A mobile robot for toxic waste cleanup is shown in Figure DP9.1(a) [23]. The closed-loop speed control is represented by Figure 9.1 with H{s) = 1. The Nichols chart in Figure DP9.1(b) shows the plot of Gc{jω) G(jω)/K versus ω. The value of the frequency at the points indicated is recorded in the following table:

(a) Determine the gain and phase margins of the closed-loop system when K =1.
(b) Determine the resonant peak in dB and the resonant frequency for K =1,
(c) Determine the system bandwidth and estimate the settling time (with a 2% criterion) and percent overshoot of this system for a step input.
(d) Determine the appropriate gain K so that the overshoot to a step input is 30%, and estimate the settling time of the system.

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