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MIT16_30F10_rec12 - Recitation 12 16.30/31 Estimation and...

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Recitation 12 16.30/31: Estimation and Control of Aerospace Systems November 29, 2010 Consider a space telescope, and let d be a unit vector aligned with the telescope’s line of sight. It is desired to point the telescope towards a star, in direction d 0 . The dynamics of the spacecraft are described by the equations of motion ˙ + �ω × J�ω = τ, where �ω is the angular velocity of the spacecraft (in body axes), J is its inertia tensor, and τ is the control torque (in body axes). In body axes, the star’s direction is not fixed, but rotates as d ˙ 0 = �ω × d 0 . Consider the control law τ = k�ω + d × d 0 . 1. Find the equilibrium points for the spacecraft, under the given control law. 2. Consider the following function: V ( �ω, d 0 ) = 1 2 �ω · J�ω + 1 2 | d d 0 | 2 . Is it a good candidate for a Lyapunov function? Study the stability of the equilibrium point(s).
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