Solve with Matlab and provide code.

The controlled process in a certain feedback control system has transfer function as below.

A controller with transfer function Gc(s) receives the system error and generates a control signal which is the input to the system transfer function. Draw root-locus diagrams as, Gc(s) is varied for three forms of Gc(s):

a) Gc (s) =k

b) Gc (s) =k(1+0.2s)

c) Gc (s) =k(1+0.2s)/(1+0.02s)

And use the root locus graph to estimate what is value of k in each case that will give stability.

Ref. Input Output 10 Gc(s) (1+0.2s)*(1+0.05s) Ref. Input Output 10 Gc(s) (1+0.2s)*(1+0.05s)