Design a lag-lead compensator for the system of Problem 8.4-1. Note that \(G_{p}(\mathrm{~s})=1 /\left(s^{2}+sight), T=1 \mathrm{~s}\), and \(H=1\).

(a) Use the lag compensator of Problem 8.4-1 and decrease its gain by a factor of 3.

(b) Design a cascaded lead compensator for a target phase margin of 55 degrees for the lag-lead combination. Why might this be hard to achieve?

(c) Plot the step responses for this system for the lag compensator of Problem 8.4-1, the lead compensator of 8.6-1, and the lag-lead design of this problem.

Problem 8.4-1

Consider the system of Fig. P8.2-2 with \(T=1 \mathrm{~s}\). The plant frequency response \(G\left(j \omega_{w}ight)\) is given in Table P8.4-1.

Fig. P8.2-2

Table P8.4-1

Transcribed Image Text:

D(z) 1-87 m(1) T S 1 s(8 + 1) C(s)