(Solution) - A satellite single axis attitude control system can be represented by -(2025 Original AI-Free Solution)

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A satellite single-axis attitude control system can be represented by the block diagram in Figure CP2.5. The variables k, a, and b are controller parameters, and J is the spacecraft moment of inertia. Suppose the nominal moment of inertia is J = 10.8E8 (slug ft2), and the controller parameters are k = 10.8E8, a = 1, and b = 8.
(a) Develop an m-file script to compute the closed-loop transfer function T(s) = ?(s)/?d(s).
(b) Compute and plot the step response to a 10° step input.
(c) The exact moment of inertia is generally unknown and may change slowly with time. Compare the step response performance of the spacecraft when J s reduced by 20% and 50%. Use the controller parameters k = 10.8E8, a = 1, and b = 8 and a 10° step input. Discuss your results.