A unity feedback system has an open-loop transfer function given by G(s) _ 250 - s[(s/10) + 1]'

The following lag compensator added in series with the plant yields a phase margin of 50°, Dc(s) = (s/1.25) + 1.

50s+ 1

(a) Using the matched pole-zero approximation, determine an equivalent digital realization of this compensator.

(b) The following transfer function is a lead network designed to add about 60° of phase at w1 = 3 radjsec, H(s)- s + 1 - O.ls + 1·
Assume a sampling period of T = 0.25 sec, and compute and plot in the z-plane the pole and zero locations of the digital implementations of H(s)

obtained using (1) Tustin's method and (2) pole-zero mapping. For each case, compute the amount of phase lead provided by the network at z1 =

ejw1T.

(c) Using log-scale for the frequency range w = 0.1 tow = 100 radjsec, plot the magnitude Bode plots for each of the equivalent digital systems found in part (a), and compare with H(s). (hint: Magnitude Bode plots are given by IH(z)i = IH(ejwT)I.

Problem