SCIENTIFIC ABSTRACT POPOV, YE.M. - POPOV, YE.P.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001342420007-8
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 25, 2000
• Sequence Number: 7
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

ROMANOVSKIY, Yu.M.; MASTRYUKOVA, T.A.; BODROV, V.P.; POPOV, Ya.M.;
KABACHNIK, M.I.
Use of high-speed computers In the analysis of mixturos of
organophosphorus compounds by their infrared spectra.''Izv. All
SSSR. Ser.khim. no.3:569-572 Mr 164. (WRA 17:4)
1. Moskovskily gosudarstvennyy universitet im. M.V.Lomonosovap
Institut elementoorganicheskikh soyedineniy AN SSSR I Institut
organicheskoy khimii im. N.D.Zelinskogo AN SSSR. "

ROSHCHUPKIN, V.P.; -POPOV, Ye.14.
Calculation of electrooptical parwreters and analysis of absoTptinn
L
band intensities in the infrared of complex molecLdes. Nii,rile comm-
pounds. Opt. i spekt. 15 no.2:202-207 Ag 163. Ovuz.4. r-1.)

POPOV, Ye.M.; SHLYAPOCHNIKOV, V.A.
Analysis of the vibrational spectra of polynitroalkanes.
Opt. i spektr. 15 no.3:325-331 S 163. (MIRA 16:10)

POPOV,, Ye.M.- SHLYAPOCHNIKOVI V.A.
2-
Electrooptical parameters of nitromethane. Opt. i spektr.
14 no.6:779-186 Je 163. (MMA 16: 8)
(Methane--Dipole moments)

POPOV,_Ye M,;-,-STOYA?IOVICH, F.M.; FEDOROV, B.P.; ANDRIANOVA, G.M.
Ultraviolet and infrared spectra of 2-thienyl sulfides. Part 6.
Zhur.ob.khim. 33 no.7:2261-22d6 Jl 163. (~HRA 16:8)
1. Institut organicheskoy khimii imeni N.D.Zelinskogo AN SSSR.
(Bithiophene--Spectra) (Sulfides)

1 17789-63 EWP(J)/E"(C)/EWT V(lm)/BDS AFFTCIASDIESD-3AJp(
T&_4_7PiZ_ _4
ACCLFdSION.NRI AP3005842 8/0032/03/015/00210202/0207-:',~'
AUMOR: Roshchupkin V, IN I
TITLE: Calculation of the Ol'qqtr*--o'O'tIGa%~ para"to" ad analysis Of the ftbsoiei~_
r f !c _~i
tion band Intensities in the lint ar44. spec"a o complex soloculea, Hitrili,
OundS
Soul=: - Optika I ektrookop v*25$ no* 9-_19630 202-207
TOPIC TAGS: elecitro;~;opticol -force constant
-nitrile compound acetcaltrIle
r
ABSTRAM: The. purpose of the work was to.dotormInes oUthe-baBla of exPe n
data, on absolute band leans.
itles lzi,the Infrared spetrm,the electro-optical C
arameters of the CC13CN K924idUlO Md to IrIte t thA'Varution in band 6n~i-
rpro
p
atom by, Cl~.'.;i
.,ties bbservod In the acetonitrile'u*rIos'with replacement of the El
-.'Xt was assuned -that solutloni'of t& olocitro-opt
Iasi problem for Clf3CX and Cal Cx~
-would help elucidate the reasons for the variation In the intensity of the
:red - absorption bonds associated with the ON stretching vibrations. Choice ok
J these molecules was dietated'by the considerations that for theis there is obxerv
1/3 i.!

~L:17799-63
r
-ACCESSION HR.''AP3005842
IZ7
larse differ8=0 In the',Intenalties'af,the A'bands and the fact that
these
a blgb degre ' of 6yMet
a rY 110 that thw direction of the dipole momen't
Gulas have
Is'kadvn*
The absolute' imtGgraZ Imtgnxtties were determined by the me
11 And B*Wells (JiChemephys.0140-5 thqd
E.B.Wilso 78#19401 the Measurements for. tr i;,
Chloroa
cetonitrile were carried out an UR-10 spectrometer with Mr, KaCl
and.MY
prisms -in a wide range 6f,pll(p partial press
it leneh of the absorption'
cell) values. The measuremeAt accuracy Is estimated-as 5$; the.accuracy in ceia&
the_eldctr~optldal parameters-10%. Experimental data on the other substi'
tin
t
tuted acetoaitriles were aken from theliterature (W.Z&Il,'Zs.phys.Chem.,14,230r'
1958). The force constants calculated for the four compounds in the series 9 e
x
....tabulitedt as are the frequencies and modes-of vibration In the C013CN molGcule.~-,
Analysis of the vibration modes-and IR absorption intensities Indicates that the!
main reason for the alteration In the intensity of the Vt hod in the spectrit ofil
j
CH3PX and CCI~W, and presumably the Intermediate substituted compounds, Is A0
chan e in the equilibrium value of the length of the CN bond or the character of,
this.14ondi-_but change in tha;character of the electro~_optical paramatie7s, of thi
n4ijhb6rin*jt C01 bond, which contributes strongly to ~the ~Il vibrations. "Thd auth~-
ors are deeply grateful to L.G.Stolyarova for synthesis of the trichloroacatoni-
trilch and Lk.A.Gribov and M.S.ARdMev for detailed discussions,of the work.:
Origa4t.has: I formula, I figure and 4 tables.

GRIBDVp L.A.; POPOV, Ye.M.
Determining the eleotrooptical
infrared absorption spectra of
spektr. 13 no.5s663-667 N 162.
(Xethane-Spectra)
parameters and intensities in
methane and ethane. opt.1
(ICRk 15s12)
(Ethanes-Spectra)

FOPOV, Ye.M.; 1-SMITIMNA, IT.Ye.
lacterization o' .OtW, icklorothionophosphate. Zhur.ob.khim.
32 no.9;308,(~-3083 6 '6;-~. (1,11FUt 15:9)
(Pho,~phorothioic acid) (Isomerization)

POPOV, Ye.M.; TSVETKOV) Ye.N.; CHZHAN ZHUN-YUT (Chang Jung-Ah
~_~iM I , T . Ya .
Room and ultraviolet absorption spectra of some unsaturated
organophoaphorus compounds. Zhxwoob.khim. 32 no*10;3255-3260
o 162. (MIRA 15:11)
(Phosphorus organic compound"pectra)

POPOV, Ye.M.; KAGAN, G.I.
Theoretical analysis of vibration spectra of vinyl alkyl sulfides.
Opt. i spek-tr. 1-1 no.6:730-734 D 161. (MIRA 14;11)
(Sulfides--Spectra) (Molecules-Vibration)

POPOVY Ye.M.; ANDREYEV, N.S.; KAGAN, G.I.
Vibrational spectra of vinyl ethers. Rotaticnall
Opt. i spektr.' 12 no.1:37-41 Ja 162. (MIRA 15:21
(Ethers--Spectra)
(Isomerism)

FOPOV, Ye.M.; KAGAN, G.I.
Vibrational spectra of vinyl alkyl others; thwetical
analysis. Opt. i spektr. 12 no.2:194-199 F 162. (HIM 15:2)
(Ethers-Spectra)

S/051/62/012/005/002/021
1-;032/E514
AUTHORS: Gribov, L.A. and
TITLE: Slectro-optical parameters of polyatomic molecules
and their calcuTation from experimental data on the
intensity and polarization in the infrared
absorption spectra
PERIODICAL: Optika i spel-,troskopiya, v.12, 110.5, 1962, 546-:i49
TEXT: The solution of the converse electro-optical problem
is discussed in a general form. It is pointed out that experi-
ment will in general yield only two quantities, namely, the
derivative of tiie dipole moment of the molecule with respect to
the normal coordinate.(except for the sign siAce the in+ensity
of the absorption band depends on the square of the derivative)
and the direction of the polarization vector. In addition,
the form of the vibrations is knoini from the solution of the
mechanical problem. It is shown that the theory put forward by
Vollkenshteyn et al. (DAN SSSR, 30, 784, l941; zhETF,'il, 6112,
1941; J.Phys., 9, 101, 1944; ZhETF, 15, 124, 1945) is, in
principle, capable of yielding this solution for a large number
Card 1/2

