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  <front>
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    <article-meta>
      <title-group>
        <article-title>Cognitive-synergetic approach to the design of automated spacecraft with onboard systems with variability properties</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Vladimir S. Kovtun</string-name>
          <email>kovtun_v11@mail.ru</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
          <xref ref-type="aff" rid="aff5">5</xref>
          <xref ref-type="aff" rid="aff6">6</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Alexander N. Pavlov</string-name>
          <email>Pavlov62@list.ru</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff5">5</xref>
          <xref ref-type="aff" rid="aff6">6</xref>
        </contrib>
        <aff id="aff0">
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          <institution>141070</institution>
          ,
          <country country="RU">Russia</country>
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          <institution>CEUR Workshop Proceedings</institution>
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          <addr-line>CEUR-WS.org</addr-line>
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          <institution>Commons License Attribution 4.0 International</institution>
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          <institution>Petersburg</institution>
          ,
          <addr-line>197198</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
        <aff id="aff4">
          <label>4</label>
          <institution>S.P. Korolev Rocket and Space Corporation Energia (RSC Energia).</institution>
          <addr-line>4A Lenin Street, Korolev, Moscow area</addr-line>
        </aff>
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          <label>5</label>
          <institution>Transport</institution>
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          <addr-line>Dec. 11-12, St.Petersburg</addr-line>
          ,
          <country country="RU">Russia</country>
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          <label>6</label>
          <institution>Vasilievsky island</institution>
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          <addr-line>39, Saint Petersburg, 199178</addr-line>
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          <country country="RU">Russia</country>
        </aff>
      </contrib-group>
      <fpage>76</fpage>
      <lpage>83</lpage>
      <abstract>
        <p>Increasing the resource support for the flight of automatic spacecraft (AS) under the existing design restrictions on the mass of onboard systems (OS) and the power of power sources is an important scientific problem. One of the ways to solve the problem is to form relationships between elements of different systems during the design and development of control systems, which allow simultaneous control of several control objects (CO) using one system, thereby providing the solution of two or more functional tasks. At the same time, the composition of on-board controls is reduced or additional functional reserves are formed while maintaining it. This provides additional resources and increases the survivability of the AS. The article discusses a general approach to the design of OS control systems that simultaneously perform several functions in synergistic interaction. The possibility of practical implementation of the system construction based on the proposed approach is shown by the example of designing a phased antenna array of an on-board radio engineering complex.</p>
      </abstract>
      <kwd-group>
        <kwd>Automatic spacecraft</kwd>
        <kwd>phased array antenna</kwd>
        <kwd>control object</kwd>
        <kwd>synergy</kwd>
        <kwd>variability</kwd>
        <kwd>onboard</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1 Introduction</title>
      <p>
        functional resources of the AS with synergetic
resources [
        <xref ref-type="bibr" rid="ref1 ref2">1,2</xref>
        ], a cognitive-synergetic*) system
approach to the development and construction of
OS
      </p>
      <p>management methods was developed. The
essence of the approach is a cognitive system
study of the characteristics of AS as an open,
nonlinear complex technical system, taking into
account the synergistic phenomena in its OS.
Based on the cognitive-synergetic approach, a
new principle of synergetic - variable design of
(A.N. Pavlov);
8882 (A.N. Pavlov).</p>
      <p>Models and Methods for Researching Information System in</p>
      <p>2020 Copyright for this paper by its authors. Use permitted under Creative</p>
      <p>To</p>
      <p>
        explain the initial provisions of the
principle, Figure 1 shows a diagram of a dynamic
model of a variable system-a process controller,
which shows two control systems CS1 and CS 2
