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ASE 370L Take Home Test 3 - ASE 370L Take Home Test 3 Drew...

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ASE 370L Take Home Test 3 April 29, 2010 Drew Rosecrans DCR544
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Satellite Attitude Controller with Control Moment Gyros It is necessary to control the attitude of a satellite in space. Based on what the satellites’ purpose is, it may be useful to keep the satellite pointed toward Earth or out into space. There are several ways to control the attitude of an object in space, but for this problem a control moment gyro (CMG) is to be used. In this problem it is important to consider gravity gradient torques due to the variation of the earth’s gravitational field over the satellite. Also aerodynamic disturbances due to the atmosphere need to be accounted for. The simplified model of the spacecraft is given by = = - θsUs Gs 1Iys2 3n2Δ Where θs is the pitch angle, Us is the CMG input torque, = . Iy 0 2 kg∙m2 , = - Δ Iz Ix , = . Ix 0 1 kg∙m2 , = . Iz 0 01 kg∙m2 , and = . / n 0 0011 rad sec is the orbital angular velocity. For this problem it is desired that the satellite be pointed toward Earth, that occurs when θs = 0 , thus the desired pitch angle θds = 0 . Now the gravity gradient term is taken care of in the plant model Gs , it is represented by =- Tgg 3n2Δθs The CMG is a constant-rate flywheel mounted on a set of gimbals that is controlled by actuators. The simplified model for the CMG is = + Gas 15s 15 The aerodynamic disturbance is due to atmospheric drag acting on the satellite and creating a torque. We can view this torque as a disturbance because it is generally much smaller than the gravity gradient torque. This disturbance torque,
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