Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

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Chapter 6 / Missile Guidance _ _ M B A : = M B v + M B ω + M B δ : = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ m n 6-40 w v 0 ⋅ P& ⋅ P& ZB o, m YB o, m ⎞ ⎛ l ⎜ p ⋅ ω ⎟ ⎟ ⎜ ⎟ ⎜ + ⎟ ⎜ mq ⋅ ω ⎟ ⎜ ⎟ ⎜ ⎠ ⎝ n r ⋅ ω XB A, B YB A, B ZB A, B ⎞ ⎟ ⎟ ⎟ ⎟ + ⎟ ⎟ ⎠ ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ l m n ξ η ζ ⋅ ξ ⋅ η ⋅ ζ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ Equation 6.10-25 The control surface deflections are dealt with in §3.11. For an agile missile the derivatives are functions of Mach number, height and lateral acceleration. The generic missile rotational dynamics are simpler and are determined by the speed and incidence dependent incidence lag (TI) where, For BTT missiles, YB ZB ( T , T ) : = ( − 1 y , 1 z ) I ω YR A, B I : = − ZR ZB Po, m ( 1 + TI ⋅ s ) ⋅ XB v & P& o, m w Equation 6.10-26 Equation 6.10-27 The angular acceleration is determined by differentiating smooth angular rates. The missile orientation quaternion is propagated using the 1 st order derivatives followed by normalisation. For STT missiles, P& YB ZB ( ω , ω ) ZB ZB YB YB ( − ( 1 + T ⋅ s ) ⋅ &P & , ( 1 + T ⋅ s ) ⋅ &P & ) I XB o, m ⋅ A, B o, m A, B I : = o, m Equation 6.10-28 Jerk is also obtained by differences at 4 kHz. The incidence lag for both types of missile control depends on Mach number limited to [1,3] and body incidence limited to ± 40°, ⎛ ⎜ ⎝ T 1 YB I , T 1 ZB I ⎞ ⎟ ⎠ : = ϕ 1 ⋅ S ( ϕ , ϕ ) : = ⋅ ( ϕ , ϕ ) 2 3 5969 ⋅ P S T 2 Equation 6.10-29 3
Chapter 6 / Missile Guidance _ _ ⎛ ⎜ ⎜ ⎜ ⎝ ϕ2 L ϕ 3 ⎞ ⎟ ⎟ ⎟ ⎠ 6-41 MV ( 30 − M ) ⋅ ( Θ ) ⎛ ⎜ m : = 0. 85 − 0. 15 ⋅ M + ⎜ m L ⎜ ⎜ m ⎝ ( ) ( ) ⎟ ⎟⎟⎟ MV 2 30 − M ⋅ Ψ Table 6-2 : Sea-Level Missile Incidence Lag (Seconds) B B 2 ⎞ ⎠ Equation 6.10-30 MACH INCIDENCE ( DEGREES ) NUMBER 0 5 10 20 30 40 1.0 1.429 1.086 0.632 0.236 0.116 0.067 1.5 1.067 0.792 0.446 0.163 0.079 0.046 2.0 0.909 0.655 0.356 0.126 0.061 0.035 2.5 0.842 0.584 0.305 0.105 0.050 0.029 3.0 0.833 0.550 0.273 0.090 0.043 0.026 The variation in incidence lag with Mach number and sea-level incidence is given in Table 6-2. Incidence lag sensitivity with respect to the missile observer states, ∂ TI ∂ X SO YB ∂ TI ∂ X SO ZB M M : = : = − − ( ) ⎟ YB 2 ⎛ ∂ ϕ ∂ ϕ ⎞ ⎜ 1 2 T ⋅ ⋅ ϕ + ϕ ⋅ I ⎜ ⎝ ∂ SO X M 2 1 ∂ SO X M ⎠ Equation 6.10-31 ( ) ⎟ ZB 2 ⎛ ∂ ϕ ∂ ϕ ⎞ ⎜ 1 3 T ⋅ ⋅ ϕ + ϕ ⋅ I ⎜ ⎝ ∂ SO X M 3 1 ∂ SO X M ⎠ Equation 6.10-32 The sensitivity of incidence lag to geodetic height depends on the change in static air pressure and temperature given in §19, ∂ ϕ ∂ X : = ⎛ ⎜ ⎜ ⎝ 5969 ⎛ ⋅ ⎜ ⎝ ∂ TS ⋅ ∂ P ∂ PS − ∂ P 1 S 02 , , 0 2 ZG ZG 16 SO M PS TS m m Decomposing the remaining Jacobians, ∂ ϕ ⎛ ⎜ ∂ ϕ2 ∂ ϕ : = 02 , , ∂ ⎜ ZA SO XM ⎝ ∂ Pm ∂ P& P ⎞ ⎟ ⎠ ⎞ ⎟ ⎟ ⎠ Equation 6.10-33 ∂ ϕ ∂ Q 2 2 A , 03 , 2 B , 06 m A ⎞ ⎟ ⎟ ⎠ Equation 6.10-34
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CRANFIELD UNIVERSITY LEIGH MOODY SE
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ABSTRACT When considering advances
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Contents _ _ LIST OF CONTENTS 1 INT
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Contents _ _ 8.2 The Scope of Moder
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Contents _ _ 17.4 Inertial Velocity
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Tables _ _ LIST OF TABLES Table 1-1
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Figures _ _ LIST OF FIGURES Figure
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Figures _ _ Figure 5-1 : Centralise
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Figures _ _ Figure 19-3 : Air Densi
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Acronyms _ _ Acronyms And Abbreviat
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Acronyms _ _ HDOP - NAVSTAR GPS Hor
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Acronyms _ _ RCS - Radar Cross Sect
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Glossary _ _ GLOSSARY A challenge w
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Glossary _ _ 0.1 Predicate Calculus
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Glossary _ _ ]A,B] Real number rang
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Glossary _ _ 0.9 Matrix Operators [
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Glossary _ _ 0.14.2 Special Vectors
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Glossary _ _ P C a , b ≡ XC YC ZC
