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

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Chapter 3 / Sensors / Gyroscopes _ _ GS γ ( ) T γ , γ , : = γ 3.4-8 R P Y Equation 3.4-7 Applying a masking matrix [GXM] to deal with the different Spin axis orientations, and relating the Spin axis to individual sensor (R,P,Y) axes, ω U C, B : = ⎛ ⎜ ⎜ ⎜ ⎝ ω ω ω XR C, Β XP C, Β XY C, Β ⎞ ⎟ ⎟ ⎟ ⎠ − GS For the configuration selected, ⎛ ⎜ γ ⊗ ⎜ ⎜ ⎝ [ GXM ] [ GXM ] : = ⎡ 0 ⎢ ⎢ 1 ⎢⎣ −1 3.4.4 Measured Angular Rate and Angular Increments ⋅ ⎡ ⎢ ⎢ ⎢ ⎣ 1 0 0 ω ω ⎤ ⎥ ⎥ ⎥⎦ YR C, Β ZR C, Β ω ω XP C, Β ZP C, Β ω ω XY C, Β YY C, Β ⎤ ⎞ ⎥ ⎟ ⎥ ⎟ ⎥ ⎟ ⎦ ⎠ Equation 3.4-8 Equation 3.4-9 Non-gyroscopic torques, and imperfect electronics, that cause application dependent measurement errors are subject to physical constraints, financial and technical trade-offs. Ignoring rotor speed variation drift, float angular velocity and acceleration, Savage’s model of a single axis mechanical gyroscope expressed in (I,O,S) axes reduces to, ω ~ I C, B : = ϕ SF ⎛ ⎜ I I ⎛ J ⎞ ⋅ ω ⋅ ω ⋅ ω − ⎜ ⎜ S − J I S JO & I ⋅ ωC, B + GSB + ⎟ C, B C, B ⎝ ⎝ HW ⎠ HW O C, B ⎞ ⎟ ⎠ Equation 3.4-10 The float inertia about the axes is denoted by (JI, JO, JS), and (HW) is the angular momentum of the rotor about the spin axis. Float dynamics, anisoelastic drift, and output rate induced errors are minimising by careful design. This leaves constant bias (GSB) and scale factor errors common to both optical and mechanical sensors. These errors are controlled by the bit pattern of MS_GS_ER listed in Table 3-9. Bits 22-23 reserved in Table 3-6 for ADC errors, are replaced by PWM errors in mechanical sensors, and fringe counting in optical systems. The anti-aliasing filter and quantised noise associated with the ADC, controlled by bits 21 and 24, are not applicable. The inertial angular rate is corrupted at the reference rate by a time delay and 2 nd order dynamics,
Chapter 3 / Sensors / Gyroscopes _ _ D ω B C, B TD U ( ϕ ( ω , ζ , ) , t ) : = ϕ ω D2L 3.4-9 C, B GS D2L GS D2L GS TD Equation 3.4-11 The output of the 2 nd order dynamics determines the cross coupling error, GS PM GS U C, B G ⋅ γ : = ω − ϕ ω D2L U ( ) C, B Table 3-9 : Gyroscope Triad Errors MS_GS_ER Sensor Error Source 17 G-dependent drift 18 G 2 -dependent drift 19 Digital compensation filter 22 Pulse count range limit 23 Pulse quantisation Equation 3.4-12 Although a time delay is not included in the Savage and IEEE models delays exist in the torquer and internal digital processor. The dynamic output is subject to a constant bias, random noise and scale factor errors effecting both mechanical and optical sensors, and a bias affecting only mechanical sensors (GSBG). A ω ~ B C, B : = ϕ SF D B ( ω + ϕ ( σ ) + ϕ ( σ ) + B ) C, B CB GS CB RN GS RN GS G Equation 3.4-13 In mechanical gyroscopes bias is caused by: • residual torques due to thermal gradient induced fluid motion • magnetic reaction torques induced by spin motor generated eddy currents in the float cylinder • residual flex-lead torques • pivot stiction • torque loop/pulse electronics In optical sensors bias results from thermal gradients in the RLG lasing path, and micro-kinks in the FOG winding. Noise in optical sensors is some 3-4 times larger than in equivalent mechanical systems, and is caused by: • Photon (quantum) shot noise; light quantised in photons at the detector • Fringe count over the output sampling period inducing quantisation noise • Residual dither from the process used to minimise lock-in bias
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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 / Seeker _ _ Th
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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 / 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 / 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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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 / 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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