a) Implement the illustrative example of standard PID controller performance presented. Demonstrate that the graphs presented in that section are correct.

b) Repeat this practical implementation for the second-order system given in Equation 4.68, i.e, determine the various control gains ( $K_P,T_I$ and $T_D$ ) which will produce similar graphs for the different cases discussed in Section 4.15.3.

\[\begin{equation*}G(s)=\frac{1}{s^{2}+1.6 s+8} \tag{4.68}\end{equation*}\]