Hi Guys, Attached is a problem from an old exam for a Process Control and Instrumentation unit. I have tried everything I know (which isn't much, it's not the main assessable portion of the unit). Other questions similar involve giving us either the characteristic closed loop equation or the controller function and deriving it from there. We take the characteristic equation and sub in s = wj (j being sqrt(-1)) and can solve for both the Im and Re parts being zero, obtaining the critical value of K and the corresponding w, then using the table becomes quite elementary. Working backwards to discover G(s) gets tricky due the s being on top (or a 1/s below) This is the only example I can find where I'm given the overall output function Y(s), so working backwards to find the characteristic equation... I just don't know how, or if it's done differently. Much of google gives tips of how to effectively use Z-N in real or simulated situations, but this is for an exam. Most of the unit is comprised of sensors, analog and digital conditioning and PLC diagrams, so these control loops/PID are kind of tacked on the end. The last time I touched Laplace was ~5 years ago. I'm sure there's a really simple solution. Please help. Thanks.