SCIENTIFIC ABSTRACT BODNER, V. A. - BODNEVAS, A. I.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000205720019-5
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 9, 2000
• Sequence Number: 19
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

Call Nr% AF 1022635
Automatic Control of A1rcr9ft Engines (Cont.)
It was approved by the Main Board of Polytechnic and
Mechanical Engineering Schoolsof the Ministry of
Higher Education, USSR.
COVERAGE: The book presents the theoretical aspects, principles
of construction, and special features of layouts'and
design of automatic devices for aircraft engines. Thq
dynamics of transient processes are investigated and
a method for selecting the characteristics of aircraft-
engine control regulating systems is given. The'book
deals with automatic-control mechanisms for reciproch-
ting and gas-turbine aircraft engines.
The book has been expanded from 336 pages (First
Edition) to 400.

T3. d
PHASE I BOOK EXPLOITATION 359
Zalmanzon, Lev Abramovich., and Cherkasov, Boris Aleksandrovich
llegulirovaniye gazoturbinnykh i pryamotochny1c4 vozdushno-reaktivnYkh
atele (Contrioliof Gas-turbine and Ramjet Engines) Moscow, Oborongiz,,
d
vig. 37U4 6
295 .500 copies printed.
Reviewers: Petrov, B. N... Corresponding Member., USSR Academy of
Sciences and2odner, V. A._A, Dr. of Technical Sciences, Prof.;
Ed.: Sotolev', 0-.11-.- Ed. of Publishing House: Belitskaya,, A. M.;
Tech. Ed.: Zudakin, .I. M.; Managing Ed. (oborongiz):
Sokolov, A. I., Eng.
PURPOSE: This is a textbook approved by the Ministry of Higher
Education for.,students of aviation vtuzes. It may also
be useful to workers specializing in the field of aircraft
engines.
COVERAGE: The book is mainly concerned with describing the physical
bases of engine control processes and with setting f0rth
methods for experimental research and design of control
Cardr-kdk devices. The close connection In the operation of the

Control of Gas-turbine (cont.) 359
elements of the control system and of the fuel supply system of the
engine is revealed in a number of examples. Characteristics of the
Individual elements of the oil system are presented. The author thanks
V. A. Bodner, B. N. Petrov, V. S. Zuyev, P. A. Korotkov, YU. P* Portnov-
Sokolov and N. V. Inozemtsev for their help in preRaring the book.
Thero are 148 references, of which 136 are Soviet (8 translations),
11 Miglish and I French.
TABLE OF
CONTUTS:
Foreword
Ch. I. Requirements for Control Systems of Gas Turbine Engines.
3
The Gas Turbine Engine as an Object of Control 7
1. Gas turbine charaoteristioo determined by the
conditions of jet aircraft operation 9
2. Gas turbine characteristics which are besio in the
design of engine control and fuel supply devices 20
Rzamples 34
Ch. II. General Principles of Control and Their Application
in the Control of the Gas Turbine Engine 36
C"Aa"

16~
24.8-3134
AUTHOR: Bodner$ V. A. (Moscow).
TITLE: Auto-oscillations-in a system-containing a compressor and
methods of eliminating such oscillations. (Avtokolebaniya
,pressorom. i metody ikb-ustraneniya).
v sisteme s kom
22RIODICAL: ulzvestiya Akademii. Nauk, OtdeleniYe Telrhnicheakikb Nauk"
.(Bulletin of the Ac.8c., 56ochnical Sciences Section),
.1957t No.8$ pp. 3-12 (U.S.S.R.)
APSTRACT: Auto-oseillations, inoluding pumping pulsations, occur
in systems with internal positive back-coupling. Howev*r,
.the Uynazic properties of the system can be changed in-tht
desired direction,zamely, from an auto-oscillatory into a
non-auto-oacillatory one by connecting to the system an
external negative back-coupling. In addition, it is shown
that there is a possibility of eliminating auto-oscillations,
by means of high speed systems with a negative back-couplin'g
and a method of selection of the parameters of sucli sy8tems
is described. The equations of motion are formulated for OL
system shown diagrammatically in Fig.4 which consists of a.
compressor, an inflow and an outflow piping, a storage space
and a regulating flap. The stability of motion is investi-
gated and formulae defining the conditions-of stability are
Csrd,V4 derived. Furthermore, the periodic movements of the air