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Glossary _ _ V ≡ V : = V • V Th
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Glossary _ _ 0.16.4 Matrix Partitio
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Glossary _ _ Only the subset of qua
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Glossary _ _ 0.19 Systeme Internati
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1 Chapter 1 / Introduction _ _ Chap
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Chapter 1 / Introduction _ _ Wherea
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Chapter 1 / Introduction _ _ • Cr
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Chapter 1 / Introduction _ _ genera
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Chapter 1 / Introduction _ _ radar
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Chapter 1 / Introduction _ _ simple
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Chapter 1 / Introduction _ _ optimi
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Chapter 1 / Introduction _ _ 1.3.9
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2 Chapter 2 / Target Modelling _ _
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Chapter 2 / Target Modelling _ _ 2.
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Chapter 2 / Target Modelling _ _
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Chapter 2 / Target Modelling _ _ t
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Chapter 2 / Target Modelling _ _ P&
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Chapter 2 / Target Modelling _ _ GO
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Chapter 2 / Target Modelling _ _ th
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Chapter 2 / Target Modelling _ _
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Chapter 2 / Target Modelling _ _ VX
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Chapter 2 / Target Modelling _ _ ma
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3 Chapter 3 / Sensors _ _ Chapter 3
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Chapter 3 / Sensors _ _ 3.1 Simulat
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Chapter 3 / Sensors _ _ Table 3-4 :
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Chapter 3 / Sensors _ _ Reference D
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Chapter 3 / Sensors _ _ 3.2-9 s s i
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Chapter 3 / Sensors _ _ 3.2-11 t o
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Chapter 3 / Sensors _ _ Figure 3-5
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Chapter 3 / Sensors _ _ Table 3-7 :
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Chapter 3 / Sensors _ _ IF ϕ LIM
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Chapter 3 / Sensors _ _ The phase e
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Chapter 3 / Sensors _ _ Taking expe
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Chapter 3 / Sensors _ _ Expressing
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Chapter 3 / Sensors _ _ INPUT; AA,
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Chapter 3 / Sensors _ _ The functio
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Chapter 3 / Inertial Navigation _ _
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Chapter 3 / Sensors / Gyroscopes _
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Chapter 3 / Sensors / Accelerometer
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Chapter 3 / Sensors / Barometric Al
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Chapter 3 / Sensors / Barometric Al
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Chapter 3 / Sensors / Radar Altimet
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Chapter 3 / Sensors / Radar _ _ 3.8
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Chapter 3 / Sensors / Radar _ _ LF
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Chapter 3 / Sensors / Radar _ _ ( )
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Chapter 3 / Sensors / Radar _ _ S :
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Chapter 3 / Sensors / Radar _ _ SN
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Chapter 3 / Sensors / Radar _ _ 2
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Chapter 3 / Sensors / Radar _ _ ⎛
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Chapter 3 / Sensors / Seeker _ _ 3.
