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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 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_ω less than or equal to 2 dB.

(b) Estimate the damping ratio of the system based on (1) M_p_ω) and (2) the phase margin. Compare the results and explain the difference, if any.

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