Auto-oscillations in a system containing a compressor and
methods of eliminating such oscillations. (Cont.)
In the case of hard excitation,oscillations with the basic
frequency and high amplitude will, be generated. : -
immediately. The frequencies of the auto-oscillations
approach the natural frequencies andtbafrequency correction
in the first approximation is determined by the speed of
movement of t1b air Amd by the hysteresis loop in the compressor
characteristic. The amplitude of the auto-oscillations is
determined by the type of the compressor characteristic and
the parameters of the system connected to the compressor.
The auto-oscillations in the system can be eliminat4d by
connecting a closed "aati-pumping" regulator (system with
back-coupling), the transfer-. function of which should be
selected from the condition of disappearance of the real
roots in the equations (3.4) and (4.21) and respectively
(6.1) and (6.6). For a given case the method of selection
of the transfer vaTue of the regulator is illustrated.
If an exti-hunting regulator is included, the system
comprising a compressor will be stable in operation at any
air consumption values, including the range of vortex
formation. A closed anti-hunting regulator permits
Card 3/4 elimination not only of the auto-oscillations but also of

Auto-oscillations in a system containing a compressor and
methods of eliminating such oscillations (Cont.)
the discontinuous.(non-periodic) movement.
There are 6 figures and 2 Slavic references.
SUBMITTED: March 7, 1957.
AVAILABLE: Library ot caigress
Card 4/4

Bom[_~g
V,/~
24-58-3-25/38
AUTHOR': Bodner, V. A. (Moscow)
TITLE: Automatic Stabilization of Potentially Unstable Systems.
(0b avtomaticheskoy stabilizatsii potentsiallno neustoychivykh
sistem)
PERIODICAL: Izvestiya Akademii Nauk SSSR, Otdeleniye Tekhnicheskikh
Nauk, 1958, Nr 3, pp 145-148 (USSR)
ABSTRACT: Numerous hydraulic and pneumatic systems applied for trans-
f orming energy aLd acting as amplif 'Lers operate ef f e-c-1.ively ,
only if the processes on the output side do not influence the
processes on the input side 9 i.e. if they are unidirectional.
Systems in which instability may occur as a result of distur-
bance of the unidirectional nature are potentially unstable.
Examples of such systems are compressors, gas turbines, jet
engines, Ltc. Disturbance of the 'unidirectional nature of such
systems of energy transformation is due to internal parasitic
back couplings. In this papdr possible methods are considered
of eliminating non-steady state regimes by means of closed
correcting circuits possessing the requi.sit-e dynamic character-
istics. It is thereby assumed that. the systems under consider-
ation possess a low degree of nonlinearity and that the methods
Card -AV4

24-58-3-25/38
Automatic Stabilization of Potentially Unstable Systems.
of the small parameter can be applied to them. The--investigat-
ions ajm~ based on oonsidering the system used for trans-
forming the energy and for amplification as an active quadri-
pole. The conclusion is arrived at that it is necessary to
eliminate internal positive back coupling. For this purpose
it is necessary to reduce to zero the elements Z12 9 Y12 9
H12 or G12 of the second diagonal of the matrix quadripole.
In contrast to servo-stabilization systems, correction sys-
tems do not contain internal amplifiers or energy transducers
and can be made of elements of the same type as the system to
be corrected. It is shown on the example of a compressor how
stability can be achieved at any operation regimes. For this
purpose the parameters of the correcting quadripole should
have a definite frequency dependence and should be functions
of the operating conditions (flow rate through the compressor).
For correcting a compressor, various correcting quadripoles can
be used which have matrices with an equal element Y1 or
12
respectively V
12 or 912
12 9 h:
There are 6 figures 'and 4 Soviet references.
Card-84

