1. Consider the system shown below. The third-order process shown is controlled by a simple proportional controller. R(S) I(s) X(s) K 4 (2s +1)'(3s +1) + N(S) 0.25 + (a) (30%) What range of permitted values for the proportional gain Kc may be employed? What are the associated borderline poles at the maximum gain for stability? (b)(20%) Estimate the percentage offset in the response signal that would be observed for a unit-step change in the set-point if the maximum allowed value for the proportional gain was employed (note that sN(s) 0 as s0). (40%) Sketch the root locus, indicating asymptotes of each branch and considering real-axis crossover also. Show details of your workings to prepare the sketch. (d)(10%) Outline briefly an 'automatic technique for plotting the root locus for this system which would be suited for implementation on a computer