β β

... η.11.3 μ,.. 15

.... 8 1....16 1.1....16 1.β.... 1.γ....4 1.4....7 1.η....45 1...5 β....51.1....51 β.β....56 β.β.1....56 β.β.β....6 β.β.γ....64 β.γ....68 β.γ.1....68 β.γ.β....7 β.γ.γ....71 β.γ.4....71 β.4....77 β.η....81 β...86 γ....87 γ.1....87

3. γ.β. - -...94 γ.γ....97 γ.γ.1....97 3.3.....99 γ.γ.γ.... 15 γ.γ.γ.1.... 16 γ.γ.γ.β.... 17 γ.γ.γ.γ.... 19 γ.γ.γ.4.... 11 γ.4.... 11 γ.4.1.... 113 γ.4.β.... 116 γ.4.γ.... 119 γ... 1 4.... 1 4.1.... 13 4.β.... 133 4.β.1.... 137 4.β.β.... 138 4.β.γ.... 14

4. 4.β.4.... 149 4.γ.... 15 4.γ.1.... 15 4.3.1.1.... 15 4.γ.1.β.... 157 4.γ.β.... 166 4.4.... 17 4.η.... 178 4... 18... 18... 184

5 ALC - Automatic Level Control ( ) ARW - angle random walk ( ); DSP - digital signal processor ( ) FPGA - field-programmable gate array ( )ν PTAT - proportional to absolute temperature ( ) SPI - serial peripheral interface ( ) - ν - ν - - ν - - ν - - ν - -- ν - ν - ν - ν - - ν - ν - ν - ν -, ν - ν - ν - ν

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7 - ν - ν - ν - ν - ; - ν - ν - ν - ; - ν - ν - ν - ν - - ν - - ν - ν - ν - ν -.

8 В. (), -, ( (), - (), - ().,, [41].. я μ, -, (),. Д1Ж.. П -.,,, 1-1η., -,,., - ().

9,.. -,,,,,., -. -(1-η ), -(1-1 ) (1-1 ),, [9]. -,..,,, - [44].,,. ( 1 1 /),,,..,,. Analog Device [34], Murata [36]. -,., (),..1, [51].

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14 я, : 1...,. 3. -,,,. ця : ( XXII,. -, β1ην БVII - «( )»,., β11ν «- β1β»,. ν γ- - «- -.»,., β1β), - (XXVIII - «- β9»,. ν «-»,, β11ν II - «-» («II»),., β11ν,.

15, β11ν БIБ -, η-,., β11ν II - «,., β1β; - «,»...,., 13). ц. 1γ-,,, β,1β...,, 65. 19 13 31.

16 1. О ц 1.1. О ДγЖ,, LabVIEW.,,,γ. Д4Ж.,,.,,.,, The Charles Stark Draper Laboratry [49]. R-R,,, (. 1.1).

17. 1.1. The Charles Stark Draper Laboratory [49]

18 1β, 14,,,. 1θ, 18, β, ββ β4.. 18 1θ (. 1.1) y x.. y x υ,,1,βη η., -.. μ -,, [9]. (JPL), [54]. (. 1.β).

19. 1.β. JPL 1,, S 1, S, S 4, S 1, C 3, C 4,.,,β ( β,7188 ) 7θ β /. [34Ж Д4] 1. 1. Analog Devices (ADXRS614) InvenSense (IDG-16) Northrop Grumman (MAG-16),,, 5 1,3 4,84-36 1,8 1

Bosch (SMG61) Silicon Sensing (SiRRS1) Sensonor (SAR 15) О»И» (-1) ОО ИИ «ОИО» (-) О (-1)... 1 () 5 - -, 3 -,8 5 1 1 3 3,3 4,1 5 -,15 5 1-7 1. DTS, Inertial Science, Kionix, Melexis, MemSense, O-Navy, SBG Systems. 1.. О ц В ИИ [8],. (, ),.,. The Charles Stark Draper Laboratry [48] (. 1.3), 8, 3 1βη 1βη, 31, 3 η βη βη,,, 4, 6,

1, 46,48 4, 4.. 1.3. The Charles Stark Draper Laboratry (,8 / /).,.,.

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3,,.,7β,β9η. Ø1,η,8β,β79.,.,. -.. 1.6. β,η. -99,1,, - -,.. 1.6.

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5 (1 γ) 1-5.. ν.. 1η.,,.,.,, - [64], [65].. 1.7 μ -,,, -.. 1.7. -, -.,.

6,,.. 1.8.. 1.8.,,,,. 18. з 1.., з η., В.,.,. [45], [33]. β.

7 β. - 1) β) 1) (θη% 7.) ) 1) β). 1.4. В я В (), () () (.1.9). β,,,.. ДЖ ДЖ.,,.,

8 β,.. Ω П U U СУ Y U Y U С С S С S. 1.9.. 1.9 μ Ω ν, β ν Y β, U β, Y, U ν B C, B S, C, S ν U ν U.,. 1.1 ( ). К ВК. 1.1.., [5],. BSAC, ADI, HSG-IMIT, Robert Bosch GmbH and Georgia Institute of Technology. BSAC,. --

9 ().,. (),. ().. -. 1.11.. 1.11. -, BSAC ADI ADXRS1η ββ.. 1.1.

3. 1.1., ADI L-L...... PTAT... HSG-IMIT [6] L-L R-R..,,,,. -. 1.13.

31. 1.13. HSG-IMIT,,, (DSP). DSP. -... Robert Bosch GmbH [5] : DRS-MM1, DRS-MMβ, DRS-MMγθ.,. DRS- MM3 L-L.. DRS-MMγ. 1.14.

3. 1.14. DRS-MM3, Robert Bosch GmbH... -. -.. SPI.,. Georgia Institute of Technology. 1.15.

33. 1.15., Georgia Institute of Technology ωεηs. δ-δ.. -.. Aδω ( ). (, ).. 3.

34 γ. BSAC, - ADI HSG-IMIT Robert Bosch GmbH. -,.. - Georgia Institute of Technology ALC

35 W. Geiger LITEF GmbH [47] 4 : ν ν ν... [17] (), (. 1.16).. 1.16.,.. [17]

36 [17],.,,,,... [18],, - (),,. (. 1.17) μ. [45]. К еи а еа Ве еа вееие / аееие а вееие / аееие а веее а веи и а аеее а веи и а аеее а веи и а аиие /вие еаи ви а авеие еаи Веие еаи Вееие ваа Д Каа иьв. 1.17.

37,.,,.,. β,, π/β,, - [5].,, -..,,,.. β- μ ν.,. 1.18.. 1.18μ ν ν ν.

38. 1.18... 1.19.. 1.19μ ν ν ν Agilent 3441A.. 1.19., (Δf ),. 1., Δf =,8. μ Q p p arctg, (1.1)

39 Q, p,. () (p; - π/β),, [8] Q, (1.) p Δ = θ,θ.. 1... 1... 41η ( β ). 1.1..,, ±1 /. 1,β4 / /.. 1.1.. 1.1 ( 1 ),, η- -.

4 C Data1C 3,34 3,33 а, 3,3 3,31 4 6 я,. 1.1. ±1 /, μ,.. / ; ( Δ = θ,θ ).,,. 1.., [17], [18],,,..,,,..,. 1.16,.

41. 1... 1. μ,,,,,,, -,,, -,,,,..,,,,,,, () ().,, ( -, ),.,

4.,.,. ωшsβ ωшs, [7].,,,θθ4.., β - 1,θθ 1-1... 41, ±1 / k = 44, / /., ( ). 4. θ,θ 1,,θθ 44, 4...