PHASE I BOOK EDWITATION sov/2656
Aytomatiaheakaye upravleniye.1 vydbialiteltnaya takhnika., VYPO 2 (Automatic
Control and Computition Tlaebnique., Nr 2) -Moscows Mashgiz., 1959. 316 P,
Errata slip inserted, 8,,000 copies printe&&
Masi V.A* Bodnerj, Doctor 6f T-echnicil Sciences., Professor, and A,M, Batkov,,
CaziM-%-ff-%kbniczl Sciences; Ed. of Publishing House: 00F. Polyakov;
Tech* Ed#-. BJ. Kodel$i Editorial Board: V.V, Solodovnikov, Doator of
Teabnigal Sciences, Professor (Chairman)i NA. Bogolyubov, Aca4emlcian;
A..Tu. 7shlinxkiy,, Correspoiding Member,, Mcrainian SSR Academy of Sciences*
Voyi KwokevIch, Doctor of Technical Sciences, Professor (Deputy Chairmani;
A,A* Iqapwov,, Doctor of Physical and Mathematical Sciences,, Professorj
BqN, Petrov,, Corresponding Membbr,, USSR Academy of Sciences-; Ya,P, Popov,,
Doctor of Technical 86iences,, Profesaorl GoSe Pospelov, Doctor of Tech-
zioai Sciences, Professory B*A* Fqsbov, Doctor of Technical Scianceep
Professorl V,,B*'VshpkovP Doctor of Technical Sciences; B,V, Anialmovp
Candidate of Technical Scioncesl V.V, Petrov,, Candidate of Technical
Saieftesej VN. Plotako*,, Candidate 9f Technical Sciences,, Docent (Sclen-
tifto ftamtm); Manadint Ede for Litersture on Machine Building azd
Instrmat Construction (Masbgis)-. N.Ve Pokrovskiyj Enginsere
cam 115

AuUmMic coutroi sad (aftt.)
80719656
PWJ=t "khts book to InUided. for scientific workers and Industrila engineers
Vko 004 IStOnsted, In PrObIfte of the design and testing of automatic
00YArol e7stowas
COMM This book to a'acUsation of articiss on automatic oantrol. The
first two articles pertain to the thoori of sonlol-dats, systems, The
ortials by VP# Poicy Is devoted to the problem of the oyathosig of Unow
eujbWW1W oystems, As a criterion for the determination of the optimum
ocautift the Minimun or, the -m, of the -man vaus of Ue square random
error ad square Opusfa error during a tims-rostriated transient process Is
foleatedo The work of F#X9 Win explains the methods of analping trouslent
"A .otsb3a proceseei In sampled-deta systems with jag-variable peramotersp
ad also tM problan of the statistIcal dynomlob of such systowas In the
work by YesPs Pow &,ot%idy to meds of the problem an diminishing the effect
of a wmber of noultzoariftes (relay type,,-dry WatIcA, baWassho etas)
" the operation at an autuatio control system by memo of vibratioma smooth'-
Los of the aft"Aftear ah"eateristleal In addition an &n"14 to made, of the
uftofim 9f Intredustag vibrations by Mesas of a self-coatnating riginse fte
orkle3a'by AD, Xaoli6y to devoted to the am problem However, ban a sti*
to ado Of. vOntional smoothing by mesas at external Veriodle action on'tho
aor& 2/i

Axitomatic Control and (Cont.) BOV12656
system and not by means or self-oscillations. In the work by V.V. Katakevich,
the theory of trigger regulators is developed, taking into account the
multivaluedness of the path characteristics. It is shown that such an analysis
damands the introduction of a many sheeted phase surface. A study is made of
setting processes, periodic motions, and their stability. In the article by
Yu.A. Mitropollskiy a study is made of systems described by nonlinear
differential equations which are essentially different from linear differ-
ential equations and which have a small parameter in such form that when the
paramter takes on the value zero, they can be exactly integrated* it is
assumed that a number of parameters in the system slowly vary with time, The
artiele by V.V. Petrov and V*Yuo Rutkovskly is devoted to a study of the problem
on the synthesis of optimum servomechanisms which guarantee the derivation of
given transient processes and which satisfy given operating conditions; the
problems of constructing circuits and the selection of the characteristics
of servomechanisms are also studied& In the work by k,v. Starikova, a
stTx4y Is made of nonlinear systems of automatic control described by differ-
ential equations with delayed argument which have two,or three nonlinear
eleweuts,, An apprexiiiLte solution of the problem uMer almly varyin external
action Is given. In the article by V.V, Kazakevich ekhd G.M. Ostrovskiy a
study is iiade of an automatic control system when there is dry friction with
diminishing characteristics in the sery otor and when derivative feedback is
introduced into the circuit. References are given at.the end of each article.
Card 3/5

