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

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Chapter 3 / Sensors / Gyroscopes _ _ The configurations shown in Figure 3-26 and Figure 3-27 contain 6 of the possible 12 sensor orientations (6 more are obtained by rotating each input axis through 180°). The negative signs in these figures indicate that the positive sensor axis is in the opposite direction to that shown. For each sensor, let the (X,Y,Z) Missile Body axes be aligned with the Input-Output-Spin (I,O,S) sensor axes such that a clockwise spinning rotor about the Spin axis implies positive output and input angular rates. The configurations in Figure 3-26 and Figure 3-27 minimise torque due to missile lateral and longitudinal acceleration respectively. For long-range missiles the spin axis of the roll gyroscope should be aligned with Z B since roll motion is often restricted and pitch manoeuvres are rare, except when terrain following. For the orientation shown in Figure 3-26 the mapping of the case inputs to the (I,O,S) axes for mechanical RPY gyroscopes is, Μ R D : = ⎡ 1 ⎢ ⎢ 0 ⎢⎣ 0 0 1 0 0 ⎤ 0 ⎥ ⎥ 1 ⎥⎦ ; Μ P D : = 3.4-6 ⎡ 0 ⎢ ⎢ 0 ⎢⎣ 1 1 0 0 0 ⎤ 1 ⎥ ⎥ 0 ⎥⎦ ; Μ Y D : = ⎡ 0 ⎢ ⎢ 0 ⎢⎣ −1 0 1 0 1 ⎤ 0 ⎥ ⎥ 0 ⎥⎦ Equation 3.4-3 For optical instruments the mappings are simply the identity matrix since these sensors are insensitive to acceleration induced errors. 3.4.3.3 Mechanical Sensor Cross-Coupling Error Unlike optical gyroscopes mechanical instruments are also affected by cross-coupling errors. Imperfect and finite bandwidth re-balancing of the float assembly supporting the rotor causes misalignment of the Spin and Input axes. The angular displacement of the float about the Output axis (γ) is usually < 0.5°. The angular rate experienced by each gyroscope is thus, ⎛ Ii ⎡ 1 0 − γ ⎞ i ⎤ ω ⎜ C, B ⎟ ⎛ 0 ⎞ i ⎢ ⎥ ⎜ ⎟ Oi ∀ i ∈ { R , P , Y } ⇒ ωC, B : = ⎢ 0 1 0 ⎥ ⋅ ⎜ ωC, B ⎟ + ⎜ γ& i ⎟ ⎢ ⎥ ⎜ Si ⎟ ⎜ ⎟ ⎣ γ i 0 1 ⎦ ⎝ ωC, B ⎠ ⎝ 0 ⎠ Equation 3.4-4 The error induced by the angular rate of the float assembly is small compared with some of the other error sources. The float angle is obtained from the typical torquer model shown in Figure 3-28 using the parameters: Float inertia J 2.5x10 -6 kg m 2 Float angular momentum H 0.005 kg m 2 /s Viscous torque coefficient C 0.004 Nm/(rad/s) Pulse-Width-Modulator (PWM) gain GSGPM 500 (rad/s)/rad Torquer bandwidth 4000 rad/s
Chapter 3 / Sensors / Gyroscopes _ _ E_W_CB 1 + - H + - TORQUER DYNAMICS 4000 s+4000 1/J C 1 s 1 s 3.4-7 E PWM GAIN FLOAT ANGLE 1 + + 1/z Figure 3-28 : Torquer Model 512 D/S 0.25 D/S + - 3 D_W_CB The PWM and torquer can be reduced to a 2 nd order lag with a damping of 0.67 and natural frequency of 160 Hz range followed by limiting and quantisation. The linear model response to a 1° step is compared to this 2 nd order closed loop response in Figure 3-29. LINEAR SYSTEM STEP RESPONSE 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 TIME (MSEC) Figure 3-29 : Closed Loop Step Response The maximum float angle depends on the PWM gain and the maximum expected angular rate, G ⋅ γ : = ω PWM MAX MAX C, B Equation 3.4-5 The PWM gain is 500 (°/s)/° for a saturation limit of 250°/s and a maximum float angle of 0.5°. The quantisation for this saturation limit, given 2 11 pulses per output cycle, is 0.244°/s. The cross-coupling misalignment angle (γ) is determined from the 2 nd order PWM dynamics when bit 3 of MS_GS_ER is set. The input to the mechanical gyroscope triad is therefore, ω U C , B : = ⎛ ⎜ ⎜ ⎜ ⎝ ω ω ω IR C, Β IP C, Β IY C, Β ⎞ ⎟ ⎟ ⎟ ⎠ − ⎛ ⎜ ⎜ ⎜ ⎝ γ γ γ R P Y ⎞ ⎟ ⎟ ⎟ ⎠ ⊗ ⎛ ⎜ ⎜ ⎜ ⎝ ω ω ω SR C, Β SP C, Β SY C, Β ⎞ ⎟ ⎟ ⎟ ⎠ Equation 3.4-6
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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 3 / Sensors / Seeker _ _ 3.
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Chapter 3 / Sensors / Fins _ _ 3.10
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Chapter 3 / Sensors / NAVSTAR GPS _
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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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6 Chapter 6 / Missile Guidance _ _
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Chapter 6 / Missile Guidance _ _ 6.
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Chapter 6 / Missile Guidance _ _ As
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Chapter 6 / Missile Guidance _ _
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Chapter 6 / Missile Guidance _ _ CD
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Chapter 6 / Missile Guidance _ _ ge
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Chapter 6 / Missile Guidance _ _ ex
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Chapter 6 / Missile Guidance _ _ &
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Chapter 6 / Missile Guidance _ _ PN
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Chapter 6 / Missile Guidance _ _ of
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Chapter 6 / Missile Guidance _ _ NO
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Chapter 6 / Missile Guidance _ _ tr
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Chapter 6 / Missile Guidance _ _ η
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Chapter 6 / Missile Guidance _ _ Au
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Chapter 6 / Missile Guidance _ _ Fo
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Chapter 6 / Missile Guidance _ _
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Chapter 6 / Missile Guidance _ _ ar
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7 Chapter 7 / Missile Trajectory Op
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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 / 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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