POPOV, Ye.M.; GRIBOV, L.A,
I
Calculation of the electrooptical parameters of certain poljratr-aic
molecules. Opt. i spektr. 12 no.6t703-71O Je 162.
(MIRA 15:5)
(Molecular spectra)

h3405
5/051/62/013/005/007/017
E039/E420
AUTHORS: Gribov, L.A., Popov, Ye.M.
TITLE: Determination of the electro-optical parameters and
calculation of intensity in the infrared absorption
of methane and ethane
PERIODICAL: Optika i spektroskopiya, V-13, no-5, 1962, 663-667
TEXT. In previous papers the method of determining the'electro-
optical parameters of multiatomic molecules from experimental
data on the intensity and polarisation of infrared absorption
bands has been developed and applied to hydrocyanic acid,
acetylene and ethylene; this work is now-extended to include
methane and ethane. Derivatives of the 'dipole moments are
calculated using normal coordinates for methane and its
deuteron-exchange compounds CH4, CD4, CH3D, CDO and CH2D2-
The following values of the electro-optical parameters for
methane are obtained
ap.) . o.65 D 0 - 03 0. 28 D
N - 'a q A A
Card 1/2

S/079/62/032/010/004/008
D204/D307
AUTHORS: Popov, Ye.M.-, Tsvetkovt Ye.N., Changp.Jung-Yff, and
MedVbd-'-,--T.Ya,
TITLE: Raman and ultraviolet spectra of some unsaturated
organic compounds of phosphorub
..PERIODICAL: Zhurnal obshchey khimiip v. 32,,'no. 10, 19629
3255 - 3260
TEXT: Raman and.UV spectra of vinyl compounds of the type 'C
0, 'C P'= S and ~'C and of the analogous
allyl derivatives were investigated in view of the lack of publica-
tions concerned with the spectra of these systems. The Raman spectra
were taken on an WCT7-51 (ISP-51) spectrographt the line intensi-
ties being measured photoelectrically with an accuracy of � 15 %.
The UV spectra were investigated on an cn -41 (S.P-41) 8pectrophoto-
meter. The compounds were tested in a solution of heptane. The cha-
racteristic vibrations of the C = C bonds in the allyl compounds
w9re very similar to those of C = C in alkenes possessing a termi-
Card 1/2

.3/07 62/032/010/004/008
Raman and ultraviolet spectra of ... D204%307
nal CH 2 group, and the UV spectra of CH2 = CH - C4H9 and CH2
CH CH 2 - (O)P(OC4H9)2 were practically the same# indicating that
in these compounds there is practically no interaction between the
C = C bonds and the P = 0, P = S or the trivalent P atom separated
from the double bond by a methylene group. In the vinyl derivatives#
the 0 = C Raman line intensities were generally.lowered and the UV
absorption bands were slightly shifted towards the shorter wave-
lengths, in comparison with hexene-1. No indication of conjugation
-in these systems was thus obtained. The assistance of M.I. Kabachnik
P.P. Shorygin and V.A. Petukhov is acknowledged. There-are 3 tables.
SUBMITTED: July 10t 1961
Card 2/2

S/020/"2/145/004/009/024
B178/B'1'02
AUT~-ORS: Gribov, LI. A., and Popov, Ye. M.
T IT, L E Valence optical scheme and theoretical considerations of
int-ensity and polarization in absorption spectra of the
fundamental vibrations of polyatomic molecules
?ZKODICAL: Akademiya nauk SSSR. Doklady, v. 145, no. 4, 1962, 761-763
TEXT: in attempt is made to find a set of electrooptical quantities 'aith
which the intensity and polarization of molecule spectra car, be analyzed.
Proceeding from
[(e) {jL) 114.q4; S-~ (AEffT - E). (1)
dQj jq
the amount of (a~/aQ.) and its direction can be determined experimentally.
1 0 1
'-L'he elements of lat4/aal and ~f)kr are the totality of the electrooptical
parameters sought. The number of the possible equations for nonsymmetrical
Ca'rd 1/2

YAGUDAYEV, M.R.; POPOV, Ye.M.; YAKOVLEv, I.P.; SHEYNKER, Yu.N.
Frequencies and intensities of infrared absorption bands of
the stretching and deformation vibrations of the Nl~ group in
primary amines. Izv. JUT SSSR Ser. khim. no.7:1189-1196 Jl 164.
(MIRA 11-8)
1. Institut khimii prirodnykh soyedineniy AN SSSR i Institut
organicheskoy khimii imeni Zelinskogo AN SSSH.

L 36665-65 FWT(m)/En(--)/EWP(J)/? Pa-4/Pr-h FsD (t)/ssD/AWAFMD (t) RM
ACCESSION NR: AP4044700 S10062164/000/00911393/1401
AUTHOR: Kogan, G. A. ; Popov, Ye. M.
TITLE: Vibration spectra and structural characteristics of polyene compounds
SOURCE: AN SSSR. Izvestiya. Seriya khimicheakaya, no. 8, 1984, 1393-1401
TOPIC TAGS: polyene compound, vibration spectrur4structure, butadiene, force
field, polyene chain length, polyene dicarboxylic acid ester, force field redistri-
bution, IR spectrum, dipole moment
ABSTRACT: The vibration spectra of 1_, 3-butadienj and trans- 1, 3, 5-hexatriene
were calculated to obtain information about the force field of conjugated molecules
and the relationship between the force field and the length of the polyene chain
was studied. Every association of the butadiene force constants agrees with the
concept oflr-electron delocalization for a system of this type. The force constarts
of the butadiene and hexatriene double bonds were much less than in compounds
with an isoprene type double bond and of ordinary carbon bonds in saturated
cardt3

hydrocarbons. Interaction of the two double bonds and of the double bond and
ordinary bonds was also indicated, Since hybridization of the carbon atom did not
change the force constant of the C-C bond, it was concluded the force field of the
butadiene was associated with IT -electron delocalization. Examination of the vi-
bration of models of polyene dicarboxylic acid eE;tersl(O=C-(C=C)n-C=O, n=2-8)
showed that increasing the length of the polyene chain did not cause significant
redistribution or equalization of the force field of the molecule in its normal
electron state. A study of the polar properties of polyene compounds involving
measurement of the absolute Integral intensity of the absorption bands in the
1600 cm-1 region in IR spectra of oL, W-substituted polyenes of the type X-(CH=
CH)n-COOC2H5, where X=-COOC2H5(n=2-8), -CH3, -N02 and -CHO (n=2-4)
showed the intramolecular effect of the substitutents tapered out rapidly with in-
creasing length of the conjugated chain. From analysis of the intensity of the bu-
tadiene IR spectra it was concluded that the double bond has a dipole moment of
about 1. 3D with the central carbon atom (C2 or C3) being the positive end of the
dipole. Molecules of linear polyenes are systems of conjugated and polar carbon
bonds, with the arrangement of the bonds as well as the charge on the atoms
;Card 2/3

L 26665-65
ACCESSION NR- AP4044700
along the polyene chain alternating. Orig. art. has: 5 tables and 2 figures

ACC -N-R-t- 821 SOURCE CO1:iE---U-ATC0T6 -A _5 To-0-070 _60 rl Ff6_2 f 6 _f6 -i
AUTHOR: Glebov, I. Aej Popov# Ye. N.
ORG: none
TITLE: Investigation of 6- and IZ-phase operation of a rectifier
generator
SOURCE: AN SSSR. Institut elektromekhaniki. Teoriya, raschet i issledovaniye
vysokoispol'zovannykh elektricheskikh mashin (Theory, design, and research of
electrical machinery in constant use). Moscow, Izd-vo Nauka, 1965, 162-167
~
ITOPIC TAGS: electric generator, s en-d conductor rectifier, electric generator unit
ABSTRACT: The excitation system of "Elektrosila" 200-, 300-Mw (built) and 500-Mw
(blueprint) turbogenerators consists (see figure) of these parts: 1 -main synchronous
generator, 2 - inductor-type h-f generator (exciter);
3 - semiconductor rectifier; 4 - reactors; 5 - magnetic
amplifier. The inductor-type generator having a
relatively high reactance causes an undesirable
current ripple in the turbogenerator field winding.
Excitation system with As a remedy, a IZ-phase rectification circuit with
inductor-type h-f generator
2

ACC NR,_ AT6016821
two 30* -shifted 3-phase windings was suggested by R. A. Lyuter. The suggestion
was experimentally verified on a 29-kw machine simulating 6- and 12-phase
conditions. Oscillographically measured the ripple ratios were 5276' for the 6-phase
circuit and 27% for the 12-phase. However. the 12-phase system had a leas favorable.
external characteristic (U,& a f (1,J). Hence, further experiments are held desirable.
Orig. art. has: 5 figures and I formula.
SUB CODE: 09. / SUBM DATE: 04Aug65 / ORIG REF: 003 OTH REF: 001

POPOV, Ye.N., kand, mer-', na-ik
Acute cholecystitis in elderly persons. Trudy inst. im. N.V.
Skl-Af.9.-60-70 163. (MIRA 18:6)
J., Moskovskiy gorodskoy nauchno-issledovatellskiy institut
1
skoroy pomoshchi ~meni Sklifosov3kogo.