Automatic Control and-(Cont.)
TANZ OF CONTMITS:
soYI2656
Perov, V.P. Synthesis of Sampled-data Systems by the Minim= Total Reproduci-
bility Error 5
Kilins, F,M. Certain Problem of the Dynamics of Sampled-data System With
,T=p-variable Parameters 50
Popov, Ye.P. On a Theory of Vibrational Smoothing of Nonlinear Characteristics
of Automatic Control Systems by Means of Self-becillations 104
Maksimov, A.D. On a Theory of 'Vibrational Smoothing of Nonlinear Characteristics
of Automatic Control Systems by Meana.,of Forced Oscillations 139
Kazakevich, V.V. Theory of Trigger Regulators Taking into Account 14altivaluedness_
of the Ch teristics i6T
Mitropoltakiy, Yu.A, Certain Equations Almost Exactly Integrable 221
Petrov, V.V., and V,Yu. Ratkovskiya, Certain Problems of Circuits and the
Selection of Characteristics of Higb-apeed Servomechanism 249
Starikova,, M.V. Asymetrical Self-oscillations of Automatic Control Systems With
Slowly Varying External Action 271
Card 4/5

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KULIMAKIN, V.S., akademik. otv.red.; BODM, V.A., doktor takhn.nauk, red.;
IVAIMNKO, A.G., doktor IWMINSXIY,,A.Ta.t sks-
demik. red.; XACHANOVA. N.A., kand.tekhn.nauk, red.; XUZHWSOV, P.I.,
doktor fiz,-zatem.nauke red,; KU1WXNKO, A.I., doktor takhn.nauk, red.;
PJTROV, B.N.0 red.; POPOV, Ye.P., doktor takhn.nauk. red.; UWOV.
G*X~$ doktor takhn-nauk, red.g KMMOV, K.K., almdemik, red,; OH1-
XATEV, P.I., kan&.takhn.nauk, red.; CMWLAKOV, N.M., kand.takhn.naukp
red.; XWOLOV, G.V., tekha.red.
EInvariancy theory and Its application to automatic devices] Teoriia
invariantnosti I as primensuie v avtomaticheakikh ustroistvakh;
trudy soveshchaniia. Moskva, Akad.nauk USSR, Otd-nie tekhn.nauko
1959. 3 81 P. (MIRA 13:7)
1. Soveshchaniye po teorii invariantnosti I eye primeneniyu v avto-
satichopkikh ustroyatvakh, Kiyev, 1958. 2. AN USSR (ror Ishlinakiy.
Khrenov) ion-korreap.AN'SM kfor Petrov),
3. Q7 (Automatic control)

AA.THOR; SOV/24-59--l--30/35
TITIE: Conference on the Iwrarlance Theory (Soveshchaniye po
teorii imariantnosti)
PERICDICAL-.Izvestiya Akademii Nauk SSSR., Otdeleniye Tekhnic-beskikh
Nauk, Energetika i Avtomatika,1959,Nr 1,pp 139-141(USSR)
ABSTRACT: A Conference on the Invariance Theoi7 and its
Application to Automation took plaoe cn October 16-20th
19C8 in Kiyev, arranged by the Departm&nt of Technical
sclences of the Academy -.f Sciences, UkrSSR, in
conjunolf.--ion with the Automation Division of the. Kiwir
Mining Seminar., The importane-e of the invarianoe theory
was described by Ishlinskiy im, his opening speech.
The papers submitted to the conference were divided into
two groups. The first group consisted of: "The Invariance
theory as a basic prinniple of efficient control and
management", V.S.Kulebakin.; "The full compensation of
the disturbanizes caused by manoeuverring in gyroscopic
systems" by A.YU.Ishlinakly; "Combined uontrol in bcth
general and quantity cont-rol" by A.G.Iv-akhnanko;
"Problem of the invariance theory in the control of
Card 1/5 deflection" bv A.I.Kmkhtenko-i "Dayariance theory to e

