Given the following ODE + 2y 3y = + 2u 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 Pl 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. You may use step responses to further clarify your answer. Given the following ODE + 2y 3y = + 2u 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 Pl 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. You may use step responses to further clarify your