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

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Chapter 6 / Missile Guidance _ _ 6.5.1.6 Stability and Observability The analytical stability of PN is considered by Rew [R.6] . Song [S.6-7] modified the PN law by oscillating the target LOS to make the system more observable and effective for mid-course guidance. Hull [H.4] optimised both control effort and information content, convergence of the shooting technique solution requiring a gradual transfer of weight from control effort to observability. 6.5.2 Conventional PN Guidance Laws For constant closing speed engagements in which the missile has a speed and lateral acceleration advantage over the target, PN laws have proven to be remarkably robust. Enhancement of the basic PN concept is introduced, reducing the target LOS rate to zero whilst compensating for, • Short range engagements dominated by the missile boost phase • Accelerating targets using sophisticated avoidance manoeuvres • High altitude engagements with increasing missile incident lag Essentially the PN guidance demands decompose into four terms: • The basic demand required to reduce the target LOS rate to zero • Compensate for the uncontrolled missile longitudinal acceleration • Augmentation to account for quasi-constant target acceleration • Compensation for gravitational acceleration Combining these terms, and expressed them in the Missile Body frame so that the autopilot can be closed around the body referenced accelerometer output, PN α Β D ≡ YΒ ZΒ T Β Β Β Β ( α , α ) : = α + α + α + α PN D PN D 6-14 PN SL PN MA PN TA GA Equation 6.5-5 Acceleration normal to the LOS is determined in different reference frames depending on the form of PN. To generate the equivalent acceleration in the Missile Body frame requires the inverse scaling, B o, m T T F ( & YB ZB F P& , &P & ) : = ( T ) &P & &P & ≡ ⋅ o, m o, m B o, m Equation 6.5-6
Chapter 6 / Missile Guidance _ _ & P& B o, m : = ⎛ ⎜ ⎜ ⎜ ⎝ T T F B F B ( ) ( ) ⎟ ( ) ( ) ⎟⎟ F −1 ⎞ ⎛ YF 5 , T ⎞ B 8 P& & ⎟ ⎜ o, m ⎟ ⋅ ⎜ F ⎟ ⎜ ZF 6 , T 9 P& & From the orthogonal properties of transformation matrices, Hence, ⎛ ⎜ ⎜ ⎜ ⎝ ∀ i ∈ &P & &P & YB o, m ZB o, m T T T 6-15 B ⎠ ⎝ o, m S S S [ 1 ( 1 ) 3 ] : T ( 1 , i ) : = T ( 2 , i ) × T ( 3 , i ) S B S B S B ⎞ ⎟ ⎟ ⎟ ⎠ B S S S S ( 1 ) : = T ( 5 ) ⋅ T ( 9 ) − T ( 6 ) ⋅ T ( 8 ) B B S S S S ( 4 ) : = T ( 8 ) ⋅ T ( 3 ) − T ( 9 ) ⋅ T ( 2 ) B B S S S S ( 7 ) : = T ( 2 ) ⋅ T ( 6 ) − T ( 3 ) ⋅ T ( 5 ) : = T F B 1 ( 1 ) B ⋅ ⎛ ⎜ ⎜ ⎜ ⎝ 6.5.2.1 Basic PN Sight-Line Rate Demand T F B − T B B B B B B B B B ⎠ Equation 6.5-7 Equation 6.5-8 Equation 6.5-9 Equation 6.5-10 Equation 6.5-11 ( ) ( ) ⎟ ( ) ( ) ⎟⎟ F ⎞ ⎛ YF 9 , − T ⎞ B 8 P& & ⎟ ⎜ o, m ⎟ ⋅ ⎜ F F ⎟ ⎜ ZF 6 , T 5 P& & B B ⎠ ⎝ o, m ⎠ Equation 6.5-12 The basic sight-line PN lateral acceleration demands, normalised by velocity (VN), reduce the inertial angular rotation of the target LOS to zero, PN α SL m N ( ) T ZS YS ω , − : = λ ⋅ V ⋅ ω For, • Constant target and missile closing speed • Non-manoeuvring target • Missile incidence and lag free guidance • Perfect missile autopilot A, S A, S Equation 6.5-13
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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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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 / Barometric Al
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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 / NAVSTAR GPS _
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Chapter 4 / Target Tracking _ _ 3.1
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Chapter 4 / Target Tracking _ _ Ine
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Chapter 5 / Missile State Observer
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Chapter 7 / Missile Trajectory Opti
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8 Chapter 8 / Simulation _ _ Chapte
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Chapter 8 / Simulation _ _ 8.1 The
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Chapter 8 / Simulation _ _ 8.3 The
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Chapter 8 / Simulation _ _ Having p
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Chapter 8 / Simulation _ _ 8.5.1 Gl
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Chapter 8 / Simulation _ _ (1) CONS
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Chapter 8 / Simulation _ _ 8.6.2 Ou
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Chapter 8 / Simulation _ _ The file
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Chapter 8 / Simulation _ _ • The
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Chapter 8 / Simulation _ _ comprehe
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Chapter 8 / Simulation _ _ WIN_RATE
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Chapter 8 / Simulation _ _ for this
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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 / Matrices _
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Appendix I / Utilities / Quaternion
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Appendix I / Utilities / Trigonomet
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