Section IV Consider the feedback control system shown in Figure Q.IV. Gp(s) and Gc(s) are respectively the plant and controller transfer functions. Answer questions 18 to 22. 1 Gp(s) = (s+a)(3+6)(8+c) = sbs Gc(s) - = K(s+d) (8+3d) Controller Process R(S) Y(s) Gc(s) Gp(s) Figure Q.IV Block diagram of a feedback control system. NOTE: the values of the parameters a, 6, c, d are likely to change between questions (see item 10 in assessment instructions). 18 3 points What is the angle between the asymptotes of the root locus plot of the system? 180 60 120 0 72 90 None of the answer choices given 19 5 points Calculate the asymptotic centroid of the system, for a = 2.8, b= 13, c=-1.5, and d=4.4. Type your answer... 20 6 points Determine the critical value of the gain K for the system, for a = 3.2, b= 11, C=-0.5, and d=4.4. The critical value of the gain K is defined as the value of the gain for which the root loci cross the imaginary axis and the stability of the system changes. Type your answer... 21 6 points Consider the characteristic equation of the system as Cheq = 94 + As3 + Bs? + Cs + D, = where A=a+b+c+3d, B= ab + 3d (a +b+c)+c(a+b), C = K + 3d (ab+c(a+b)) + abc, D=Kd+ 3abcd. = Use the Routh-Hurwitz criterion to find the maximum value of K for the system to be stable, for a = 3.6, b= 17, C=-2.7, and d=5.1. Type your answer... 22 to 5 points Determine the value of gain K for the system, for a = 5.4, b= 19, C=-0.6, and d=5.4 so that the point s =-62.1 is a closed-loop pole. Type your