Sketch the root-locus plot for the system shown below R(S) + C(s) K S2 + 3s + a s(s + 2)(s + b) Rectala 1 S2 + 7s + 20 a= 10 where K is an adjustable parameter and a = 10 + p and b = 4 + . The values of p and q are the two last digits of your student number. For example, if your student number is 12345678, p = 7 and q = 8, therefore a = 17 and b = 4.8. You must provide calculations for the following: (a) The angle which each asymptote makes with the real axis (b) The real axis intercept value of any asymptotes (c) Break-away or break-in locations of the root-locus at the real axis (a) The angle of departure and/or angle of arrival of any complex roots (e) The points at which the root-locus cross the imaginary axis Hint: For part (e), it is recommended you substitute s = jw into the characteristic equation (see Lecture/Tutorial 6, Q2) and solve the resulting polynomial with help of a computation engine rather than using Routh-Hurwitz Stability Criterion method