43 - (. 1.3), [9] : (, )ν,, ;,.

44 аеь авеие аи и а еаи. 1.3.. 1.4.

45 К еи а еа Ве еа вееие / аееие а вееие / аееие а веее а веи и а аиие /вие еаи ви а аеее а веи и а аеее а веи и а авеие еаи Веие еаи Вееие ваа Д Каа иьв. 1.4. 1.5. О я В 1, β,. 1.5.. 1.5.

46,,,,,,,. = 1/1θ T, T = 1/,.. 1.6,.,, k 1 k (k = k 1 ± Δk),,, ΔA, Δ. k k1 k1 k Δ Δ. 1.6..,., (1.1), t

( A ( ) p A 4 p Q 47 ).,,5, Q=1 p=β7 1,7% - 3%..,,.. [55].,.. 1.7. a. 1.7., Q = 4.,,.

48,. η, θ, γ 4 -.,,,,.., I. МШsЭ sтчt.,,.. sтчэ,,.. МШst. sint.,,.,.. sint. cost.,. 1.8,. 1.9..

49. 1.8.. 1.9. ( ),,,,. МШsЭ,...

5,,, МШsЭμ,.,,,,,,,..,,, [5]. В 1 1. -, μ,,...,,.

. я В ця 51.1. я я. OXYZ. Ω 1, Ω, Ω 3. O O 1, x, y, z. (O 1,1,β,γ) OXYZ., (O 1,1,,3). β.1, [5]: - β βν - = const ν -,. -. Z.. O O1 3 const X y z x Y..1. (α, β, ) μ 1 3 1 3. (.1) 1 μ 3

5 e e M I I I M I I I. (.) μ e z e y e x F mz F my F mx. (.3) (β.1) (β.β), μ - 1-, - Ω -, - ()*( ).,,,, μ.. sin 4 sin ) ( ) ( cos ) ( ) ( ) ) 3( ( sin ) ( ) ( cos ) ( ) ( ) ) 3( ( 3 1 1 3 1 3 1 e z e y e x U h Sl t t V S t U S t t V C t U C I I n I I I I t m U I I c n I t t V S t U S t t V C t U C I I n I I I I t m U I I c n I F z c z n mz F y c y n my F x c x n mx U V U V U f V U V U f z z y y x x. (.4), (β.4)., Σ,.

53 (.4) (Э) (Э). (Э) (t).,. : t t t t B t B t s c s c sin cos ) ( sin cos ) (. (.5), s,, s. (.1.5) (.1.4),, I, - ) (t : B U A X t ) (. (.6) μ A (, ). g g g g q q q q A. (.7) A Q p q. 1 p. J J g.,.

54, p p -. B U. U =, V, U, V ) ( U, V U U - V -.,,.,, U,,, U. U U U -.,, ku, k, 4k U U ( 4 = ββ - U U - ). B μ C S C S B. (.8) S C - ( S C), 1. S, C. B 8. -

55 (.6) - I, B,, A. (.6). -,., : Y C) X ( D) U y (, (.9) Y -,, X. D U Y, y -. C β μ., Y U, (.6): t d Y Y U K Y Y K Y Y dt K, (.1) dt K, K, K,, Y -., (.6), (.9), (.1),,, (,, s const), (Bs), μ

Bs Bs Q I I 56 S C. (.11) U ( U,, Ω(t), U, μ I 1 Qp p I Q ) k U, (.1) k F 4U h 4 sin. (.13) I ( k) U., (t) B S (β.1) μ.. я В k BS k B 1 S ku. (.14)..1. [3] (),., 5, (.6): 5, A B. ANSYS 7.,...., / ( ).

57... ANSYS 7. 5., 1-7 + I I I I I I 3,3,7 3,85 7,4 3,85 7,1 I I ( I I I I ),914 Q 1 4,,69,73

58 η (),.., 1-9,.. < 1 3, 4,7 F /, / 1,74 / 1,48,49 /,78 1,11 /,585 h, 4 + 1,5, 1/16 5 A, μ (A ) 1 =, 1 4 E q q q q (.15) (A ) = 1 1 1 1 1 1,487, (.16) (A ) 3 = 1 1 1 1 1 1,881 5 g g g g, (.17)

59 (A ) 4 = 5,637 1 5 1 1 1 1, (.18) ( ) q 5: =β : q 1 p Q 4 1, (.19) I I I 5 5,637 1, (.) I 7 1 1,487 1, (.1) 7 = : I I / c 5 1,8811. 7 g (.) B (.8). C S - - U ( V ) ( ),. S,. U, V, /β. IЩ Д1/ψЖ.. B μ C U F sin 1 1 U 4, h Ip B (.3) I = 3,851-7 I I, = 8.851 - /.

6 (.3), U ( V ) U ( V)., 1- (.3). U U Л 1 Л 43 ψ.. U S U, Л 11 Л 33 ψ.,. μ S U = C U = C U h h h - h. (.4), ( ): 7 B,9634,199 1 1,,178 13, 4 B 13, 4. (.5) μ 1- β, - 1,η, 3- η, 4-7., b 1 η-θ (. 5), b 1 γ -4.... () [5] X (,,, ) c s c s T,

61 Y Y, U Y, U ) (, T., (..3), ( ), (), - (), ()...3.,, «MicroCAP θ.β.θ.» [6Ж γ,(7γ)*1-4 γ,(7γ)*1-3 ( 1 ). () ( ), μ 1 ( ) t C ПТ sin( ) 1 ( ) t C ПТ cos( ), i=1..4, (.6) i - ν () ( =.11, =.788); - (=β7 ).,, MicroCAP. β.4-.6.

6..4...5.

63..θ...7...7. : 4349 619 1,498,15 619 4349,15 1,498 C. (.7) 7,37,41 155,8 34,46,41 7,37 34,46 158,8

64,, =6 =5..,.,,,,. (β.1.9), D,. () ( ), θ 4 β.7., 1,. D:,17,15,19,15,15,17,15,19 D, (.8),8,7,6,1,7,8,1,6 A, B, C D,, μ,....3. [5]...8 μ,,, -.

65 а Д1 и Д - авеие аи и а еаи S C S C 7 1 5 5 Ц И U а Д3 и Д4 - авеие а β а Д5 и Д6 - авеие аи β..8. () Y = (Y,U,Y,U ) T,. Y Y,. θ.., Matlab θ.η. (..9)...9. Matlab 6.5. β.9 μ State-Space - ν Control - ν Out data...1 Control.

66..1. Control «Control» 4 YД Ж. 4-. 4 ( Amp Betcos, Amp Bet sin, Amp Gam cos, Amp Gam sin) ( SinWave). 4- ( PID Controller, PID Controller1, PID Controller, PID Controllerγ),. 4 U[].,. β,, U γ4

k 67 F l U 3 34 (.9) h V (t). V,,γ,. p p 1 1 p U d V 3 4 k k Fl 3 h k U 3 4 (.3) γ, 4 (. 5), F = 1,74, l = 1,48, h = 4. = 8,851-1 / k = 111 : 9,49 1 V d 5 (.31) (p/) - 1, d. V,, d,9491 5 V (.3), η V = β. (t) d =,1 = 3,71 -..11:

68 (t)..11. (t).3. μ,, μ,,,. μ - A, B C.., g А ( Ω) U, - U, Ω,,..3.1.,,. t,

69,.,, μ -,,,,, -,, -. ( ) A, μ - - 1η ( 1η, β ) - - 5...1 β.13 V (p) U γ4 (p) (), U γ4 =dv...1. V (p)

7..13. U γ4 (p).3.. g, (-5/c β9/c) =-5/c =9/c U =β (..14) U ()...14. U () U () (...14),,β.