that have a synergistic energy relationship. Each
of the systems initially
consists
of control
subsystems CSS1, CSS2 and control objects
CO1, CO2 [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. In turn, each CO is represented
by its own state blocks SB1, SB2, which are
onboard AS systems, and output blocks OB1, OB2.
      </p>
      <p>* ) cognitive-synergetic approach - "cognizing
joint
activity": adjective
"cognitive" from</p>
      <p>Latin
cognitio knowledge, cognition; "synergetic" adjective
from "synergy" - from</p>
      <p>Greek. συν-prefix with the
meaning of compatibility and εϱγον "activity".</p>
      <p>In addition to these, the following set
designations are introduced: X1, X2 - States of
CO1, CO2; Y1, Y2-outputs of CO1, CO2;
Ξdisturbing effects; U1, U2-control effects on CO1,
CO2. In this case, the control is carried out
through the sets of input actions V1 and V2, built
on the binary relations of Cartesian products V1
= U1× Ξ, V2 = U2× Ξ.</p>
      <p>As can be seen from Figure 1, the traditional
control of SB2 in CS2 through CSS2 is replaced
by control through SB1, taking into account the
second feedback between OB2 and CSS1. In this
case, the output of OB1 is connected to the first
input of CSS1. The control action U1 is formed
taking into account the fact that when SB1
performs its functions, the processes
simultaneously form the control action U2 for
SB2. At the same time, the condition of
maintaining the functionality of SB1 is met,
including after the termination of control over the
U2 line. SB1 as part of CO1 is the "control
subsystem" for SB2 in CO2. The presence of
control over the U2 line creates a functional
reserve for the control of the CO2. If you do not
use the line, then you need to use an additional
CSS2 to control the OP2. Thus, CS1 has the
"property of variability" in the form of existing
control options SB1 or SB1 and SB2, i.e. it is
simultaneously a process control system in two
on-Board systems SB1 and SB2.</p>
      <p>The criterion for evaluating the properties of a
variable process control system can be the
coefficient of variability (Kvar), which is equal to
the maximum possible number of processes
controlled by a single system. In this case, Kvar =
2. the use of synergistic phenomena as a result of
process interactions makes it possible to design
systems that control several processes at once.</p>
      <p>
        In contrast to the property of
multifunctionality of systems, in which a separate
system-process controller performs several
functional purposes due to its structure in the
form of a set of elements and relationships
between them, variable systems implement
additional functions due to the interaction of
systems, in the presence of synergistic
relationships in the processes. The
multifunctionality in figure 1 would be denoted by the
set of outputs of the CO1. For example, jet
flywheels (JF) with regenerative rotor control
windings simultaneously perform the functions
of a power gyroscope and an electric power
generator when the rotor is decelerated [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. Thus,
each JF is a two-function system. Therefore, if
the considered principle of synergetic - variable
design of control systems is observed, a
multifunctional system can also become variable.
      </p>
      <p>The design task is to obtain and use a priori
information about the variability properties of
regulatory systems to create new methods for
controlling AS. This expands the scope of
searching for solutions to functional problems in
the complex process of flight control of the
vehicle, complementing its structural and
functional onboard resources with synergistic
resources. In addition, the variability of process
control systems can provide pre-prepared
technical measures that increase the survivability
of on-Board systems. The calculated reserve for
parrying abnormal flight situations in case of
failures are elements of other variable control
systems used in the new functional purpose.</p>
    </sec>
    <sec id="sec-2">
      <title>2 Phased array antenna as a control object</title>
      <p>
        Currently, flat phased array antennas (PAA)
are increasingly used on Board the AS in solving
problems of providing personal satellite
communications, including retransmission of
signals from a personal mobile subscriber trunk
and exchange of special control information with
ground vehicles via the main communication
channel [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. Due to a number of technical
advantages, large-sized mirror antennas are
gradually being "replaced" by PAA. The primary
element of the PAA are radio signal emitters that
provide electronic movement of the beam in one
plane [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. Circular controlled (switchable) left or
right direction of rotation polarization of
radiation and signal reception is created in a
system of orthogonally polarized emitters with a
