In this exercise, validate the work done in lecture and expand it by doing the following for the system given below , a) design a proportional controller using ziegler-nichols tuning rule. (done in class) b) design a pd controller using ziegler-nichols tuning rule. c) design a pi controller using ziegler-nichols tuning rule. (done in class) d) design a pid controller using ziegler-nichols tuning rule. (time response given in lecture) for each case, plot the time response for your design to verify the stability of the closed-loop system. consider looking for an independent verification of system stability & the steady state error.