71, μ U. k.3.3. 4-...15 (V, U, V, U )...15. (V, U, V, U) (t), t, V U..15 (V ),β. (t)..11.,1.,,β..3.4.,,

7., Q [5]: = I I p cos( ), (.33) cos 1 k ( ) β,, I, ΔI = I β + I - I α, p β,, k Q p 1 Q p,, Q 1 p arctg -...16 β.17 p p. μ p p (.34) k..16.

73..17.,,.,., [5],, (.11) 1 1. (.35) 1 k Q, υ,, 1., [13], μ 1 1 Q k. (.36),,

74.,, k. -..18 ( ) β.19 ( ) ( Q = 1):..18. Y,U,Y,U ( ) (t), t, Y U

75..19. Y,U,Y,U ( ) (t), t, Y U..18 β.19, 4-η,,γ. * B s = (B * s ) const + (B * s ) var, (B * s ) const, (B * s ) var = k (B * s ) const sin( t), <k<1,,. G (B * s ) var. - Matlab 6.5,,. A,.

76,,..,., ( ) ( ).,. (...),,,1, 1,.... ( ), 7%,. 1θ.,, 1θ...1 β.

77. U /U,..1. (U /U ). Δφ,,... ( )..4. В U =U Ω (β.1).

78 = = c,,, U =,16 U = -1, γβ., : =,14 c; / c k = -13,51. B, A, B, C,, μ ( -4 +θη), ( = 1 ), η, 1.,,,,. k k k k,., - 4 +θη, μ - - 4 =,1768 c, k = -1,5861 / c, B / c - +θη =,143 c, k = -13,568. B (t) k(t),, (- 4 ), ( ) () (+65 ),,.β.3.4:

79, / c t, C..3. c k, / B..4. k k 4 +θη, 4 :,9 / ; k k,17%,1 %.. t, C k k

8 6. 6., /,9,, ppm,16 18,,, / 5, 16,,.., Simulink (.1), : ( )ν ;,,.

81.5. ця я В, (,..5),. 1...6. U β [ ] U [ ] иа а ве еа 48, иа 3 3. 96 Ц k(3) U β U [ ] [ ] е в ее а 1 еи еаи аи k U β [ ] U [ ] S S 16 S S k Uii(n)..5.

8..6.,., ( k ),,,.. D. () (), U β

83 U sin(βπi/k) cos(βπi/k). U β sin(βπi/k), U β cos(βπi/k), U sin(βπi/k), U cos(βπi/k) k,.. k, 4 - S β, C β, S,., 1θ 4 S β, C β, S,,.,..7,, 1 θ. S1 (а Д1) а иьв U1, U13, U1, U3, U3, U41, U4, U51, U5: S (а Д) S3 (а Д3, Д4) S4 (а Д5) TиТ = 1/3 T S5 (а Д6) /4 - T/3 / - T/3 3/4 - T/3 UТТmax = 1В U3max=4В - T/3..7. UТТμ n U11( n) U k S ( n) S k S ( i) S k S ( n) S ( n 1) П И i, (.37) n U1( n) U kп ( n) ФИ ( Т) Ф ( n) ( n 1) i, (.38) n U13( n) U k S ( n) S k S ( i) S k S ( n) S ( n 1) П И i, (.39) n U14( n) U kп ( n) ФИ ( Т) Ф ( n) ( n 1) i, (.4)

84 U 1( n) U13( n), (.41) U ( n) U14( n), (.4) U 3( n) U11( n), (.43) U 4( n) U1( n), (.44) n U3( n) U k ( n) Ф ( Т) Ф ( n) ( n 1) П И i, (.45) n U 41( n) U kп S ( n) S kи S ( i) S k S ( n) S ( n 1) i, (.46) n U 4( n) U kп S ( n) S kи S ( i) S k S ( n) S ( n 1) i, (.47) U51( n) U 4( n), (.48) U5( n) U 41( n), (.49) n=(16, 3, 64), n=1 1, U, kп, kи, k, S,, S,, Smax. - -, 4- S β, C β, S,.,,,., U Y...8. x(n) - аеа y(n) иеие..8. μ

85 y( n) x( n) gy( M), (.5) g, M - ( ). μ H 1 z) 1 gz (. (.51) (..9): G M 1 j ( ) H ( e ). (.5) jm 1 ge..9., 3.4. [6],..,,, -.,, - 1/3T.

86 В β 1.,, μ,.,.. Ansys, MicroCAP Matlab Mathcad. 3. : γ /; 1θ. 4.. 5.,., 6.

87 3. я ц В,. 1., (..6),, [1]. -. 3.1. В (), (). μ ν ν ν -, ν, ν (),,.,,,,.

88 μ,,,, μ,.. ( ). - () - ().. 3.1.. γ.1. (), ().. () β ().,..,.

89 (1 θ).. 1..,. 3.,.,, (). U β U ДУ ДУ β U U U ПД ПДβ U «48» О 1 1 СУС 6 8. 3..., ( ) (). β,,.. 3.3.

9. 3.3., 7. 7. η,η β γ,η В О «48» β,8,4 β,8,4 β,8,4 9θ ±,1 48 ±,1 9θ ±,1

91 В U 7 () U,1 η,,1 η,, 4 4 37,5,15 37,5,15 В U U,9,5,9,5, 4 4 В В 1β + 1β γ β,β,. γ.4, «θочэтюц 4». θωi δ -78γ δ-мкын β θωi-17 AНЯКЧЭОМС. γ.1.4. U U.. θωi-17β ( ). δ-78γ θωi, θωi 9η-1. ADSθ-185.

9. 3.4. μ.. μ, ν ν. μ - 7 T=1/γ (γγγ,γ ), μ γ, ν

93 β. δ-card.,,,,. μ, X ; ν ν..,. -,.,.,, : 1.,..,

94 (,, ). 3. μ,,,,,,. 3.. - - я я (p ). p (),, μ,,,.,,. (p β ),,,.. = p = p β. (),, μ.,, Q [43]., Q,, Д], [61],. [14],, μ (Q air ),

95 (Q clamping ), (Q TED ), (Q volume ) (Q surface )., μ Q -1 = Q -1 air + Q -1 clamping + Q -1 TED + Q -1-1 volume + Q surface. (3.1),,, μ (. 1 1.γ),,,,. () [5]: sin 4 F k 4U. (3.) h I..,,. : 1. ν.. μ 3. ν 4. ν 5. ; 6.. (. 3.5):

96,,, ν 1, PCI, COM ; β, 1 COM, ;. 3.5.. γ.5 μ 11-6 (.48111.βθβ),, AРТХОЧЭ γγββa, 1, β, -, - -, 1 - β7, β - 4, -17,.. 3.6 μ - (- 17) ν - ν -.

97. 3.6., 3.3..,. 3.3.1. [15], [16],,,,,. μ,,.. h,,.,,.,., h C S C, (3.3)

98 S,,,. r 1 c = 1 U 1, U1, 1 =,1,β. μ h 1,31 U S r, (3.4) max 1 U max -,,.,.. 3.7.,,. 3.7.. 3.7,.,,,.

99 8. 8. β, β, ДЖ,, ДЖ h γ γ h 4 4 h 41 4,399 4,383,16 4,374,148 6 3,881 4,4 -,159 4,98 -,7 54 3,354 3,54 -,186 3,368 -,373 13,89,734,75,55,58 16,745,765 -,,594 -,14 61 3,773 4,176 -,43 3,93 -,88 5 4,748 4,44,36 4,55 -,345 71 4,767 4,311,456 3,397,47 19 3,67 3,314,356 3,398 -,486 47,448,54 -,56,184 -,53 8, - β,4, - 17%., ( 8),.,. 3.3.. [1],

1, (p Q). p Q μ. -, - (48 ). ( ). ().,,,,. μ p N T, ДЖ, (3.5) N ζ T N, μ Q pt N, (3.6) ln A / A A, A., Q p, (3.7) At ln 1 At T, (3.8) T T, -. β 9.