SOLOMIKA, Ye.N.; POPOV, Ye.Y.
Disorders of the large arteries of the extremities in protracted
septic endocarditis. Sov.med. 24 no.l:~57-63 Ja 160.
(MIRA 13:5)
1. Oz obahchey i gospitalluoy terapayticheskoy (sav. - doystvitall-
nyy chlen AMR SSSR prof. Ye.K. Tareyev) i khirurgichoskoy (zav. -
prof. A.W. Telikoretskiy) kliniki sanitarno-gigiyenicheskogo fakull-
teta I Nookovskogo ordens. Lenina, meditsinskogo institute, imeni
L.M. Sechenova na baze 24-y gorodskoy bollnitey (glavnyy vrach
V.P. Uspensk17).
(WIDOCARDITIS complications)
(LEG blood supply)

Popov, YC.-
"Acute
bo('ies nnd inLtv.urents." Yoscow ol' L-nin inS4.
I.I.on for th(,. Dc,.-roc
i Icni I. 'Ei. schcriov.
of Doctor in Z-J~erdcal Scienc,~.
Kniz)iaya letopis
ljo. 1~1, lll,',1~6. 1-:oc cow

POPOVIV Ye.N. (Moskva, 8--ya ul. OktyabrIskogo polya,d-5.kv-5)
Perforation of the aorta In esophageal trauma caused by
foreign bodies. Grud. khir. I no.3-91-97 Ny-Je 159. WIRA 15:3)
1. Iz Moskovskogo nauchno-isoledovatellskogo inatituta skoroy
pomoshchi Imeni N.V. Sklifosovskogo (dir. - zasluzhennyy vrach
'USSR M.M. Tarazov, glavnyy kh:Lrurg - prof. B.A. Petrov)
i kafodry obstichoy i gospitallnoy khirurgii (zav, - prof,
A.N. Velikoretskiy) I MoskovBkogo ordena Lanina maditsirwkogo
instituta imeni I.M. Sechenova (dir. - prof. V.V. Kovanov).
'AORTA-WOUNDS, All INJURIES)
(F.SOPHAGUS-FMEIGN BMIES)

SOLODOV, Aleksandr Vasillyevich; EOPOV, Ye P. retgenzent; PETROV,
F.S., dots., red.; K?,V-UCHKOVA, V.11., tekhn. red.
(Linea-v autoriztic control systeme with variable parameters]
Lineinye sistemy avtomaticheskogo upravleniia s peremennymi
parametrami. Moskva, Fizmatgiz, 1962. 324 P. (MIRA 15:6)
1. Chlon-korrespondent Akademil nauk SSSR (for Popov).
(Automatic control)

POPOV9 Ye.P. (Leningrad)
Study of self-oscillatory systems with logic devices. Izv. AN
SSSR. Otd. tekh. nauk. Energ. i avtom. no.4:116-121 Jl-Ag 162.
(MIRA 15:9)
(Automatic control)

Po~~Ov, 'Ye. F. Lt. Col.
110 i "I
.,alculatAne the Col~pr,--,tdon of A# Ilor-Cylindriall Snlrpl 3pri-P..9,11 Prik.
mat. i mekh. 4, No-1, 1040

P-~ j PT-'V 3y~. P.
"Ti-.---ory and Design of Duc-11-ile Elastic Cc--.pouqd--," Leningrad, 1947

USSR/Springs, Spiral Feb 1947
Mathematics, Applied
"Calculation of Springs," E. P. Popov, 22 pp
"Inzhenernyy Sbornik" Vol III, No 2
Treatment of non-linear characteristics (relation-
ship between load and displacement) in a spiral
spring of arbitrary form subjected to an axial
load) when a number of the coils are brought into
contact.
16yo

Uz --- % r- - -" -.'- .-
P. nd&M stadM tanWh abo&A,
Ro&j
--rXimm Mblems of the Statics of Thb
Gosudantv. lidat. Tehn.-Teor. LV 'doecow-Leningrad,
1949. 170 pp. (I pfart).
This is a seff-contained monograp ; devoted to a sys-
ternatic exposition o(solutionsof a bm..c classof elastostatic
RMblams on large deflections of thin , f ~ds'knd Vat-Rades.
The theory, including a careful derivanon of the K;rchhoff
eauffibri QAAUQDL,45 contained j!, the first chapter
(49 pp.). Th remainini two chapters 003 pp.) de.-I with
the appi'cations of the theory to diverse problems on deflec-
tion and stability of thin rods deforme(I in one plane. The
book eum'manzes all significant publishcd results on prob-
'ems o( this catEg-,ry up to 1948, A distinguishing feature of
the work is that the "act solutions are nresented in a form
suitable for numerical computation, so teat they can be used
directly by a strew analyst. The bibliof,-raphy contains 85
items, the earliest of which is dated 1867.
L S. Soholmikaff (Los Angeles, Calif.).
Sourass Xathe=tiGal
VOI 13

redaktor; , S.N.,
ROSTOVTSEV, G.G.; PAIIOVKO, Ya.G. _Nt UN
retBenzent; PAVIAVA, T.P., tekhniche_~kiy redaktor.
[Structural mechanics of the airplane] StroitelInaia mekhanika
samoleta. Vol. 1. (Geueral course] Obshchii kurs. Leningrad,
Leningradekaia Krasnoznamennaia voenno-vozdushnaia inzhenernaia
akademiia. 1950. 437 P. [Microfilm] (MLR& 8:1)
(Airplanes--Design and construction)

POPOV, To.P..(leningrad)
Accounting for the nonlinearity influence in designing servosystems.
Avtom. i telem. 14 no,6:690-711 N-D '53- (MIBA 10:3)
(servo.echaniame)

POPOV, Ye.P.; SOBOLICV, O.K., redaktor; AKHLAXOV, S.N., tekhnicheskiy
(Dynamics of automatic control systems] Dinamika sistem aytomatiche-
skogo regultrovaniia. Koekva, Gos. izd-vo tekhniko-teoret. lit-ry,
1954. 798 p. (KLRA 8:2)
(Automatic control)

USSR/Engineering - Automatic Control
Card 1/1 pub. 41-1/13
Author : Popov. Ye.-P., Leningrad
FD-1107
Title : Approximate study of self-excited oscillations and forced oscillations
of nonlinear systems of high order on the basis of the harmonic lin-
earization of nonlinearities
Periodical : Izv. AN SSSR. Otd. tekh. nauk 5. 3-38) MY 1954
Abstract : Extends one of the variants of the method of harmonic balance of Yxylov
and Bogolyubov to a new group of problems, developing a more direct
m~_thod for obtaining the approximate dependence of the frequency and
amplitude of self-excited oxcillations 'and forced oscillations (with a
given forced frequency) on the parameters of the system, as well as for
finding the ranges of their existence. The'presented method consists of
a combination of the method of harmonic balance of M. M. Krylov and N. N.
Bogolyubov and the method of determining stability limits of linear sys-
tems resulting from the analytical expression of Mikhaylov's criterion.
Twenty-two referc..nces. Diagrams
Institution
Submitted January 23, 1954

POPOV, E.P.
RepI7 to M.A.Aizerman's and I.M.Sairnow's note on X.F.Popor's article.
Izv. AN SSSR Otd.tekh. nauk no.lOgI89-191 0 154. (MIRA 8:3)
(Vibrations)(Aizerman, 1A.A.YZalruova, I.K.)

POPOV Ye.p.
Reply to N.K.Aleksandrovskii's and G.K.-Xrug's remarks concerning
my article Offonlinearity effects in the design of servomechanisma.0
(Avtow. I. telem. 14 no,6 '53.) Avtom. i telem. 15 no.4:362-363
ji-Ag 154. (KIJA 7:11)
(Servomechanisms)

Yj
USSR
1 ox in-, tQ Tr, ~tm- t
r de-,v,~ Fry ~v
1c, n t;;"
i,c ut I -i!i~ llx-~t~ clascL L.-f lll~~T i-
the

Z7
USSHIPhydics Mechanics
Card 1/1 flub. 2.2 - 6/48
Authors Popov, E. P.
title Thorough determination of the first approxima-ti.on durinIg the study of auto-
oscillations of nonlinear hinh-order systems
Periodical Dok. AN SSSR 98/3, 345-348, Sep 21, 1954
Abstract, -,A perfect solution for the cases where hisher harmonics of the argument must
be taken into consideration for the calculation of the first harmonies of a
nonlinear function (harmonic linearization) is described. It was established
that the first harmonics of the function (f~ is determined not only by the
first harmonies (x) but also by certain combination members composed of all
(X) harmonies. The role of these combination members, in solving the problem
of auto-oscillation of nonlinear high-order systems, is explained. Formulas
for the coefficients of harmonic linearization.. are included. Five USSR re-
ferences (1934-1954). Graphs; drawing.
Institution
Presented by: Academician 11. It'. Bogolyzfbov, June 9, 1954

