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A satellite single-axis attitude control system can be represented by the block diagram in Figure 1. 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 = 10.8e^8 (slug ft^2), and the controller parameters are k = 10.8e^8, a = 1, and 6 = 8. Develop a m-file script to compute the closed loop transfer function T(s) = ?(s)/?_d (s). (10 marks) Compute and plot the step response to a 10° step input. (5 marks) The exact moment of inertia is generally unknown and may change slowly with time. Compare the step response performance of the spacecraft when J is reduced by 20% and 50%. Use the controller parameters k = 10.8e^8, a = 1, and b = 8 and a 10° step input. Discuss your results. (15 marks)

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