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

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Chapter 3 / Sensors / Seeker<br />

_ _<br />

The segmented design of the motor’s commutator results in a fixed<br />

frequency sinusoidal torque disturbance and an induced magnetic<br />

component modelled so that they can operate out-of-phase. The torque<br />

disturbance characteristics are listed in Table 3-19.<br />

Table 3-19 : Complex Gimbal Torque Characteristics<br />

MATH DESCRIPTION PITCH YAW UNITS<br />

KG1 Flexi-lead torque 0.005 0.025 Nm<br />

KG2 Motor torque amplitude 0.002 0.02 Nm<br />

KG3 Motor torque frequency 30 15 rad/rad<br />

KG4 Motor torque phase offset [ -π , π ] [ -π , π ] rad<br />

KG5 Magnetic torque amplitude 0.005 0.01 Nm/Amp<br />

KG6 Magnetic torque frequency 25 50 Hz<br />

KG7 Magnetic torque phase offset [ -π , π ] [ -π , π ] rad<br />

The friction torque disturbances (SKτF) comprise stiction, viscous and<br />

coulomb damping. Stiction is the torque needed to induce motion in a<br />

stationary gimbal. Viscous friction arises from resistance to motion due to<br />

eddy currents, induced magnetic fields and lubrication. Coulomb friction is<br />

due to abnormal loads on gimbal bearings when subject to vibration. These<br />

torque disturbances, characterised using data listed in Table 3-20, oppose<br />

the motion of the gimbals. When the applied torque is greater than Stiction,<br />

τ<br />

F<br />

: =<br />

Ψ&<br />

H<br />

B<br />

H<br />

H<br />

( sign ( K , Ψ&<br />

) + K ) ⋅ Ψ&<br />

SK<br />

≥<br />

3.9-11<br />

SK<br />

G10Ψ<br />

K<br />

G9Ψ<br />

When the applied torque is less than stiction,<br />

⎧<br />

⎪<br />

⎪<br />

⎨<br />

⎪<br />

⎪<br />

⎪⎩<br />

τ<br />

τ<br />

SK MΨ<br />

SK MΨ<br />

τ<br />

+<br />

+<br />

SK MΨ<br />

+<br />

τ<br />

τ<br />

SK EΨ<br />

SK EΨ<br />

τ<br />

≤<br />

<<br />

SK EΨ<br />

−<br />

≥<br />

Ψ&<br />

SK<br />

H<br />

B<br />

SK<br />

K<br />

SK<br />

K<br />

<<br />

G8Ψ<br />

K<br />

G8Ψ<br />

G8Ψ<br />

SK<br />

⇒<br />

K<br />

B<br />

G9Ψ<br />

⇒<br />

⇒<br />

τ<br />

⇒<br />

∧<br />

SK<br />

τ<br />

SK FΨ<br />

SK FΨ<br />

τ<br />

SK FΨ<br />

G11Ψ<br />

: =<br />

: =<br />

: =<br />

−<br />

τ<br />

B<br />

Equation 3.9-14<br />

SK MΨ<br />

SK<br />

SK<br />

K<br />

K<br />

+<br />

G8Ψ<br />

G8Ψ<br />

τ<br />

SK EΨ<br />

⎫<br />

⎪<br />

⎪<br />

⎬<br />

⎪<br />

⎪<br />

⎪⎭<br />

Equation 3.9-15

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