Question 2 System representing the simplified version of the satellite with flexible solar panels is given as in Figure 2. For the system model the flexible panels using a rigid sheet with moment of inertia Jp connected to the main satellite body by a torsional compliant element with spring constant k and damping constant b. The moment of inertia of the satellite is Js. The angle of the satellite body from the inertial reference is and the angle of the panel from the inertial reference is denoted as o. Thrusters are used to command an external torque of 7 about the axis of the satellite body. Rotational spring k and damper b at joint Figure 2: Single Link Robot Arm Jp The physical parameters are Js = 5kgm, Jp = 1kgm, k = 0.15Nm, b = 0.05Nms. The torque is limited by T 5Nm. a) Derive the equations of motion (EOM) of the satellite. b) Linearize the evaluated EOM evaluated in previous section. c) Evaluate the transfer function for both outputs (s), and (s), considering the input 7. d) Design a PID controller for the system (you are free to specify design criteria), and explain the effects of P-I-D gains.