combined phase center.
      </p>
      <p>Each PAA contains a construction plane on
which the working surface is placed, formed
from the receiving and transmitting modules
(RTM) (figure 2), combined in panels. The
external surface of the modules consists of a set
of emitters of the same type.</p>
      <p>
        Each RТM consists of an antenna web made
in the form of a multi-layer printed circuit Board
divided into cells (for example, see figure 2, a
total of 64 square cells, with an 8×8 placement).
In this case, the RTM contains an emitter, a
matching circuit, a power amplifier (which is the
main consumer of electricity), an attenuator and
a phase shifter in each cell of the modular
element. Control units for attenuators and phase
shifters, power supply, switchgear, and beam
control and correction devices are used one at a
time for several RTM [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], and their placement on
panels is positioned with the placement of the
RTM and is performed inside the web at the
joints of modular elements. High-frequency
currents flowing along asymmetric micro strip
lines and RTM emitters do not create permanent
magnetic moments [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. In addition, currents that
have their own magnetic moments flow through
the primary and secondary power supply circuits
of the RTM in the PAA [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ].
      </p>
      <p>The diagram of the current circuits of the
secondary power supply of the RTM, projected
on the working surface of the PAA module, is
shown in figure 3, where the current directions in
the modules are shown. The primary power
supply is indicated by a line with a voltage of
100 V, and the secondary power supply is
indicated by a line with a voltage of 5 V. At the
same time, Figure 3a shows the scheme of
separate power supply of modules from
secondary power sources (SPS) SPS1 and SPS2
with multidirectional current flow, and in figure
3b — with the possibility of powering the
module from one of the two SPS.</p>
      <p>The arrows show the current directions in the
PPM. For example, the current consumption of
the RTM 30...40 mA, the area of the circuit that
it covers in one cell is ~2.5 × 10-3 m2. The
number of RTM in the PAA, consisting of four
panels, each of which has 64 modular elements
containing 64 RTM, will be 16384 pcs. As a
result of the calculation, the total current in the
secondary power supply circuits of the RTM is
~500 ...650 A, and the total area of the circuits is
~41 m2.</p>
    </sec>
    <sec id="sec-3">
      <title>3 Power gyroscope system as a control object</title>
      <p>
        The system of power gyroscopes (PG) is
designed to control the angular motion of the AS.
The control is carried out according to the law of
conservation of the kinetic moment for the AS as
a closed system by exchanging between the
kinetic moments of the AS body and the PG
system. However, the system is not completely
closed, since it is affected by external forces that
create disturbing moments, among which the
most significant are the moments of gravitational
forces, light pressure and magnetic moment. In
this case, the total vector of the kinetic moment
of the G (t) is defined as the sum of the vectors
of the kinetic moments of the body K (t) and the
PG system H (t) [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]:
t
G (t)= K (t)+ H (t), G (t) = G 0(t)+  M в (t)dt,
0
where G 0(t - the initial value vector G (t) ; M в
= M sd+ M ge+ M gm+ M gs+ M mm - the main
vector of external torque; M sd – moment of
force of light pressure F sd; M ge, M gs, M gm –
highlights from the gravitational forces of the
Earth, Sun and moon, respectively; M mm - is the
magnetic moment, M mm = L cm× B E, where
M mm = L cm× B E - is the intrinsic magnetic
moment AS; B E - vector of the magnetic field of
the Earth (MFE).
      </p>
      <p>
        Under the action of M в , the kinetic moment
accumulates in the PG system [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ] to the
maximum possible values ("saturation") of the
region S of the available values. As an example,
Figure 4 shows variants of the S region for
different configurations of single-stage PG (jet
flywheels).
      </p>
      <p>In this case, the matrices A of the guide
cosines of the kinetic moments of the rotors
of the same type of flywheels are given
and for comparative analysis, the
1 ...4
evaluation of the regions s by an inscribed
sphere with radius R =  carried out .</p>
      <p>After "saturation" of the PG system, it is
unloaded from the accumulated kinetic
moment. One of the most common methods
used for many years is the magnetic
unloading method using magnetic Executive
bodies (MEB) [11]. The applied methods for
unloading PG from the accumulated kinetic
moment using the control magnetic moment
include the following actions [12]:
- measurement of the current value of the