11 β Δ f= Пβ- П β Пβ, П, Δ f, Q Qβ 1 41 746, 678,8 67,3 16117 14 46 997, 996,9,1 3814 35849 3 47 741,6 74,5 37,1 35897 5598 4 6 6, 188, 38 1588 49 5 61 551,9 538,6 13,3 386 3879 6 5 59, 578,6 11,5 18157 913 7 71 575, 566,5 8,5 35 36 8 54 578,8 553,6 5,3 9 99 9 13 74,8 533,8 7, 8744 1475 1 16 791,7 59,5 199, 4193 4464 11 19 533,3 515,5 17,9 6454 13418 1 66 318, 314,7 3,5 56 15 9. - (.. 3.8). β,, β (.. 3.9). U β,. 3.8., β β

1 U,. 3.9., β β. 3.1.. 3.1. β. β., ±β (.. 3.11).

13 U β,. 3.11. β, ±β. :,.,,.,, (..) (..).,,.,,,,. (.. 3.1).

14 45 4 35 3 Ampl G 5 15 1 5 993,5 994 994,5 995 995,5 996 996,5 997 997,5 w,. 3.13).. 3.1. 4θ U=θ,η, (. 6 5 4 Ampl B, B 3 1 993,5 994 994,5 995 995,5 996 996,5 997 997,5 w,. 3.13. 4θ β. 3.1 γ.13..., (. 3.14).

15 w, 996,9 996,7 996,5 996,3 996,1 995,9 995,7 1 6 11 16 1 6 Ampl G,. 3.14. 4θ,. 3.3.3.,, (, ). ( 41) 1.

16 1.. 41 1 1 1 1,1,1,1,1 U () 6,89,5 1 ()* 1 * - 41 β 4,5 /, γ /. 3.3.3.1. ( 41) N, γ, 11. 3.15. Ω, / N1,... N,... N3,... N4,... N5,... N +,... N -,... 11. Ki, // 1 56,69 51,76 59,31 6,36 56,7-6,4-4,35-77,3 1 58,7 3,4 59,36 115,96 58,6-55,61-57,5-7,59 3 57,58-1,1 57,15 5,5 57,31-157,48-193, -7,1 5 56,83-185,87 56, 48,14 56,6-4,39-351,7-68,94

17 4 14 N+,N-, 4-51 -31-11 9 9 49-6 -16-6 -36 Уая, а/. 3.15. 41, 1,. 41 K = -7β,β4 // = -4,45 %.. 3.16, ± /.. 3.16. U β ±β / 3.3.3.. (U4-U41)/β (. β.7), γθ.,. (. γ.18) 41, (. 3.17), 486β.

18. 3.17. 41 37541,5 лн Аллн 17.6.14 11_49. ц 41 1, Сиа SinB, / ча 1, 1, 189,47 YARW =3,56 17,76 1,,1,1,1 1 1 1 1 Вя ия, к. 3.18. 41,. 3.17,. μ, μ,, ν μ

19,. [].,. 3.3.13 = = 17,76 /..,. 3.3.3.3. - ЩШХШsК.ОбО. μ β (, ), β μ U_beta = As_beta *(1 +.15 * sin(w_omega_beta * tau * CountPeriod)), (3.9) AsИЛОЭК βν w_omega_beta ν ЭКЮ = 1β8./f_pribora, f_pribora (1β8 - )ν ωшючэθоытшн. (β),,,1 (,,, )., ШЭЧψ = AЦЩSψ/(.1η*AsИЛОЭК), AЦЩSψ, UИЛОЭК,,7., аишцоркилоэк,. 41 4,γ..

11. 3.3.3.4. Δ μ Δ = ΔA cos / A sin, (3.1) - (. ). β. 3.19. И. Оц 41-3 8 13 18 3 -,5-1 -1,5 Δφ, - -,5-3 -3,5-4 -4,5 Вя,. 3.19.. 41, μ

111 Δ = γ,9η ; Δ β = 1,β. - β.. 3.,, β.,76e+3,69e+3 лн Аллн 5.9.13. ц 41 1,E+4 1,E+3 Сиа CosB, у 1,E+ 1,16E+ 8,78E+ 1,E+1 5,53E+ 1,E+,1 АЦ CosB "Гц",1,1 1 1 1 1 1 ЦА CosB "Гц" 1,96E-1 1,E-1 1,66E-1 Вя ия, к. 3.. (β), μ, β, 8,78.., β,θ7.. θ,11. ;, β 1,66 1-1..,,119.. 4,7 1 -...,

1β. / 11., /, %, 1β., 1 13 134, 4,57,7 5, 16 349,6 1,4 13, 3 19 1,7 1,36 5,5 5, 4 54 197,1 3,95 4, 6,1 5 61 185,1,48 4 6,3 6 71 13, - 5, 7 41 17,76 4,45 4,3 1,7 ( γθ ),.,. : 1... :,. 3.,. 3.4. я 13.

113 13., /,9 1,7,, %,16 1,7,18,48, / 5 5, 16 4 ( 41)., A, B, C D.. 3.4.1., B (. β) 14 15., 14. β p β, 7 746, p, 7 678,77 β Q β 1 4 1 Q 1 4 16118, 7 678,7 ΔJ/J,914 η,θ 1-3 А β /.

4 1 1,181 6,961 4 5 1 4 6,961 1,181 4 5 114 1,181 6,961 1 4 4 5 6,961 1,181 A, (3.11) А β /. 4,887 1 5,1389 1 1,1917 1 6, 9631 5,1389 1 4,887 1 6, 9631 1,1917 1 A 1,1917 1 6,963 1 6,59 1 5,83 1 6,9631 1,1917 1 5,83 1 6,59 1 1 5 4 5 4 5 5 4 4 5 5 4 5 4 5 4 4 5, (3.1) A. a 1,,,., B h β, 4 h, 4 15. 4,γβη ( ) 3,943 ( ) β F, 1,74 β F,,49 F, 1,15 β p β, 7 746, p, 7 678,77 β l, 1,48 β l,,78 l, 1,17 β, / U, / U, / 1,5 / 7.56 5 / 7 4 / 1/16 T 1/3 T I I I, γ.8η 1-7

115 :,983,1949 7 1 B 1,,3138 1, 657 (3.13) : 7, 4688 8, 5791 7 1 B 1,, 783 (3.14) b 1 U β, β (. 15, «β, / U»).

116 3.4.. D, 16. 16. D, C 4349 619 7,37,41 619 4349,41 7,37 1,498,15 155,8 34,46,15 1,498 34,46 158,8 = 89.5 89.5 183.7 183.7 D D,17,15,8,7,15,17,7,8,19,15,6,1,15,19,1,6,51,11 D,51,3751 3 3 3 3,11,51 3,3751,51 3 3 3,151,751,51 3 3 3,1751 3,751,151,1751,51 3 3 3 3 μ S,5 4 C,5 4 S,5 4 C,5 4

117 β,.. 3.1,.. 3.1., 1 η D (. 1θ), β.η. 48 (1θ, γ ).. 3., 1 γ. μ s=4, =4.

118. 3... 3., η, γ., β65-35,.. 3.3.. 3.3., 1 γ, μ s =,γ1, =,βη.

