The system with \(\mathrm{G}(s)=\frac{900}{s(s+1)(s+9)}\) is to be compensated such that its gain cross over frequency becomes same as its uncompensated phase cross over frequency and provides phase margin of \(45^{\circ}\). To achieve this goal, one may use

(a) a lag compensator that contributes attenuation of \(20 \mathrm{~dB}\) and phase lag of \(45^{\circ}\) at frequency of \(3 \sqrt{3} \mathrm{rad} / \mathrm{sec}\).

(b) a lead compensator that contributes amplification of \(20 \mathrm{~dB}\) and phase lead of \(45^{\circ}\) at frequency of \(3 \mathrm{rad} / \mathrm{sec}\).

(c) a lag-lead compensator that contributes amplification of \(20 \mathrm{~dB}\) and a phase lag of \(45^{\circ}\) at frequency of \(\sqrt{3} \mathrm{rad} / \mathrm{sec}\).

(d) a lag-lead compensator that contributes an attenuation of \(20 \mathrm{~dB}\) and phase lead of \(45^{\circ}\) at frequency of \(3 \mathrm{rad} / \mathrm{sec}\).