulik A., Kozij A. Sensor unit fault-tolerance enhancement by means of failure diagnosis and
serviceability restoration. Proc. IFAC Workshop on Intelligent Autonomous Vehicles. Sauthamp-
ton, UK, 1993. P. 516–521.
18. Кулик А.С. Сигнально-параметрическое диагностирование систем управления. Харьков : Гос.
аэрокосмич. ун-т «ХАИ», Бизнес-Информ, 2000. 260 с. (Kulik A.S. Signal-parametric diagnostics of
control systems. Kharkov : State Aerospace University «KhAI», Bisnes-Inform, 2000. 260 p.)
19. Кулик А.С. Элементы теории рационального управления объектами. Харьков : Нац. аэро-
косм. ун-т им. Н. Е. Жуковского «ХАИ», 2016. 256 с. (Kulik A.S. Elements of the theory of ra-
tional control of objects. Kharkov : National Aerospace University «KhAI», 2016. 256 p.)
Submitted 03.03.2023
|
| id | nasplib_isofts_kiev_ua-123456789-210932 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0572-2691 |
| language | English |
| last_indexed | 2026-03-19T00:30:37Z |
| publishDate | 2023 |
| publisher | Інститут кібернетики ім. В.М. Глушкова НАН України |
| record_format | dspace |
| spelling | Kulik, A. 2025-12-21T10:37:24Z 2023 The principle of control by diagnosis as a result of the systematic application of fundamental control principles / A. Kulik // Проблеми керування та інформатики. — 2023. — № 1. — С. 7–22. — Бібліогр.: 19 назв. — англ. 0572-2691 https://nasplib.isofts.kiev.ua/handle/123456789/210932 62-52 10.34229/1028-0979-2023-1-1 The subject of study is the principle of management by diagnosis. The goal is to establish the principle of management by diagnosis as a result of the systemic application of fundamental management principles. The scientific novelty lies in the formulation of a new principle of management by diagnosis and the development of instrumental tools enabling the operability of automatic control objects under various destabilizing conditions. Предметом вивчення є принцип керування за діагнозом. Мета полягає у формуванні принципу керування за діагнозом як результату системного застосування фундаментальних принципів керування. Наукова новизна полягає у формуванні нового принципу керування за діагнозом та розробці низки інструментальних засобів, застосування яких дозволяє забезпечити працездатність обʼєктів автоматичного керування в умовах дії різнотипних дестабілізуючих впливів. en Інститут кібернетики ім. В.М. Глушкова НАН України Проблеми керування та інформатики Проблеми динаміки керованих систем The principle of control by diagnosis as a result of the systematic application of fundamental control principles Принцип керування за діагнозом як результат системного застосування фундаментальних принципів керування Article published earlier |
| spellingShingle | The principle of control by diagnosis as a result of the systematic application of fundamental control principles Kulik, A. Проблеми динаміки керованих систем |
| title | The principle of control by diagnosis as a result of the systematic application of fundamental control principles |
| title_alt | Принцип керування за діагнозом як результат системного застосування фундаментальних принципів керування |
| title_full | The principle of control by diagnosis as a result of the systematic application of fundamental control principles |
| title_fullStr | The principle of control by diagnosis as a result of the systematic application of fundamental control principles |
| title_full_unstemmed | The principle of control by diagnosis as a result of the systematic application of fundamental control principles |
| title_short | The principle of control by diagnosis as a result of the systematic application of fundamental control principles |
| title_sort | principle of control by diagnosis as a result of the systematic application of fundamental control principles |
| topic | Проблеми динаміки керованих систем |
| topic_facet | Проблеми динаміки керованих систем |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210932 |
| work_keys_str_mv | AT kulika theprincipleofcontrolbydiagnosisasaresultofthesystematicapplicationoffundamentalcontrolprinciples AT kulika principkeruvannâzadíagnozomâkrezulʹtatsistemnogozastosuvannâfundamentalʹnihprincipívkeruvannâ AT kulika principleofcontrolbydiagnosisasaresultofthesystematicapplicationoffundamentalcontrolprinciples |