UM/ Engineering, Follow-up systems
Card 1/1 S Pub. 22 - (11/149
Authors j Popov, E. P.
Unmodulated frequencies of a non-linear system of a high order during
slowly varying external-affecting force
PorlodIcal : Dok. A14,SSSR 98/4, 545-547, Oct. 1, 1954
Abstmat t Using a sample-equation, an aporoximative method is described in
connection with the determination of an effect of a slowly-varying
feeding force on the frequency carriers 9f automatic control and
measuring devices of following-up systems. -Five references (1937-
1954
Institution :
Presented by : Academician N. N. Bogolyubov, June 8, 1954
(3-on741

SOV/124-57-5-5180
Translation from: Referativnyy zhurnal. Mekhanika, 1957., Nr 5, p 12 (USSR)
AUTHOR: Popov, Ye. P.
TITLE: The Approximate Determination of Self-sustained and Forced
Oscillations in Automatic Control Systems (Priblizhennoye oprede-
leniye avtokolebaniy i vynuzfidennykh kolebaniy v sistemakh
avtomaticheskogo regulirovaniya)
PERIODICAL: Tr. 2-go Vses. soveshch. po teorii avtomat. regulirovaniya. !"7.b't.-
Vol. 1. Moscow- Le.6ingrad, lzd-vo AN SSSR, 1955, pp 219-248
ABSTRACT: The paper describes the applipation of N. M. Kryl(jvls and N. N.'.
Bogolyubov's harmonic -equilibrium method to the iniestigation of the
periodic modes of oscillation of some nonlinear systems. In accord-
ance with the nature of their nonlinear connections, the systems under
investigation are divided into three classes. The author describes
the harmonic linearization of systems of the various classes, as well
as that of systems having a tag. The determination of the periodic
mode of oscillation (as well as the clarification of its relationship to
the system parameters) is reduced to the solution of equations
Card 1/2 obtained by equating to zero the coordinates of a certain nominal

SOV/124-57-5-5180
The Approximate Determination of Self-sust V ned and Forced Osc;llations (cont.)
frequency curve constructed for a linearized system. Graphs are adduced for the
relationships corresponding to some characteristic cases. The author describes
some approximate stability evaluations which are based either on the averaging of
the variable coefficients of the perturbed-motion equations or on an analysis of the
nature of the nominal frequency curve at points corresponding to possible modes of
oscillation. The general premises are illustrated by a number of specific configu-
rations. Neither the question of a substantiation of the methods described in the
paper under review nor the evaluation of their accuracy are examined. Undoubtedly,
many of these methods will produce satisfactbry results only on condition of
definite limitations in the properties of the systems investigated. It is noted that in
the majority of cases the experiments produce good qualitative and quantitative
agreement with the calculations made in accordance with the methods described.
N. N. Krasovkkiy
Card 212

USSR/Mathematies - Automatic Regulation FD-2237
Card 1/1 Pub.41-5/17
Author : Popov, Ye. P., Leningrad
Title : On the small parameter in the method of harmonic linearization
Periodical : Izv. AN SSSRY Otd, Tekh. Nauk 2, 41-59, Feb 1955
Abstract : Makes an attempt to show the possibility of derivirg formulae for harmonic
linearization by the small parameter method; demonstrates the complete con-
currence of results obtained by the small parameter method and the harmonic
linearization method not only for single-value and loop characteristics
F (x), but for more general types of nonlinearities F (x, px). Shows the
simultaneous existence of autoresonance and filters in problems on the
theory of regulation. Formulae, diagrams. Thirteen USSR references.
Institution:
Submitted : November 17, 1954

P. (Prof.)
"Ar!plication of t he Method of Harmonic Linerization to the Itesearch on Transitional
Processes in Non-linear S:-stcms,"
naper read at the Session of the Acad. Sci. UiS% on Scientific Problems of Automatic
Production, 115-20 October 19~Y6.
Avtomatika i telenekhanika, 149. 2, p. 182-192, 1957.
9015229

I OBOIST, O.K.. redaktor; KURASHOTA, N.Ya.,
J"P'X4'Iei'FS-N!'4h Por
(Autowtic control; fundamental concepts] Avtomaticheakc-et reguliro-
vents; onnovnye poniatiia. Moskva. Goa. izd-vo tekhniko-teoret.
lit-ry, 1956. 296 p. (MLRA 10:2)
(Automatic control)

on the up* atha aaamak ;4pAwLz&..
in tb4
9 P P,~p- 'D~44-dy Akad
v "k ~S?7 'T Tw
,
-Js TM I", Truasl~u.n
Method in whwh a tlvtm nonline-ar equa

. tAbll~htlljj the Mcth~l ~ smali p-rameter
;
7 h cvmiderLd wbicti mavm 11
approximate a u,lutjgl A 'hc quA
t" to thc tivcn

POPOV, Ye. P.
"Damping Diagrams of Nonlinear Processes in Automatic Systems,"
by Ye. P. Popov, Leningrad, Avtomatika, No 4, 1956, pp 6-18
The article presents an approximate method of evaluating the quality
of transient processes in nonlinear systems simultaneously with the deter-
mination of autooscillations and the separation of areas of stability.
This method is based on one of the varieties of the harmonic balance method
and is called the harmonic linearization method.
Whereas previously a solution to a nonlinear problem was sought for,
which solution was close to a nondamping sinusoidal solution (i.e., close
to a solution to a linear system located at the stability boundary), the
author proposes a new method in which the solution to a nonlinear problem,
close to a linear rapidly damping solution far from the stability boundary,
is found.
. This approximate method of investigating the quality of nonlinear
transitory processes yields entirely satisfactory results.

POFOV) YE. P.
"Approximate methods of studying of nonli:jear oscillations In alatc,
Matic control systems."
Paper presented at the Intl. Symposium on Nonlinear Vibrations, Kiev, USSR,
9-19 Eep 61
Institute of laectrical Engineering of the USSR Academy of Sciences, Leningrad

7
~1112311 2/12 6
Appr.,).dmat;~., 3ttudy of Trqasient izv. Akad. N aux,
Of 0. t e kht. Nauk
Proccajes
3-23
Ul. S. 3 .
TF-C-,L: EYI. f at I~jrt _x (: x al I
ay if I g 3y". 3 tabi I i
t ~_ r~~3 rl~t "I'ly t.j trLE:
4 n,-

t
-

r t it C."I

by ,vn,,~j.CjCjIJ_ng certrdn relay
Sys tem~j, In 08tiMa-ti-,ig accuracy of__the- Wtjjod~ it yras
ino-a fu,-
asstated- that-th px%-a-aa ~si6l is obta
,
-
1
b6~ rar~itory pre,66-as f,,r- th- sa;rv
the

US;;14yehaniJ
Card 1A P11b. 2? 10/54
Authors i ToIpov, Ye. P.
Title s On the application of the hArMOnIC linearization method tc the theory of
automatic control
Periodical I D(**'AN SSSFt 106/2, 211-2-14.. Jan 11, 1956
~Abstraet 9 Proof is presented.that the introduction or a small pnrameter into the
harmonic linearization method makes the latter more effective and pricti-
cal in its application to the automatic control theory.- Seven USSR
references (1934-1955).
Institution
Presented by: Academician N. IN. Bogolvubov, July 9,~ 1955

o
SUBJECT USSR / PHYSICS CARD 1 / 2 PA - 1746
AUTHOR POPOV'Z.P.
TITLE '-K-Ce-neralization of the Asymptotic Method developed by
N.N.BOGOLJUBOV in the Theory of Nonlinear Oscillations.
PERIODICAL Dokl.kkad.Nauk, 111, fasc.2, 308-311 (1956)
Issued: 1 / 19577-
In the case of many technical problems, particularly in the theory of automatic
regulation it is neoossary to investigate quickly declining dying down oscil-
lation processes. For this purpose the asymptotic solution of a differential
equation of the type: d 2 x/dt2 + 2b dx/dt + a2x f(x,dx/dt) is necessary.
Here E denotes a small parameter, b and c real constants, f(x,dx/dt) - an
assumed real function. In the case of 0 the solution of the above equa-
tion in the case of complex roots of the characteristic equation
2 2 -bt 2
p + 2bp + a =0 takes the form x - a cos V, a - a 0e V t + Vo Ve' 7b
In accordance with the idea of the asymptotic method developed by N.N.BOGOL-
JUBOV the solution of the given differential equation is sought near W 0
in the form x = a cos T + t9j(a'T) + E 2 92 (a,T) + ..., but with the following
expressions for a(t) and T(t): da/dt --ba +F_ ~j (a) + F2
2 , ~2 (a) . .....
d'V/dt + E B, (a) + E B 2(a) +..., where 4) - has the same value as above.
These expressions for x,da/dt and dT/dt are considered to be formal series, and
INSTITUTION: Leningrad Aix-force Academy "A.F.UOZAJSKIJ"

