Suppose that the following continuous-time lead compensator D(s) = lO(s + 1)

s + 10 is to be used in controlling the plant G(s) = 20 s(s + l)(s + 10) ·

If this system is to be implemented using a digital computer at a sampling interval O.lsec, determine the transfer function D(z) of the controller using:

(a) Pole-zero matching method

{b) Tustin's conversion method

{c) Bilinear transformation method