Given the following ODE ў + 2ў — Зу —й+ 2и 1. Write down a state space realization for the system 2. Compute the transfer function of the system from the SS computed in part 1 3. Now design a PI/PID controller for the system with BW 5 rad/s. Decide on whether you need a PID or if a PI will suffice, based on phase requirements from the zeros in the controller. If a PID is required then use tau 1/100 (time constant for the pseudo pole). Show all work. 4. Plot T and S and comment on your observations regarding the command following and output disturbance rejection properties of your design.