119 η, γ,. 3.4.. 3.4. η, γ. μ s =,βθ, =,βη., s c η, γ.,. 3.4.3. A, B, C D, γ.4.1 γ.4.. А =,.. p. 1. /(c ). Ω k, μ Ω =,6 / k = -3,18 = 4 (. 16) β, 36 γ. 8,3. ( ),. 3.5.

1. 3.5., ( 1γ) μ - ( )ν -. ( 1 ),. В 3 1. 1 (. 1.)..,,. 3.. 4., μ 1..; 1,7 / (. 19);,48% (. 19);

11 ββ,7 (. 13). 5. μ, μ, ; ;, ;,, ;. 6.. 7.,. 8.. -, -.

1 4. О В,,.,,., [13].,,.,,,,.,. 17,. 17., 17% -,9,9

13,, : 1. ;. (, γ ( γ.γ.1) ( γ.γ.β) ); 3.., 17,.,, (.. γ.γ). 4.1. я β(t), [5]: 1 I p cos Q 1 Q I cos Q I V V I U U, (4.1) I cos C Vβ - cos(э) ν C Uβ - cos(э) ν ν. (4.1) (Ω ), U - (k).

14, (4.1),,,, β = C Vβ =, -,. 18. I p cos Q Ω 1 Q I cos Q I V V 18. k I U I cos U - I U I cos U -.,,.,,.. 4.1.. 4.1. μ h 1 l tmaxh l tmax R S R1 S U Gk e e, (4.)

15 G ν k ν h ν Δ 1, ν α ν l ν S. U,,. i 1 i i, (4.3) (4.1.) μ μ t tmax h 1 l tmax h l t max R1 S max R S Gk 1 l e le R1 S 1 RS 1 Δ : 1, Δ = 1 μ l R 1 l R 1 e e tmax tmax 1 R e tmax h 1 R1 S l h 1 l tmaxh l RS l 1 1 1 R e R e tmax h R1 S l R S h 1l tmaxh l RS l 1 R e R S β = 1,η99 ; Δ = 1,θ7η.., (4.4), (4.5), (4.6) β,, ( ).

16,., μ M SLU h, (4.7) η ν S ν L ν h., α,, sтчα α, μ h h Lsin t, (4.8) h ν h ν., M μ M. (4.9) h Lsin t SLU (4.9) ( )μ M a b1 sin t a1 cost, (4.1) a, b 1, a 1, μ a = f 1 (h ); b 1 = f (h ); a 1 = f 3 (h )., M h, h.

, γ, 4,, ( 19): 19. -, γ, 4 a dt t L h SLU sin sin dt t L h SLV dt t L h t L h SLU f sin 1 sin 1 a 1 dt t L h t SLU sin cos sin cos dt t L h t SLV tdt t L h t L h SLU f cos sin 1 sin 1 b 1 dt t L h t SLU sin sin sin sin dt t L h t SLV tdt t L h t L h SLU f sin sin 1 sin 1 μ 17

a 18 cos A SLU L t h [ h L h Lsin t h L h L t htg L arctg ] h L a A SLU 1 SLU tg 1 cos 1 cos 1 tg Lh Lsin t tg t L sin L h, (4.11) t cos htg L arctg L h h L t h L h L SLU cos 1 tg A 1 b tg Lh Lsin t, (4.1) t cos t h tg L L arctg L h h Lsin t L h h L h L SLU cos 1 1 (4.13) : a t Lcos t h tg L SLV h [ ] arctg h L h Lsin t h L h L h L,, (4.14) a SLV 1 SLV tg 1 cos 1 cos 1 tg Lh Lsin t tg t cos htg L arctg L h h L t h L h L t L sin L h, (4.15)

19 t cos t h tg L L SLV 1 arctg cos 1 tg L h h Lsin t L h h L h L b SLV cos 1 tg Lh Lsin t 1. (4.16), γ, 4: a t SLU Lcos t h tg L h [[ ] f f arctg h L h Lsin t h L h L h L sin t Lcos t h tg L h [ arctg ] ] h L h L t h L h L h L SLU f f SL 1 a 1 1 cos 1 cos 1 tg Lh Lsin t tg Lh Lsin t, (4.17) t SLU ftg cos t L h tg L cos 1 tg L h h Lsin t L h h L h L [ arctg ] t SLU ftg cos t L h tg L [ arctg ] cos 1 tg L h h Lsin t L h h L h L, (4.18)

13 t cos h tg L SLV L [ ] cos 1 tg L h h Lsin t L h h L h L t 1 arctg b cos [ arctg tg L h h L t L h h L h L SLU ftg t L cos 1 sin SLU ftg 1 SLU ftg 1 cos 1 cos 1 tg Lh Lsin t tg Lh Lsin t a a1 b1 A ; A1 ; B 1. U U U t htg L ]. (4.19),, β. β,,...,,. μ β = 6., = η.ββ..,. 1%.,. μ μ 11 A A 11 ( h) 6,4191 ; A A 1 ( h) 4,41 μ 1 A 11 ( h) 6,419 1 ; A 1 ( h) 8,381 1 ; A 1 ( h) 7,351 11 ; 1 ( h) 7,7 1. βμ μ

( ),1591 131 1 A A 1 h ; A A 1 ( h) 1,488 1 9 A f ( h) 1,655 1 ; A f ( ) 1 h 15 ; A 1 ( h) 4,431 11 ; f 1 ( h) 7,547 1 β%... \ Ω, % k, % 9 11 - [9] μ,,,.,,,. β U 3, γ 4.,, U γ,, γ, 4, U 3 ± U γ.,,, η, θ.

13. μ,, U,.., (4.1.3),,,.,, U ΔU, U + + ΔU,.. 4... 4.. ΔU ΔU,,, ΔU = ΔU, μ U U П h Δh, h.. U U П 1.,, μ h П,

U11( n) U U13( n) U k П k П 133 n S ( n) S kи S ( i) S k S ( n) S ( n 1) i U 1 U n U П S ( n) S kи S ( i) S k S ( n) S ( n 1) 1 i U (4.) μ n U П U11( n) U kп S ( n) S kи S ( i) S k S ( n) S ( n 1) 1 i U (4.1) U1( n) U k 1 U n П ( n) kи ( i) k ( n) ( n 1) i U П (4.), β, U 1 U 1, U γ : U31( n) U k ( n) Ф ( Т) Ф ( n) ( n 1) 1 n П И i, (4.3) U3( n) U k ( n) Ф ( Т) Ф ( n) ( n 1) n П И i βμ. (4.4) n U П U 41( n) U kп S ( n) S kи S ( i) S k S ( n) S ( n 1) 1 i U, П (4.5) n U П U 4( n) U kп S ( n) S kи S ( i) S k S ( n) S ( n 1) 1 i U. (4.6) 4.. я., (.4): ( I ); ( n ); ν.

134. [19]: ν ν ν ν.,,. [57], -. μ -,, ;, -,,,,., sin kxy kx ky [58Ж.,, -, 1 1-4.

135 [59Ж,,,.,,,,,,,.. 4.γ,.

