A unity feedback system has the plant transfer function $G_{p}(s)=\frac{1}{(s+1)(2 s+1)}$
- Determine the frequency at which the plant has a phase lag of $90^{\circ}$.
- An integral controller with transfer function $G_1(s)=\frac{k}{s}$ is placed in the feedforward path of the feedback system. Find the value of $k$ such that the compensated system has an open-loop gain margin of $2.5$.
- Determine the steady state errors of the compensated system to unit-step and unit-ramp inputs.