Question: A satellite single-axis attitude control system can be represented by the block diagram in Figure. 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 6 = 8.
(a) Develop an m-file script to compute the closed loop transfer function T(s) = θ(s)/θd(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 / is 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.
