Autonomous, self-driven vehicles can be used in warehouses, airports, and many other applications. These vehicles follow a wire embedded in the floor and adjust the steerable front wheel to maintain proper direction. The sensing coils, mounted on the front wheel assembly, detect an error in the direction of travel and adjust the steering. The overall control system open-loop transfer function is

\[D G(s)=\frac{K}{s(s+\pi)^{2}}=\frac{K_{v}}{s(s / \pi+1)^{2}}\]

It is desired to have a bandwidth of the closed-loop system exceed \(2 \pi \mathrm{rad} / \mathrm{s}\).

(a) Set \(K_{v}=2 \pi\) and sketch the Bode diagram.

(b) Using the Bode diagram, obtain the logarithmic-magnitude vs. phase angle curve.