136. 4.3.,,. μ

137. ;,..,,,., -. 4..1... [46], [11].. μ β.4, Ω, Ω 3 μ I c I I I I (4.7) I c I I I I., β,.. β,,, μ G, (4.8) 1 k k

138 1 1 k k p, (4.9) 1 k I I I -,, I k p - G (t), β,.. β,. (4.β8) (4.β9), : G p T, (4.3) T,..., (4.8), k.,, (4.3) (4.β8) -.. 4θ (. 3.3.β),., γ,β, G =,794,, =,3.., k =,999. 4..., k, Simulink. (4.7): I s s s ( s) c ( s) I s ( s) I I I s ( s) (4.31) I s s s ( s) c ( s) I s ( s) I I I s ( s). p

139 (.. 4.4): M веш I s + s + c I s + [(I -I ) + I ]s M веш I s - [(I -I ) + I ]s I s + s + c. 4.5).. 4.4. Matlab (.. 4.5. Matlab μ Step1, Step, Gain, Gain1. θ μ Transfer Fcn : 1 I s s c PID Controller, PID Controller 1: I s I I I s. (4.3). (4.33)

14 Transfer Fcn1 : 1 I s s c PID Controller, PID Controller : I s I I I s. (4.34). (4.35) Scope. To Workspace.. 4.6 4.7. β β,87. Q β = Q = 1. β a) β t b) t

141 β c) t. 4.6. β p β = p. a) 1", b) 1, c)βº β a) t β b) t

14 β c). 4.7. β p =.99 p β. ) 1", Л) 1, М) βº, [46]:. 4.β9 k = 1,, p 1 ;,,. (4.β9); (4.3) (4.β8). 4..3.,,.,,.,.1.,, t

143. μ. 4.8 -,. 4.9 -.. 4.8. (V, U, V, U ) (t), t, V U ( = ) V = -7.γ4 νu =,9 νv = -1,9 ν U =,η.

144. 4.9. (V, U, V, U ) (t), t, V U ( = β,9. ) V = -7.1β νu =,9 νv = -1,η ν U = =,5. ( =,9..) β.,. ΔV =.β, ΔV =,8η, ΔU = ΔU =.

(). 145. 4.1, 4.11 V, V Vb, -6,5 1 3 4 5 6 7-6,6 y =,1x - 7,3314-6,7-6,8-6,9-7 -7,1-7, -7,3-7,4 ая я,. 4.1. β (V b ) 1,5 1 y =,51x - 1,966,5 Vg, 1 3 4 5 6 7 -,5-1 -1,5 - -,5 ая я,. 4.11. (V g ),,, V β,,.. 4.1-4.14 (V, U,V ) ( U ):

146-6,5,1,,3,4,5,6-6,6 Vb -6,7-6,8-6,9 y = 1,4918x - 7,33-7 -7,1-7, аа. 4.1. (V ),5, y =,1x,15 Ug,1,5 5 1 15 5 аа. 4.13. (U ) 3,5 Vg 1,5 1,5 y = -,98x + 3,71 5 1 15 5 аа. 4.14. (V ) V, B C (.6), (.9) g β() = : q BC BS GS SV V B C, (4.36) B C, V S u u V c44 SV c X X, μ (4.37), β

147 (S Vβ ) (c 44 ) (.. 4.1),.. 4.15. 411, β. β β.. U = γ,9 γ 4., 15, 1, 5,, -4, -,,, 4,S in G -5, -1, S in B S in B орто S in B пряо - - cos cos. U=3.9 B -15, -,. 4.15. SТЧβ. 4.15, SТЧβ,,,.. 4.16 V. 4β7.

148 V β A. 4.16. (V ) (A ), (k ).. 4.16 4,4β, c 44 = = ββ89,η /, β S Vβ = = 4,4θ 1-7 1/., (4.γ7) μ k S V c = 14.. 44, (). 4θ (. 4..1). V β. 4θ. 4.17. V 5 1 15 5 3-1 - -3-4 -5-6 -7 y = -4,64x + 351,77-8. 4.17. (V ) β (A β ). 4θ =4,βθ γ,8γ 1-8 1/ 4ηη / =,55.., μ =,55..,βγβ.. = 1,4.. A β

149, 9,β%.,,,. 4..4., β.1, X Y U : [5]: ; Y CX. (4.38) ν ( ); ( μ ).., : X BS GS. (4.39) ( ), μ

Y us us 15. (4.4) G S, G C, B C β,... (. 4.γ8), μ Y 11 1 31 41 1 3 4 13 3 33 43 14 4 34 44 BS GS 1 3 4 B B B B S S S S 14 4 34 44 GS GS G S G S. (4.41),,,,. 4.18:. 4.18.,. 4.18, -,.,, (4.41) (. 4.19): β

151. 4.19.,. 4.19,,,,, β. βμ ( β).. β1,. 1., β- β X,, X,, U β 9,,13,3,84 V β 3,3,47 5,5,13 β

15 9,γ,,47,1γ. 4.3. (.. 3.1 3.14) [3], [4], [5]..,, [6]. μ,.,, [53].,,.,,,. U β U β. β,,..,,,.. 4.3.1. 4.3.1.1., μ

ηfu h (1 ) h 153 U k x (1 ) h, (4.4) F k, = 8,85 1-1β / -, F - h, С, Ф -,, μ -, U ; -,.. ( ) (4.4)., U С [5].. (4.4),, 1: M U x k ku n x 1 n h (1 ) h n x h. (4.43),,, βμ I 3 ku l l c B sin t 4kU S h. (4.44) h [6], [4]: sin t, (4.45) μ 1 sint cost, (4.46) t β =, μ ku l 4kU l a c 3 h h 3 b (4.3.3)

154 I a b 3 BS sint. (4.47) (4.46) (4.43), β β : I a A1 BS sin -a B1 BS cos, (4.48) 1 1 А1 a a sin b a sin sin d a 4a 3b a 4 3 3, (4.49) 3 B 1 =,.. P ( ) a b. (4.48) β (.. 4.): AI 4A B AI 1 a 1 a 1 S. (4.5) I a I. 4.. β, Q = 1, U = 1, p β = 7 [1] (. 4.1),, μ = m n,

155 3 1 3 a 4 a m 1 9 n 1 a a a 4. (4.51) 4.β1.. 1, 1.,. Simulink,,, : U I c I I I I BS sint k x (1 ) h, (4.5) I c I I I I. (4.53) Simulink. 4.:

156. 4.. Simulink, γ 4,.. 71 (U = 3,5 U = η ). 4.3. Simulink,. 4 35 3 Аа, [] 5 15 Uв = 5В Uв = 3,5В оь 1 5 555 56 565 57 F [] 575 58 585. 4.3.. μ p = βηθθ,η, Q = 35, p β = βη7η, Q β = 36, h β = 4,η, h = γ,4, U ( ) = 1,9

157,,. 4.3,.,,,, [8]. : (U); ; ;.,,, ; ν,,.,. 4.3.1..,, (Δh/h)., [5].

158 [5].,,,. h h,, 79. β-, =,8. 6 V V V V V,551 V = 1η, V 1 1 -β β.. 4.4.

159 V V, - -15-1 -5 5 1 15 V, = -3,61-3 -,31-3 -1,531-3 -7,651-7,651-1,531-3,31-3 3,61-3 V, =,8 6,91-4 -7,81-4 1,11-3 6,51-3 1,411 -,541-3,981-5,731-7,81 -.. 4.4.

16. 4.4, = =,796.,.., V -,, +. μ 6 V V,551 SignV. (4.54) 1 SignV 3. 4.5.

161 V V, - -15-1 -5 5 1 15 3. V, = -1,1-3 -5,741-4 -,551-5 -6,381-5 6,381-5,551-5 5,741-4 1,1-3 V, =,8-5,661-4 -3,181-4 -1,411-4 3,541-5 3,181-4 1,71-3,871-3 5,91-3. 4.5. «sign»

16,,.. = =,8.,,., μ V V (4.55) S 1 max,.. 4.6, h = h (1-) S 1 max, max, h, sin.. 4.6. (M V ) (M VK ), V = const (t) = S sint + c cost sint, c S. (). 1+ =1,79β

163. V max., V V. 4.,,,.,, c S. k c,, Q,. 4. t=, U +U U -U t = 4 T V sin kc 1 sin V max kc 1 max T T t = 4 U -U U +U 3T t = 4 V sin kc 1 sin V max kc 1 max, μ U -U V,. k c U max V max, U max V max. μ M s V V 1 V V 1 1 1 s 6 max max V,551. (4.56) (4.η6), V max =γ, 5. 4.7.