0 PC)

AUTHOR: FOMINA, Ye.N. 103-10-9/10
.TITLEs Seminar on the Automatic Control Theovf in Leningrad (1955-1956)
(Obahcheleningradskly seminar po teorii avtomaticheakogo reguli-
rovaniya (1955-1956 gg.))
PERIODICALt Avtomatik& i Telemekhanika, 1957# Vol* 18, Nr lo, PP* 947-949
(USSR)
ABSTRACT3 On January 21, 1955, P.A.Lebedev delivered a lecture on
"Stability of a non-Stabilized Movement in the Final Time
Interval".
On February 2, 1955, T.K.Sokolov discussed the "Question of the
Characteristics of Quality in the Theory of Automatic Control".
D.A.Bashkirov discussed the "Finding out of Roots of Algebraic
Equations According to the Method of the Successive Divisions".
On June 6, 1955 I.A.Orurk discussed the "Application of Integral
Equations on the Occasion of the Investigation of the
Transition Processes in Complicated Linear and Nonlinear Systems".
N.G.Barinov discussed the "Problem of the Construction of Trans-
ition Characteristics in Automatic Control Systems."
On September 27, 1956 Xt&L.Po2ov discussed the "Approximate
Investigation of Transition Processes in some Nonlinear
Automatic Systems According to the Method of the Harmonic Lineari-
Card 1/2 zation."

PHASE I BOOK EXPLOITATION 3716
Avtomaticheskoye upravleniye i vychislitel'naya tekhnika, vyp. 1.
(Automatic Control and-Computing Technique, v. 1) Moscow,
Mashgiz, 1958. 302 p. 7,000 copies printed. I
Ed.: Solodovnikov, V.V., Doctor of Technical Sciences, Professor;
Scientific Ed. of Publishing House: Polyakov,,G.F.; Tech. Ed.:
Sokolova, T.F.; Managing Ed. for Literature on Machine Build'ing
and Instrument Making (Mashgiz): Pokrovskiy, N.V., Engineer.
PURPOSE: The book is intended for engineers and scientific person-
nel.
COVERAGE: The book is a,collection of eleven articles presented at
a seminar an the theory and technique of automatic control and
computing machines. The seminar was organized by the Scientific
and Technical Society of Instrument Making, the Moscow Higher
Card 1/4

Automatic Control and (Cont.) 376
Technical School imeni Bauman, and the-Moscow Aviation Institute
imeni S.Ordzhonikidze. The Mogcow Physics and Engineering In-
stitute also participated iri the seminar. The first five arti-
cles outline the theory of automatic control, the.next four de-
scribe automatic control systems and system .components, and the
last two articles discuss differential. analyzers. No person-
alities are mentioned.
TABLE'OF CONTENTS:
Foreword
3
Solodovnikov, V.V. Basic Principles of Engineering Cybernetics 5
Kuzin, L.T. Some Problems in Synthesizing Pulse Servomechanism
Systems Subject to Steady-state Random Signals 22
Card 2/4

Automatic Control and (Cont.) 376
Popov, Ye.P. Selecting the Parameters of Self-oscillatory Auto-
ti
mat ~coH`trol Systems 59
Rayevskiy, S.Ya. Description of Random Processes by Means of the
Complex Frequency Function, and Some Problems of Control System
Quality 80
Kuzovkov, N.T. Some New Applications of the Method of Logarithmic
Frequency Characteristics to the Analysis of Automatic Control
Systems ' 100
Ruzskiy, Yu.Ye. Electric Hydraulic Controllers 134
Chelomey, V.N. Study of Pneumatic and Hydraulic Servomechanisms 166
Rozenblat, M.A. Magnetic Amplifiers for Automatic Control Systems 182
Card 3/4

S/112/59/000/012/056/097
A052/AOOl
Translation from. Referativnyy zhurmal, Elektrotekhnika, 1959, No. 12, p. 158,
# 24999
AUTHOR-, PopovA Y2..P.
TTTIE- On Selection of Parameters of Natural-Oscillation Automatic Control
Systems
PERIODICAL: V sb.: Avtomat. upravleniye i vychisl. tekhn. No. 1, Moscow, Mash-
giz, 1958, pp. 59-79
TEXT: An approximate analytical method of investigation of natural-oscil-
lation automatic control systems is described. The method is connected with the
use of Mikhaylov's linear criterion and is called the harmonic linearization method.
The latter is considered in application to automatic systems containing any number
of nonlinearities at a slowly varying input action, Suggestions on the analysis of
the obtained periodic stability solutions are made. Examples of calculation of
natural-oscillation conditions in the systems are givL=n. A.S.B.
Translator's note- This is the full translation of the original Russian abstract.
Card 1/1

Effia
r 'r,
L 7
I
-1 A I
I.: An, 4- 4
U F-F-,

SOV/24--59-1-8/35
AUTHOR: Popov, Ye.p.
TITLE: IlQpmerftc Linearazation Applied tc Is,-,5,a-te the Stability
Regions of Nonlinear Automatic Systems (0 vydelenii
oblastey ustoye-bi-iosti nelineyn7ldi avtomati~:-.heskikh
sistem na osno-vie garmoai~,heskoy linearizatsii)
PERIODICAL:Izvestiya Akademii Nauk SSSR, Otdeleniye Tekhnicheskikh
Naiik.,, Energetika i A-ktoma-tVk,9,,l9591,!,Tr lvpp 53-454 (USSR)
ABSTRACT: The systems are those that ha-ie one nonlinearity only
and which ar-- described by differentlial
equations with constaut. i,,oeffi!_,ients. It is asslim d
thatb a periodic t-o the e~-atioras -xists at -,-he
boundax~j between the regions of stability and instability
and tbat ~he solutic-nis withJr, the unstable x-agion are
also periodic. The cscillW,-ions are assumeci to be of
nearly sinusoidal wave shape,, with rsespe,:.t to the -variable
appearing i-n the nonlinear function (bixt not necessarily
with respect to the ot-her variab_161s). This a5sumption
is essential -to the harmonio, 11-raearization approximation.
The necessa:~,y a-ad sufficient. c;aarlit. ions fcx, the system
Card 1/2 to be stable a.1-- soug4t-j t..ap, ~5affi4.~ient are

6
"0V/24-59-1-8/35
Harmonic Linearization Applied to Locate the Stability Itegions of
Nonlinear Automatic Systems
found to be exactly those that Lyapunov2s direct
rigorous method gives. It is pointed out that the
method lacks mathematical rigoux but that, since it is
a very effective one for practical purposes, it should
be given a sounder mathematical basis. The method is
extensively illustrated by examples; Nyquist diagrams
are used to derive the sufficient conditions. There are
9 figu--res and 9 references of which 7 are Soviet and
2 German.
SUBMITTED: 22nd May 1958
Card 2/2

POPOV, Te.P.
Theor7 of vibrational smoothing of nonlinear characteristics of
automatic control systems with the aid of self-oscillations. Avtom.
upr. i vych. tekh. no.2:104-138 '59. (MIRA 13:2)
(Automatic control)

67476
/.c, 94-00
AUTHOR: Popov, Ye.P. (LeninLrad) SOV/24-59-4-12/33
----------
TITLE. The Effects of Noise Caused by Vibration on t1le Stability
and Response of a Non-linear Automatic System A
PERIODICAL: Izvostiya Akadetaii nauk SSSR, Otdeleniye tekhnicheskikh
nauk, Energetilka i avtomatika, 1959, Nr 4, PP 97 -- 105 (USSR)
ABSTRACT: A general approximate treatment is givens The system
(Figure- 1) has one non-linear unit, which is iacluded in
the internal feedback loop. Units 1, 2 and 3 are linear
-is are the feedback and the object. The non-linear
differential ec.;Uatlon describing the system is (1.1),
where F(x) is the non-linear function and the other
functions are operator polynomials with constant coefficients.
The external vibration noise f,(t) �s defined by Eq (1.2);
f1(t) is the input, which varies much more slowly than
Yt), in accordance with the condition giv-en. It is
assumed that the linear transfer function R(p)/Q(p) contains
no harmonics generated by the non-linearity; an approximate
Cardl/3 solution for x is sought in the form Eq (1-3), in 'Th
P~_~