SOV/24-59-1-30/35
Conference on the Invariance Theory
in the combined, nonlinear systems of control with the
disturbance determined by the modulus" by G.M.Ulanov;
"The fVndamental principles of desi&rn and structural
properties of the combined system orcontrol" by
B.N.Petrov. The second group consisted of: "The
calculation of the seiTomechanism of the combined system
of operation by the method of logarithmic frequency
characteristics" by V.A.Bessekerskiy and S.M.Fedorov;
"On the application of disturbances control in a highly
controlled system" by V.M.Yeintsevich; "Thp. stability
of a symmetrically coupled system with combined control"
by L.V.T-c,;ukejmik; "The independent and combined control
of the parameters of aircraft motion" by G.S.Pospelov;
"On problems of synthesis of linear systems of combined
control" by P.I.Chinayev; "0a the theory of uniform
type of coupled systems of autcmatuio contr%--il with a
symmetric cross-coupling" by V.T.Morozovskiy; "A new
method of application of the classical method of
computation of power-oompensating servomechanisms" by
V.N.Yavorskiy; 110a application of the principle of
Card 2/5 compensation for designing automatic stalbilising systems"

Z!, OV/24-5 9-1-30/35
-he Invar-anee Theory-
Conference on 4. L
by V.A.Bodner. Others who gabmitted papers were:
P.I.Dekhtyarenkc-; G.K,,Nechaye-v-. V.I.Nechiporenk-o;
A.I.Sud-Zloche-,,skiT.- A.N.Miiyakh and
B.Ye.Dibyshkin; Ook.Kryz-har-cvskiy-,*V.G.Vasi-L'L;e,,r.-,
V.I.Kostyuk and ot'hers. The confferan-lle az;.:;epted the
motion which empha~~isei the fc.,11ow:Lng points:
1) the in-iariance thecry t.,~-_omes generally accepted as
a method of .3ojapansating the effect o-IL" external
distui,ba=s s 7 -hod of exte:-L~nal dist-av"bances was
2) the compews at i on me44
fIrst elaborat-ad in t1ie USSR by Plnofessor G.V.Shchipanov;
fu:::ther mathema-~i~--al analysis JUL this field. was carried
out by N.N.Luzin, P.I. A.G.Ivakhnenko,
B.N.Petrov, V.S-Nalebaldu and A.Pj..IshIinskiy-.
3) the Soviet scientists developed the invariance theory
and related to it a Lon-linear system of automatic control;
4) the compenzation meth,:d bas been sufficiently
developed so that its appli~.ations in the engineering
fields be--ame praaticable;
Card 3/5 5) the --ompensation method 'has 'Llean employed writh great.

Conference-on the Invariance Theory
S'OV/24-59-1-30/35
success during the last 10 years in the navy, aviationv
artillery2 power stations,etc; therefore, it is
advisable that:
1) the compensation method should be generally adopted;
2) the theoretical principles and the experimental
data of automation and other dynamical systems affected
b the deviation of control should be propagated;
D~ the problems of compensation and the invariance
3
theory should be discussed in schools and factories
where automation is being introduced;
4) the papers submitted to this conference should be
published;
5) preparation should be made for the International
Convention on Automation in 1960;
6) research should be intensified in (a) the control
and operation of linear systems with a time coefficient,
and delaying action, non-linear systems and systems with
multi-controls, self-control and computing systems,
(b) method of analysis and synthesis (c) methods of
measurements of disturbing factors, W determination of
Card. 4/5 disturbances by the statistical method and (e)

conference
SOV/24-59--l-30/35
on the Invarianee Theory
standardisation, of the terminology in the field of
control and operation;
in view of the slackness of the Commission on
Automation, Academy of Sciences, USSR, formed April lstj
1941 under Prof ess=- G.V- the oonference
asks for a fresh mo-ve in this matter-,
8) this report should be gablished in the scientific
press.

