Electronics and computers are being used to control automobiles. Figure P9.14 is an example of an automobile control system, the steering control for a research automobile. The control stick is used for steering. A typical driver has a reaction time of $T=0.2 \mathrm{~s}$.
(a) Using the Nichols chart, determine the magnitude of the gain $K$ that will result in a system with a peak magnitude of the closed-loop frequency response $M_{p o}$ less than or equal to $2 \mathrm{~dB}$.
(b) Estimate the damping ratio of the system based on (1) $M_{p \omega}$ and (2) the phase margin. Compare the results and explain the difference, if any.
(c) Determine the closed-loop 3-dB bandwidth of the system.