Consider a system with a zero-order hold, a process

and T = 0.1 s.
(a) Let D(z) = K and determine the transfer function G(z)D(z).
(b) Determine the characteristic equation of the closed-loop system,
(c) Calculate the maximum value of K for a stable system.
(d) Determine K such that the overshoot is less than 30%.
(e) Calculate the closed-loop transfer function T(z) for K of part (d) and plot the step response.
(f) Determine the location of the closed-loop roots and the overshoot if K is one-half of the value determined in part (c). (g) Plot the step response for the K of part (f).

Gp(s) = s(s + 10),