Consider the system of Problem 8.4-1.
(a) Design a unity-dc-gain phase-lead compensator that yields a phase margin of approximately \(45^{\circ}\).
(b) Obtain the system step response of part (a) using MATLAB, and find the rise time \({ }_{t_{r}}\) and the percent overshoot.
(c) Compare the step-response parameters of part (b) with Problem 8-2(c) and (e).

Problem 8.4-1

Fig. p8.2-2

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Consider the system of Fig. P8.2-2 with T = 1 s. The plant frequency response G(jo) is given in Table P8.4-1. (a) Let D(z) = 1. If the system is stable, find its phase margin. (b) Let the digital controller realize a gain K, that is, D(z)= K. Find K such that the system phase margin is 45. (c) Obtain the system step response of part (b) using MATLAB, and find the rise time t, and the percent overshoot. (d) Design a unity-dc-gain phase-lag compensator that yields a phase margin of approximately 45. (e) Obtain the system step response of part (d) using MATLAB, and find the rise time t,, and the percent overshoot. TABLE P8.4-1 Frequency Response for PROBLEM 8.4-1 |G(jow)| G(jo) dB ZG(jow) 9.95473 -98.56 4.91192 -106.98 3.20693 -115.10 2.34103 -122.83 ww (1) 0.1 0.099 0.2 0.199 0.3 0.297 0.4 0.394 19.96 13.82 10.12 7.38