164 5. V V, - -15-1 -5 67,5 135 V +V, 5 1 15 3 3 V -V, 3 3 5 15 (V +V)(1 -), 1 3 16,5 3 (V -V)(1+), 3 3 3 3 7 V =, -,31-3 -,31-3 -1,531-3 -,771-3,31-3,31-3 V =,8, -,711-3 -,711-3 -,641-3 -,451-3.173,573

165 V = 3 V = 15. 4.7., μ ;.

166 4.3.., μ Δ = ηs/(h ±Δh)... 4.8, 4.9 ΔU (.. 1.) 4 (. 4.8), γ (. 4.9)., -. γ = 4 = γ,γ. 11 1 9 8 7 U 6 5 4 3 3 5 7 9 11 13 15 17 19 С DP4. 4.8. ΔU () 4 () 1 9 8 7 U1 6 5 4 3 1 1 3 5 7 9 11 13 15 17 19 C DP3. 4.9. ΔU () γ (). 4.8, 4.9,,, -

167, (γ,γ ) γ 4.,. 4.3.. 4.3. 4β7 1,7η.,, (4.β): h l tmaxh l tmax R S R1 S U Gk e e. (4.57) β sin(э),. 4.31: U (t), t,. 4.31. U (t) β sin(э), G = 9,8, k =,9 -

168 (.. 4.3 4.γ3):,. 4.3. ( η.ββ..),,. 4.33. ( 1η.ββ..).. 4.3. 4.33. 4.34. 4.35.,. 4.34. ( η.ββ..)

169. 4.35. ( 1η.ββ.). 4.36 1η,., -.. 4.36.. 4.γθμ,,.,,

17. μ K S S S 1 3, S i i-. = 1η.ββ. h = 4, =,β89ν = 5,ββ.. K =,8θν = 1,ββ.. K =,6. Simulink «Fcn», 4.57. -. 4.37.. 4.37. -. 4.37 μ Nelin SNb βν Nelin SNg ν k CH beta, k CH gamma ν k CH β.,,,,,,,,.

171,, θ..,,,... 4.38,, -η.ββ.., β - γ.η.. h = β... 4.38., h = β. 4.39. 4.39.,,. -η.ββ.., β - γ.η.,,,,. h = 1, = η.ββ.., β = γ.η... 4.4:

17. 4.4., h = 1 μ ν ;., [56],,. 4.4. я ц я я 1θ ( θ). 41 4,θ ( 1β).,,. () (.36)μ ( ), ( ): = +, (4.58) = /(β Q β ), (4.59) = k Н k, (4.6) k Н = u Bs / β, (4.61)

173 Sl 4 k U A k, (4.6) h If k Н, k -. 6 9. β Δ f = f β - - f β h, 6. f β, ΔП, Q Q β 1 41 746, 67,5 16117,9 14,53 4,4 4,3,6 46 997,,13 3814, 35849,16-19,5,4 3 48 666,31 7,49 35577,9 4536,84-4,6,3 4 61 551,947 13,3 386,97 3879,6 3,9 4,4 5 5 59,3 11,46 18157,4 913,8 4,5 7,7,4 6 54 578,89 5,6 9,89 989,946 3,4 4, 1,9 7 13 74,8 7, 8744,97 1474,5,5,7,9 8 16 791,7 199,4 4193,73 4463,68,6 1,4,9 9 19 533,37 17,86 6454,45 13418,13 3,4 5,5,9 : Q β (. 4.41), Q β (. 4.4), Δ f (. 4.43) h (. 4.44).,, 5 15 ПП 1 5 5 1 15 5 3 35 4 45 5 Qb. 4.41. Q b

174 1,4 1, 1 ПП,8,6,4, 5 1 15 5 3 35 4 45 5 Qb. 4.4. Q b 5 15 ПП 1 5 5 1 15 5 delf, 4.4γ. Δ f 5 15 ПП 1 5,5 3 3,5 4 4,5 5 h,. 4.44. h

175, () Q Δ f, h.,,. β 41 16. 7. 7. β U Aβ U A k β k A β A k β k U β U k β k k β k β,. 41,, β, β. k β.,,

176 otnb = AЦЩSψ/(.1η*AsИЛОЭК) 1,. U Aβ (..7) k β. k (4.θβ).. 4.45 U Aβ. 41, 8 f = γ4β77θ μ 41 U A k A k U k k U Aβ 1 1 6,6 1,3 1 1,3 1,3 8. 16 14 1 1 ПП 8 6 4 1 3 4 5 6 7 8 9 1 UAb,. 4.45. U Aβ. 4.45, U Aβ = 7,η U Aβ,, -, U Aβ ΔU,,.,,, U Aβ = 7,η. k β,. 41 k β = 5 = 9,β.

177 U Aβ = 7,η, k β = 5, γ9,9., U Aβ k β (K),, 8 U Aβ = 7,5 k β = 5, K, K =4,ββη / /c K =,77η / /c.. 4.46., / /c. 4.46., 41,,. 1θ, μ f = γγβ4, β9.. 1θ 9. U A k A k U k k 1 1 5 5,75 1.3 5 1 1 5,3 1.3 = 9,9, =,7βη / /cμ U Aβ = 7,5 k β = 3 = γ8β,γ, = =,16 / /c.., μ, 1..

178. (U Aβ k β ),. 3. U Aβ k β,.. 4. 4.5. я (...6). UТТ,, μ n U П U11( n) U kп S ( n) S kи S ( i) S k S ( n) S ( n 1) 1 i U, (4.63) U1( n) U kп 1 n S ( n) U П ( n) kи ( i) k ( n) ( n 1) 1 S i max U n U П U13( n) U kп S ( n) S kи S ( i) S k S ( n) S ( n 1) 1 i U U14( n) U k П (4.64), (4.65) n S ( n) U П ( n) kи ( i) k ( n) ( n 1) 1 1 S i max U 1 (4.66) U 1( n) U13( n), (4.67) U ( n) U14( n), (4.68) U 3( n) U11( n), (4.69) U 4( n) U1( n), (4.7) U31( n) U k ( n) Ф ( Т) Ф ( n) ( n 1) n П И i, (4.71) U3( n) U k ( n) Ф ( Т) Ф ( n) ( n 1) n П И i, (4.7) n U П U 41( n) U kп S ( n) S kи S ( i) S k S ( n) S ( n 1) 1 i U (4.73)

179 n U П U 4( n) U kп S ( n) S kи S ( i) S k S ( n) S ( n 1) 1 i U n=(16, 3, 64), n=1 1, U, U, U, k, k, k, S,, S,, S 1 П И max (4.74) U51( n) U 4( n), (4.75) U5( n) U 41( n), (4.76) -.,, Ф U,. () 1/1θ. S. UТТ, S,,.. 3. я я 3. 1. U 1 U, β.. β U П 1. U S β, S, C β, C... 1 S max,

18 [63], 31., 7,, γ1. 31., / 1,7 1,1,, % 1,7,5,48,36, / 5 5,,7 37,6 В 4 1..., -. 3.,,.

181 4.,,. 5. μ ν ν,,,,, ν 6.,.

