(a) Comp1de the poles and zeros of the discrete-time systems that result from discretizing the continuous-time system with transfer function G s = 10(s2 +0.2s+2)

() (s 2 +0.5s+l)(s+10)'

for sampling intervals ranging from Ts = lsec to T8 = O.Olsec.

(b) Create a root locus plot showing the evolution of the poles and zeros computed in part

(a) as a function of T8 •

{c) Repeat parts

(a) and

(b) for G(s) = (s +  0.1

+ 2i)(s + 0.1- 2i) .

(s + 0.1

+ i)(s + 0.1- i)(s + 0.1

+ 0.5i)(s + 0.1- 0.5i)

{d) Repeat parts (a), {b), and

(c) for different discretization methods.

Problem