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Chapter 3 / Sensors / Seeker _ _ 5
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Chapter 3 / Sensors / Seeker _ _
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Chapter 3 / Sensors / Seeker _ _ th
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Chapter 3 / Sensors / Seeker _ _ Th
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Chapter 3 / Sensors / Seeker _ _ Th
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Chapter 3 / Sensors / Fins _ _ 3.10
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Chapter 3 / Sensors / Fins _ _ thro
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Chapter 3 / Sensors / NAVSTAR GPS _
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Chapter 3 / Sensors / Helmet Mounte
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Chapter 3 / Sensors / Helmet Mounte
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Chapter 3 / Sensors / Air Data Syst
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Chapter 4 / Target Tracking _ _ 3.1
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Chapter 4 / Target Tracking _ _ Ine
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Chapter 4 / Target Tracking _ _ ran
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Chapter 5 / Missile State Observer
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5 Chapter 5 / Missile State Observe
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Chapter 8 / Simulation _ _ with the
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Chapter 8 / Simulation _ _ Figure 8
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Chapter 8 / Simulation _ _ Table 8-
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Chapter 8 / Simulation _ _ 8.8 Disc
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9 Chapter 9 / Performance _ _ Chapt
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Chapter 9 / Performance _ _ 9.1 Air
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Chapter 9 / Performance _ _ XM ( >
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Chapter 9 / Performance _ _ 9.3 PN
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Chapter 9 / Performance _ _ The eff
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Chapter 9 / Performance _ _ VXMVOM
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Chapter 9 / Performance _ _ VXMVOM
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Chapter 9 / Performance _ _ 9.4 CLO
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Chapter 9 / Performance _ _ AR_BOM
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Chapter 9 / Performance Chapter 9 /
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Initially the position error falls
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values of CN are not always a relia
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crude initialisation introduces err
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9.5.3 Singer Filter Tuning The Sing
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9.6.2 CLOS Study The CLOS study sho
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Chapter 10 / Conclusions _ _ 10-2
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Chapter 10 / Conclusions _ _ 10.3 T
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Chapter 10 / Conclusions _ _ 10.7 M
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Chapter 11 / Future Research _ _ 11
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Chapter 11 / Future Research _ _
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Chapter 11 / Future Research _ _ To
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References _ _ B.4 BAZARAA M.S., SH
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References _ _ F.1 FOX J.E., “A C
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References _ _ H.5 #HULL D.G., RADK
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References _ _ L.2 LOOZE D.P., HSU
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References _ _ N.4 NABAA N., BISHOP
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References _ _ R.3 RUSNACK I., “O
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References _ _ S.15 SINGER R.A.,
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References _ _ Y.2 YUAN P., CHERN J
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Bibliography _ _ B.13 BABA Y., YAMA
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Bibliography _ _ B.40 BECKER J.C.,
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Bibliography _ _ C.33 CORTINA E., O
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Bibliography _ _ E.8 ERSHOV A.A.,
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Bibliography _ _ G.34 GUTMAN P., VE
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Bibliography _ _ H.35 HUSSAIN A.M.,
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Bibliography _ _ K.14 KATZIR S., CL
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Bibliography _ _ L.19 LEFAS C.C,
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Bibliography _ _ M.16 MAYNE D.Q., P
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Bibliography _ _ P.1 PAINTER J.H.,
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Bibliography _ _ R.32 RONG LI X., Z
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Bibliography _ _ S.47 SPEYER J.L.,
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Bibliography _ _ V.5 VIAN J.L., MOO
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Bibliography _ _ W.29 WATSON G.A.,
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Appendix A / Geometric Points _ _ 1
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Appendix A / Geometric Points _ _ 1
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Appendix B / Frames of Reference _
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Appendix C / Axis Transforms _ _ 16
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Appendix C / Axis Transforms _ _ YP
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Appendix C / Axis Transforms _ _ B
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Appendix C / Axis Transforms _ _ YB
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Appendix C / Axis Transforms _ _ Us
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Appendix C / Axis Transforms _ _ No
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Appendix C / Axis Transforms _ _ B
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Appendix C / Axis Transforms _ _
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Appendix D / Point Mass Dynamics _
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Appendix E / Earth Geometry _ _ 18-
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Appendix E / Earth Geometry _ _ ELL
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Appendix E / Earth Geometry _ _ (dx
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Appendix E / Earth Geometry _ _ Int
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Appendix E / Earth Geometry _ _ 18.
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Appendix E / Earth Geometry _ _ 19-
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Appendix E / Earth Geometry _ _ P S
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Appendix E / Earth Geometry _ _ 19.
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Appendix E / Earth Geometry _ _ ∂
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Appendix G / Gravity _ _ 20-2
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Appendix G / Gravity _ _ g : = g +
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Appendix G / Gravity _ _ d −6 2
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Appendix G / Gravity _ _ 20-8
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Appendix H / Steady State Tracking
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Appendix I / Utilities _ _ 22.1-2
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Appendix I / Utilities _ _ Cartesia
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Appendix I / Utilities _ _ Matrix P
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Appendix I / Utilities _ _ 22.1-8
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Appendix I / Utilities / General Ut
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Appendix I / Utilities / WGS 84 Tar
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Appendix I / Utilities / Axis Trans
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Appendix I / Utilities / Point Mass
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Appendix I / Utilities / Earth, Atm
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Appendix I / Utilities / Digital Ma
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Appendix I / Utilities / Digital Fi
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Appendix I / Utilities / Matrices _
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Appendix I / Utilities / Quaternion
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Appendix I / Utilities / Trigonomet
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Appendix I / Utilities / Vectors _
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Appendix I / Utilities / Covariance
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