SOV/204-59-3-3/33
AUTHORS:Bodner V. A.. Selezne-,,, V. P.1, Ov--.haz.-ov, V. Ye. (Moscow)
ped Systems of Arbitrary Period
TITLE: The Theory of Inertial Dam
that are Invariant with Respo-ot to Chwiges in the ObjeGt-,
PERIODICAL: Izvestiya Akademii nauk SSSR,. Otd(~leniye -"-ekhnicheski-kh
aauk, Energetika i avtomatika, 1959, Nr 3, PP 11-18 (USSR)
ABSTRACT: The paper deals with inertial gu~danoe systems contain-
ing more than one feedback loop. FJ-g 1 shows the geueral
system the authors envisage as moving at a i,-onstant speed
at a fixed distance from the sw7face of a spherical earth;
Eqs (1.1) are the equations of motior, and Fig 921 shows the
corresponding struottiral diagram. la-~ platfo= is assumed
-1-1o i-otate about the verti.-a). at ~k rl,lated to the lat-
rJ).3 .1.
itude ~ and longitude % by , , A) sin where w 3
is the angulw~ ,relo:zity of the. ea~,,.`.%. Eq (1,2) is found by
differentiating the first equation -n (
W - 1.1). Then (1-3)
gives thq compensation condition \'tbe :-orn-4.itioya that the
system is invariant with respect to --L perturbation (ac..,el-
eration) ). The rbsult syst-zin is at tt-e boundary bezveen
Card 1/3

SOV/24-159-3-3/33
The Theory of Inortial Damped Systems of Arbitrary Period that a-re
Invariant with Respect to Chwzges in the Object
stability and instability; damping may be introduced via
the dotted unit shown in Fig 3, or via the unit K_ (full
line). Eqs(1.6) and (1.5) relate r-3speotively to these two
cases. However. both forms of damping cause the condition
U 3~)to be vioiated. The next paragraphs (Eqs (1-7) to
lHo illustrate the pc,int that; ' If ouch a system is used
as an indicator of looatioii in a c1cCed-loop conti,,-ol system,
the damping introdv_~_ed by these internal feedbacks is lost
and the larger system beoomes unstable. The second major
division of the paper deals with s-.vs-11-emz in whicuh the infor-
mation about the position of 1-1he objeot 'Ln terrestrial co-
ordinates is supplied by scme non-dnert:Lal system not speci-
fied; this latter infcrxatlon i,:.~ als:~ assumea t-~ be very
much more acOurate than th- inforzation sapplied by the in.-
ertial svstem. This topL~ is traated very cursorily. The
third major division is ccucerned With the ~'rrjrs in-l-'roduced
by erroi-s in them inforruatizin supplied to tha inej!tial system;
the errors are assumed random, and the uacal Xesult is
reached. The last section drals witti -1~1_,e effects of the
Card 2/3

SOV/24-5,9-3-3/33
The Theory of In -ertial Damped Systems of Axr-'Atraa~y Period that are
Invariaat with Respect to Cha-uges the ritjeot
finite spe-ed of the obje,3t zn th- ,,rorkizigr of the inertial
system, and it is shown that tLie system ~,*eases tQ funQtion
properly when the ascape i~, appnoa,2hed. The paper
contains 6 figurBe and 4 referonc~~E, 3 if whi3h are Soviet
and I English.
19r-9.
SUBMITTED- February 18, L
Card 3/3

SOV/24-59-4-15/33
AUTHORS: Bodner.-V,A-. and Kazakevich, V.V,, (Moscow)
7
TITLE: .5tability of Compressors'as Non-linear Elements in
Extended Systems
pERIODICAL-. Izvestiya Akademii nauk SSSR, Otdeleni ze tekhnicheskikh
nauk, Energetika J avtomatika, 1959, Nr , pp 116-125 (USSR)
ABSTRACT: The compressor is one supplying compressed air toremote
polnt's'throughnarrow pipes; the compressor is controlled
by the pressure prevailing at a fairly distant point.
The equations of motion (taken from Ref 1) are (1-1),
where u, p and (J are, respectively, the speed,
pressure and density, d is the diameter of the pipe,
a and m are coefficients representing viscous resisiance
and y is the ratio of the specific heats. It is
assumed that the pipe (Figure 1) is loaded at the ends
by acoustic impedances Z 1 and Z. the boundary
conditions are then (1.2), where p and p. are the
total pressures at the input and the output, respectivelyl
p and p are the constant components of those
01 02
Card 111.5

