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.

Agas contained within a piston-cylinder assembly e end nation about same energy states, 1 and 2, where pi 10 bar, v undergoes two processes, a and b, between the sam 0.1 m3, ui-400 kj and p2 1 bar, v2 1.0 m2, u2 200 kj: process a: process from 1 to 2 during which the pressure- volume relation is pv constant process b: constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to +20 0 state 2 kinetic and potential energy effects can be ignored. for each of the processes a and b, (a) sketch the process on p-v coordinates, (b) evaluate the work, in kj, and (c) evaluate process the heat transfer, in kj