The system $$900/s(s+1)(s+9)$$ is to be such that its gain crossover frequency becomes same as its uncompensated phase crossover frequency and provides at $${45^0}$$ phase margin . To achieve this, one may use

If $$X = {\mathop{\rm Re}\nolimits} G\left( {j\omega } \right),\,\,$$ and $$y = {\rm I}mG\left( {j\omega } \right)$$ then for $$\omega \to {0^ + },\,\,$$ the Nyquist plot for $$G\left( s \right) = 1/\left[ {s\left( {s + 1} \right)\left( {s + 2} \right)} \right]$$

Consider the feedback system shown below which is subjected to a unit step input. The system is stable and has following parameters $${k_p} = 4,\,\,{k_i} = 10,\,\,\omega = 500\,\,$$ and $$\xi $$ $$=0.7.$$ The steady state value of $$z$$ is

$$R-L-C$$ circuit shown in figure

For a step input $${e_{i,}}$$ the overshoot in the output $${e_{0,}}$$ will be