67476
SOV/24-59-4-12/33
The Effects of Noise Caused by Vibration on the Stability and
Response of a Non-linear Automatic System
x0(t) varies slowly and A and 0 are the amplitude and
the phase of the forced oscillations at the input to the
non-linear unit; these can vary slowly as x (t) varies.
The subsequent steps are a standard harmonic linearization
treatment; Figure 2 illustrates typical results obtained
from a saturation-type non-linearity.
The second section of the paper deals with the derivation
of'the linear equation for the response to the input
(other than noise). The linearization of Eq (2.2) is used-,
odd symmetrical functions (i.e. typical non-linearities)
a.re considered; then Eq (2-3) applies, which simplifies
the calculations. The response to the useful signal is
then described by Eq (2.6), where the gain k depends on
the amplitude B and frequency S), of the noise input.
Eq (2.7) gives the stability limit indicated by the
characteristic equation; Eq (2.8) is the transfer function
of the open-loop system and Eq (2.9) is the same for the
closed-loop system.
Card2/3 The third section deals with special cases frequently
------------------------ - - ;r -

P -
T- IT L V
c.
P &,I i cl
-ine-a-
"j; I
3
d f _r e i
s olut or, n c'.
So lu n E j.
T, - -j 7. 1 -- f I i
u'd J
help
s e ji ju
mIS "-"T 0
L! T J.
C 1-ut- Y7
a
Card ys t c
and "~T

sl.l.,791 5~/ooo/06/00-,,/029
On the Determi.nat-ion of the -Higher Harrmcnics in _140-n-Srx -, ical
Self-Excited Ose-Mations
characteristic co,,nposed. of straight line sectioDs r.~Y
Ayzerman , M , A. , and Gantimakher , F. R. ( Pr i.Ittlachnalla
a
riaterfiatika i Ylekharika, 1956, I~r SUCIL-1 - sclltltiOl
has proved difficult for tyiany systems other than of tha
oAn-off type. In the present Daper. another method (,j'
analysis of self-excited oscillations is presented. using
a Fourier expansion with a finite number o-.L' hilgher
harmonies (including a zero harutoni,,~ in tho case of non-
symmetrical oscillations), The method is based on using
the results of harmonio linear iz q'U ion consi,lered ;F~s the
zero approx.-Lmation wi.th subseqLient inopro)ve-iments
determining the higher The mathod is
applicable to many systems with non-linear c'P_ara,:.ter_JsL'i,_-S
more general. than a. succession of st-ra-ight line sections,
but nevertheless with other substantial limitations.
The general equation doscrib:LnG the motion of a non-
Card linear system contains the non-lineai characte-7ist-ic J~n
2/1+ the form of a function of the dis.placement, A 12fftitation
is introduced by which the higher derifitives of this
function are finite. The periodic ;oltition of tLie

?g (~ /(I /
On the Determination of 15`ie T Eher in
Self-Excited Oscillations
equation of motion is ro7tmu_lated, dJ_sti_,)gu_-Slli7Dg tile 2;er,,-
and fundamental harmordes. is:z slhuwn tll-iat, ac.".,epting
thie above limitation orl the non-1.4noaiitly., the zaro and
fundamental htarmonil -i sol.utlf oris can -z:e apprroxilraat-4~_,ly
derived from two selparate. equal aons A -on6itiOll
is formulated ( 'the f iltering ppoperlv-~y 1) by Bq (1.10) .
The devrea of its fulfilment dp_~,-,.ides Mae impc,~,-taucq of
takin- account of the higher haimoalcs J-n the dec-11-ed
I?
Solution. If important, an appi-c-)xi-mation fl)~~ each of tte
higher harmonics is given. Tl'Yji!z in turn, leads to a
fresh approximation for t~ie zeri.- and f-undamental
harmonies. This improvement- corstllitu~-Jes a sig-nifleant
computationa-1 adivantage of the it-ethod presented here.
Successive approximations can be introduced by using the
corrected values of the zerc. anr fundamental harmonics in
the subsequert step of' approxim,! ting the higher
knother advantage is the facili~ y of doaling with non-
Card symmetrical conditions which ar,, expressed by the presenr.~e
3 /L of a constanl~ in the equation ri " motion, An example of
the method deais with an on-off sv~3tew. It is seen
V

SHUVALOV, likolay Konstantinovich; POPOV. TGOP., prof., doktor tekhn.
nauk, rateenzent; TOR0307, A.A., prof., doktor takhn.nauk,
retsenzent; DSKCHIMO, O.P., kand.takhn.nauk, retoonzent;
WSWQV. A.D.. kand.tekhu.neuk. nauchnyy red.; APTEKKAH. M.A..
red.; TSZ, R.K.. takhn.red.
(systems of program control operating on a combined principle]
Sistemy program-nogo regrallrovaniia, rabotsiushchie na kombi-
nirovennon printsipe. Leningrad, Gos.soiuznoe izd-vo sudostroit.
promyehl., 1960. 74 p. (MIRA 13:6)
(Automatic control) (Programming (Electronic computers))

E 5 4-
ri s 9 Z
0 ~:f
R2 98
H h A .-a a
Ar - - -
41; 0 -.13
md 4 1
41 It
o I
wiJ 5
Id
ik;115:1 lid
.13-
P4 .9
7H
ol
-14 1.

SCLODOTNIKOV, V.V., prof., doktor takhn.nauk, red.; BOGOLYUBOY, N.N.,
akademik, red.; ISaINSKIY. A.Tu.. skademik. red.; KAZAMICH,
Y.Y., prof.. doktor tekhn.nauk, red.; LTAPUNOV. A.A., prof..
doktor fiz.-mat.nauk, red.; PWROT, B.N., red.;.PCPOT. Te.P.,
prof.. doktor tekhn.nauk, red.; POSMOV. G.S., ~7r-or.-,-doktor
tekhn.nauk. red.; RTABOV. B.A.. prof.. doktor tekhn.nauk, red.;
ANISIMOV, M., dotsent. kand.takhn.nauk. red.; PIEROV. V.V..
dotsent, doktor tekhn.nauk, red.; FLOTNIKOV. V.N., dotsent,
kand.tekhn.nauk. red.; USHAKOV, V.B., doktor tekhn.nauk, red.;
POLYAKOV, G.F., red.izd-ve; SOKOLOVA, T.F., tekhn.red.
[Automatic control and computer engineering] Avtomatichookoe
upravlenie i vychislitellnaia tekhalka. Moskva, Gos.nauchno-
tekhn.izd-vo mashinostroit.lit-ry. No.3. 196o. 489 p.
(MIRA 13:7)
1. Chlen-korrespondent AN SSSR (for B.N.Petrov).
(Automatic control) (Electronic calculating machines)

PHM I BOOK EXPWITATION SOV/4479
Popov, Ye. P.,, and I.P. Pal'tov
Priblizhennyye wtody isaledovanlys nelineyaykh aytomaticheakikh sistem, (Approximto
Methods for Analyzing Nonlinear Automatic System) Moscov, Tizmatgiz, 1960,
792 P. 10,000 copies printed.
Ed.: O.K. Sobolev; Tech. Ed.: B.A. TuwArkina.
PURPOSE: Thio'book is intended for engineers and scientists concerned vith the
theory and practical applicationa of automatic control system, particularly
those vhich deal with nonlinearities in automatic control, stabIlization and
regulating systemaj, and servomechanism. The book is 4160 suit" for students
and aspirants.
COVERAGE: The book presents a comprehensive treatment of various approximate methods
for analyzing the characteristics of nonlinear automatic systems. These zwthods
are based largely on the theoretical concepts of hamaDnic balance and equivalent
linearization; also treated am the specialized-sma31-parawter method and statis-
tical linearization. A wide variety of nonlinearities is consid-ored,,and many
Card-l/-g--

31327
S/569 61/001/000/012/019
(11-3 D274YIIMOO
AUTHORt POPOTI Ye. P. (USSR)
TITLEs Some synthesis problems of nonlinear control systems
SOURCEs International Federation of Automatic Control. lat
Congreast Moscow, 1960. Teoriya nopr*ryvnykh mistem.
Spetsiallnyye matematicheakiye problemy. Moscowt
Izd-vo AN SSSRy 1961. Trudy, v. 1, 389-403
TEXT s Synthesis problems are considered which can be solved by describ-
ing function technique and by statistical linearization. Two types of
robloms are discu8sedi problems related to the free motion of the system
atability, sustained oscillationsp tr=siont processes) and problems re-
T
lat*d to the system response to disturbances and controller action (steady~
state and dynamic error, effect of vibration and random noise). System
configuration and order of differential equations are assumed as arbitrary.
Neverthelesag for convenience, a certain typical configuration is consi-
dered (shovn in figures)., with one- and two nonlinearities respectively.
Card 1/14

Some synthesis problems...
31327
3/589/61/001/000/012/019
ID274/D306
Transient processes, sustained oscillations, stabilitys For the case of
symmetrical oscillatory processesq viz.
da, d -,,r (a) ('%)
x = a $in --i- . a 9 (a) 9
t dt
the describing function is
x + IL(-al px
F(x) q(&) q' (a (6)
CO
The performance measure of the transient process in nonlinear systems of
high order by means of Eq. (5) in analogous to that used in linear theory,
namely the root-locus method, with the basic difference, however, that the
damping factor ~ and the frequency w are not constant, but vary with
the oscillation amplitude a . From Eq. (5), the characteristic equation
Card 2/14