О 18 μ 1. ( - 4, -,η ).., (. γ.17),. 3., (Q), Q. 4.. (-),.,, [45],,,. : 1.,,, β. 1...

183.,,,,. 3.,. 4. μ ;, ;. 5. 1 / γ7,θ..

184 1. /.. Д.Ж // 8- μ. -. 1.. 1β7-138.. Precision micromechanical gyro: pathway to advance / V. Doronin [et al.] // Proc. Navigation Technology for the 3-rd Millenium. Boston. 1996.. 469-475. 3. KЮЭТЧ, J., SЦЫОčЧТФ, A., ψкуsтć, I. θскsо-locking control of the Coriolis meter's resonance frequency based on virtual instrumentation // Sensor and Actuators A: Physical, ISSN 94-446, 3, vol.14. No.1. P. 86-93. 4. Cenk Acar. Robust Micromashined Vibratory Gyroscopes: dissertation, University of California. Irvine. 4.48 p. 5...,.....μ «-», ββ. 1ββ. 6... Micro-Cap θ..μ, β1. γ44. 7...,....μ, 197. β1θ. 8.....μ, β7. 4. 9. ( )μ β8η848 /.. Д.Ж.. β7.1β.9ην.β7.7.97.. β1 1... μ.γγ.η71. -,...».., β8. 4η.

185 11..... IV. (19γ-γβ.) /....., 19ηη. η11. 1......μ -. 19θγ. 771. 13..,....μ. β4. 8γβ. 14.... ( - )..μ.... β1. 74. 15., /.. Д.Ж..γ.θηββ. -,...».., βθ. 1θ. 16.... ββ, β, 1μ.γγ.ηθ77. -,...».., β8. β1. 17.... μ.... -. β8. 1η8. 18.... μ..... β1γ. βθη. 19... RR-μ.... -. 9. 1βη.. A. Haarahiltunen, A. Vurpala, H. Savin Modeling the effect of mobile ion contamination on the stability of a micromechanical resonator // Journal of Applied Physics. Published by the American Institute of Physics doi: 1.163/1.36511. 11.4355. 11. P. 1-5.

186 1. μ - /...,..,..., β7. θθ.. /.. Д.Ж // - «,,,», 7η- «,»... μ.. β1γ.. 4γ. 3... μ...-.. -. β7. 18β. 4.,.. /..,... μ VI. /.....-.μ, βη,. 149 153. 5. /.. Д.Ж //., 4. 9.4-9. 6.....μ. 1991. βηη. 7.. /.. Д.Ж // - «,,,», 75- «,»... μ.. β1γ.. γ-31.

187 8... μ // ББVIII - «- β9».. β9.. ηθ-6. 9., ω.ψ. μ / ω.ψ.,.. //. 11. βγ.. γθ-4. 3...,... RR- μ. // БIБ μ.β1β. -. β1β..β9-31. 31. /... Д.Ж,. η/η8θ.. β1γ. θ1. 3. / -,...».... Д.Ж IζTAS Ref. Nr 3-53-44ηθ.., β4. 8γ. 33. μ β178η48 / Д.Ж.. 19.4.ν.β.1... 3. 34. Analog Devices. URL: http://www.analog.com/ru/products/sensors/mems-gyroscopes.html ( β4.η.β1η) 35. BOSCH. URL: http://www.boschsemiconductors.de/en/ubk_semiconductors/safe/airbag_systems/angular_rate_sensors /angular_rate_sensors.html ( β4.η.β1η) 36. murata. URL: http://www.murata.com/eneu/products/sensor/gyro ( β4.η.β1η)

188 37. SТХТМШЧ SОЧsТЧР. URL: http://www.siliconsensing.com/products/gyroscopes/ ( β4.η.β1η) 38. Systron Donner. URL: http://www.systron.com/inertial-sensors/single-axis-gyroscope ( 4.5.15) 39. ISense. URL: http://www.isense.ru/perspektivnyie-razrabotki/ ( β4.η.β1η) 4. ««. URL: http://www.elektropribor.spb.ru/prod/rprod_list ( β4.η.β1η) 41... /.. Д.Ж //. β4. 1 (44).. 17-118. 4.,....μ, 19θβ. 19θ. 43.,.. //. ββ. 1(γη).. ηβ-56. 44... - μ..... β14. 1γ. 45... μ..... β14. 188. 46... μ.. θ. 47. TСО ЦТМЫШЦОМСКЧТМКХ ωшытшхтs ЫКЭО sочsшы µωηrs II / GОТРОЫ А. ДОЭ КХ.Ж // Symposium Gyro Technology. Stuttgart. 3. P. 5.1-5.9. 48. Planar inertial sensor: Patent US 4598585 / Burton Boxenhorn filed 19.3.84; boxenhorn 8.7.86. 49. Symmetrical micromechanical gyroscope: Patent US 538 / Jonathan J. Bernstein filed 9.4.91; boxenhorn.4.91.

189 5. Mikko Saukoski. System and circuit design for a capacitive MEMS gyroscope: Doctoral Dissertation. Helsinki University of Technology Faculty of Electronics, Communications and Automation Department of Micro and Nanosciences. 8. 71 p. 51. Ajit Sharma. CMOS systems and circuits for sub-degree per hour MEMS gyroscopes: Ph.D. Dissertation. Georgia institute of technology. 7. 164 p. 5... μ.... -.-.. -,. 3 c. 53... // 1. μ...., β4.. 4η-51. 54. High Performance MEMS Micro-Gyroscope / Sam Y. Bae [et al.] // Proc. SPIE 4755. Design, Test, Integration, and Packaging of MEMS/MOEMS. 9 p. 55...,..,....μ -, 19η9. 91θ. 56...,.. - -. μ, β4. 1θ4. 57..Srikantha Phani, Ashwin A Seshia Identification of Anisoelasticity and Nonproportional Damping in MEMS Gyroscopes // NSTI-Nanotech. Vol.. 4. P. 343-346. 58. Dynamically balanced microelectromechanical devices: Patent US 657163 / Marc S. Weinberg, Kaplesh Kumar, A. Thomas King filed 3.3.; boxenhorn 3.6.3. 59., μ βγ4θβγ9 /..,.... 17.7.7ν. 1.β.9.

19 6. Digital readout electronics for micro-machined gyroscopes with enhanced sensor designs / T. Link [et al.] // HSG-IMIT. University Stuttgart. Tshinghua University. Symposium Gyro Technology.. PP. 5.-5.11. 61. /.. Д.Ж // γ- - «- -.»μ., β1β.. θ7-7. 6... - μ...., β8. 141. 63. R-R., /.. Д.Ж // ББII μ., β1η.. 63-68. 64. /.. Д.Ж //... 8.., 1.. 1-18. 65. The mode matching technology for MEMS gyroscopes with mutually spaced ОТРОЧПЫОЪЮОЧМОs / A. TКЫКsШЯ ДОЭ КХ.Ж // IЧЭОЫЧКЭТШЧКХ ωшчпоыочмо «εтмыш- and Nanoelectronics β1β»μ ψшшф ШП КЛsЭЫКМЭs. Moscow, Zvenigorod. 1. P. 3-33.

В - «...» ИИИИИИИИИИИИ.... - γ..,.., γγ..,..,.. «, ( 74θ/19-1β ββ.1.β1β.) ( 9β4-γ4/14 (153-135-14)-1/353-14 1θ.9.β14.),, μ 1..48111.βθβ.48111.β48ν..48111.βθβ,.48111.β48; 3..48111.β48,.48111.β48-1,.48111.βθβ,.4β1γβ.7.4β1γβ.7β. γ γγ........

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