Consider a discrete$-$time unity$-$gain negativefeedback system $($as shown in Figure $1)$ where the open$-$loop plant has transfer function

$G(z)=\frac{1}{z(z-1)}$

Figure $1$: Closed$-$Loop System.

Suppose $D(z)$ is to be designed to give the system a bandwidth of $1ra\frac{d}{s}$ and a phase margin of $75.$

$($A$)$ Should a lag compensator or a lead compensator be used?

$($B$)$ On the axes at the right, make a sketch showing how you could geometrically determine the pole and the zero of $D(z)$ to give the specified bandwidth and phase margin.

$($C$)$ On the magnitude and phase plots given in Figure $2,$ sketch the magnitude and phase plots of the compensated loop transfer function.

Figure $2$: Magnitude and Phase Plots $.$