A mobile robot for toxic waste cleanup is shown in Figure DP9.1(a) [23]. The closed-loop

Chapter 0, Problem DP9.1

(choose chapter or problem)

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{jco) G(jio)/K versus co. The value of the frequency at the points indicated is recorded in the following table: Point 1 2 3 4 5 co 2 5 10 20 50 (a) Determine the gain and phase margins of the closed-loop system when K - \. (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.