Design a PD controller for the system shown in Figure P9.2

Step 1 of 6

For the PD controller transfer junction, the equation of the gain is given as follows:

\(G(S)=\left(\mu_{0}+S K_{0}\right)\)

Here,

\(G(S)=\frac{K}{S(S+8)(S+25)}\).

The dominant pole consideration diamante can be used for the PD controller transfer junction as follows:

\(G^{\prime}(S)=\frac{R}{S(S+8)}\)

Further the compensated characteristic equation for the PD controller transfer junction is:

\(\begin{aligned}
1+G^{\prime}(S) \mu(S) & =0 \\
1+\frac{\mu}{S(S+8)} & =0 \\
{\left[S^{2}+8 S+K\right] } & =0 \\
\Delta^{2}+2 \xi \omega_{n}+\omega_{n} & =0 \\
2 \xi \omega_{n} & =8 \\
\xi \omega_{n} & =4
\end{aligned}\)