The pitch attitude motion of a rigid spacecraft is described by
where J is the principal moment of inertia, and u is the input torque on the vehicle [7]. Consider the PD controller
(a) Obtain a block diagram of the control system. Design a control system to meet the following specifications: (1) closed-loop system bandwidth about 10 rad/s, and (2) percent overshoot less than 20% to a 10° step input. Complete the design by developing and using an interactive m-file script, (b) Verify the design by simulating the response to a 10° step input, (c) Include a closed-loop transfer function Bode plot to verify that the bandwidth requirement is satisfied.