Some synthesis problems ...
31327
S/569J61/001/000/012/019
D274/D306
2(p) + R(P) rq(a) + q'(') (p (7)
L w )I - 0
in obtainod. With the change of variables p + JW, one obtains
+ j u)) + B( + JW) Z-q(a) + jqI(a) 0 (8)
_7
Expansion in series
Q,
+ jw) 2( + jw _)
dp
(jw)' d2
+ f60 +
21 dp2
0 (A))'
+ - n
nI dp
Card 3/14

31327
S/569/61/001/000/012/019
Some synthesis problemso.. D274/D306
in convenient; if is sufficiently small, then
2( + jW) = Q(jU)) + dQ
p jW
The methods of determining ~ (a) &n4 (;j(&) from Eq. (8) differ. Four
such graphic methods are considered~ The graphs obt,,).ined in determining
and co are called damping-measure diagrams of nonlinear transient
processes. These graphs yield much information on the synthesis of non-
linear systems. By drawing up such diagrams with respect to various
system-parameters, the most convenient parameters can be selected. It is
noted that with small the use of Eq. (10) instead of Eq. (9) consi-
derably simplifies the problem. Transient processes with non-symmetrical
oscillations: Such oscillations are assumed to have two components:
0
X = X (t) + X*(t)
0 dy
x .a a(t) sin y(t) (A) (17)
dt
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Some synthesis problems... D274/D306
where x * in the periodic component, and x 0-the aperiodic. Thit describ-
ing function is
x 0)X +
F(X) - F 0(x0a) + q(a YX
, co
where
Jf2
0 1
F "(.0 + -a sin
y)
dy
(19)
211

217
q F(x0+ a sin V )sin 'Y d q, F(X0 +
0
(20)
+ a si n cos 1~ dy
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Some synthesis problems ... D274/D306
Hence,
0 0
Q(P)xO + R(P)F (x 'ft) - 0 (21)
0 V (&Px 0
Q(P)X* + R(P) [q(a~lx + P x = 0 (22)
Eq. 22 permits obtaining the two- variables (a and W) as a function of
x0 and the parameter k. From
X (a, 9 x0M = 0 2 Y(a. Cog X0 'k) = 0 (23)
one obtains a(k) and w(a) by the same methods as above. By graphic
means one obtains the new function
FO = 4)(X"k) (24)
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31327
S/569/61/001/000/012/019
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called displacement function. 71ais function is related to the aperiodic
component (Eq. (21) ). Thus, instead of Eq. (21), one obtains
COX 0 + R(P),I)(x 09 k) '. 0 (25)
The solution of Eq. (25) yields the sought-for characteristics of the
transient process. Steady--state and dynamic error.- Let the nonlinear
system be subjected to the disturbanpes f l(t)9 f2(t)t f,(t). The system
equations are
Q(p)x + R(P)F(X) - Sl(P)fl 2(p)f2(t) + S3(P)f;3(t) 8)
The forced oscillations are sought in the form
x - A f sin(Q.- t' + Y ) -
(29)
The describing function is set up and Eq, (28) is reduced. By assigning
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3- 7
Vy'569/61/001/000/012/019
Some synthesis problems... 1;2.74/D306
-various values of A f and Cj,)f for k = const,~ and by calculating in
each case B and (0 the solution to the problem is obtained and shown in
figure. (It was alss'umed that f I =B sin f2 - f3 - 0.) From this
olution, the steady~-staU error of fh~.- nonlinear system under sinusoidal
:
disturbances can b* determined. This error is nonlinearly dependent on B.
If the system has self-sustained oscillations, the obtained forced oscilla-
tions will occur only under certain conditions. further, the steady~state
ystem operating under self-sustaining conditions.
error is considered of a s-
After transformations, the equation
= 0 Y"A.-,,?qMqk) - 0 (39)
in obtained., whence the functions A(k) and Q (A) can be found by any of
the graphical methods described above. Knoving A for any M and k, one
obtains
x0 0(.]W,k) (40)
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Some synthesis problemoooo
S)1.32?
t$UOJOI/001/000/012/019
11274/11306
expressing x 0 by the gain factors of the elementst the steady-state error
can be determined. It is noted that the limits of stability k of non-
linear systems can depend on M (i.e.. on the external disturbance),, unlike
linear systems; this has to be taken into account in practice. Furthert
the dynamic error is found for a self-sustaining systemy assuming x 0 not a
constant, but a slowl-y changing function of time. By linearization, one
obtains
+ k (k)R(p)_7xo - S (P)f
n 1
(44)
whence linear theory can be used for the determination of the dynamic error.
In many cases, a simpler solution can be obtained without determining the
displacement function. Thus, for odd symmetrical nonlinearities F(x), the
gain factor of the slowly varying component of the nonlinear element can be
directly determined from
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Some synthesis problems.-
/-, 0
OF
k o
x0 0
31,32 L/569/61/001/000/012/019
D274/D306
(45)
Effect of -vibration- and random noise: System (28) in considered. After
transformations. and using Eqs. (18), (19) and (20), system (28) decomposes
into two equations 4t
2(p)x0 + R(p)F0(x 0', Ard
ql(p)fl(t) + S3(P)f3(t)
(48)
0
Q(p) + R(p) q(AB,x
0
ql(AB~x B
p S 2(p) x
B AB
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Some synthesis problems...
sin (P x* M 0
x on T P) 9
3132"f
S/569'61/001/000/012/019
D27~XO6
(49)
for signal and noise respectively. From Eq. (49) one obtains the equation
for determining the amplitude A. of the vibration at the nonlinearity
input, viz.
2 0 2 0
I (AB9 g2B9x Ik + T AB~ Q BIX Pk
2 ( 1) 0 B2 9 (50)
Aj 2
x (QB9k) + Y2(QB'k)
a a
vhence the displacement function
F0 - ~(xO'B9C)B9k) (51)
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/001/000/012/019
4 D306
Some synthesis problems... D2 7~YME
Is obtained by graphic means. In this came, the -signal characteristic
depends not onl on the form of.the nonlin*arity and on k (as was the
case in Eq. (241 )~ but also on the amplitude B and rrequoncy Q or
the external-disturbance. In most cases it is possible to forego the
solution of Eqs. (50) and (51). This applie
f:(in particular if Eq. (45 is
used. In the case of random noises~ when t) represents a statj-'Lonary
random process with power spectrum density w f (CO), statistical lineariza,
tion to used. Thereby, Eq. (28) becomes
2(p)3cM + R(p)F M (xM9 L$.) - SI(P)fl(t) + S3(p)f3(t) (57)
Q(P)xr + R(P)qr(%-' C.)xr - S2(p)f2(t) (58)
for the signal and the noise respectively* From Eq. (58) follows
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62 ac
x 2 IT
+00
31327
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D274/D306
(59)
20W) + B(jw)qr(xmt 6x)
00
whence the mean-square value (5x of the random noise x r can be graphi-
cally determined. Thereupon, the displacement function is found, which can
be linearized in many cases, viz.
F11 - kn( 6:rtk)% - (61)
Introducing Eq. (61) in Eq. (57)9 a linear equation for the signal is ob-
tained. Linear theory can be used thereafterg taking into account, how-
ever, that k n changes with configuration, parameters and external noise.
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The above considerations remain valid for systems with several nonlineari-
ties. It is noted that the method has been tested in practice and found
satisfactory. There are 10 figures and 21 referencess 17 Soviet-bloc and
4 DOU-SOTiet-blov. Th* references to the English-language publications
read as follows: R. J. Kochenburger, Trans. Amer. Inst. Electr. Engra.
69, part 1, 1950; E. V. Grensted, Proc. Inst. Electr. Engineers, v. 1029
part C, 1955.
Card 14/14

POPOV, Ye. P.
"On Self-Adjusting Control Systems Without Sample Disturbances. 11
Paper presented at IFAG International Federation of Automatic Control
Symposium on Self Adjusting System Theory, Rome 26-28 Apr 62

39548
S/024/62/000/004/005/007
/6' 90a 0 E14o/E435
AUTHOR: Popov, Ye.P. (Leningrad)
TITLE: On the investigation of self-oscillatory systems with
logical devices
PERIODICAL: Akademiya nauk SSSR. Izvestiya.-Otdeleniye
tekhnicheskikh nauk. Energetika 1 avtomatika,.no.4,
1962, 116-121
TEXT: The author considers systems in which the control signal
takes on only the values +1, 0, -1, in accordance with the
logical conditions connected with the instantaneous values of the
regulated coordinate and its derivatives. The steady-state in
such systems is usually oscillatory, while transients are damped
oscillations mergi ng into the steady-state. In this article the
method of harmonic linearization is applied to the study of such
systems. While the logical conditions can frequently be
described in analytic form, it is more convenient in many cases to
give them graphically, as in Fig.l. Here, fov example, the value
+1 for the control signal is obtained when the deviation u of the
Beard 1/3

