8.4-1. Consider the system of Fig. P8.2-2 with 71 s. The plant frequency response G(jw) 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 f,, 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(jw)| G(jw) dB ZG(jw) 0.1 0.099 9.95473 19.96 -98.56 0.2 0.199 4.91192 13.82 -106.98 0.3 0.297 3.20693 10.12 -115.10 0.4 0.394 2.34103 7.38 -122.83

Fig: 1