1~01F/ 2 4 - I I
L~5/33.
:C4-
1
Stability of Compressors as Non-linear ements n xtended Systems
pressures; Q I and Q2 are flows (in volume terms)
and q, and q 2 -are excess flows (again in volume terms).
The equations. are linearized (Ref 1) as (1,3 and (1.4),
with the symbols defined at the top of p 117; the
boundary conditions.are put as (1-5). It is assumed that
h11 and h 21 are constant for the purposes of examining
the stability, though this is not so In unstable modes
(variation in aF/DQ 2 is used as a test for instability).
In the second section, the equatlons are solved using the
form given by Bqs_(2.1) and (2.2), which with (1-3).and
(1-4) give (2*3) for the input pipe and (2.4) for the
output pipe; the corresponding solutions are (2.5) and
(2.6), where Z 11 and Z 22 are the wave impedances of
the pipes. Eq (-2-7) gives the constants A and B ;
this system has a solution only if (2*8) is complied with.
The two equations derived from (2.8) are (2.9).
Card 2/5

sov/24-5_9-4-15/33
Stability of Compressors as Non-linear Elements in Extended Systems
Then (2.8) is put as (2.10), with E I]. ` "E12 0
In section 3, the compressor is assumed to be connected
to a pipe terminated by an impedance Z. . with an
impedance Z1 at the input by the compressor (here
II= 0) . The substitutions at the top of p 119 are then
made, to give (3-1), which then splits up into Eqs (3.2)
and (3-3); these equations show that the natural
frequencies of the system depend only on the pipe and V/
terminating Impedance and that there are two series of
frequencies given by Eq 0A). First, the roots
corresponding to tho + sign are consid.*ered, with
1z 214-4 Z22 ; we thea have Eq (3-5), which leads to a
contradiction. Therefore, z and we have
2j>> Z22 1z
Eq (3-6). Then the -sign is taken, again with t 2 Z 2 2
this gives Eq (3-7). The case (Z 2j-_'> Z22 gives
Card 3/5 Eq (3-8). This argument shows that the minus stgn must

Stability of Compressors as Non sov/24-%9-4-15/3~
..linear Elements in Extended ystems
be taken and Eq (.3.9) gives the frequencies.
The subsequent analysis deals with the stability limits,
which are given by Eq (3-13); the case Y = 0 is
considered in detail. Here, Eq (3.12) becomes (3,15),
which implies Rcr(3-16) and (3-17); these define,
respectively, the regions of' dynamic and static stability.
Figure 2 Illustrates this. -Figure 3 shows lines of
constant decrement.
The next section dea,la with the effects of radiation
from the open end of' the pipe,.assumed fitted with an
infinite flange. Figure 4 illustrates the results in
general terms. Ecl;(3-19) onwards deal with the effects
of an impedance Z. connected at the compressor end;
at no point can the system then become absolutely umsthble.
The system is, respectively, leant and most stable when
the two equations for R apply. The final two sections
.W I
deal with other special cases, the significance of which
Card 4/5

SOV/24-59-4-15/33
Stability of.Compressors as Non-linear Elements in Extended Systems
11 -is clear from the conditions in the text immediately I/
preceding the equations.
There are 3 figures and 3 Soviet referenbes.
SUBMITTED: February 27, 1959
Card 5/5

69935
S/024/59/000/06/012/028
4, "9 --. 0 V E023/E235
AUTHORS: Bopgx,,~~ and Kozlov, M. S. (Moscow)
TITLE: Response of a Control System Conta-ining Slow Coordinate
Sensons q
PERIODICAL: Izvestiya Akademii nauk SSSR, Otdeleniye
tekhnicheskikb nauk, Energetika i avtomatika, 1959,
Nr 6, pp 99-107 (US�R) I
ABSTRACT: Closed-loop systems of autoptlot.type are considered;
Fig 1 shows the way in which the system is to be
considered as regards deviation in a lateral direction
from a specified path. Fig 2 relates similarly to
deviation in a vertical plane and to control of the--
speed. Eq (1.2) is the control law applicable to Fig 1;
Fig 3 shows the equivalent block diagram. Eq (1-3)
relates to the lateral acceleration arising from wind
forces. After this general introduction, section 2
deals with undamped systems; the equations are compiled
on the basis of Fig 3. Up to (2.4) it is assumed that
(1.1) is complied vrith; past that point it is assumed
that klk2 - 1/R - n/R'(n