On the investigation of
S/024/62/ooo/ooVOW007
E140/E435
controlled coordinate from its required value exceeds a prescribed
value ul and, at the same time, the derivative PU-.- v has the
same sign (velocity directed towards increasing the deviation) or
has opposite sign but small value. The broken line ABCD
describes the stable limit cycle in the linear approximation,
and methods for calculating the points-ABCD are given in the paper
as well as for determining the transient process to the same
approximation (Fig.2). The phase plane is used here only for-
illustration, the method being suitable for systems of arbitrary
order and in not connected with the construction of hodographs
in the complex plane. There-are 9 figures.
SUBMITTED: may.ll,-1962
Card 2/3

32691
S/040/62/026/001/007/023
1~4006 0/77), D237/D3O4
AUTHOR; POPOVI Ye*PV (Leningrad)
TITLE: On peculiarities occurring upon the introduction of a
small parameter in investigating non-linear oscillations
in automatic systems
PFRIODICAL. Akademiya nauk SSSR. Otdeleniye tekhnicheskikh nauk. Pri-
kladnaya matematika i mekhanika, v. 26, no. 1, 1962, 62-69
TEXT: The author draws attention to a somewhat different formulation of
the small parameter problem in equations of dynamics of non-linear auto-
matic systems which may pmvide a basis for developing a strict theory for
various widely used approximate methods of investigation of automatic
systems containing strong non-linearity y=F(x,px) where (p=d/dt). 4hen
the remaining equations can be reduced to a single linear equation of
high order. In automatic systems non-linearities are often encountered
which differ sharply from the corresponding linear function y=k Ix -:.k2px-.
Also, for the x variable processes are often observed which are nearly
Card 1/2

PUPKOV, K.k.; POPOV, 'Ye.-P~, teFim. naluz., letienzer.'.'
BARPTOVA,, Z.S., irizh.,. red.
[Statistical calculation of nordinear systems of au'~cmatic
control] SLatisticheskii raschet nelineinykh sistem avtc,-
maticheskogo upravlanJia. Xloskva, Ma-zhincistroenle,, 19b5 p.
(MdRA 18!4",

L 0093-67 CID
ACC NRt AT6016441 SOURCE CODE- UR/0000/65/000 0061 0350
AUTHOR: Popov, Ye. P.; Loskutov, G. M.; Yi1supov, R. M. 15Y_
ORG: none
TITLE: On self-adjusting control systems without test perturbation effects
SOURCE- International Federation of Automatic Control. International Congress. 2d, Basel,
1963. DiskrebWe I samonastralvayushchlyesya sistemy (Discrete and-R`&-pfFv-e--Wy-s5i'ms);
trudy kongressa. Moscow, Izd-vo Nauka, 1965, 338-350
TOPIC TAGS- auto natic control theory, self adaptive control, optimal automatic control
A~BSTRACT: A self-adjusting control system is one which during operation (1) determines the
~dynamlc characteristics of the system by automatic search or calculates them from measure-
*Anto; (2) by some test determines the adjustment, parameters, or regulator structures
n
e
6eseary for standardizing (or optimizing) the system; and (3) carries out the adjusting, pa-
rameter, or regulator structure values derived. The literature contains very little informa-
tion on the synthesis and analysis of self-adjusting control systems for essentially stationary
plants, while the drawback of many proposed systems Is that special test signals must be used
Card 1/2

L o4993-67
-kd C N R. AT6016441
to check dynamic characteristics of the signal. The present authors propose one of the pos-
sible principles for creating a self-adjusting control system for a certain class of nonsta-
tionary plants. The chief merit of the principle is that it can take into account conditions
both internal (system ~hrameteis) and external (noise and control effects) In system opera-
tion. The report gives only the 6sic features of the proposed principle of designing a self-
adjusting control system, but It Is to be hoped that this principle can be applied in many cases
where it is desirable to use natural oscillations of a system without Introducing perturbing test
signals. The generallp'ase and several particular cases are studied and some of the points In-
volved are discus sed. ~' OrIg. art. has: 28 formulas and 2 figures.
SUB CODE: 09, W1 SUBM DATE: 29Sep65/ ORIG REF: 006
Card 2/2

ACC NRt AM6022150 Monograph UR/
Beackerskiy, Viktor Antonovich; Popov,_X~jgeniy Pavlovich
Theory of automatic control systems (Teoriya sistem avtomaticheskogo
regulirovaniya) Moscow, Izd-vo "Nauka," 1966. 992 p. illus.,
biblio., index. 15,500 coplas printed.
TOPIC TAGS: automatic control 6ystem, nonlineary1control system, linear;
automatic control system, control system stability, automatic
c o n t r o I t a c h n o I o g ycz3y, 3-Q 4-t~
U 2E AND cM-ely material of courses on
RPO 1OVERACE: This book covers
P
"Automatic control theory" of schools of higher technical education.;
It may also be useful as a handbook or textbook by a wide circle of
engineers, students, and scientists. The book was planned as a
rovised edition of Ye. P. Popov's book "Automatic Control System
Dynamics" (Gostekhizdat, 1959), however, due to the rapid advances
in the field of automatic control in recent years. it had to be
entirely rewritten. Parts 11, 111, and IV were written by V. A.
Besekerskiy and Parts I and IV by Ye, Ps Popov,
TABLE OF CONTENTSt
Foreword -- 8
Corti 1/3 UDCt 62-50

ACC NR: AM6022150
Part I; General Information on Automatic Control Systems
Ch. 1. Types of automatic control systems -- 9
Ch. 2. C;ntrol programs and laws. Self-tuning systems -- 40
Part Ili Conventional Linear Systems of Automatic Control
Ch. 3. Linearization of differential equations for automatic
control systems -- 62
Ch. 4. Dynamic elements and their characteristics -- 76
Ch. 5. Forming the initial differential equations of automatic
control systems -- 137
Ch. 6. Stability criteria -- 184
Ch. 7. Plotting the curve of the transient processes in automatic
control systems -- 224
Ch. 8. Evaluating the quality of control -- 267
Ch. 9. Improving the accuracy of automatic control systems 3241
Ch. 10. Improving quality of the control process -- 353
Ch. 11. Random processes in automatic control systems -- 402
Ch. 126 Methods of automatic control system synthesis -- 460
Part III: Special Linear Systems of-Automatic Control
Ch. 13. Variable parameter systems -- 513.
Ch, 14. Lagging system and systems with the distributed param-
542
Ch, Pulse systems -- 571
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ACC INPt AH602215O
Part IV: Nonlinear Automatic Control Systems
Ch. 16. Forming equations of nonlinear automatic control
systems -- 599
Ch. 17. Precise methods of*investigating stability and self-
oscillations -- 634
Ch. 18. Approximate methods of investigating stability and self-
oscillation -- 702
Ch. 19. Slowly varying processes in self-oscillatLon systems 785
Ch. 20. Quality evaluation of control processes 813
Ch. 21. Forced oscillations in nonlinear systems 847
Ch. 22. Random processes in nonlinear systems 873
Ch. 23. Optimal systems of automatic control 893
Part Vs Digital and Self-Tuning Automatic Control Systems
Ch. 24. Control systems with digital computers -- 916
Ch. 25. Extremal and self-tuning systems -- 952
Appendix 1. H-function table -- 974
iAppendix 2. Integral table -- 978
Bibliography -- 981
Index -- 986
SUB CODE: 1307 SUBM DATEt 17Sap6S/ ORIG REPI 093/ OTH RM 007
Card

!~QPOV, Ys.P, 41n,-h.; PYLSTOLOV, A.A., kand. le'~,=. nauk, dot6ent;
in.2"
Study of the drying of s:Lngle-phase (XAS transformers u2ing
a zero sequence cirau-it. izv. vys. ucheb. zav.; energ. I no.!-'.*
16,22. N 164 (KI?A 18."l)
1. Chelyabinskly insLitut mekimnivatsii A elektrlfikatsai
,gellskogo khozyuystva. Predzitavlnnn kafedroy proizved-stra -4
raspredeleniya elektrcenergii v sel'Ekvri khozya3-stve.

-,~F
I yea~:a
dr -9Y-1-1 -
: ~: P - - - - -
I..;�ng if "he MCF-se:-Iss 5j--glC-Dh3Se tr!.:Sf --.- :2 i' -
zero sfiquence current. Biul. tekh,--5kor,. !nfom. Gr--E..n.-
issl. fnst. nauc-. ! tekh. 'Unform. 1-7 no.12438-4C. P 164.
(MUFl'. 188? 3)