H in
accumulated kinetic moment vector
the PG system;
- measurement of the MFE induction

vector B ;</p>
      <p>- determination of the unit vector of the
unloading moment mr = Lr  B ;</p>
      <p>Lr B
- generation of a control signal for current
loops by changing the magnitude and
direction of current flow in the MEB to
ensure the conditions for unloading the PG
from the accumulated kinetic moment
mr  h &lt; 0,</p>
      <p>
 H
h =  .</p>
      <p>H
(1)</p>
    </sec>
    <sec id="sec-4">
      <title>4 Design of a phased array antenna with a controlled intrinsic magnetic moment</title>
      <p>In the design of the PAA, the magnitude
and direction of the current in the circuit of
RTM are defined by p modes PAA –
"receiving", "transmission",
"receptiontransmission" of radio signals of different
power, where p = 1,2,...,P – number of
modes of PAA, each of which is provided by
the power supply in the q's of the circuits of
the secondary power RTM, where q =
1,2,...,Q – the set of current circuits.</p>
      <p>The result for each PAA module
calculates the magnitude and direction of the
vectors the intrinsic magnetic moments.</p>
      <p>At the same time, they can have both
positive L+p1...L+pn ,n = 1,2,...,N ,N  Q
(Figure
5)
and
negative
directions
L−p1...L−pm ,m = 1,2,...,M ,M  Q (Figure 6).
+
L p2
+</p>
      <p>L p1
</p>
      <p>L+p(n−1)
+</p>
      <p>L pq</p>
      <p>
        The values of the magnetic moment
vectors differ due to the difference in the
areas and currents of the contours. Therefore,
when ground testing of the PAA in q RTM ,
in each p operating mode, the values of
currents in the power I pq circuits are
measured and their areas S pq are determined.
To determine the area, thermographs
(thermal imagers) are used. The areas are
determined by images of electric (or thermal)
fields of the power supply circuits of the
RTM obtained from thermographs (thermal
imagers) [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
      </p>
      <p></p>
      <p>Directions normal n pq to each current
circuit power RTM determined on the basis
of the logic of the switches of the antenna
array according to the algorithm of switching
of power circuit. according to these data, the
magnetic moments of the RTM are
calculated
 </p>
      <p>Lpq = I pqS pqnpq</p>
      <p>According to the proper magnetic
moments of each module, the magnetic
moments are calculated for the PAA panel as
a whole, in each p-th mode of its operation
 Q 
Lp =  Lpq</p>
      <p>q=1
in this case, the values can take both n and
m values (see figures 5,6).</p>
      <p>Therefore, the design calculation and
experimental method can determine the
intrinsic magnetic moment of the PAA panel
in each p operating mode. Without losing the
functionality of the PAA, with the help of
different variations in the switching of the
power supply of the modules, magnetic
moments of different signs are formed.</p>
      <p>Due to the purposeful creation of a
controlled power path for individual
modules, the operating modes of the PAA
panels are created, in which only positive (
   
