For a process with transfer function $G_{(s)}=\frac{2(4s+1)}{s(15s+3)(2s+1)},$ which is controlled with a

Proportional$-$Integral controller, sketch and explain the root$-$locus diagram for fixed integral

time ${}_{\text{I}},$ for the following cases $($check and show your results with MATLAB$)$:

a$.{}_{\text{I}}>15($Larger than process time constants$)$

bin between the process time constants$)$

c$.{}_{\text{I}}<mn\; id="EditorElement\_1717560">2</mn><mtext\; id="EditorElement\_1717504"></mtext><mi\; id="EditorElement\_1717505">(</mi>$Smaller than the process time constants$)$