Operational spacecraft undergo substantial mass property and configuration changes during their lifetime [25]. For example, the inertias change considerably during operations. Consider the orientation control system shown in Figure AP9.1.
(a) Plot the Bode diagram, and determine the gain and phase margins when ωn2 = 15,267.
(b) Repeat part (a) when ω2 = 9500. Note the effect of changing ωn2 by 38%. part (a) when T = 0.1 s. Describe the effect of the100% increase in the time delay T.
(c) Using the phase margin, predict the overshoot for a step input for parts (a) and (b).

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Controller 775s + 10) s(s 2) Dynamics R(s) Orientation command- Yis) Orientation angle 305.3 Sensor s t S s + 1