Lp := L+ ) or negative ( Lp := L− ) intrinsic
magnetic moments are summed up. There
are variants of operating modes in which the
vectors of different signs are mutually
compensated, in such cases the panel is
"magnetically balanced" ( Lp  0 ). When
the power is turned off for all the PAA
modules, the grille is also "magnetically
balanced".</p>
    </sec>
    <sec id="sec-5">
      <title>5 Algorithm for using a phased array antenna to unload the system of power gyroscopes from the accumulated kinetic moment</title>
      <p>The algorithm for unloading the PG from
the accumulated kinetic moment using the
PAA as the MEB includes the following
steps:
1) measurement of the value of the kinetic

moment vector H accumulated in the PG
system;</p>
      <p>2) the choice to fulfill the condition of
unloading PG (1) for mr = mp , mp = LLpp  BB ,
    
Lp := L− Lp := L+ V , where p
modes of
operation of the PAA ( p = 1,..., P ), providing
unloading PG from the accumulated kinetic
moment;</p>
      <p>3) determining the values of the vector's
 h M p projections unloading point on the
direction vector h ,
 h M p = Lp  B ( h  mp ) ,</p>
      <p> 
where m  , L
p p

– the value vectors m p ,
 
Lp for p modes of operation of the PAA;

4) selection of the p mode of operation
of the PAA at the maximum value
max  h M p for unloading the PG system;
5) unloading of the PG by switching on

the p mode of operation of the PAA with
 
the control of the condition mp  h ≥ 0 (2),
 
where m p is the value of the vector m p for

the p mode;</p>
      <p>6) re-selecting the PAA mode after
condition (2) is met by replaying steps 1) -4);
7) completion of PG unloading when the

value H ≈ 0 is obtained by selecting the
"magnetically balanced" mode of operation
of the PAA.</p>
      <p>Evaluating the effectiveness of the control
moment.</p>
      <p>For the case of unidirectional arrangement
of magnetic moments of current circuits in
the secondary power supply circuits of the
previously considered PAA, the order of
values of the total value of the intrinsic
magnetic moment is</p>
      <p>L = Lp </p>
      <p>~ 1× 104 А∙м2.</p>
      <p>The control moment is estimated for an
AS containing a PAA and located in a

geostationary orbit, where B ~1×10-7 Tl. In
this case, we consider the case of the
standard orbital orientation of the AS on the
 
GSO, when the vectors L and B are
mutually perpendicular. Then the order of
values of the control moment ML modulo
will be equal to</p>
      <p> </p>
      <p>M L = L  B ~ 1× 10-3 Н∙м.</p>
      <p>Comparative estimates have shown that
the magnetic control moment has the same
order of magnitude as the total moments of
gravitational forces and light pressure forces
acting on the AS [13].</p>
    </sec>
    <sec id="sec-6">
      <title>6 Conclusions</title>
      <p>Based on the cognitive-synergetic system
approach to AS flight control, a new
principle of synergetic - variable design of
control systems have been developed. the
variable control system designed according
to this principle contains a control subsystem
that has the ability to regulate the operation
of several on-board systems, which allows:
to reduce the weight of the on-board flight
controls of the AS; to reduce the on-board
power consumption by eliminating
additional consumers; to obtain an additional
functional reserve on board the AS.</p>
      <p>The synergetic energy relationship
between the phased array control system
(PAA CS) and the power gyroscope system
(PG CS) is considered. Thus in CS PAA
control object is a PAA, and a control
subsystem - chain primary and secondary
power transmit-receive modules (RTM). In
CS PG, the object is PG, and control
subsystem the kinetic moment in PG
magnetic Executive body (MEB) system of
orientation AS.</p>
      <p>The synergistic energy relationship
between the two control systems in the form
of magnetic moments of current circuits in
the power supply circuits of the RTM
interacting with the MPZ and the kinetic
moment in the PG system allowed for the
design revision of the CS PAA for its use as
MEB. Thus, CS PAA is endowed with the
property of variability, which allows it to
become a regulatory system for two physical
processes at once: control of radio signals of
satellite communication in the PAA and
control of the kinetic moment in the PG
system. An additional functional resource
was obtained on Board the AS for unloading
the PG from the accumulated kinetic
moment, which can replace or Supplement
the existing one.</p>
      <p>Application of the principle of
synergeticvariable design of control systems makes it
possible to solve the problems of additional
resource provision of the AS and increase its
survivability.</p>
      <p>The technical solution is protected by a
patent of the Russian Federation [14].</p>
    </sec>
    <sec id="sec-7">
      <title>Acknowledgments</title>
      <p>Research carried out on this topic was carried
out with partial financial support from RFBR
grants (No. 17-29-07073, 18-07-01272,
18-0801505, 19–08–00989, 20-08-01046), under the
budget theme 0073–2019–0004.
Cosmonautics and rocket science. 2009.</p>
      <p>No. 55. P. 60 – 68.
[11] Sheremetyevsky N. N., Bikhman R. I.</p>
      <p>Simple reliable system of kinetic
moment reset for artificial Earth satellites
oriented in the orbital coordinate system
// In the collection "Management in
space" Vol. 1. M. - "Science". 1976. P.
110-118.
[12] Kovalenko A.P. Magnetic control
systems for space aircraft. - Moscow:
Mashinostroenie, 1975. 320 p.
[13] 13. Kovtun V.S., Banit Yu.R. Patent RU
2176972 C1. MKI B 64 G 1/24 / Method
for determining the magnetic moment of
solar batteries of a spacecraft with a
system of power gyroscopes //
Inventions 2001. No. 35.
[14] Kovtun V. S., Platonov V.N., Frolov I.</p>
      <p>V., Ermakov P.N. Patent RU 2604268
C2 B64G 1/36/ Method for forming
control actions on a spacecraft with a
phased antenna array // Inventions 2016.
No. 34.</p>
    </sec>
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